Server job assigning logic, submarine movement syncing, submarine collision improvements, spawnpoints in levels

Farseer Physics Engine 3.5/Common/ConvexHull/ChainHull.cs

@@ -0,0 +1,143 @@
+using System.Collections.Generic;
+using Microsoft.Xna.Framework;
+
+namespace FarseerPhysics.Common.ConvexHull
+{
+    /// <summary>
+    /// Andrew's Monotone Chain Convex Hull algorithm.
+    /// Used to get the convex hull of a point cloud.
+    /// 
+    /// Source: http://www.softsurfer.com/Archive/algorithm_0109/algorithm_0109.htm
+    /// </summary>
+    public static class ChainHull
+    {
+        //Copyright 2001, softSurfer (www.softsurfer.com)
+
+        private static PointComparer _pointComparer = new PointComparer();
+
+        /// <summary>
+        /// Returns the convex hull from the given vertices..
+        /// </summary>
+        public static Vertices GetConvexHull(Vertices vertices)
+        {
+            if (vertices.Count <= 3)
+                return vertices;
+
+            Vertices pointSet = new Vertices(vertices);
+
+            //Sort by X-axis
+            pointSet.Sort(_pointComparer);
+
+            Vector2[] h = new Vector2[pointSet.Count];
+            Vertices res;
+
+            int top = -1; // indices for bottom and top of the stack
+            int i; // array scan index
+
+            // Get the indices of points with min x-coord and min|max y-coord
+            const int minmin = 0;
+            float xmin = pointSet[0].X;
+            for (i = 1; i < pointSet.Count; i++)
+            {
+                if (pointSet[i].X != xmin)
+                    break;
+            }
+
+            // degenerate case: all x-coords == xmin
+            int minmax = i - 1;
+            if (minmax == pointSet.Count - 1)
+            {
+                h[++top] = pointSet[minmin];
+
+                if (pointSet[minmax].Y != pointSet[minmin].Y) // a nontrivial segment
+                    h[++top] = pointSet[minmax];
+
+                h[++top] = pointSet[minmin]; // add polygon endpoint
+
+                res = new Vertices(top + 1);
+                for (int j = 0; j < top + 1; j++)
+                {
+                    res.Add(h[j]);
+                }
+
+                return res;
+            }
+
+            top = -1;
+
+            // Get the indices of points with max x-coord and min|max y-coord
+            int maxmax = pointSet.Count - 1;
+            float xmax = pointSet[pointSet.Count - 1].X;
+            for (i = pointSet.Count - 2; i >= 0; i--)
+            {
+                if (pointSet[i].X != xmax)
+                    break;
+            }
+            int maxmin = i + 1;
+
+            // Compute the lower hull on the stack H
+            h[++top] = pointSet[minmin]; // push minmin point onto stack
+            i = minmax;
+            while (++i <= maxmin)
+            {
+                // the lower line joins P[minmin] with P[maxmin]
+                if (MathUtils.Area(pointSet[minmin], pointSet[maxmin], pointSet[i]) >= 0 && i < maxmin)
+                    continue; // ignore P[i] above or on the lower line
+
+                while (top > 0) // there are at least 2 points on the stack
+                {
+                    // test if P[i] is left of the line at the stack top
+                    if (MathUtils.Area(h[top - 1], h[top], pointSet[i]) > 0)
+                        break; // P[i] is a new hull vertex
+
+                    top--; // pop top point off stack
+                }
+                h[++top] = pointSet[i]; // push P[i] onto stack
+            }
+
+            // Next, compute the upper hull on the stack H above the bottom hull
+            if (maxmax != maxmin) // if distinct xmax points
+                h[++top] = pointSet[maxmax]; // push maxmax point onto stack
+            int bot = top;
+            i = maxmin;
+            while (--i >= minmax)
+            {
+                // the upper line joins P[maxmax] with P[minmax]
+                if (MathUtils.Area(pointSet[maxmax], pointSet[minmax], pointSet[i]) >= 0 && i > minmax)
+                    continue; // ignore P[i] below or on the upper line
+
+                while (top > bot) // at least 2 points on the upper stack
+                {
+                    // test if P[i] is left of the line at the stack top
+                    if (MathUtils.Area(h[top - 1], h[top], pointSet[i]) > 0)
+                        break; // P[i] is a new hull vertex
+
+                    top--; // pop top point off stack
+                }
+
+                h[++top] = pointSet[i]; // push P[i] onto stack
+            }
+
+            if (minmax != minmin)
+                h[++top] = pointSet[minmin]; // push joining endpoint onto stack
+
+            res = new Vertices(top + 1);
+
+            for (int j = 0; j < top + 1; j++)
+            {
+                res.Add(h[j]);
+            }
+
+            return res;
+        }
+
+        private class PointComparer : Comparer<Vector2>
+        {
+            public override int Compare(Vector2 a, Vector2 b)
+            {
+                int f = a.X.CompareTo(b.X);
+                return f != 0 ? f : a.Y.CompareTo(b.Y);
+            }
+        }
+    }
+}

Farseer Physics Engine 3.5/Common/ConvexHull/GiftWrap.cs

@@ -0,0 +1,90 @@
+using Microsoft.Xna.Framework;
+
+namespace FarseerPhysics.Common.ConvexHull
+{
+    /// <summary>
+    /// Giftwrap convex hull algorithm.
+    /// O(nh) time complexity, where n is the number of points and h is the number of points on the convex hull.
+    /// 
+    /// See http://en.wikipedia.org/wiki/Gift_wrapping_algorithm for more details.
+    /// </summary>
+    public static class GiftWrap
+    {
+        //Extracted from Box2D
+
+        /// <summary>
+        /// Returns the convex hull from the given vertices.
+        /// </summary>
+        /// <param name="vertices">The vertices.</param>
+        public static Vertices GetConvexHull(Vertices vertices)
+        {
+            if (vertices.Count <= 3)
+                return vertices;
+
+            // Find the right most point on the hull
+            int i0 = 0;
+            float x0 = vertices[0].X;
+            for (int i = 1; i < vertices.Count; ++i)
+            {
+                float x = vertices[i].X;
+                if (x > x0 || (x == x0 && vertices[i].Y < vertices[i0].Y))
+                {
+                    i0 = i;
+                    x0 = x;
+                }
+            }
+
+            int[] hull = new int[vertices.Count];
+            int m = 0;
+            int ih = i0;
+
+            for (; ; )
+            {
+                hull[m] = ih;
+
+                int ie = 0;
+                for (int j = 1; j < vertices.Count; ++j)
+                {
+                    if (ie == ih)
+                    {
+                        ie = j;
+                        continue;
+                    }
+
+                    Vector2 r = vertices[ie] - vertices[hull[m]];
+                    Vector2 v = vertices[j] - vertices[hull[m]];
+
+                    float c = MathUtils.Cross(ref r, ref v);
+                    if (c < 0.0f)
+                    {
+                        ie = j;
+                    }
+
+                    // Collinearity check
+                    if (c == 0.0f && v.LengthSquared() > r.LengthSquared())
+                    {
+                        ie = j;
+                    }
+                }
+
+                ++m;
+                ih = ie;
+
+                if (ie == i0)
+                {
+                    break;
+                }
+            }
+
+            Vertices result = new Vertices(m);
+
+            // Copy vertices.
+            for (int i = 0; i < m; ++i)
+            {
+                result.Add(vertices[hull[i]]);
+            }
+
+            return result;
+        }
+    }
+}

Farseer Physics Engine 3.5/Common/ConvexHull/Melkman.cs

@@ -0,0 +1,132 @@
+using Microsoft.Xna.Framework;
+
+namespace FarseerPhysics.Common.ConvexHull
+{
+    /// <summary>
+    /// Creates a convex hull.
+    /// Note:
+    /// 1. Vertices must be of a simple polygon, i.e. edges do not overlap.
+    /// 2. Melkman does not work on point clouds
+    /// </summary>
+    /// <remarks>
+    /// Implemented using Melkman's Convex Hull Algorithm - O(n) time complexity.
+    /// Reference: http://www.ams.sunysb.edu/~jsbm/courses/345/melkman.pdf
+    /// </remarks>
+    public static class Melkman
+    {
+        //Melkman based convex hull algorithm contributed by Cowdozer
+
+        /// <summary>
+        /// Returns a convex hull from the given vertices.
+        /// </summary>
+        /// <returns>A convex hull in counter clockwise winding order.</returns>
+        public static Vertices GetConvexHull(Vertices vertices)
+        {
+            if (vertices.Count <= 3)
+                return vertices;
+
+            //We'll never need a queue larger than the current number of Vertices +1
+            //Create double-ended queue
+            Vector2[] deque = new Vector2[vertices.Count + 1];
+            int qf = 3, qb = 0; //Queue front index, queue back index
+
+            //Start by placing first 3 vertices in convex CCW order
+            int startIndex = 3;
+            float k = MathUtils.Area(vertices[0], vertices[1], vertices[2]);
+            if (k == 0)
+            {
+                //Vertices are collinear.
+                deque[0] = vertices[0];
+                deque[1] = vertices[2]; //We can skip vertex 1 because it should be between 0 and 2
+                deque[2] = vertices[0];
+                qf = 2;
+
+                //Go until the end of the collinear sequence of vertices
+                for (startIndex = 3; startIndex < vertices.Count; startIndex++)
+                {
+                    Vector2 tmp = vertices[startIndex];
+                    if (MathUtils.Area(ref deque[0], ref deque[1], ref tmp) == 0) //This point is also collinear
+                        deque[1] = vertices[startIndex];
+                    else break;
+                }
+            }
+            else
+            {
+                deque[0] = deque[3] = vertices[2];
+                if (k > 0)
+                {
+                    //Is Left.  Set deque = {2, 0, 1, 2}
+                    deque[1] = vertices[0];
+                    deque[2] = vertices[1];
+                }
+                else
+                {
+                    //Is Right. Set deque = {2, 1, 0, 2}
+                    deque[1] = vertices[1];
+                    deque[2] = vertices[0];
+                }
+            }
+
+            int qfm1 = qf == 0 ? deque.Length - 1 : qf - 1;
+            int qbm1 = qb == deque.Length - 1 ? 0 : qb + 1;
+
+            //Add vertices one at a time and adjust convex hull as needed
+            for (int i = startIndex; i < vertices.Count; i++)
+            {
+                Vector2 nextPt = vertices[i];
+
+                //Ignore if it is already within the convex hull we have constructed
+                if (MathUtils.Area(ref deque[qfm1], ref deque[qf], ref nextPt) > 0 && MathUtils.Area(ref deque[qb], ref deque[qbm1], ref nextPt) > 0)
+                    continue;
+
+                //Pop front until convex
+                while (!(MathUtils.Area(ref deque[qfm1], ref deque[qf], ref nextPt) > 0))
+                {
+                    //Pop the front element from the queue
+                    qf = qfm1; //qf--;
+                    qfm1 = qf == 0 ? deque.Length - 1 : qf - 1; //qfm1 = qf - 1;
+                }
+
+                //Add vertex to the front of the queue
+                qf = qf == deque.Length - 1 ? 0 : qf + 1; //qf++;
+                qfm1 = qf == 0 ? deque.Length - 1 : qf - 1; //qfm1 = qf - 1;
+                deque[qf] = nextPt;
+
+                //Pop back until convex
+                while (!(MathUtils.Area(ref deque[qb], ref deque[qbm1], ref nextPt) > 0))
+                {
+                    //Pop the back element from the queue
+                    qb = qbm1; //qb++;
+                    qbm1 = qb == deque.Length - 1 ? 0 : qb + 1; //qbm1 = qb + 1;
+                }
+                //Add vertex to the back of the queue
+                qb = qb == 0 ? deque.Length - 1 : qb - 1; //qb--;
+                qbm1 = qb == deque.Length - 1 ? 0 : qb + 1; //qbm1 = qb + 1;
+                deque[qb] = nextPt;
+            }
+
+            //Create the convex hull from what is left in the deque
+            if (qb < qf)
+            {
+                Vertices convexHull = new Vertices(qf);
+
+                for (int i = qb; i < qf; i++)
+                    convexHull.Add(deque[i]);
+
+                return convexHull;
+            }
+            else
+            {
+                Vertices convexHull = new Vertices(qf + deque.Length);
+
+                for (int i = 0; i < qf; i++)
+                    convexHull.Add(deque[i]);
+
+                for (int i = qb; i < deque.Length; i++)
+                    convexHull.Add(deque[i]);
+
+                return convexHull;
+            }
+        }
+    }
+}

Farseer Physics Engine 3.5/Common/Curve.cs

@@ -0,0 +1,273 @@
+#if !XNA && !WINDOWS_PHONE && !XBOX && !ANDROID
+
+#region License
+
+/*
+MIT License
+Copyright © 2006 The Mono.Xna Team
+
+All rights reserved.
+
+Authors:
+Olivier Dufour (Duff)
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
+*/
+
+#endregion License
+
+using System;
+
+namespace Microsoft.Xna.Framework
+{
+    public enum CurveLoopType
+    {
+        Constant,
+        Cycle,
+        CycleOffset,
+        Oscillate,
+        Linear
+    }
+
+    public enum CurveContinuity
+    {
+        Smooth,
+        Step
+    }
+
+    public enum CurveTangent
+    {
+        Flat,
+        Linear,
+        Smooth
+    }
+
+    public class Curve
+    {
+#region Private Fields
+
+        private CurveKeyCollection keys;
+        private CurveLoopType postLoop;
+        private CurveLoopType preLoop;
+
+#endregion Private Fields
+
+#region Public Properties
+
+        public bool IsConstant
+        {
+            get { return keys.Count <= 1; }
+        }
+
+        public CurveKeyCollection Keys
+        {
+            get { return keys; }
+        }
+
+        public CurveLoopType PostLoop
+        {
+            get { return postLoop; }
+            set { postLoop = value; }
+        }
+
+        public CurveLoopType PreLoop
+        {
+            get { return preLoop; }
+            set { preLoop = value; }
+        }
+
+#endregion Public Properties
+
+#region Public Constructors
+
+        public Curve()
+        {
+            keys = new CurveKeyCollection();
+        }
+
+#endregion Public Constructors
+
+#region Public Methods
+
+        public void ComputeTangent(int keyIndex, CurveTangent tangentInType, CurveTangent tangentOutType)
+        {
+            throw new NotImplementedException();
+        }
+
+        public void ComputeTangent(int keyIndex, CurveTangent tangentType)
+        {
+            ComputeTangent(keyIndex, tangentType, tangentType);
+        }
+
+        public void ComputeTangents(CurveTangent tangentInType, CurveTangent tangentOutType)
+        {
+            throw new NotImplementedException();
+        }
+
+        public void ComputeTangents(CurveTangent tangentType)
+        {
+            ComputeTangents(tangentType, tangentType);
+        }
+
+        public Curve Clone()
+        {
+            Curve curve = new Curve();
+
+            curve.keys = keys.Clone();
+            curve.preLoop = preLoop;
+            curve.postLoop = postLoop;
+
+            return curve;
+        }
+
+        public float Evaluate(float position)
+        {
+            CurveKey first = keys[0];
+            CurveKey last = keys[keys.Count - 1];
+
+            if (position < first.Position)
+            {
+                switch (PreLoop)
+                {
+                    case CurveLoopType.Constant:
+                        //constant
+                        return first.Value;
+
+                    case CurveLoopType.Linear:
+                        // linear y = a*x +b with a tangeant of last point
+                        return first.Value - first.TangentIn*(first.Position - position);
+
+                    case CurveLoopType.Cycle:
+                        //start -> end / start -> end
+                        int cycle = GetNumberOfCycle(position);
+                        float virtualPos = position - (cycle*(last.Position - first.Position));
+                        return GetCurvePosition(virtualPos);
+
+                    case CurveLoopType.CycleOffset:
+                        //make the curve continue (with no step) so must up the curve each cycle of delta(value)
+                        cycle = GetNumberOfCycle(position);
+                        virtualPos = position - (cycle*(last.Position - first.Position));
+                        return (GetCurvePosition(virtualPos) + cycle*(last.Value - first.Value));
+
+                    case CurveLoopType.Oscillate:
+                        //go back on curve from end and target start 
+                        // start-> end / end -> start
+                        cycle = GetNumberOfCycle(position);
+                        if (0 == cycle%2f) //if pair
+                            virtualPos = position - (cycle*(last.Position - first.Position));
+                        else
+                            virtualPos = last.Position - position + first.Position +
+                                         (cycle*(last.Position - first.Position));
+                        return GetCurvePosition(virtualPos);
+                }
+            }
+            else if (position > last.Position)
+            {
+                int cycle;
+                switch (PostLoop)
+                {
+                    case CurveLoopType.Constant:
+                        //constant
+                        return last.Value;
+
+                    case CurveLoopType.Linear:
+                        // linear y = a*x +b with a tangeant of last point
+                        return last.Value + first.TangentOut*(position - last.Position);
+
+                    case CurveLoopType.Cycle:
+                        //start -> end / start -> end
+                        cycle = GetNumberOfCycle(position);
+                        float virtualPos = position - (cycle*(last.Position - first.Position));
+                        return GetCurvePosition(virtualPos);
+
+                    case CurveLoopType.CycleOffset:
+                        //make the curve continue (with no step) so must up the curve each cycle of delta(value)
+                        cycle = GetNumberOfCycle(position);
+                        virtualPos = position - (cycle*(last.Position - first.Position));
+                        return (GetCurvePosition(virtualPos) + cycle*(last.Value - first.Value));
+
+                    case CurveLoopType.Oscillate:
+                        //go back on curve from end and target start 
+                        // start-> end / end -> start
+                        cycle = GetNumberOfCycle(position);
+                        virtualPos = position - (cycle*(last.Position - first.Position));
+                        if (0 == cycle%2f) //if pair
+                            virtualPos = position - (cycle*(last.Position - first.Position));
+                        else
+                            virtualPos = last.Position - position + first.Position +
+                                         (cycle*(last.Position - first.Position));
+                        return GetCurvePosition(virtualPos);
+                }
+            }
+
+            //in curve
+            return GetCurvePosition(position);
+        }
+
+#endregion Public Methods
+
+#region Private Methods
+
+        private int GetNumberOfCycle(float position)
+        {
+            float cycle = (position - keys[0].Position)/(keys[keys.Count - 1].Position - keys[0].Position);
+            if (cycle < 0f)
+                cycle--;
+            return (int) cycle;
+        }
+
+        private float GetCurvePosition(float position)
+        {
+            //only for position in curve
+            CurveKey prev = keys[0];
+            CurveKey next;
+            for (int i = 1; i < keys.Count; i++)
+            {
+                next = Keys[i];
+                if (next.Position >= position)
+                {
+                    if (prev.Continuity == CurveContinuity.Step)
+                    {
+                        if (position >= 1f)
+                        {
+                            return next.Value;
+                        }
+                        return prev.Value;
+                    }
+                    float t = (position - prev.Position)/(next.Position - prev.Position); //to have t in [0,1]
+                    float ts = t*t;
+                    float tss = ts*t;
+                    //After a lot of search on internet I have found all about spline function
+                    // and bezier (phi'sss ancien) but finaly use hermite curve 
+                    //http://en.wikipedia.org/wiki/Cubic_Hermite_spline
+                    //P(t) = (2*t^3 - 3t^2 + 1)*P0 + (t^3 - 2t^2 + t)m0 + (-2t^3 + 3t^2)P1 + (t^3-t^2)m1
+                    //with P0.value = prev.value , m0 = prev.tangentOut, P1= next.value, m1 = next.TangentIn
+                    return (2*tss - 3*ts + 1f)*prev.Value + (tss - 2*ts + t)*prev.TangentOut + (3*ts - 2*tss)*next.Value +
+                           (tss - ts)*next.TangentIn;
+                }
+                prev = next;
+            }
+            return 0f;
+        }
+
+#endregion
+    }
+}
+
+#endif

Farseer Physics Engine 3.5/Common/CurveKey.cs

@@ -0,0 +1,167 @@
+#if !XNA && !WINDOWS_PHONE && !XBOX && !ANDROID
+
+#region License
+
+/*
+MIT License
+Copyright © 2006 The Mono.Xna Team
+
+All rights reserved.
+
+Authors:
+Olivier Dufour (Duff)
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
+*/
+
+#endregion License
+
+using System;
+
+namespace Microsoft.Xna.Framework
+{
+    public class CurveKey : IEquatable<CurveKey>, IComparable<CurveKey>
+    {
+#region Private Fields
+
+        private CurveContinuity continuity;
+        private float position;
+        private float tangentIn;
+        private float tangentOut;
+        private float value;
+
+#endregion Private Fields
+
+#region Properties
+
+        public CurveContinuity Continuity
+        {
+            get { return continuity; }
+            set { continuity = value; }
+        }
+
+        public float Position
+        {
+            get { return position; }
+        }
+
+        public float TangentIn
+        {
+            get { return tangentIn; }
+            set { tangentIn = value; }
+        }
+
+        public float TangentOut
+        {
+            get { return tangentOut; }
+            set { tangentOut = value; }
+        }
+
+        public float Value
+        {
+            get { return value; }
+            set { this.value = value; }
+        }
+
+#endregion
+
+#region Constructors
+
+        public CurveKey(float position, float value)
+            : this(position, value, 0, 0, CurveContinuity.Smooth)
+        {
+        }
+
+        public CurveKey(float position, float value, float tangentIn, float tangentOut)
+            : this(position, value, tangentIn, tangentOut, CurveContinuity.Smooth)
+        {
+        }
+
+        public CurveKey(float position, float value, float tangentIn, float tangentOut, CurveContinuity continuity)
+        {
+            this.position = position;
+            this.value = value;
+            this.tangentIn = tangentIn;
+            this.tangentOut = tangentOut;
+            this.continuity = continuity;
+        }
+
+#endregion Constructors
+
+#region Public Methods
+
+#region IComparable<CurveKey> Members
+
+        public int CompareTo(CurveKey other)
+        {
+            return position.CompareTo(other.position);
+        }
+
+#endregion
+
+#region IEquatable<CurveKey> Members
+
+        public bool Equals(CurveKey other)
+        {
+            return (this == other);
+        }
+
+#endregion
+
+        public static bool operator !=(CurveKey a, CurveKey b)
+        {
+            return !(a == b);
+        }
+
+        public static bool operator ==(CurveKey a, CurveKey b)
+        {
+            if (Equals(a, null))
+                return Equals(b, null);
+
+            if (Equals(b, null))
+                return Equals(a, null);
+
+            return (a.position == b.position)
+                   && (a.value == b.value)
+                   && (a.tangentIn == b.tangentIn)
+                   && (a.tangentOut == b.tangentOut)
+                   && (a.continuity == b.continuity);
+        }
+
+        public CurveKey Clone()
+        {
+            return new CurveKey(position, value, tangentIn, tangentOut, continuity);
+        }
+
+        public override bool Equals(object obj)
+        {
+            return (obj is CurveKey) ? ((CurveKey) obj) == this : false;
+        }
+
+        public override int GetHashCode()
+        {
+            return position.GetHashCode() ^ value.GetHashCode() ^ tangentIn.GetHashCode() ^
+                   tangentOut.GetHashCode() ^ continuity.GetHashCode();
+        }
+
+#endregion
+    }
+}
+
+#endif

Farseer Physics Engine 3.5/Common/CurveKeyCollection.cs

@@ -0,0 +1,176 @@
+#if !XNA && !WINDOWS_PHONE && !XBOX && !ANDROID
+
+#region License
+
+/*
+MIT License
+Copyright © 2006 The Mono.Xna Team
+
+All rights reserved.
+
+Authors:
+Olivier Dufour (Duff)
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
+*/
+
+#endregion License
+
+using System;
+using System.Collections;
+using System.Collections.Generic;
+
+namespace Microsoft.Xna.Framework
+{
+    public class CurveKeyCollection : ICollection<CurveKey>, IEnumerable<CurveKey>, IEnumerable
+    {
+#region Private Fields
+
+        private List<CurveKey> innerlist;
+        private bool isReadOnly = false;
+
+#endregion Private Fields
+
+#region Properties
+
+        public CurveKey this[int index]
+        {
+            get { return innerlist[index]; }
+            set
+            {
+                if (value == null)
+                    throw new ArgumentNullException();
+
+                if (index >= innerlist.Count)
+                    throw new IndexOutOfRangeException();
+
+                if (innerlist[index].Position == value.Position)
+                    innerlist[index] = value;
+                else
+                {
+                    innerlist.RemoveAt(index);
+                    innerlist.Add(value);
+                }
+            }
+        }
+
+        public int Count
+        {
+            get { return innerlist.Count; }
+        }
+
+        public bool IsReadOnly
+        {
+            get { return isReadOnly; }
+        }
+
+#endregion Properties
+
+#region Constructors
+
+        public CurveKeyCollection()
+        {
+            innerlist = new List<CurveKey>();
+        }
+
+#endregion Constructors
+
+#region Public Methods
+
+        public void Add(CurveKey item)
+        {
+            if (item == null)
+                throw new ArgumentNullException("Value cannot be null.", (Exception) null);
+
+            if (innerlist.Count == 0)
+            {
+                innerlist.Add(item);
+                return;
+            }
+
+            for (int i = 0; i < innerlist.Count; i++)
+            {
+                if (item.Position < innerlist[i].Position)
+                {
+                    innerlist.Insert(i, item);
+                    return;
+                }
+            }
+
+            innerlist.Add(item);
+        }
+
+        public void Clear()
+        {
+            innerlist.Clear();
+        }
+
+        public bool Contains(CurveKey item)
+        {
+            return innerlist.Contains(item);
+        }
+
+        public void CopyTo(CurveKey[] array, int arrayIndex)
+        {
+            innerlist.CopyTo(array, arrayIndex);
+        }
+
+        public IEnumerator<CurveKey> GetEnumerator()
+        {
+            return innerlist.GetEnumerator();
+        }
+
+        public bool Remove(CurveKey item)
+        {
+            return innerlist.Remove(item);
+        }
+
+        IEnumerator IEnumerable.GetEnumerator()
+        {
+            return innerlist.GetEnumerator();
+        }
+
+        public CurveKeyCollection Clone()
+        {
+            CurveKeyCollection ckc = new CurveKeyCollection();
+            foreach (CurveKey key in innerlist)
+                ckc.Add(key);
+            return ckc;
+        }
+
+        public int IndexOf(CurveKey item)
+        {
+            return innerlist.IndexOf(item);
+        }
+
+        public void RemoveAt(int index)
+        {
+            if (index != Count && index > -1)
+                innerlist.RemoveAt(index);
+            else
+                throw new ArgumentOutOfRangeException(
+                    "Index was out of range. Must be non-negative and less than the size of the collection.\r\nParameter name: index",
+                    (Exception) null);
+        }
+
+#endregion Public Methods
+    }
+}
+
+#endif

Farseer Physics Engine 3.5/Common/Decomposition/BayazitDecomposer.cs

@@ -0,0 +1,243 @@
+using System.Collections.Generic;
+using System.Diagnostics;
+using Microsoft.Xna.Framework;
+
+namespace FarseerPhysics.Common.Decomposition
+{
+    //From phed rev 36: http://code.google.com/p/phed/source/browse/trunk/Polygon.cpp
+
+    /// <summary>
+    /// Convex decomposition algorithm created by Mark Bayazit (http://mnbayazit.com/)
+    /// 
+    /// Properties:
+    /// - Tries to decompose using polygons instead of triangles.
+    /// - Tends to produce optimal results with low processing time.
+    /// - Running time is O(nr), n = number of vertices, r = reflex vertices.
+    /// - Does not support holes.
+    /// 
+    /// For more information about this algorithm, see http://mnbayazit.com/406/bayazit
+    /// </summary>
+    internal static class BayazitDecomposer
+    {
+        /// <summary>
+        /// Decompose the polygon into several smaller non-concave polygon.
+        /// If the polygon is already convex, it will return the original polygon, unless it is over Settings.MaxPolygonVertices.
+        /// </summary>
+        public static List<Vertices> ConvexPartition(Vertices vertices)
+        {
+            Debug.Assert(vertices.Count > 3);
+            Debug.Assert(vertices.IsCounterClockWise());
+
+            return TriangulatePolygon(vertices);
+        }
+
+        private static List<Vertices> TriangulatePolygon(Vertices vertices)
+        {
+            List<Vertices> list = new List<Vertices>();
+            Vector2 lowerInt = new Vector2();
+            Vector2 upperInt = new Vector2(); // intersection points
+            int lowerIndex = 0, upperIndex = 0;
+            Vertices lowerPoly, upperPoly;
+
+            for (int i = 0; i < vertices.Count; ++i)
+            {
+                if (Reflex(i, vertices))
+                {
+                    float upperDist;
+                    float lowerDist = upperDist = float.MaxValue;
+                    for (int j = 0; j < vertices.Count; ++j)
+                    {
+                        // if line intersects with an edge
+                        float d;
+                        Vector2 p;
+                        if (Left(At(i - 1, vertices), At(i, vertices), At(j, vertices)) && RightOn(At(i - 1, vertices), At(i, vertices), At(j - 1, vertices)))
+                        {
+                            // find the point of intersection
+                            p = LineTools.LineIntersect(At(i - 1, vertices), At(i, vertices), At(j, vertices), At(j - 1, vertices));
+
+                            if (Right(At(i + 1, vertices), At(i, vertices), p))
+                            {
+                                // make sure it's inside the poly
+                                d = SquareDist(At(i, vertices), p);
+                                if (d < lowerDist)
+                                {
+                                    // keep only the closest intersection
+                                    lowerDist = d;
+                                    lowerInt = p;
+                                    lowerIndex = j;
+                                }
+                            }
+                        }
+
+                        if (Left(At(i + 1, vertices), At(i, vertices), At(j + 1, vertices)) && RightOn(At(i + 1, vertices), At(i, vertices), At(j, vertices)))
+                        {
+                            p = LineTools.LineIntersect(At(i + 1, vertices), At(i, vertices), At(j, vertices), At(j + 1, vertices));
+
+                            if (Left(At(i - 1, vertices), At(i, vertices), p))
+                            {
+                                d = SquareDist(At(i, vertices), p);
+                                if (d < upperDist)
+                                {
+                                    upperDist = d;
+                                    upperIndex = j;
+                                    upperInt = p;
+                                }
+                            }
+                        }
+                    }
+
+                    // if there are no vertices to connect to, choose a point in the middle
+                    if (lowerIndex == (upperIndex + 1) % vertices.Count)
+                    {
+                        Vector2 p = ((lowerInt + upperInt) / 2);
+
+                        lowerPoly = Copy(i, upperIndex, vertices);
+                        lowerPoly.Add(p);
+                        upperPoly = Copy(lowerIndex, i, vertices);
+                        upperPoly.Add(p);
+                    }
+                    else
+                    {
+                        double highestScore = 0, bestIndex = lowerIndex;
+                        while (upperIndex < lowerIndex)
+                            upperIndex += vertices.Count;
+
+                        for (int j = lowerIndex; j <= upperIndex; ++j)
+                        {
+                            if (CanSee(i, j, vertices))
+                            {
+                                double score = 1 / (SquareDist(At(i, vertices), At(j, vertices)) + 1);
+                                if (Reflex(j, vertices))
+                                {
+                                    if (RightOn(At(j - 1, vertices), At(j, vertices), At(i, vertices)) && LeftOn(At(j + 1, vertices), At(j, vertices), At(i, vertices)))
+                                        score += 3;
+                                    else
+                                        score += 2;
+                                }
+                                else
+                                {
+                                    score += 1;
+                                }
+                                if (score > highestScore)
+                                {
+                                    bestIndex = j;
+                                    highestScore = score;
+                                }
+                            }
+                        }
+                        lowerPoly = Copy(i, (int)bestIndex, vertices);
+                        upperPoly = Copy((int)bestIndex, i, vertices);
+                    }
+                    list.AddRange(TriangulatePolygon(lowerPoly));
+                    list.AddRange(TriangulatePolygon(upperPoly));
+                    return list;
+                }
+            }
+
+            // polygon is already convex
+            if (vertices.Count > Settings.MaxPolygonVertices)
+            {
+                lowerPoly = Copy(0, vertices.Count / 2, vertices);
+                upperPoly = Copy(vertices.Count / 2, 0, vertices);
+                list.AddRange(TriangulatePolygon(lowerPoly));
+                list.AddRange(TriangulatePolygon(upperPoly));
+            }
+            else
+                list.Add(vertices);
+
+            return list;
+        }
+
+        private static Vector2 At(int i, Vertices vertices)
+        {
+            int s = vertices.Count;
+            return vertices[i < 0 ? s - 1 - ((-i - 1) % s) : i % s];
+        }
+
+        private static Vertices Copy(int i, int j, Vertices vertices)
+        {
+            while (j < i)
+                j += vertices.Count;
+
+            Vertices p = new Vertices(j);
+
+            for (; i <= j; ++i)
+            {
+                p.Add(At(i, vertices));
+            }
+            return p;
+        }
+
+        private static bool CanSee(int i, int j, Vertices vertices)
+        {
+            if (Reflex(i, vertices))
+            {
+                if (LeftOn(At(i, vertices), At(i - 1, vertices), At(j, vertices)) && RightOn(At(i, vertices), At(i + 1, vertices), At(j, vertices)))
+                    return false;
+            }
+            else
+            {
+                if (RightOn(At(i, vertices), At(i + 1, vertices), At(j, vertices)) || LeftOn(At(i, vertices), At(i - 1, vertices), At(j, vertices)))
+                    return false;
+            }
+            if (Reflex(j, vertices))
+            {
+                if (LeftOn(At(j, vertices), At(j - 1, vertices), At(i, vertices)) && RightOn(At(j, vertices), At(j + 1, vertices), At(i, vertices)))
+                    return false;
+            }
+            else
+            {
+                if (RightOn(At(j, vertices), At(j + 1, vertices), At(i, vertices)) || LeftOn(At(j, vertices), At(j - 1, vertices), At(i, vertices)))
+                    return false;
+            }
+            for (int k = 0; k < vertices.Count; ++k)
+            {
+                if ((k + 1) % vertices.Count == i || k == i || (k + 1) % vertices.Count == j || k == j)
+                    continue; // ignore incident edges
+
+                Vector2 intersectionPoint;
+
+                if (LineTools.LineIntersect(At(i, vertices), At(j, vertices), At(k, vertices), At(k + 1, vertices), out intersectionPoint))
+                    return false;
+            }
+            return true;
+        }
+
+        private static bool Reflex(int i, Vertices vertices)
+        {
+            return Right(i, vertices);
+        }
+
+        private static bool Right(int i, Vertices vertices)
+        {
+            return Right(At(i - 1, vertices), At(i, vertices), At(i + 1, vertices));
+        }
+
+        private static bool Left(Vector2 a, Vector2 b, Vector2 c)
+        {
+            return MathUtils.Area(ref a, ref b, ref c) > 0;
+        }
+
+        private static bool LeftOn(Vector2 a, Vector2 b, Vector2 c)
+        {
+            return MathUtils.Area(ref a, ref b, ref c) >= 0;
+        }
+
+        private static bool Right(Vector2 a, Vector2 b, Vector2 c)
+        {
+            return MathUtils.Area(ref a, ref b, ref c) < 0;
+        }
+
+        private static bool RightOn(Vector2 a, Vector2 b, Vector2 c)
+        {
+            return MathUtils.Area(ref a, ref b, ref c) <= 0;
+        }
+
+        private static float SquareDist(Vector2 a, Vector2 b)
+        {
+            float dx = b.X - a.X;
+            float dy = b.Y - a.Y;
+            return dx * dx + dy * dy;
+        }
+    }
+}

Farseer Physics Engine 3.5/Common/Decomposition/CDT/Delaunay/DelaunayTriangle.cs

@@ -0,0 +1,420 @@
+/* Poly2Tri
+ * Copyright (c) 2009-2010, Poly2Tri Contributors
+ * http://code.google.com/p/poly2tri/
+ *
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without modification,
+ * are permitted provided that the following conditions are met:
+ *
+ * * Redistributions of source code must retain the above copyright notice,
+ *   this list of conditions and the following disclaimer.
+ * * Redistributions in binary form must reproduce the above copyright notice,
+ *   this list of conditions and the following disclaimer in the documentation
+ *   and/or other materials provided with the distribution.
+ * * Neither the name of Poly2Tri nor the names of its contributors may be
+ *   used to endorse or promote products derived from this software without specific
+ *   prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+ * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
+ * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+ * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+ * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+ * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+
+// Changes from the Java version
+//   attributification
+// Future possibilities
+//   Flattening out the number of indirections
+//     Replacing arrays of 3 with fixed-length arrays?
+//     Replacing bool[3] with a bit array of some sort?
+//     Bundling everything into an AoS mess?
+//     Hardcode them all as ABC ?
+
+using System;
+using System.Collections.Generic;
+using System.Diagnostics;
+using FarseerPhysics.Common.Decomposition.CDT.Delaunay.Sweep;
+using FarseerPhysics.Common.Decomposition.CDT.Util;
+
+namespace FarseerPhysics.Common.Decomposition.CDT.Delaunay
+{
+    internal class DelaunayTriangle
+    {
+        /** Neighbor pointers */
+
+        /** Flags to determine if an edge is a Delauney edge */
+        public FixedBitArray3 EdgeIsConstrained;
+
+        /** Flags to determine if an edge is a Constrained edge */
+        public FixedBitArray3 EdgeIsDelaunay;
+        public Util.FixedArray3<DelaunayTriangle> Neighbors;
+
+        /** Has this triangle been marked as an interior triangle? */
+
+        public Util.FixedArray3<TriangulationPoint> Points;
+
+        public DelaunayTriangle(TriangulationPoint p1, TriangulationPoint p2, TriangulationPoint p3)
+        {
+            Points[0] = p1;
+            Points[1] = p2;
+            Points[2] = p3;
+        }
+
+        public bool IsInterior { get; set; }
+
+        public int IndexOf(TriangulationPoint p)
+        {
+            int i = Points.IndexOf(p);
+            if (i == -1) throw new Exception("Calling index with a point that doesn't exist in triangle");
+            return i;
+        }
+
+        //TODO: Port note - different implementation
+        public int IndexCW(TriangulationPoint p)
+        {
+            int index = IndexOf(p);
+            switch (index)
+            {
+                case 0:
+                    return 2;
+                case 1:
+                    return 0;
+                default:
+                    return 1;
+            }
+        }
+
+        //TODO: Port note - different implementation
+        public int IndexCCW(TriangulationPoint p)
+        {
+            int index = IndexOf(p);
+            switch (index)
+            {
+                case 0:
+                    return 1;
+                case 1:
+                    return 2;
+                default:
+                    return 0;
+            }
+        }
+
+        public bool Contains(TriangulationPoint p)
+        {
+            return (p == Points[0] || p == Points[1] || p == Points[2]);
+        }
+
+        public bool Contains(DTSweepConstraint e)
+        {
+            return (Contains(e.P) && Contains(e.Q));
+        }
+
+        public bool Contains(TriangulationPoint p, TriangulationPoint q)
+        {
+            return (Contains(p) && Contains(q));
+        }
+
+        /// <summary>
+        /// Update neighbor pointers
+        /// </summary>
+        /// <param name="p1">Point 1 of the shared edge</param>
+        /// <param name="p2">Point 2 of the shared edge</param>
+        /// <param name="t">This triangle's new neighbor</param>
+        private void MarkNeighbor(TriangulationPoint p1, TriangulationPoint p2, DelaunayTriangle t)
+        {
+            if ((p1 == Points[2] && p2 == Points[1]) || (p1 == Points[1] && p2 == Points[2]))
+            {
+                Neighbors[0] = t;
+            }
+            else if ((p1 == Points[0] && p2 == Points[2]) || (p1 == Points[2] && p2 == Points[0]))
+            {
+                Neighbors[1] = t;
+            }
+            else if ((p1 == Points[0] && p2 == Points[1]) || (p1 == Points[1] && p2 == Points[0]))
+            {
+                Neighbors[2] = t;
+            }
+            else
+            {
+                Debug.WriteLine("Neighbor error, please report!");
+                // throw new Exception("Neighbor error, please report!");
+            }
+        }
+
+        /// <summary>
+        /// Exhaustive search to update neighbor pointers
+        /// </summary>
+        public void MarkNeighbor(DelaunayTriangle t)
+        {
+            if (t.Contains(Points[1], Points[2]))
+            {
+                Neighbors[0] = t;
+                t.MarkNeighbor(Points[1], Points[2], this);
+            }
+            else if (t.Contains(Points[0], Points[2]))
+            {
+                Neighbors[1] = t;
+                t.MarkNeighbor(Points[0], Points[2], this);
+            }
+            else if (t.Contains(Points[0], Points[1]))
+            {
+                Neighbors[2] = t;
+                t.MarkNeighbor(Points[0], Points[1], this);
+            }
+            else
+            {
+                Debug.WriteLine("markNeighbor failed");
+            }
+        }
+
+        public void ClearNeighbors()
+        {
+            Neighbors[0] = Neighbors[1] = Neighbors[2] = null;
+        }
+
+        public void ClearNeighbor(DelaunayTriangle triangle)
+        {
+            if (Neighbors[0] == triangle)
+            {
+                Neighbors[0] = null;
+            }
+            else if (Neighbors[1] == triangle)
+            {
+                Neighbors[1] = null;
+            }
+            else
+            {
+                Neighbors[2] = null;
+            }
+        }
+
+        /**
+         * Clears all references to all other triangles and points
+         */
+
+        public void Clear()
+        {
+            DelaunayTriangle t;
+            for (int i = 0; i < 3; i++)
+            {
+                t = Neighbors[i];
+                if (t != null)
+                {
+                    t.ClearNeighbor(this);
+                }
+            }
+            ClearNeighbors();
+            Points[0] = Points[1] = Points[2] = null;
+        }
+
+        /// <param name="t">Opposite triangle</param>
+        /// <param name="p">The point in t that isn't shared between the triangles</param>
+        public TriangulationPoint OppositePoint(DelaunayTriangle t, TriangulationPoint p)
+        {
+            Debug.Assert(t != this, "self-pointer error");
+            return PointCW(t.PointCW(p));
+        }
+
+        public DelaunayTriangle NeighborCW(TriangulationPoint point)
+        {
+            return Neighbors[(Points.IndexOf(point) + 1)%3];
+        }
+
+        public DelaunayTriangle NeighborCCW(TriangulationPoint point)
+        {
+            return Neighbors[(Points.IndexOf(point) + 2)%3];
+        }
+
+        public DelaunayTriangle NeighborAcross(TriangulationPoint point)
+        {
+            return Neighbors[Points.IndexOf(point)];
+        }
+
+        public TriangulationPoint PointCCW(TriangulationPoint point)
+        {
+            return Points[(IndexOf(point) + 1)%3];
+        }
+
+        public TriangulationPoint PointCW(TriangulationPoint point)
+        {
+            return Points[(IndexOf(point) + 2)%3];
+        }
+
+        private void RotateCW()
+        {
+            var t = Points[2];
+            Points[2] = Points[1];
+            Points[1] = Points[0];
+            Points[0] = t;
+        }
+
+        /// <summary>
+        /// Legalize triangle by rotating clockwise around oPoint
+        /// </summary>
+        /// <param name="oPoint">The origin point to rotate around</param>
+        /// <param name="nPoint">???</param>
+        public void Legalize(TriangulationPoint oPoint, TriangulationPoint nPoint)
+        {
+            RotateCW();
+            Points[IndexCCW(oPoint)] = nPoint;
+        }
+
+        public override string ToString()
+        {
+            return Points[0] + "," + Points[1] + "," + Points[2];
+        }
+
+        /// <summary>
+        /// Finalize edge marking
+        /// </summary>
+        public void MarkNeighborEdges()
+        {
+            for (int i = 0; i < 3; i++)
+                if (EdgeIsConstrained[i] && Neighbors[i] != null)
+                {
+                    Neighbors[i].MarkConstrainedEdge(Points[(i + 1)%3], Points[(i + 2)%3]);
+                }
+        }
+
+        public void MarkEdge(DelaunayTriangle triangle)
+        {
+            for (int i = 0; i < 3; i++)
+                if (EdgeIsConstrained[i])
+                {
+                    triangle.MarkConstrainedEdge(Points[(i + 1)%3], Points[(i + 2)%3]);
+                }
+        }
+
+        public void MarkEdge(List<DelaunayTriangle> tList)
+        {
+            foreach (DelaunayTriangle t in tList)
+                for (int i = 0; i < 3; i++)
+                    if (t.EdgeIsConstrained[i])
+                    {
+                        MarkConstrainedEdge(t.Points[(i + 1)%3], t.Points[(i + 2)%3]);
+                    }
+        }
+
+        public void MarkConstrainedEdge(int index)
+        {
+            EdgeIsConstrained[index] = true;
+        }
+
+        public void MarkConstrainedEdge(DTSweepConstraint edge)
+        {
+            MarkConstrainedEdge(edge.P, edge.Q);
+        }
+
+        /// <summary>
+        /// Mark edge as constrained
+        /// </summary>
+        public void MarkConstrainedEdge(TriangulationPoint p, TriangulationPoint q)
+        {
+            int i = EdgeIndex(p, q);
+            if (i != -1) EdgeIsConstrained[i] = true;
+        }
+
+        public double Area()
+        {
+            double b = Points[0].X - Points[1].X;
+            double h = Points[2].Y - Points[1].Y;
+
+            return Math.Abs((b*h*0.5f));
+        }
+
+        public TriangulationPoint Centroid()
+        {
+            double cx = (Points[0].X + Points[1].X + Points[2].X)/3f;
+            double cy = (Points[0].Y + Points[1].Y + Points[2].Y)/3f;
+            return new TriangulationPoint(cx, cy);
+        }
+
+        /// <summary>
+        /// Get the index of the neighbor that shares this edge (or -1 if it isn't shared)
+        /// </summary>
+        /// <returns>index of the shared edge or -1 if edge isn't shared</returns>
+        public int EdgeIndex(TriangulationPoint p1, TriangulationPoint p2)
+        {
+            int i1 = Points.IndexOf(p1);
+            int i2 = Points.IndexOf(p2);
+
+            // Points of this triangle in the edge p1-p2
+            bool a = (i1 == 0 || i2 == 0);
+            bool b = (i1 == 1 || i2 == 1);
+            bool c = (i1 == 2 || i2 == 2);
+
+            if (b && c) return 0;
+            if (a && c) return 1;
+            if (a && b) return 2;
+            return -1;
+        }
+
+        public bool GetConstrainedEdgeCCW(TriangulationPoint p)
+        {
+            return EdgeIsConstrained[(IndexOf(p) + 2)%3];
+        }
+
+        public bool GetConstrainedEdgeCW(TriangulationPoint p)
+        {
+            return EdgeIsConstrained[(IndexOf(p) + 1)%3];
+        }
+
+        public bool GetConstrainedEdgeAcross(TriangulationPoint p)
+        {
+            return EdgeIsConstrained[IndexOf(p)];
+        }
+
+        public void SetConstrainedEdgeCCW(TriangulationPoint p, bool ce)
+        {
+            EdgeIsConstrained[(IndexOf(p) + 2)%3] = ce;
+        }
+
+        public void SetConstrainedEdgeCW(TriangulationPoint p, bool ce)
+        {
+            EdgeIsConstrained[(IndexOf(p) + 1)%3] = ce;
+        }
+
+        public void SetConstrainedEdgeAcross(TriangulationPoint p, bool ce)
+        {
+            EdgeIsConstrained[IndexOf(p)] = ce;
+        }
+
+        public bool GetDelaunayEdgeCCW(TriangulationPoint p)
+        {
+            return EdgeIsDelaunay[(IndexOf(p) + 2)%3];
+        }
+
+        public bool GetDelaunayEdgeCW(TriangulationPoint p)
+        {
+            return EdgeIsDelaunay[(IndexOf(p) + 1)%3];
+        }
+
+        public bool GetDelaunayEdgeAcross(TriangulationPoint p)
+        {
+            return EdgeIsDelaunay[IndexOf(p)];
+        }
+
+        public void SetDelaunayEdgeCCW(TriangulationPoint p, bool ce)
+        {
+            EdgeIsDelaunay[(IndexOf(p) + 2)%3] = ce;
+        }
+
+        public void SetDelaunayEdgeCW(TriangulationPoint p, bool ce)
+        {
+            EdgeIsDelaunay[(IndexOf(p) + 1)%3] = ce;
+        }
+
+        public void SetDelaunayEdgeAcross(TriangulationPoint p, bool ce)
+        {
+            EdgeIsDelaunay[IndexOf(p)] = ce;
+        }
+    }
+}

Farseer Physics Engine 3.5/Common/Decomposition/CDT/Delaunay/Sweep/AdvancingFront.cs

@@ -0,0 +1,180 @@
+/* Poly2Tri
+ * Copyright (c) 2009-2010, Poly2Tri Contributors
+ * http://code.google.com/p/poly2tri/
+ *
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without modification,
+ * are permitted provided that the following conditions are met:
+ *
+ * * Redistributions of source code must retain the above copyright notice,
+ *   this list of conditions and the following disclaimer.
+ * * Redistributions in binary form must reproduce the above copyright notice,
+ *   this list of conditions and the following disclaimer in the documentation
+ *   and/or other materials provided with the distribution.
+ * * Neither the name of Poly2Tri nor the names of its contributors may be
+ *   used to endorse or promote products derived from this software without specific
+ *   prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+ * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
+ * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+ * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+ * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+ * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+
+// Changes from the Java version
+//   Removed BST code, but not all artifacts of it
+// Future possibilities
+//   Eliminate Add/RemoveNode ?
+//   Comments comments and more comments!
+
+using System;
+using System.Text;
+
+namespace FarseerPhysics.Common.Decomposition.CDT.Delaunay.Sweep
+{
+    /**
+     * @author Thomas Åhlen (thahlen@gmail.com)
+     */
+
+    internal class AdvancingFront
+    {
+        public AdvancingFrontNode Head;
+        protected AdvancingFrontNode Search;
+        public AdvancingFrontNode Tail;
+
+        public AdvancingFront(AdvancingFrontNode head, AdvancingFrontNode tail)
+        {
+            Head = head;
+            Tail = tail;
+            Search = head;
+            AddNode(head);
+            AddNode(tail);
+        }
+
+        public void AddNode(AdvancingFrontNode node)
+        {
+            //_searchTree.put(node.key, node);
+        }
+
+        public void RemoveNode(AdvancingFrontNode node)
+        {
+            //_searchTree.delete( node.key );
+        }
+
+        public override string ToString()
+        {
+            StringBuilder sb = new StringBuilder();
+            AdvancingFrontNode node = Head;
+            while (node != Tail)
+            {
+                sb.Append(node.Point.X).Append("->");
+                node = node.Next;
+            }
+            sb.Append(Tail.Point.X);
+            return sb.ToString();
+        }
+
+        /// <summary>
+        /// MM:  This seems to be used by LocateNode to guess a position in the implicit linked list of AdvancingFrontNodes near x
+        ///      Removed an overload that depended on this being exact
+        /// </summary>
+        private AdvancingFrontNode FindSearchNode(double x)
+        {
+            // TODO: implement BST index 
+            return Search;
+        }
+
+        /// <summary>
+        /// We use a balancing tree to locate a node smaller or equal to given key value
+        /// </summary>
+        public AdvancingFrontNode LocateNode(TriangulationPoint point)
+        {
+            return LocateNode(point.X);
+        }
+
+        private AdvancingFrontNode LocateNode(double x)
+        {
+            AdvancingFrontNode node = FindSearchNode(x);
+            if (x < node.Value)
+            {
+                while ((node = node.Prev) != null)
+                    if (x >= node.Value)
+                    {
+                        Search = node;
+                        return node;
+                    }
+            }
+            else
+            {
+                while ((node = node.Next) != null)
+                    if (x < node.Value)
+                    {
+                        Search = node.Prev;
+                        return node.Prev;
+                    }
+            }
+            return null;
+        }
+
+        /// <summary>
+        /// This implementation will use simple node traversal algorithm to find a point on the front
+        /// </summary>
+        public AdvancingFrontNode LocatePoint(TriangulationPoint point)
+        {
+            double px = point.X;
+            AdvancingFrontNode node = FindSearchNode(px);
+            double nx = node.Point.X;
+
+            if (px == nx)
+            {
+                if (point != node.Point)
+                {
+                    // We might have two nodes with same x value for a short time
+                    if (point == node.Prev.Point)
+                    {
+                        node = node.Prev;
+                    }
+                    else if (point == node.Next.Point)
+                    {
+                        node = node.Next;
+                    }
+                    else
+                    {
+                        throw new Exception("Failed to find Node for given afront point");
+                        //node = null;
+                    }
+                }
+            }
+            else if (px < nx)
+            {
+                while ((node = node.Prev) != null)
+                {
+                    if (point == node.Point)
+                    {
+                        break;
+                    }
+                }
+            }
+            else
+            {
+                while ((node = node.Next) != null)
+                {
+                    if (point == node.Point)
+                    {
+                        break;
+                    }
+                }
+            }
+            Search = node;
+            return node;
+        }
+    }
+}

Farseer Physics Engine 3.5/Common/Decomposition/CDT/Delaunay/Sweep/AdvancingFrontNode.cs

@@ -0,0 +1,64 @@
+/* Poly2Tri
+ * Copyright (c) 2009-2010, Poly2Tri Contributors
+ * http://code.google.com/p/poly2tri/
+ *
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without modification,
+ * are permitted provided that the following conditions are met:
+ *
+ * * Redistributions of source code must retain the above copyright notice,
+ *   this list of conditions and the following disclaimer.
+ * * Redistributions in binary form must reproduce the above copyright notice,
+ *   this list of conditions and the following disclaimer in the documentation
+ *   and/or other materials provided with the distribution.
+ * * Neither the name of Poly2Tri nor the names of its contributors may be
+ *   used to endorse or promote products derived from this software without specific
+ *   prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+ * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
+ * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+ * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+ * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+ * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+
+// Changes from the Java version
+//   Removed getters
+//   Has* turned into attributes
+// Future possibilities
+//   Comments!
+
+namespace FarseerPhysics.Common.Decomposition.CDT.Delaunay.Sweep
+{
+    internal class AdvancingFrontNode
+    {
+        public AdvancingFrontNode Next;
+        public TriangulationPoint Point;
+        public AdvancingFrontNode Prev;
+        public DelaunayTriangle Triangle;
+        public double Value;
+
+        public AdvancingFrontNode(TriangulationPoint point)
+        {
+            Point = point;
+            Value = point.X;
+        }
+
+        public bool HasNext
+        {
+            get { return Next != null; }
+        }
+
+        public bool HasPrev
+        {
+            get { return Prev != null; }
+        }
+    }
+}

Farseer Physics Engine 3.5/Common/Decomposition/CDT/Delaunay/Sweep/DTSweepConstraint.cs

@@ -0,0 +1,66 @@
+/* Poly2Tri
+ * Copyright (c) 2009-2010, Poly2Tri Contributors
+ * http://code.google.com/p/poly2tri/
+ *
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without modification,
+ * are permitted provided that the following conditions are met:
+ *
+ * * Redistributions of source code must retain the above copyright notice,
+ *   this list of conditions and the following disclaimer.
+ * * Redistributions in binary form must reproduce the above copyright notice,
+ *   this list of conditions and the following disclaimer in the documentation
+ *   and/or other materials provided with the distribution.
+ * * Neither the name of Poly2Tri nor the names of its contributors may be
+ *   used to endorse or promote products derived from this software without specific
+ *   prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+ * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
+ * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+ * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+ * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+ * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+
+namespace FarseerPhysics.Common.Decomposition.CDT.Delaunay.Sweep
+{
+    internal class DTSweepConstraint : TriangulationConstraint
+    {
+        /// <summary>
+        /// Give two points in any order. Will always be ordered so
+        /// that q.y > p.y and q.x > p.x if same y value 
+        /// </summary>
+        public DTSweepConstraint(TriangulationPoint p1, TriangulationPoint p2)
+        {
+            P = p1;
+            Q = p2;
+            if (p1.Y > p2.Y)
+            {
+                Q = p1;
+                P = p2;
+            }
+            else if (p1.Y == p2.Y)
+            {
+                if (p1.X > p2.X)
+                {
+                    Q = p1;
+                    P = p2;
+                }
+                else if (p1.X == p2.X)
+                {
+                    //                logger.info( "Failed to create constraint {}={}", p1, p2 );
+                    //                throw new DuplicatePointException( p1 + "=" + p2 );
+                    //                return;
+                }
+            }
+            Q.AddEdge(this);
+        }
+    }
+}

Farseer Physics Engine 3.5/Common/Decomposition/CDT/Delaunay/Sweep/DTSweepContext.cs

@@ -0,0 +1,236 @@
+/* Poly2Tri
+ * Copyright (c) 2009-2010, Poly2Tri Contributors
+ * http://code.google.com/p/poly2tri/
+ *
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without modification,
+ * are permitted provided that the following conditions are met:
+ *
+ * * Redistributions of source code must retain the above copyright notice,
+ *   this list of conditions and the following disclaimer.
+ * * Redistributions in binary form must reproduce the above copyright notice,
+ *   this list of conditions and the following disclaimer in the documentation
+ *   and/or other materials provided with the distribution.
+ * * Neither the name of Poly2Tri nor the names of its contributors may be
+ *   used to endorse or promote products derived from this software without specific
+ *   prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+ * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
+ * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+ * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+ * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+ * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+
+namespace FarseerPhysics.Common.Decomposition.CDT.Delaunay.Sweep
+{
+    /**
+     * 
+     * @author Thomas Åhlén, thahlen@gmail.com
+     *
+     */
+
+    internal class DTSweepContext : TriangulationContext
+    {
+        // Inital triangle factor, seed triangle will extend 30% of 
+        // PointSet width to both left and right.
+        private const float ALPHA = 0.3f;
+
+        public DTSweepBasin Basin = new DTSweepBasin();
+        public DTSweepEdgeEvent EdgeEvent = new DTSweepEdgeEvent();
+
+        private DTSweepPointComparator _comparator = new DTSweepPointComparator();
+        public AdvancingFront aFront;
+
+        public DTSweepContext()
+        {
+            Clear();
+        }
+
+        public TriangulationPoint Head { get; set; }
+        public TriangulationPoint Tail { get; set; }
+
+        public void RemoveFromList(DelaunayTriangle triangle)
+        {
+            Triangles.Remove(triangle);
+            // TODO: remove all neighbor pointers to this triangle
+            //        for( int i=0; i<3; i++ )
+            //        {
+            //            if( triangle.neighbors[i] != null )
+            //            {
+            //                triangle.neighbors[i].clearNeighbor( triangle );
+            //            }
+            //        }
+            //        triangle.clearNeighbors();
+        }
+
+        public void MeshClean(DelaunayTriangle triangle)
+        {
+            MeshCleanReq(triangle);
+        }
+
+        private void MeshCleanReq(DelaunayTriangle triangle)
+        {
+            if (triangle != null && !triangle.IsInterior)
+            {
+                triangle.IsInterior = true;
+                Triangulatable.AddTriangle(triangle);
+                for (int i = 0; i < 3; i++)
+                {
+                    if (!triangle.EdgeIsConstrained[i])
+                    {
+                        MeshCleanReq(triangle.Neighbors[i]);
+                    }
+                }
+            }
+        }
+
+        public override void Clear()
+        {
+            base.Clear();
+            Triangles.Clear();
+        }
+
+        public void AddNode(AdvancingFrontNode node)
+        {
+            //        Console.WriteLine( "add:" + node.key + ":" + System.identityHashCode(node.key));
+            //        m_nodeTree.put( node.getKey(), node );
+            aFront.AddNode(node);
+        }
+
+        public void RemoveNode(AdvancingFrontNode node)
+        {
+            //        Console.WriteLine( "remove:" + node.key + ":" + System.identityHashCode(node.key));
+            //        m_nodeTree.delete( node.getKey() );
+            aFront.RemoveNode(node);
+        }
+
+        public AdvancingFrontNode LocateNode(TriangulationPoint point)
+        {
+            return aFront.LocateNode(point);
+        }
+
+        public void CreateAdvancingFront()
+        {
+            AdvancingFrontNode head, tail, middle;
+            // Initial triangle
+            DelaunayTriangle iTriangle = new DelaunayTriangle(Points[0], Tail, Head);
+            Triangles.Add(iTriangle);
+
+            head = new AdvancingFrontNode(iTriangle.Points[1]);
+            head.Triangle = iTriangle;
+            middle = new AdvancingFrontNode(iTriangle.Points[0]);
+            middle.Triangle = iTriangle;
+            tail = new AdvancingFrontNode(iTriangle.Points[2]);
+
+            aFront = new AdvancingFront(head, tail);
+            aFront.AddNode(middle);
+
+            // TODO: I think it would be more intuitive if head is middles next and not previous
+            //       so swap head and tail
+            aFront.Head.Next = middle;
+            middle.Next = aFront.Tail;
+            middle.Prev = aFront.Head;
+            aFront.Tail.Prev = middle;
+        }
+
+        /// <summary>
+        /// Try to map a node to all sides of this triangle that don't have 
+        /// a neighbor.
+        /// </summary>
+        public void MapTriangleToNodes(DelaunayTriangle t)
+        {
+            AdvancingFrontNode n;
+            for (int i = 0; i < 3; i++)
+            {
+                if (t.Neighbors[i] == null)
+                {
+                    n = aFront.LocatePoint(t.PointCW(t.Points[i]));
+                    if (n != null)
+                    {
+                        n.Triangle = t;
+                    }
+                }
+            }
+        }
+
+        public override void PrepareTriangulation(Triangulatable t)
+        {
+            base.PrepareTriangulation(t);
+
+            double xmax, xmin;
+            double ymax, ymin;
+
+            xmax = xmin = Points[0].X;
+            ymax = ymin = Points[0].Y;
+
+            // Calculate bounds. Should be combined with the sorting
+            foreach (TriangulationPoint p in Points)
+            {
+                if (p.X > xmax)
+                    xmax = p.X;
+                if (p.X < xmin)
+                    xmin = p.X;
+                if (p.Y > ymax)
+                    ymax = p.Y;
+                if (p.Y < ymin)
+                    ymin = p.Y;
+            }
+
+            double deltaX = ALPHA*(xmax - xmin);
+            double deltaY = ALPHA*(ymax - ymin);
+            TriangulationPoint p1 = new TriangulationPoint(xmax + deltaX, ymin - deltaY);
+            TriangulationPoint p2 = new TriangulationPoint(xmin - deltaX, ymin - deltaY);
+
+            Head = p1;
+            Tail = p2;
+
+            //        long time = System.nanoTime();
+            // Sort the points along y-axis
+            Points.Sort(_comparator);
+            //        logger.info( "Triangulation setup [{}ms]", ( System.nanoTime() - time ) / 1e6 );
+        }
+
+
+        public void FinalizeTriangulation()
+        {
+            Triangulatable.AddTriangles(Triangles);
+            Triangles.Clear();
+        }
+
+        public override TriangulationConstraint NewConstraint(TriangulationPoint a, TriangulationPoint b)
+        {
+            return new DTSweepConstraint(a, b);
+        }
+
+        #region Nested type: DTSweepBasin
+
+        public class DTSweepBasin
+        {
+            public AdvancingFrontNode bottomNode;
+            public bool leftHighest;
+            public AdvancingFrontNode leftNode;
+            public AdvancingFrontNode rightNode;
+            public double width;
+        }
+
+        #endregion
+
+        #region Nested type: DTSweepEdgeEvent
+
+        public class DTSweepEdgeEvent
+        {
+            public DTSweepConstraint ConstrainedEdge;
+            public bool Right;
+        }
+
+        #endregion
+    }
+}

Farseer Physics Engine 3.5/Common/Decomposition/CDT/Delaunay/Sweep/DTSweepPointComparator.cs

@@ -0,0 +1,69 @@
+/* Poly2Tri
+ * Copyright (c) 2009-2010, Poly2Tri Contributors
+ * http://code.google.com/p/poly2tri/
+ *
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without modification,
+ * are permitted provided that the following conditions are met:
+ *
+ * * Redistributions of source code must retain the above copyright notice,
+ *   this list of conditions and the following disclaimer.
+ * * Redistributions in binary form must reproduce the above copyright notice,
+ *   this list of conditions and the following disclaimer in the documentation
+ *   and/or other materials provided with the distribution.
+ * * Neither the name of Poly2Tri nor the names of its contributors may be
+ *   used to endorse or promote products derived from this software without specific
+ *   prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+ * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
+ * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+ * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+ * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+ * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+
+using System.Collections.Generic;
+
+namespace FarseerPhysics.Common.Decomposition.CDT.Delaunay.Sweep
+{
+    internal class DTSweepPointComparator : IComparer<TriangulationPoint>
+    {
+        #region IComparer<TriangulationPoint> Members
+
+        public int Compare(TriangulationPoint p1, TriangulationPoint p2)
+        {
+            if (p1.Y < p2.Y)
+            {
+                return -1;
+            }
+            else if (p1.Y > p2.Y)
+            {
+                return 1;
+            }
+            else
+            {
+                if (p1.X < p2.X)
+                {
+                    return -1;
+                }
+                else if (p1.X > p2.X)
+                {
+                    return 1;
+                }
+                else
+                {
+                    return 0;
+                }
+            }
+        }
+
+        #endregion
+    }
+}

Farseer Physics Engine 3.5/Common/Decomposition/CDT/Delaunay/Sweep/PointOnEdgeException.cs

@@ -0,0 +1,43 @@
+/* Poly2Tri
+ * Copyright (c) 2009-2010, Poly2Tri Contributors
+ * http://code.google.com/p/poly2tri/
+ *
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without modification,
+ * are permitted provided that the following conditions are met:
+ *
+ * * Redistributions of source code must retain the above copyright notice,
+ *   this list of conditions and the following disclaimer.
+ * * Redistributions in binary form must reproduce the above copyright notice,
+ *   this list of conditions and the following disclaimer in the documentation
+ *   and/or other materials provided with the distribution.
+ * * Neither the name of Poly2Tri nor the names of its contributors may be
+ *   used to endorse or promote products derived from this software without specific
+ *   prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+ * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
+ * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+ * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+ * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+ * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+
+using System;
+
+namespace FarseerPhysics.Common.Decomposition.CDT.Delaunay.Sweep
+{
+    internal class PointOnEdgeException : NotImplementedException
+    {
+        public PointOnEdgeException(string message)
+            : base(message)
+        {
+        }
+    }
+}

Farseer Physics Engine 3.5/Common/Decomposition/CDT/ITriangulatable.cs

@@ -0,0 +1,48 @@
+/* Poly2Tri
+ * Copyright (c) 2009-2010, Poly2Tri Contributors
+ * http://code.google.com/p/poly2tri/
+ *
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without modification,
+ * are permitted provided that the following conditions are met:
+ *
+ * * Redistributions of source code must retain the above copyright notice,
+ *   this list of conditions and the following disclaimer.
+ * * Redistributions in binary form must reproduce the above copyright notice,
+ *   this list of conditions and the following disclaimer in the documentation
+ *   and/or other materials provided with the distribution.
+ * * Neither the name of Poly2Tri nor the names of its contributors may be
+ *   used to endorse or promote products derived from this software without specific
+ *   prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+ * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
+ * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+ * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+ * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+ * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+
+using System.Collections.Generic;
+using FarseerPhysics.Common.Decomposition.CDT.Delaunay;
+
+namespace FarseerPhysics.Common.Decomposition.CDT
+{
+    internal interface Triangulatable
+    {
+        IList<TriangulationPoint> Points { get; } // MM: Neither of these are used via interface (yet?)
+        IList<DelaunayTriangle> Triangles { get; }
+        TriangulationMode TriangulationMode { get; }
+        void PrepareTriangulation(TriangulationContext tcx);
+
+        void AddTriangle(DelaunayTriangle t);
+        void AddTriangles(IEnumerable<DelaunayTriangle> list);
+        void ClearTriangles();
+    }
+}

Farseer Physics Engine 3.5/Common/Decomposition/CDT/Orientation.cs

@@ -0,0 +1,40 @@
+/* Poly2Tri
+ * Copyright (c) 2009-2010, Poly2Tri Contributors
+ * http://code.google.com/p/poly2tri/
+ *
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without modification,
+ * are permitted provided that the following conditions are met:
+ *
+ * * Redistributions of source code must retain the above copyright notice,
+ *   this list of conditions and the following disclaimer.
+ * * Redistributions in binary form must reproduce the above copyright notice,
+ *   this list of conditions and the following disclaimer in the documentation
+ *   and/or other materials provided with the distribution.
+ * * Neither the name of Poly2Tri nor the names of its contributors may be
+ *   used to endorse or promote products derived from this software without specific
+ *   prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+ * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
+ * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+ * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+ * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+ * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+
+namespace FarseerPhysics.Common.Decomposition.CDT
+{
+    internal enum Orientation
+    {
+        CW,
+        CCW,
+        Collinear
+    }
+}

Farseer Physics Engine 3.5/Common/Decomposition/CDT/Polygon/Polygon.cs

@@ -0,0 +1,272 @@
+/* Poly2Tri
+ * Copyright (c) 2009-2010, Poly2Tri Contributors
+ * http://code.google.com/p/poly2tri/
+ *
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without modification,
+ * are permitted provided that the following conditions are met:
+ *
+ * * Redistributions of source code must retain the above copyright notice,
+ *   this list of conditions and the following disclaimer.
+ * * Redistributions in binary form must reproduce the above copyright notice,
+ *   this list of conditions and the following disclaimer in the documentation
+ *   and/or other materials provided with the distribution.
+ * * Neither the name of Poly2Tri nor the names of its contributors may be
+ *   used to endorse or promote products derived from this software without specific
+ *   prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+ * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
+ * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+ * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+ * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+ * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+
+// Changes from the Java version
+//   Polygon constructors sprused up, checks for 3+ polys
+//   Naming of everything
+//   getTriangulationMode() -> TriangulationMode { get; }
+//   Exceptions replaced
+// Future possibilities
+//   We have a lot of Add/Clear methods -- we may prefer to just expose the container
+//   Some self-explanitory methods may deserve commenting anyways
+
+using System;
+using System.Collections.Generic;
+using System.Linq;
+using FarseerPhysics.Common.Decomposition.CDT.Delaunay;
+
+namespace FarseerPhysics.Common.Decomposition.CDT.Polygon
+{
+    internal class Polygon : Triangulatable
+    {
+        protected List<Polygon> _holes;
+        protected PolygonPoint _last;
+        protected List<TriangulationPoint> _points = new List<TriangulationPoint>();
+        protected List<TriangulationPoint> _steinerPoints;
+        protected List<DelaunayTriangle> _triangles;
+
+        /// <summary>
+        /// Create a polygon from a list of at least 3 points with no duplicates.
+        /// </summary>
+        /// <param name="points">A list of unique points</param>
+        public Polygon(IList<PolygonPoint> points)
+        {
+            if (points.Count < 3) throw new ArgumentException("List has fewer than 3 points", "points");
+
+            // Lets do one sanity check that first and last point hasn't got same position
+            // Its something that often happen when importing polygon data from other formats
+            if (points[0].Equals(points[points.Count - 1])) points.RemoveAt(points.Count - 1);
+
+            _points.AddRange(points.Cast<TriangulationPoint>());
+        }
+
+        /// <summary>
+        /// Create a polygon from a list of at least 3 points with no duplicates.
+        /// </summary>
+        /// <param name="points">A list of unique points.</param>
+        public Polygon(IEnumerable<PolygonPoint> points) : this((points as IList<PolygonPoint>) ?? points.ToArray())
+        {
+        }
+
+        public Polygon()
+        {
+        }
+
+        public IList<Polygon> Holes
+        {
+            get { return _holes; }
+        }
+
+        #region Triangulatable Members
+
+        public TriangulationMode TriangulationMode
+        {
+            get { return TriangulationMode.Polygon; }
+        }
+
+        public IList<TriangulationPoint> Points
+        {
+            get { return _points; }
+        }
+
+        public IList<DelaunayTriangle> Triangles
+        {
+            get { return _triangles; }
+        }
+
+        public void AddTriangle(DelaunayTriangle t)
+        {
+            _triangles.Add(t);
+        }
+
+        public void AddTriangles(IEnumerable<DelaunayTriangle> list)
+        {
+            _triangles.AddRange(list);
+        }
+
+        public void ClearTriangles()
+        {
+            if (_triangles != null) _triangles.Clear();
+        }
+
+        /// <summary>
+        /// Creates constraints and populates the context with points
+        /// </summary>
+        /// <param name="tcx">The context</param>
+        public void PrepareTriangulation(TriangulationContext tcx)
+        {
+            if (_triangles == null)
+            {
+                _triangles = new List<DelaunayTriangle>(_points.Count);
+            }
+            else
+            {
+                _triangles.Clear();
+            }
+
+            // Outer constraints
+            for (int i = 0; i < _points.Count - 1; i++)
+            {
+                tcx.NewConstraint(_points[i], _points[i + 1]);
+            }
+            tcx.NewConstraint(_points[0], _points[_points.Count - 1]);
+            tcx.Points.AddRange(_points);
+
+            // Hole constraints
+            if (_holes != null)
+            {
+                foreach (Polygon p in _holes)
+                {
+                    for (int i = 0; i < p._points.Count - 1; i++)
+                    {
+                        tcx.NewConstraint(p._points[i], p._points[i + 1]);
+                    }
+                    tcx.NewConstraint(p._points[0], p._points[p._points.Count - 1]);
+                    tcx.Points.AddRange(p._points);
+                }
+            }
+
+            if (_steinerPoints != null)
+            {
+                tcx.Points.AddRange(_steinerPoints);
+            }
+        }
+
+        #endregion
+
+        public void AddSteinerPoint(TriangulationPoint point)
+        {
+            if (_steinerPoints == null)
+            {
+                _steinerPoints = new List<TriangulationPoint>();
+            }
+            _steinerPoints.Add(point);
+        }
+
+        public void AddSteinerPoints(List<TriangulationPoint> points)
+        {
+            if (_steinerPoints == null)
+            {
+                _steinerPoints = new List<TriangulationPoint>();
+            }
+            _steinerPoints.AddRange(points);
+        }
+
+        public void ClearSteinerPoints()
+        {
+            if (_steinerPoints != null)
+            {
+                _steinerPoints.Clear();
+            }
+        }
+
+        /// <summary>
+        /// Add a hole to the polygon.
+        /// </summary>
+        /// <param name="poly">A subtraction polygon fully contained inside this polygon.</param>
+        public void AddHole(Polygon poly)
+        {
+            if (_holes == null) _holes = new List<Polygon>();
+            _holes.Add(poly);
+            // XXX: tests could be made here to be sure it is fully inside
+            //        addSubtraction( poly.getPoints() );
+        }
+
+        /// <summary>
+        /// Inserts newPoint after point.
+        /// </summary>
+        /// <param name="point">The point to insert after in the polygon</param>
+        /// <param name="newPoint">The point to insert into the polygon</param>
+        public void InsertPointAfter(PolygonPoint point, PolygonPoint newPoint)
+        {
+            // Validate that 
+            int index = _points.IndexOf(point);
+            if (index == -1)
+                throw new ArgumentException(
+                    "Tried to insert a point into a Polygon after a point not belonging to the Polygon", "point");
+            newPoint.Next = point.Next;
+            newPoint.Previous = point;
+            point.Next.Previous = newPoint;
+            point.Next = newPoint;
+            _points.Insert(index + 1, newPoint);
+        }
+
+        /// <summary>
+        /// Inserts list (after last point in polygon?)
+        /// </summary>
+        /// <param name="list"></param>
+        public void AddPoints(IEnumerable<PolygonPoint> list)
+        {
+            PolygonPoint first;
+            foreach (PolygonPoint p in list)
+            {
+                p.Previous = _last;
+                if (_last != null)
+                {
+                    p.Next = _last.Next;
+                    _last.Next = p;
+                }
+                _last = p;
+                _points.Add(p);
+            }
+            first = (PolygonPoint) _points[0];
+            _last.Next = first;
+            first.Previous = _last;
+        }
+
+        /// <summary>
+        /// Adds a point after the last in the polygon.
+        /// </summary>
+        /// <param name="p">The point to add</param>
+        public void AddPoint(PolygonPoint p)
+        {
+            p.Previous = _last;
+            p.Next = _last.Next;
+            _last.Next = p;
+            _points.Add(p);
+        }
+
+        /// <summary>
+        /// Removes a point from the polygon.
+        /// </summary>
+        /// <param name="p"></param>
+        public void RemovePoint(PolygonPoint p)
+        {
+            PolygonPoint next, prev;
+
+            next = p.Next;
+            prev = p.Previous;
+            prev.Next = next;
+            next.Previous = prev;
+            _points.Remove(p);
+        }
+    }
+}

Farseer Physics Engine 3.5/Common/Decomposition/CDT/Polygon/PolygonPoint.cs

@@ -0,0 +1,48 @@
+/* Poly2Tri
+ * Copyright (c) 2009-2010, Poly2Tri Contributors
+ * http://code.google.com/p/poly2tri/
+ *
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without modification,
+ * are permitted provided that the following conditions are met:
+ *
+ * * Redistributions of source code must retain the above copyright notice,
+ *   this list of conditions and the following disclaimer.
+ * * Redistributions in binary form must reproduce the above copyright notice,
+ *   this list of conditions and the following disclaimer in the documentation
+ *   and/or other materials provided with the distribution.
+ * * Neither the name of Poly2Tri nor the names of its contributors may be
+ *   used to endorse or promote products derived from this software without specific
+ *   prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+ * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
+ * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+ * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+ * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+ * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+
+// Changes from the Java version
+//   Replaced get/set Next/Previous with attributes
+// Future possibilities
+//   Documentation!
+
+namespace FarseerPhysics.Common.Decomposition.CDT.Polygon
+{
+    internal class PolygonPoint : TriangulationPoint
+    {
+        public PolygonPoint(double x, double y) : base(x, y)
+        {
+        }
+
+        public PolygonPoint Next { get; set; }
+        public PolygonPoint Previous { get; set; }
+    }
+}

Farseer Physics Engine 3.5/Common/Decomposition/CDT/Polygon/PolygonSet.cs

@@ -0,0 +1,65 @@
+/* Poly2Tri
+ * Copyright (c) 2009-2010, Poly2Tri Contributors
+ * http://code.google.com/p/poly2tri/
+ *
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without modification,
+ * are permitted provided that the following conditions are met:
+ *
+ * * Redistributions of source code must retain the above copyright notice,
+ *   this list of conditions and the following disclaimer.
+ * * Redistributions in binary form must reproduce the above copyright notice,
+ *   this list of conditions and the following disclaimer in the documentation
+ *   and/or other materials provided with the distribution.
+ * * Neither the name of Poly2Tri nor the names of its contributors may be
+ *   used to endorse or promote products derived from this software without specific
+ *   prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+ * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
+ * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+ * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+ * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+ * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+
+// Changes from the Java version
+//   Replaced getPolygons with attribute
+// Future possibilities
+//   Replace Add(Polygon) with exposed container?
+//   Replace entire class with HashSet<Polygon> ?
+
+using System.Collections.Generic;
+
+namespace FarseerPhysics.Common.Decomposition.CDT.Polygon
+{
+    internal class PolygonSet
+    {
+        protected List<Polygon> _polygons = new List<Polygon>();
+
+        public PolygonSet()
+        {
+        }
+
+        public PolygonSet(Polygon poly)
+        {
+            _polygons.Add(poly);
+        }
+
+        public IEnumerable<Polygon> Polygons
+        {
+            get { return _polygons; }
+        }
+
+        public void Add(Polygon p)
+        {
+            _polygons.Add(p);
+        }
+    }
+}

Farseer Physics Engine 3.5/Common/Decomposition/CDT/Sets/ConstrainedPointSet.cs

@@ -0,0 +1,114 @@
+/* Poly2Tri
+ * Copyright (c) 2009-2010, Poly2Tri Contributors
+ * http://code.google.com/p/poly2tri/
+ *
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without modification,
+ * are permitted provided that the following conditions are met:
+ *
+ * * Redistributions of source code must retain the above copyright notice,
+ *   this list of conditions and the following disclaimer.
+ * * Redistributions in binary form must reproduce the above copyright notice,
+ *   this list of conditions and the following disclaimer in the documentation
+ *   and/or other materials provided with the distribution.
+ * * Neither the name of Poly2Tri nor the names of its contributors may be
+ *   used to endorse or promote products derived from this software without specific
+ *   prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+ * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
+ * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+ * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+ * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+ * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+
+using System.Collections.Generic;
+
+namespace FarseerPhysics.Common.Decomposition.CDT.Sets
+{
+    /*
+     * Extends the PointSet by adding some Constraints on how it will be triangulated<br>
+     * A constraint defines an edge between two points in the set, these edges can not
+     * be crossed. They will be enforced triangle edges after a triangulation.
+     * <p>
+     * 
+     * 
+     * @author Thomas Åhlén, thahlen@gmail.com
+     */
+
+    internal class ConstrainedPointSet : PointSet
+    {
+        private List<TriangulationPoint> _constrainedPointList;
+
+        public ConstrainedPointSet(List<TriangulationPoint> points, int[] index)
+            : base(points)
+        {
+            EdgeIndex = index;
+        }
+
+        /**
+         * 
+         * @param points - A list of all points in PointSet
+         * @param constraints - Pairs of two points defining a constraint, all points <b>must</b> be part of given PointSet!
+         */
+
+        public ConstrainedPointSet(List<TriangulationPoint> points, IEnumerable<TriangulationPoint> constraints)
+            : base(points)
+        {
+            _constrainedPointList = new List<TriangulationPoint>();
+            _constrainedPointList.AddRange(constraints);
+        }
+
+        public int[] EdgeIndex { get; private set; }
+
+        public override TriangulationMode TriangulationMode
+        {
+            get { return TriangulationMode.Constrained; }
+        }
+
+        public override void PrepareTriangulation(TriangulationContext tcx)
+        {
+            base.PrepareTriangulation(tcx);
+            if (_constrainedPointList != null)
+            {
+                TriangulationPoint p1, p2;
+                List<TriangulationPoint>.Enumerator iterator = _constrainedPointList.GetEnumerator();
+                while (iterator.MoveNext())
+                {
+                    p1 = iterator.Current;
+                    iterator.MoveNext();
+                    p2 = iterator.Current;
+                    tcx.NewConstraint(p1, p2);
+                }
+            }
+            else
+            {
+                for (int i = 0; i < EdgeIndex.Length; i += 2)
+                {
+                    // XXX: must change!!
+                    tcx.NewConstraint(Points[EdgeIndex[i]], Points[EdgeIndex[i + 1]]);
+                }
+            }
+        }
+
+        /**
+         * TODO: TO BE IMPLEMENTED!
+         * Peforms a validation on given input<br>
+         * 1. Check's if there any constraint edges are crossing or collinear<br>
+         * 2. 
+         * @return
+         */
+
+        public bool isValid()
+        {
+            return true;
+        }
+    }
+}

Farseer Physics Engine 3.5/Common/Decomposition/CDT/Sets/PointSet.cs

@@ -0,0 +1,84 @@
+/* Poly2Tri
+ * Copyright (c) 2009-2010, Poly2Tri Contributors
+ * http://code.google.com/p/poly2tri/
+ *
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without modification,
+ * are permitted provided that the following conditions are met:
+ *
+ * * Redistributions of source code must retain the above copyright notice,
+ *   this list of conditions and the following disclaimer.
+ * * Redistributions in binary form must reproduce the above copyright notice,
+ *   this list of conditions and the following disclaimer in the documentation
+ *   and/or other materials provided with the distribution.
+ * * Neither the name of Poly2Tri nor the names of its contributors may be
+ *   used to endorse or promote products derived from this software without specific
+ *   prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+ * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
+ * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+ * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+ * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+ * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+
+using System.Collections.Generic;
+using FarseerPhysics.Common.Decomposition.CDT.Delaunay;
+
+namespace FarseerPhysics.Common.Decomposition.CDT.Sets
+{
+    internal class PointSet : Triangulatable
+    {
+        public PointSet(List<TriangulationPoint> points)
+        {
+            Points = new List<TriangulationPoint>(points);
+        }
+
+        #region Triangulatable Members
+
+        public IList<TriangulationPoint> Points { get; private set; }
+        public IList<DelaunayTriangle> Triangles { get; private set; }
+
+        public virtual TriangulationMode TriangulationMode
+        {
+            get { return TriangulationMode.Unconstrained; }
+        }
+
+        public void AddTriangle(DelaunayTriangle t)
+        {
+            Triangles.Add(t);
+        }
+
+        public void AddTriangles(IEnumerable<DelaunayTriangle> list)
+        {
+            foreach (DelaunayTriangle tri in list) Triangles.Add(tri);
+        }
+
+        public void ClearTriangles()
+        {
+            Triangles.Clear();
+        }
+
+        public virtual void PrepareTriangulation(TriangulationContext tcx)
+        {
+            if (Triangles == null)
+            {
+                Triangles = new List<DelaunayTriangle>(Points.Count);
+            }
+            else
+            {
+                Triangles.Clear();
+            }
+            tcx.Points.AddRange(Points);
+        }
+
+        #endregion
+    }
+}

Farseer Physics Engine 3.5/Common/Decomposition/CDT/TriangulationConstraint.cs

@@ -0,0 +1,46 @@
+/* Poly2Tri
+ * Copyright (c) 2009-2010, Poly2Tri Contributors
+ * http://code.google.com/p/poly2tri/
+ *
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without modification,
+ * are permitted provided that the following conditions are met:
+ *
+ * * Redistributions of source code must retain the above copyright notice,
+ *   this list of conditions and the following disclaimer.
+ * * Redistributions in binary form must reproduce the above copyright notice,
+ *   this list of conditions and the following disclaimer in the documentation
+ *   and/or other materials provided with the distribution.
+ * * Neither the name of Poly2Tri nor the names of its contributors may be
+ *   used to endorse or promote products derived from this software without specific
+ *   prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+ * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
+ * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+ * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+ * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+ * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+
+/**
+ * Forces a triangle edge between two points p and q
+ * when triangulating. For example used to enforce
+ * Polygon Edges during a polygon triangulation.
+ * 
+ * @author Thomas Åhlén, thahlen@gmail.com
+ */
+namespace FarseerPhysics.Common.Decomposition.CDT
+{
+    internal class TriangulationConstraint
+    {
+        public TriangulationPoint P;
+        public TriangulationPoint Q;
+    }
+}

Farseer Physics Engine 3.5/Common/Decomposition/CDT/TriangulationContext.cs

@@ -0,0 +1,84 @@
+/* Poly2Tri
+ * Copyright (c) 2009-2010, Poly2Tri Contributors
+ * http://code.google.com/p/poly2tri/
+ *
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without modification,
+ * are permitted provided that the following conditions are met:
+ *
+ * * Redistributions of source code must retain the above copyright notice,
+ *   this list of conditions and the following disclaimer.
+ * * Redistributions in binary form must reproduce the above copyright notice,
+ *   this list of conditions and the following disclaimer in the documentation
+ *   and/or other materials provided with the distribution.
+ * * Neither the name of Poly2Tri nor the names of its contributors may be
+ *   used to endorse or promote products derived from this software without specific
+ *   prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+ * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
+ * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+ * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+ * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+ * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+
+using System.Collections.Generic;
+using System.Runtime.CompilerServices;
+using FarseerPhysics.Common.Decomposition.CDT.Delaunay;
+
+namespace FarseerPhysics.Common.Decomposition.CDT
+{
+    internal abstract class TriangulationContext
+    {
+        public readonly List<TriangulationPoint> Points = new List<TriangulationPoint>(200);
+        public readonly List<DelaunayTriangle> Triangles = new List<DelaunayTriangle>();
+        private int _stepTime = -1;
+
+        public TriangulationContext()
+        {
+            Terminated = false;
+        }
+
+        public TriangulationMode TriangulationMode { get; protected set; }
+        public Triangulatable Triangulatable { get; private set; }
+
+        public bool WaitUntilNotified { get; private set; }
+        public bool Terminated { get; set; }
+
+        public int StepCount { get; private set; }
+        public virtual bool IsDebugEnabled { get; protected set; }
+
+        public void Done()
+        {
+            StepCount++;
+        }
+
+        public virtual void PrepareTriangulation(Triangulatable t)
+        {
+            Triangulatable = t;
+            TriangulationMode = t.TriangulationMode;
+            t.PrepareTriangulation(this);
+        }
+
+        public abstract TriangulationConstraint NewConstraint(TriangulationPoint a, TriangulationPoint b);
+
+        [MethodImpl(MethodImplOptions.Synchronized)]
+        public void Update(string message)
+        {
+        }
+
+        public virtual void Clear()
+        {
+            Points.Clear();
+            Terminated = false;
+            StepCount = 0;
+        }
+    }
+}

Farseer Physics Engine 3.5/Common/Decomposition/CDT/TriangulationMode.cs

@@ -0,0 +1,40 @@
+/* Poly2Tri
+ * Copyright (c) 2009-2010, Poly2Tri Contributors
+ * http://code.google.com/p/poly2tri/
+ *
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without modification,
+ * are permitted provided that the following conditions are met:
+ *
+ * * Redistributions of source code must retain the above copyright notice,
+ *   this list of conditions and the following disclaimer.
+ * * Redistributions in binary form must reproduce the above copyright notice,
+ *   this list of conditions and the following disclaimer in the documentation
+ *   and/or other materials provided with the distribution.
+ * * Neither the name of Poly2Tri nor the names of its contributors may be
+ *   used to endorse or promote products derived from this software without specific
+ *   prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+ * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
+ * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+ * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+ * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+ * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+
+namespace FarseerPhysics.Common.Decomposition.CDT
+{
+    internal enum TriangulationMode
+    {
+        Unconstrained,
+        Constrained,
+        Polygon
+    }
+}

Farseer Physics Engine 3.5/Common/Decomposition/CDT/TriangulationPoint.cs

@@ -0,0 +1,82 @@
+/* Poly2Tri
+ * Copyright (c) 2009-2010, Poly2Tri Contributors
+ * http://code.google.com/p/poly2tri/
+ *
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without modification,
+ * are permitted provided that the following conditions are met:
+ *
+ * * Redistributions of source code must retain the above copyright notice,
+ *   this list of conditions and the following disclaimer.
+ * * Redistributions in binary form must reproduce the above copyright notice,
+ *   this list of conditions and the following disclaimer in the documentation
+ *   and/or other materials provided with the distribution.
+ * * Neither the name of Poly2Tri nor the names of its contributors may be
+ *   used to endorse or promote products derived from this software without specific
+ *   prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+ * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
+ * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+ * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+ * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+ * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+
+using System.Collections.Generic;
+using FarseerPhysics.Common.Decomposition.CDT.Delaunay.Sweep;
+
+namespace FarseerPhysics.Common.Decomposition.CDT
+{
+    internal class TriangulationPoint
+    {
+        // List of edges this point constitutes an upper ending point (CDT)
+
+        public double X, Y;
+
+        public TriangulationPoint(double x, double y)
+        {
+            X = x;
+            Y = y;
+        }
+
+        public List<DTSweepConstraint> Edges { get; private set; }
+
+        public float Xf
+        {
+            get { return (float) X; }
+            set { X = value; }
+        }
+
+        public float Yf
+        {
+            get { return (float) Y; }
+            set { Y = value; }
+        }
+
+        public bool HasEdges
+        {
+            get { return Edges != null; }
+        }
+
+        public override string ToString()
+        {
+            return "[" + X + "," + Y + "]";
+        }
+
+        public void AddEdge(DTSweepConstraint e)
+        {
+            if (Edges == null)
+            {
+                Edges = new List<DTSweepConstraint>();
+            }
+            Edges.Add(e);
+        }
+    }
+}

Farseer Physics Engine 3.5/Common/Decomposition/CDT/TriangulationUtil.cs

@@ -0,0 +1,175 @@
+/* Poly2Tri
+ * Copyright (c) 2009-2010, Poly2Tri Contributors
+ * http://code.google.com/p/poly2tri/
+ *
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without modification,
+ * are permitted provided that the following conditions are met:
+ *
+ * * Redistributions of source code must retain the above copyright notice,
+ *   this list of conditions and the following disclaimer.
+ * * Redistributions in binary form must reproduce the above copyright notice,
+ *   this list of conditions and the following disclaimer in the documentation
+ *   and/or other materials provided with the distribution.
+ * * Neither the name of Poly2Tri nor the names of its contributors may be
+ *   used to endorse or promote products derived from this software without specific
+ *   prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+ * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
+ * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+ * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+ * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+ * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+
+namespace FarseerPhysics.Common.Decomposition.CDT
+{
+    /**
+     * @author Thomas Åhlén, thahlen@gmail.com
+     */
+
+    internal class TriangulationUtil
+    {
+        public static double EPSILON = 1e-12;
+
+        /// <summary>
+        ///   Requirements:
+        /// 1. a,b and c form a triangle.
+        /// 2. a and d is know to be on opposite side of bc
+        /// <code>
+        ///                a
+        ///                +
+        ///               / \
+        ///              /   \
+        ///            b/     \c
+        ///            +-------+ 
+        ///           /    B    \  
+        ///          /           \ 
+        /// </code>
+        ///    Facts:
+        ///  d has to be in area B to have a chance to be inside the circle formed by a,b and c
+        ///  d is outside B if orient2d(a,b,d) or orient2d(c,a,d) is CW
+        ///  This preknowledge gives us a way to optimize the incircle test
+        /// </summary>
+        /// <param name="pa">triangle point, opposite d</param>
+        /// <param name="pb">triangle point</param>
+        /// <param name="pc">triangle point</param>
+        /// <param name="pd">point opposite a</param>
+        /// <returns>true if d is inside circle, false if on circle edge</returns>
+        public static bool SmartIncircle(TriangulationPoint pa, TriangulationPoint pb, TriangulationPoint pc,
+                                         TriangulationPoint pd)
+        {
+            double pdx = pd.X;
+            double pdy = pd.Y;
+            double adx = pa.X - pdx;
+            double ady = pa.Y - pdy;
+            double bdx = pb.X - pdx;
+            double bdy = pb.Y - pdy;
+
+            double adxbdy = adx * bdy;
+            double bdxady = bdx * ady;
+            double oabd = adxbdy - bdxady;
+            //        oabd = orient2d(pa,pb,pd);
+            if (oabd <= 0) return false;
+
+            double cdx = pc.X - pdx;
+            double cdy = pc.Y - pdy;
+
+            double cdxady = cdx * ady;
+            double adxcdy = adx * cdy;
+            double ocad = cdxady - adxcdy;
+            //      ocad = orient2d(pc,pa,pd);
+            if (ocad <= 0) return false;
+
+            double bdxcdy = bdx * cdy;
+            double cdxbdy = cdx * bdy;
+
+            double alift = adx * adx + ady * ady;
+            double blift = bdx * bdx + bdy * bdy;
+            double clift = cdx * cdx + cdy * cdy;
+
+            double det = alift * (bdxcdy - cdxbdy) + blift * ocad + clift * oabd;
+
+            return det > 0;
+        }
+        /*
+        public static bool InScanArea(TriangulationPoint pa, TriangulationPoint pb, TriangulationPoint pc,
+                                      TriangulationPoint pd)
+        {
+            double pdx = pd.X;
+            double pdy = pd.Y;
+            double adx = pa.X - pdx;
+            double ady = pa.Y - pdy;
+            double bdx = pb.X - pdx;
+            double bdy = pb.Y - pdy;
+
+            double adxbdy = adx*bdy;
+            double bdxady = bdx*ady;
+            double oabd = adxbdy - bdxady;
+            //        oabd = orient2d(pa,pb,pd);
+            if (oabd <= 0)
+            {
+                return false;
+            }
+
+            double cdx = pc.X - pdx;
+            double cdy = pc.Y - pdy;
+
+            double cdxady = cdx*ady;
+            double adxcdy = adx*cdy;
+            double ocad = cdxady - adxcdy;
+            //      ocad = orient2d(pc,pa,pd);
+            if (ocad <= 0)
+            {
+                return false;
+            }
+            return true;
+        }
+        */
+
+        public static bool InScanArea(TriangulationPoint pa, TriangulationPoint pb, TriangulationPoint pc, TriangulationPoint pd)
+        {
+            double oadb = (pa.X - pb.X) * (pd.Y - pb.Y) - (pd.X - pb.X) * (pa.Y - pb.Y);
+            if (oadb >= -EPSILON)
+            {
+                return false;
+            }
+
+            double oadc = (pa.X - pc.X) * (pd.Y - pc.Y) - (pd.X - pc.X) * (pa.Y - pc.Y);
+            if (oadc <= EPSILON)
+            {
+                return false;
+            }
+            return true;
+        }
+
+        /// Forumla to calculate signed area
+        /// Positive if CCW
+        /// Negative if CW
+        /// 0 if collinear
+        /// A[P1,P2,P3]  =  (x1*y2 - y1*x2) + (x2*y3 - y2*x3) + (x3*y1 - y3*x1)
+        ///              =  (x1-x3)*(y2-y3) - (y1-y3)*(x2-x3)
+        public static Orientation Orient2d(TriangulationPoint pa, TriangulationPoint pb, TriangulationPoint pc)
+        {
+            double detleft = (pa.X - pc.X) * (pb.Y - pc.Y);
+            double detright = (pa.Y - pc.Y) * (pb.X - pc.X);
+            double val = detleft - detright;
+            if (val > -EPSILON && val < EPSILON)
+            {
+                return Orientation.Collinear;
+            }
+            else if (val > 0)
+            {
+                return Orientation.CCW;
+            }
+            return Orientation.CW;
+        }
+    }
+}

Farseer Physics Engine 3.5/Common/Decomposition/CDT/Util/FixedArray3.cs

@@ -0,0 +1,118 @@
+/* Poly2Tri
+ * Copyright (c) 2009-2010, Poly2Tri Contributors
+ * http://code.google.com/p/poly2tri/
+ *
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without modification,
+ * are permitted provided that the following conditions are met:
+ *
+ * * Redistributions of source code must retain the above copyright notice,
+ *   this list of conditions and the following disclaimer.
+ * * Redistributions in binary form must reproduce the above copyright notice,
+ *   this list of conditions and the following disclaimer in the documentation
+ *   and/or other materials provided with the distribution.
+ * * Neither the name of Poly2Tri nor the names of its contributors may be
+ *   used to endorse or promote products derived from this software without specific
+ *   prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+ * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
+ * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+ * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+ * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+ * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+
+using System;
+using System.Collections;
+using System.Collections.Generic;
+
+namespace FarseerPhysics.Common.Decomposition.CDT.Util
+{
+    internal struct FixedArray3<T> : IEnumerable<T> where T : class
+    {
+        public T _0, _1, _2;
+
+        public T this[int index]
+        {
+            get
+            {
+                switch (index)
+                {
+                    case 0:
+                        return _0;
+                    case 1:
+                        return _1;
+                    case 2:
+                        return _2;
+                    default:
+                        throw new IndexOutOfRangeException();
+                }
+            }
+            set
+            {
+                switch (index)
+                {
+                    case 0:
+                        _0 = value;
+                        break;
+                    case 1:
+                        _1 = value;
+                        break;
+                    case 2:
+                        _2 = value;
+                        break;
+                    default:
+                        throw new IndexOutOfRangeException();
+                }
+            }
+        }
+
+        #region IEnumerable<T> Members
+
+        public IEnumerator<T> GetEnumerator()
+        {
+            return Enumerate().GetEnumerator();
+        }
+
+        IEnumerator IEnumerable.GetEnumerator()
+        {
+            return GetEnumerator();
+        }
+
+        #endregion
+
+        public bool Contains(T value)
+        {
+            for (int i = 0; i < 3; ++i) if (this[i] == value) return true;
+            return false;
+        }
+
+        public int IndexOf(T value)
+        {
+            for (int i = 0; i < 3; ++i) if (this[i] == value) return i;
+            return -1;
+        }
+
+        public void Clear()
+        {
+            _0 = _1 = _2 = null;
+        }
+
+        public void Clear(T value)
+        {
+            for (int i = 0; i < 3; ++i) if (this[i] == value) this[i] = null;
+        }
+
+        private IEnumerable<T> Enumerate()
+        {
+            for (int i = 0; i < 3; ++i) yield return this[i];
+        }
+    }
+}

Farseer Physics Engine 3.5/Common/Decomposition/CDT/Util/FixedBitArray3.cs

@@ -0,0 +1,118 @@
+/* Poly2Tri
+ * Copyright (c) 2009-2010, Poly2Tri Contributors
+ * http://code.google.com/p/poly2tri/
+ *
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without modification,
+ * are permitted provided that the following conditions are met:
+ *
+ * * Redistributions of source code must retain the above copyright notice,
+ *   this list of conditions and the following disclaimer.
+ * * Redistributions in binary form must reproduce the above copyright notice,
+ *   this list of conditions and the following disclaimer in the documentation
+ *   and/or other materials provided with the distribution.
+ * * Neither the name of Poly2Tri nor the names of its contributors may be
+ *   used to endorse or promote products derived from this software without specific
+ *   prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+ * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
+ * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+ * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+ * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+ * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+
+using System;
+using System.Collections;
+using System.Collections.Generic;
+
+namespace FarseerPhysics.Common.Decomposition.CDT.Util
+{
+    internal struct FixedBitArray3 : IEnumerable<bool>
+    {
+        public bool _0, _1, _2;
+
+        public bool this[int index]
+        {
+            get
+            {
+                switch (index)
+                {
+                    case 0:
+                        return _0;
+                    case 1:
+                        return _1;
+                    case 2:
+                        return _2;
+                    default:
+                        throw new IndexOutOfRangeException();
+                }
+            }
+            set
+            {
+                switch (index)
+                {
+                    case 0:
+                        _0 = value;
+                        break;
+                    case 1:
+                        _1 = value;
+                        break;
+                    case 2:
+                        _2 = value;
+                        break;
+                    default:
+                        throw new IndexOutOfRangeException();
+                }
+            }
+        }
+
+        #region IEnumerable<bool> Members
+
+        public IEnumerator<bool> GetEnumerator()
+        {
+            return Enumerate().GetEnumerator();
+        }
+
+        IEnumerator IEnumerable.GetEnumerator()
+        {
+            return GetEnumerator();
+        }
+
+        #endregion
+
+        public bool Contains(bool value)
+        {
+            for (int i = 0; i < 3; ++i) if (this[i] == value) return true;
+            return false;
+        }
+
+        public int IndexOf(bool value)
+        {
+            for (int i = 0; i < 3; ++i) if (this[i] == value) return i;
+            return -1;
+        }
+
+        public void Clear()
+        {
+            _0 = _1 = _2 = false;
+        }
+
+        public void Clear(bool value)
+        {
+            for (int i = 0; i < 3; ++i) if (this[i] == value) this[i] = false;
+        }
+
+        private IEnumerable<bool> Enumerate()
+        {
+            for (int i = 0; i < 3; ++i) yield return this[i];
+        }
+    }
+}

Farseer Physics Engine 3.5/Common/Decomposition/CDT/Util/PointGenerator.cs

@@ -0,0 +1,38 @@
+using System;
+using System.Collections.Generic;
+
+namespace FarseerPhysics.Common.Decomposition.CDT.Util
+{
+    internal class PointGenerator
+    {
+        private static readonly Random RNG = new Random();
+
+        public static List<TriangulationPoint> UniformDistribution(int n, double scale)
+        {
+            List<TriangulationPoint> points = new List<TriangulationPoint>();
+            for (int i = 0; i < n; i++)
+            {
+                points.Add(new TriangulationPoint(scale*(0.5 - RNG.NextDouble()), scale*(0.5 - RNG.NextDouble())));
+            }
+            return points;
+        }
+
+        public static List<TriangulationPoint> UniformGrid(int n, double scale)
+        {
+            double x = 0;
+            double size = scale/n;
+            double halfScale = 0.5*scale;
+
+            List<TriangulationPoint> points = new List<TriangulationPoint>();
+            for (int i = 0; i < n + 1; i++)
+            {
+                x = halfScale - i*size;
+                for (int j = 0; j < n + 1; j++)
+                {
+                    points.Add(new TriangulationPoint(x, halfScale - j*size));
+                }
+            }
+            return points;
+        }
+    }
+}

Farseer Physics Engine 3.5/Common/Decomposition/CDT/Util/PolygonGenerator.cs

@@ -0,0 +1,98 @@
+/* Poly2Tri
+ * Copyright (c) 2009-2010, Poly2Tri Contributors
+ * http://code.google.com/p/poly2tri/
+ *
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without modification,
+ * are permitted provided that the following conditions are met:
+ *
+ * * Redistributions of source code must retain the above copyright notice,
+ *   this list of conditions and the following disclaimer.
+ * * Redistributions in binary form must reproduce the above copyright notice,
+ *   this list of conditions and the following disclaimer in the documentation
+ *   and/or other materials provided with the distribution.
+ * * Neither the name of Poly2Tri nor the names of its contributors may be
+ *   used to endorse or promote products derived from this software without specific
+ *   prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+ * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
+ * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+ * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+ * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+ * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+
+using System;
+using FarseerPhysics.Common.Decomposition.CDT.Polygon;
+
+namespace FarseerPhysics.Common.Decomposition.CDT.Util
+{
+    internal class PolygonGenerator
+    {
+        private static readonly Random RNG = new Random();
+
+        private static double PI_2 = 2.0*Math.PI;
+
+        public static Polygon.Polygon RandomCircleSweep(double scale, int vertexCount)
+        {
+            PolygonPoint point;
+            PolygonPoint[] points;
+            double radius = scale/4;
+
+            points = new PolygonPoint[vertexCount];
+            for (int i = 0; i < vertexCount; i++)
+            {
+                do
+                {
+                    if (i%250 == 0)
+                    {
+                        radius += scale/2*(0.5 - RNG.NextDouble());
+                    }
+                    else if (i%50 == 0)
+                    {
+                        radius += scale/5*(0.5 - RNG.NextDouble());
+                    }
+                    else
+                    {
+                        radius += 25*scale/vertexCount*(0.5 - RNG.NextDouble());
+                    }
+                    radius = radius > scale/2 ? scale/2 : radius;
+                    radius = radius < scale/10 ? scale/10 : radius;
+                } while (radius < scale/10 || radius > scale/2);
+                point = new PolygonPoint(radius*Math.Cos((PI_2*i)/vertexCount),
+                                         radius*Math.Sin((PI_2*i)/vertexCount));
+                points[i] = point;
+            }
+            return new Polygon.Polygon(points);
+        }
+
+        public static Polygon.Polygon RandomCircleSweep2(double scale, int vertexCount)
+        {
+            PolygonPoint point;
+            PolygonPoint[] points;
+            double radius = scale/4;
+
+            points = new PolygonPoint[vertexCount];
+            for (int i = 0; i < vertexCount; i++)
+            {
+                do
+                {
+                    radius += scale/5*(0.5 - RNG.NextDouble());
+                    radius = radius > scale/2 ? scale/2 : radius;
+                    radius = radius < scale/10 ? scale/10 : radius;
+                } while (radius < scale/10 || radius > scale/2);
+                point = new PolygonPoint(radius*Math.Cos((PI_2*i)/vertexCount),
+                                         radius*Math.Sin((PI_2*i)/vertexCount));
+                points[i] = point;
+            }
+            return new Polygon.Polygon(points);
+        }
+    }
+}

Farseer Physics Engine 3.5/Common/Decomposition/CDTDecomposer.cs

@@ -0,0 +1,75 @@
+/*
+* Farseer Physics Engine:
+* Copyright (c) 2012 Ian Qvist
+*/
+
+using System.Collections.Generic;
+using System.Diagnostics;
+using FarseerPhysics.Common.Decomposition.CDT;
+using FarseerPhysics.Common.Decomposition.CDT.Delaunay;
+using FarseerPhysics.Common.Decomposition.CDT.Delaunay.Sweep;
+using FarseerPhysics.Common.Decomposition.CDT.Polygon;
+using Microsoft.Xna.Framework;
+
+namespace FarseerPhysics.Common.Decomposition
+{
+    /// <summary>
+    /// 2D constrained Delaunay triangulation algorithm.
+    /// Based on the paper "Sweep-line algorithm for constrained Delaunay triangulation" by V. Domiter and and B. Zalik
+    /// 
+    /// Properties:
+    /// - Creates triangles with a large interior angle.
+    /// - Supports holes
+    /// - Generate a lot of garbage due to incapsulation of the Poly2Tri library.
+    /// - Running time is O(n^2), n = number of vertices.
+    /// - Does not care about winding order.
+    /// 
+    /// Source: http://code.google.com/p/poly2tri/
+    /// </summary>
+    internal static class CDTDecomposer
+    {
+        /// <summary>
+        /// Decompose the polygon into several smaller non-concave polygon.
+        /// </summary>
+        public static List<Vertices> ConvexPartition(Vertices vertices)
+        {
+            Debug.Assert(vertices.Count > 3);
+
+            Polygon poly = new Polygon();
+
+            foreach (Vector2 vertex in vertices)
+                poly.Points.Add(new TriangulationPoint(vertex.X, vertex.Y));
+
+            if (vertices.Holes != null)
+            {
+                foreach (Vertices holeVertices in vertices.Holes)
+                {
+                    Polygon hole = new Polygon();
+
+                    foreach (Vector2 vertex in holeVertices)
+                        hole.Points.Add(new TriangulationPoint(vertex.X, vertex.Y));
+
+                    poly.AddHole(hole);
+                }
+            }
+
+            DTSweepContext tcx = new DTSweepContext();
+            tcx.PrepareTriangulation(poly);
+            DTSweep.Triangulate(tcx);
+
+            List<Vertices> results = new List<Vertices>();
+
+            foreach (DelaunayTriangle triangle in poly.Triangles)
+            {
+                Vertices v = new Vertices();
+                foreach (TriangulationPoint p in triangle.Points)
+                {
+                    v.Add(new Vector2((float)p.X, (float)p.Y));
+                }
+                results.Add(v);
+            }
+
+            return results;
+        }
+    }
+}

Farseer Physics Engine 3.5/Common/Decomposition/EarclipDecomposer.cs

@@ -0,0 +1,403 @@
+/*
+* C# Version Ported by Matt Bettcher and Ian Qvist 2009-2010
+* 
+* Original C++ Version Copyright (c) 2007 Eric Jordan
+*
+* This software is provided 'as-is', without any express or implied
+* warranty.  In no event will the authors be held liable for any damages
+* arising from the use of this software.
+* Permission is granted to anyone to use this software for any purpose,
+* including commercial applications, and to alter it and redistribute it
+* freely, subject to the following restrictions:
+* 1. The origin of this software must not be misrepresented; you must not
+* claim that you wrote the original software. If you use this software
+* in a product, an acknowledgment in the product documentation would be
+* appreciated but is not required.
+* 2. Altered source versions must be plainly marked as such, and must not be
+* misrepresented as being the original software.
+* 3. This notice may not be removed or altered from any source distribution.
+*/
+
+using System;
+using System.Collections.Generic;
+using System.Diagnostics;
+using Microsoft.Xna.Framework;
+
+namespace FarseerPhysics.Common.Decomposition
+{
+    /// <summary>
+    /// Convex decomposition algorithm using ear clipping
+    /// 
+    /// Properties:
+    /// - Only works on simple polygons.
+    /// - Does not support holes.
+    /// - Running time is O(n^2), n = number of vertices.
+    /// 
+    /// Source: http://www.ewjordan.com/earClip/
+    /// </summary>
+    internal static class EarclipDecomposer
+    {
+        //box2D rev 32 - for details, see http://www.box2d.org/forum/viewtopic.php?f=4&t=83&start=50 
+
+        /// <summary>
+        /// Decompose the polygon into several smaller non-concave polygon.
+        /// Each resulting polygon will have no more than Settings.MaxPolygonVertices vertices.
+        /// </summary>
+        /// <param name="vertices">The vertices.</param>
+        /// <param name="tolerance">The tolerance.</param>
+        public static List<Vertices> ConvexPartition(Vertices vertices, float tolerance = 0.001f)
+        {
+            Debug.Assert(vertices.Count > 3);
+            Debug.Assert(!vertices.IsCounterClockWise());
+
+            return TriangulatePolygon(vertices, tolerance);
+        }
+
+        /// <summary>
+        /// Triangulates a polygon using simple ear-clipping algorithm. Returns
+        /// size of Triangle array unless the polygon can't be triangulated.
+        /// This should only happen if the polygon self-intersects,
+        /// though it will not _always_ return null for a bad polygon - it is the
+        /// caller's responsibility to check for self-intersection, and if it
+        /// doesn't, it should at least check that the return value is non-null
+        /// before using. You're warned!
+        ///
+        /// Triangles may be degenerate, especially if you have identical points
+        /// in the input to the algorithm.  Check this before you use them.
+        ///
+        /// This is totally unoptimized, so for large polygons it should not be part
+        /// of the simulation loop.
+        /// </summary>
+        /// <remarks>
+        /// Only works on simple polygons.
+        /// </remarks>
+        private static List<Vertices> TriangulatePolygon(Vertices vertices, float tolerance)
+        {
+            //FPE note: Check is needed as invalid triangles can be returned in recursive calls.
+            if (vertices.Count < 3)
+                return new List<Vertices>();
+
+            List<Vertices> results = new List<Vertices>();
+
+            //Recurse and split on pinch points
+            Vertices pA, pB;
+            Vertices pin = new Vertices(vertices);
+            if (ResolvePinchPoint(pin, out pA, out pB, tolerance))
+            {
+                List<Vertices> mergeA = TriangulatePolygon(pA, tolerance);
+                List<Vertices> mergeB = TriangulatePolygon(pB, tolerance);
+
+                if (mergeA.Count == -1 || mergeB.Count == -1)
+                    throw new Exception("Can't triangulate your polygon.");
+
+                for (int i = 0; i < mergeA.Count; ++i)
+                {
+                    results.Add(new Vertices(mergeA[i]));
+                }
+                for (int i = 0; i < mergeB.Count; ++i)
+                {
+                    results.Add(new Vertices(mergeB[i]));
+                }
+
+                return results;
+            }
+
+            Vertices[] buffer = new Vertices[vertices.Count - 2];
+            int bufferSize = 0;
+            float[] xrem = new float[vertices.Count];
+            float[] yrem = new float[vertices.Count];
+            for (int i = 0; i < vertices.Count; ++i)
+            {
+                xrem[i] = vertices[i].X;
+                yrem[i] = vertices[i].Y;
+            }
+
+            int vNum = vertices.Count;
+
+            while (vNum > 3)
+            {
+                // Find an ear
+                int earIndex = -1;
+                float earMaxMinCross = -10.0f;
+                for (int i = 0; i < vNum; ++i)
+                {
+                    if (IsEar(i, xrem, yrem, vNum))
+                    {
+                        int lower = Remainder(i - 1, vNum);
+                        int upper = Remainder(i + 1, vNum);
+                        Vector2 d1 = new Vector2(xrem[upper] - xrem[i], yrem[upper] - yrem[i]);
+                        Vector2 d2 = new Vector2(xrem[i] - xrem[lower], yrem[i] - yrem[lower]);
+                        Vector2 d3 = new Vector2(xrem[lower] - xrem[upper], yrem[lower] - yrem[upper]);
+
+                        d1.Normalize();
+                        d2.Normalize();
+                        d3.Normalize();
+                        float cross12;
+                        MathUtils.Cross(ref d1, ref d2, out cross12);
+                        cross12 = Math.Abs(cross12);
+
+                        float cross23;
+                        MathUtils.Cross(ref d2, ref d3, out cross23);
+                        cross23 = Math.Abs(cross23);
+
+                        float cross31;
+                        MathUtils.Cross(ref d3, ref d1, out cross31);
+                        cross31 = Math.Abs(cross31);
+
+                        //Find the maximum minimum angle
+                        float minCross = Math.Min(cross12, Math.Min(cross23, cross31));
+                        if (minCross > earMaxMinCross)
+                        {
+                            earIndex = i;
+                            earMaxMinCross = minCross;
+                        }
+                    }
+                }
+
+                // If we still haven't found an ear, we're screwed.
+                // Note: sometimes this is happening because the
+                // remaining points are collinear.  Really these
+                // should just be thrown out without halting triangulation.
+                if (earIndex == -1)
+                {
+                    for (int i = 0; i < bufferSize; i++)
+                    {
+                        results.Add(buffer[i]);
+                    }
+
+                    return results;
+                }
+
+                // Clip off the ear:
+                // - remove the ear tip from the list
+
+                --vNum;
+                float[] newx = new float[vNum];
+                float[] newy = new float[vNum];
+                int currDest = 0;
+                for (int i = 0; i < vNum; ++i)
+                {
+                    if (currDest == earIndex) ++currDest;
+                    newx[i] = xrem[currDest];
+                    newy[i] = yrem[currDest];
+                    ++currDest;
+                }
+
+                // - add the clipped triangle to the triangle list
+                int under = (earIndex == 0) ? (vNum) : (earIndex - 1);
+                int over = (earIndex == vNum) ? 0 : (earIndex + 1);
+                Triangle toAdd = new Triangle(xrem[earIndex], yrem[earIndex], xrem[over], yrem[over], xrem[under],
+                                              yrem[under]);
+                buffer[bufferSize] = toAdd;
+                ++bufferSize;
+
+                // - replace the old list with the new one
+                xrem = newx;
+                yrem = newy;
+            }
+
+            Triangle tooAdd = new Triangle(xrem[1], yrem[1], xrem[2], yrem[2], xrem[0], yrem[0]);
+            buffer[bufferSize] = tooAdd;
+            ++bufferSize;
+
+            for (int i = 0; i < bufferSize; i++)
+            {
+                results.Add(new Vertices(buffer[i]));
+            }
+
+            return results;
+        }
+
+        /// <summary>
+        /// Finds and fixes "pinch points," points where two polygon
+        /// vertices are at the same point.
+        /// 
+        /// If a pinch point is found, pin is broken up into poutA and poutB
+        /// and true is returned; otherwise, returns false.
+        /// 
+        /// Mostly for internal use.
+        /// 
+        /// O(N^2) time, which sucks...
+        /// </summary>
+        /// <param name="pin">The pin.</param>
+        /// <param name="poutA">The pout A.</param>
+        /// <param name="poutB">The pout B.</param>
+        /// <param name="tolerance"></param>
+        private static bool ResolvePinchPoint(Vertices pin, out Vertices poutA, out Vertices poutB, float tolerance)
+        {
+            poutA = new Vertices();
+            poutB = new Vertices();
+
+            if (pin.Count < 3)
+                return false;
+
+            bool hasPinchPoint = false;
+            int pinchIndexA = -1;
+            int pinchIndexB = -1;
+            for (int i = 0; i < pin.Count; ++i)
+            {
+                for (int j = i + 1; j < pin.Count; ++j)
+                {
+                    //Don't worry about pinch points where the points
+                    //are actually just dupe neighbors
+                    if (Math.Abs(pin[i].X - pin[j].X) < tolerance && Math.Abs(pin[i].Y - pin[j].Y) < tolerance && j != i + 1)
+                    {
+                        pinchIndexA = i;
+                        pinchIndexB = j;
+                        hasPinchPoint = true;
+                        break;
+                    }
+                }
+                if (hasPinchPoint) break;
+            }
+            if (hasPinchPoint)
+            {
+                int sizeA = pinchIndexB - pinchIndexA;
+                if (sizeA == pin.Count) return false; //has dupe points at wraparound, not a problem here
+                for (int i = 0; i < sizeA; ++i)
+                {
+                    int ind = Remainder(pinchIndexA + i, pin.Count); // is this right
+                    poutA.Add(pin[ind]);
+                }
+
+                int sizeB = pin.Count - sizeA;
+                for (int i = 0; i < sizeB; ++i)
+                {
+                    int ind = Remainder(pinchIndexB + i, pin.Count); // is this right    
+                    poutB.Add(pin[ind]);
+                }
+            }
+            return hasPinchPoint;
+        }
+
+        /// <summary>
+        /// Fix for obnoxious behavior for the % operator for negative numbers...
+        /// </summary>
+        /// <param name="x">The x.</param>
+        /// <param name="modulus">The modulus.</param>
+        /// <returns></returns>
+        private static int Remainder(int x, int modulus)
+        {
+            int rem = x % modulus;
+            while (rem < 0)
+            {
+                rem += modulus;
+            }
+            return rem;
+        }
+
+        /// <summary>
+        /// Checks if vertex i is the tip of an ear in polygon defined by xv[] and  yv[].
+        /// </summary>
+        /// <param name="i">The i.</param>
+        /// <param name="xv">The xv.</param>
+        /// <param name="yv">The yv.</param>
+        /// <param name="xvLength">Length of the xv.</param>
+        /// <remarks>
+        /// Assumes clockwise orientation of polygon.
+        /// </remarks>
+        /// <returns>
+        /// 	<c>true</c> if the specified i is ear; otherwise, <c>false</c>.
+        /// </returns>
+        private static bool IsEar(int i, float[] xv, float[] yv, int xvLength)
+        {
+            float dx0, dy0, dx1, dy1;
+            if (i >= xvLength || i < 0 || xvLength < 3)
+            {
+                return false;
+            }
+            int upper = i + 1;
+            int lower = i - 1;
+            if (i == 0)
+            {
+                dx0 = xv[0] - xv[xvLength - 1];
+                dy0 = yv[0] - yv[xvLength - 1];
+                dx1 = xv[1] - xv[0];
+                dy1 = yv[1] - yv[0];
+                lower = xvLength - 1;
+            }
+            else if (i == xvLength - 1)
+            {
+                dx0 = xv[i] - xv[i - 1];
+                dy0 = yv[i] - yv[i - 1];
+                dx1 = xv[0] - xv[i];
+                dy1 = yv[0] - yv[i];
+                upper = 0;
+            }
+            else
+            {
+                dx0 = xv[i] - xv[i - 1];
+                dy0 = yv[i] - yv[i - 1];
+                dx1 = xv[i + 1] - xv[i];
+                dy1 = yv[i + 1] - yv[i];
+            }
+
+            float cross = dx0 * dy1 - dx1 * dy0;
+
+            if (cross > 0)
+                return false;
+
+            Triangle myTri = new Triangle(xv[i], yv[i], xv[upper], yv[upper], xv[lower], yv[lower]);
+
+            for (int j = 0; j < xvLength; ++j)
+            {
+                if (j == i || j == lower || j == upper)
+                    continue;
+                if (myTri.IsInside(xv[j], yv[j]))
+                    return false;
+            }
+            return true;
+        }
+
+        private class Triangle : Vertices
+        {
+            //Constructor automatically fixes orientation to ccw
+            public Triangle(float x1, float y1, float x2, float y2, float x3, float y3)
+            {
+                float cross = (x2 - x1) * (y3 - y1) - (x3 - x1) * (y2 - y1);
+                if (cross > 0)
+                {
+                    Add(new Vector2(x1, y1));
+                    Add(new Vector2(x2, y2));
+                    Add(new Vector2(x3, y3));
+                }
+                else
+                {
+                    Add(new Vector2(x1, y1));
+                    Add(new Vector2(x3, y3));
+                    Add(new Vector2(x2, y2));
+                }
+            }
+
+            public bool IsInside(float x, float y)
+            {
+                Vector2 a = this[0];
+                Vector2 b = this[1];
+                Vector2 c = this[2];
+
+                if (x < a.X && x < b.X && x < c.X) return false;
+                if (x > a.X && x > b.X && x > c.X) return false;
+                if (y < a.Y && y < b.Y && y < c.Y) return false;
+                if (y > a.Y && y > b.Y && y > c.Y) return false;
+
+                float vx2 = x - a.X;
+                float vy2 = y - a.Y;
+                float vx1 = b.X - a.X;
+                float vy1 = b.Y - a.Y;
+                float vx0 = c.X - a.X;
+                float vy0 = c.Y - a.Y;
+
+                float dot00 = vx0 * vx0 + vy0 * vy0;
+                float dot01 = vx0 * vx1 + vy0 * vy1;
+                float dot02 = vx0 * vx2 + vy0 * vy2;
+                float dot11 = vx1 * vx1 + vy1 * vy1;
+                float dot12 = vx1 * vx2 + vy1 * vy2;
+                float invDenom = 1.0f / (dot00 * dot11 - dot01 * dot01);
+                float u = (dot11 * dot02 - dot01 * dot12) * invDenom;
+                float v = (dot00 * dot12 - dot01 * dot02) * invDenom;
+
+                return ((u > 0) && (v > 0) && (u + v < 1));
+            }
+        }
+    }
+}

Farseer Physics Engine 3.5/Common/Decomposition/FlipcodeDecomposer.cs

@@ -0,0 +1,152 @@
+using System.Collections.Generic;
+using System.Diagnostics;
+using Microsoft.Xna.Framework;
+
+namespace FarseerPhysics.Common.Decomposition
+{
+    /// <summary>
+    /// Convex decomposition algorithm created by unknown
+    /// 
+    /// Properties:
+    /// - No support for holes
+    /// - Very fast
+    /// - Only works on simple polygons
+    /// - Only works on counter clockwise polygons
+    /// 
+    /// More information: http://www.flipcode.com/archives/Efficient_Polygon_Triangulation.shtml
+    /// </summary>
+    internal static class FlipcodeDecomposer
+    {
+        private static Vector2 _tmpA;
+        private static Vector2 _tmpB;
+        private static Vector2 _tmpC;
+
+        /// <summary>
+        /// Decompose the polygon into triangles.
+        /// 
+        /// Properties:
+        /// - Only works on counter clockwise polygons
+        /// 
+        /// </summary>
+        /// <param name="vertices">The list of points describing the polygon</param>
+        public static List<Vertices> ConvexPartition(Vertices vertices)
+        {
+            Debug.Assert(vertices.Count > 3);
+            Debug.Assert(vertices.IsCounterClockWise());
+
+            int[] polygon = new int[vertices.Count];
+
+            for (int v = 0; v < vertices.Count; v++)
+                polygon[v] = v;
+
+            int nv = vertices.Count;
+
+            // Remove nv-2 Vertices, creating 1 triangle every time
+            int count = 2 * nv; /* error detection */
+
+            List<Vertices> result = new List<Vertices>();
+
+            for (int v = nv - 1; nv > 2; )
+            {
+                // If we loop, it is probably a non-simple polygon 
+                if (0 >= (count--))
+                {
+                    // Triangulate: ERROR - probable bad polygon!
+                    return new List<Vertices>();
+                }
+
+                // Three consecutive vertices in current polygon, <u,v,w>
+                int u = v;
+                if (nv <= u)
+                    u = 0; // Previous 
+                v = u + 1;
+                if (nv <= v)
+                    v = 0; // New v   
+                int w = v + 1;
+                if (nv <= w)
+                    w = 0; // Next 
+
+                _tmpA = vertices[polygon[u]];
+                _tmpB = vertices[polygon[v]];
+                _tmpC = vertices[polygon[w]];
+
+                if (Snip(vertices, u, v, w, nv, polygon))
+                {
+                    int s, t;
+
+                    // Output Triangle
+                    Vertices triangle = new Vertices(3);
+                    triangle.Add(_tmpA);
+                    triangle.Add(_tmpB);
+                    triangle.Add(_tmpC);
+                    result.Add(triangle);
+
+                    // Remove v from remaining polygon 
+                    for (s = v, t = v + 1; t < nv; s++, t++)
+                    {
+                        polygon[s] = polygon[t];
+                    }
+                    nv--;
+
+                    // Reset error detection counter
+                    count = 2 * nv;
+                }
+            }
+
+            return result;
+        }
+
+        /// <summary>
+        /// Check if the point P is inside the triangle defined by
+        /// the points A, B, C
+        /// </summary>
+        /// <param name="a">The A point.</param>
+        /// <param name="b">The B point.</param>
+        /// <param name="c">The C point.</param>
+        /// <param name="p">The point to be tested.</param>
+        /// <returns>True if the point is inside the triangle</returns>
+        private static bool InsideTriangle(ref Vector2 a, ref Vector2 b, ref Vector2 c, ref Vector2 p)
+        {
+            //A cross bp
+            float abp = (c.X - b.X) * (p.Y - b.Y) - (c.Y - b.Y) * (p.X - b.X);
+
+            //A cross ap
+            float aap = (b.X - a.X) * (p.Y - a.Y) - (b.Y - a.Y) * (p.X - a.X);
+
+            //b cross cp
+            float bcp = (a.X - c.X) * (p.Y - c.Y) - (a.Y - c.Y) * (p.X - c.X);
+
+            return ((abp >= 0.0f) && (bcp >= 0.0f) && (aap >= 0.0f));
+        }
+
+        /// <summary>
+        /// Cut a the contour and add a triangle into V to describe the 
+        /// location of the cut
+        /// </summary>
+        /// <param name="contour">The list of points defining the polygon</param>
+        /// <param name="u">The index of the first point</param>
+        /// <param name="v">The index of the second point</param>
+        /// <param name="w">The index of the third point</param>
+        /// <param name="n">The number of elements in the array.</param>
+        /// <param name="V">The array to populate with indicies of triangles.</param>
+        /// <returns>True if a triangle was found</returns>
+        private static bool Snip(Vertices contour, int u, int v, int w, int n, int[] V)
+        {
+            if (Settings.Epsilon > MathUtils.Area(ref _tmpA, ref _tmpB, ref _tmpC))
+                return false;
+
+            for (int p = 0; p < n; p++)
+            {
+                if ((p == u) || (p == v) || (p == w))
+                    continue;
+
+                Vector2 point = contour[V[p]];
+
+                if (InsideTriangle(ref _tmpA, ref _tmpB, ref _tmpC, ref point))
+                    return false;
+            }
+
+            return true;
+        }
+    }
+}

Farseer Physics Engine 3.5/Common/Decomposition/Seidel/Edge.cs

@@ -0,0 +1,60 @@
+using System.Collections.Generic;
+
+namespace FarseerPhysics.Common.Decomposition.Seidel
+{
+    internal class Edge
+    {
+        // Pointers used for building trapezoidal map
+        public Trapezoid Above;
+        public float B;
+        public Trapezoid Below;
+
+        // Montone mountain points
+        public HashSet<Point> MPoints;
+        public Point P;
+        public Point Q;
+
+        // Slope of the line (m)
+        public float Slope;
+
+
+        public Edge(Point p, Point q)
+        {
+            P = p;
+            Q = q;
+
+            if (q.X - p.X != 0)
+                Slope = (q.Y - p.Y) / (q.X - p.X);
+            else
+                Slope = 0;
+
+            B = p.Y - (p.X * Slope);
+            Above = null;
+            Below = null;
+            MPoints = new HashSet<Point>();
+            MPoints.Add(p);
+            MPoints.Add(q);
+        }
+
+        public bool IsAbove(Point point)
+        {
+            return P.Orient2D(Q, point) < 0;
+        }
+
+        public bool IsBelow(Point point)
+        {
+            return P.Orient2D(Q, point) > 0;
+        }
+
+        public void AddMpoint(Point point)
+        {
+            foreach (Point mp in MPoints)
+            {
+                if (!mp.Neq(point))
+                    return;
+            }
+
+            MPoints.Add(point);
+        }
+    }
+}

Farseer Physics Engine 3.5/Common/Decomposition/Seidel/MonotoneMountain.cs

@@ -0,0 +1,166 @@
+using System;
+using System.Collections.Generic;
+using System.Diagnostics;
+
+namespace FarseerPhysics.Common.Decomposition.Seidel
+{
+    internal class MonotoneMountain
+    {
+        // Almost Pi!
+        private const float PiSlop = 3.1f;
+
+        // Triangles that constitute the mountain
+        public List<List<Point>> Triangles;
+        private HashSet<Point> _convexPoints;
+        private Point _head;
+
+        // Monotone mountain points
+        private List<Point> _monoPoly;
+
+        // Used to track which side of the line we are on
+        private bool _positive;
+        private int _size;
+        private Point _tail;
+
+        public MonotoneMountain()
+        {
+            _size = 0;
+            _tail = null;
+            _head = null;
+            _positive = false;
+            _convexPoints = new HashSet<Point>();
+            _monoPoly = new List<Point>();
+            Triangles = new List<List<Point>>();
+        }
+
+        // Append a point to the list
+        public void Add(Point point)
+        {
+            if (_size == 0)
+            {
+                _head = point;
+                _size = 1;
+            }
+            else if (_size == 1)
+            {
+                // Keep repeat points out of the list
+                _tail = point;
+                _tail.Prev = _head;
+                _head.Next = _tail;
+                _size = 2;
+            }
+            else
+            {
+                // Keep repeat points out of the list
+                _tail.Next = point;
+                point.Prev = _tail;
+                _tail = point;
+                _size += 1;
+            }
+        }
+
+        // Remove a point from the list
+        public void Remove(Point point)
+        {
+            Point next = point.Next;
+            Point prev = point.Prev;
+            point.Prev.Next = next;
+            point.Next.Prev = prev;
+            _size -= 1;
+        }
+
+        // Partition a x-monotone mountain into triangles O(n)
+        // See "Computational Geometry in C", 2nd edition, by Joseph O'Rourke, page 52
+        public void Process()
+        {
+            // Establish the proper sign
+            _positive = AngleSign();
+            // create monotone polygon - for dubug purposes
+            GenMonoPoly();
+
+            // Initialize internal angles at each nonbase vertex
+            // Link strictly convex vertices into a list, ignore reflex vertices
+            Point p = _head.Next;
+            while (p.Neq(_tail))
+            {
+                float a = Angle(p);
+                // If the point is almost colinear with it's neighbor, remove it!
+                if (a >= PiSlop || a <= -PiSlop || a == 0.0f)
+                    Remove(p);
+                else if (IsConvex(p))
+                    _convexPoints.Add(p);
+                p = p.Next;
+            }
+
+            Triangulate();
+        }
+
+        private void Triangulate()
+        {
+            while (_convexPoints.Count != 0)
+            {
+                IEnumerator<Point> e = _convexPoints.GetEnumerator();
+                e.MoveNext();
+                Point ear = e.Current;
+
+                _convexPoints.Remove(ear);
+                Point a = ear.Prev;
+                Point b = ear;
+                Point c = ear.Next;
+                List<Point> triangle = new List<Point>(3);
+                triangle.Add(a);
+                triangle.Add(b);
+                triangle.Add(c);
+
+                Triangles.Add(triangle);
+
+                // Remove ear, update angles and convex list
+                Remove(ear);
+                if (Valid(a))
+                    _convexPoints.Add(a);
+                if (Valid(c))
+                    _convexPoints.Add(c);
+            }
+
+            Debug.Assert(_size <= 3, "Triangulation bug, please report");
+        }
+
+        private bool Valid(Point p)
+        {
+            return p.Neq(_head) && p.Neq(_tail) && IsConvex(p);
+        }
+
+        // Create the monotone polygon
+        private void GenMonoPoly()
+        {
+            Point p = _head;
+            while (p != null)
+            {
+                _monoPoly.Add(p);
+                p = p.Next;
+            }
+        }
+
+        private float Angle(Point p)
+        {
+            Point a = (p.Next - p);
+            Point b = (p.Prev - p);
+            return (float)Math.Atan2(a.Cross(b), a.Dot(b));
+        }
+
+        private bool AngleSign()
+        {
+            Point a = (_head.Next - _head);
+            Point b = (_tail - _head);
+            return Math.Atan2(a.Cross(b), a.Dot(b)) >= 0;
+        }
+
+        // Determines if the inslide angle is convex or reflex
+        private bool IsConvex(Point p)
+        {
+            if (_positive != (Angle(p) >= 0))
+                return false;
+            return true;
+        }
+    }
+}

Farseer Physics Engine 3.5/Common/Decomposition/Seidel/Node.cs

@@ -0,0 +1,41 @@
+using System.Collections.Generic;
+
+namespace FarseerPhysics.Common.Decomposition.Seidel
+{
+    // Node for a Directed Acyclic graph (DAG)
+    internal abstract class Node
+    {
+        protected Node LeftChild;
+        public List<Node> ParentList;
+        protected Node RightChild;
+
+        protected Node(Node left, Node right)
+        {
+            ParentList = new List<Node>();
+            LeftChild = left;
+            RightChild = right;
+
+            if (left != null)
+                left.ParentList.Add(this);
+            if (right != null)
+                right.ParentList.Add(this);
+        }
+
+        public abstract Sink Locate(Edge s);
+
+        // Replace a node in the graph with this node
+        // Make sure parent pointers are updated
+        public void Replace(Node node)
+        {
+            foreach (Node parent in node.ParentList)
+            {
+                // Select the correct node to replace (left or right child)
+                if (parent.LeftChild == node)
+                    parent.LeftChild = this;
+                else
+                    parent.RightChild = this;
+            }
+            ParentList.AddRange(node.ParentList);
+        }
+    }
+}

Farseer Physics Engine 3.5/Common/Decomposition/Seidel/Point.cs

@@ -0,0 +1,61 @@
+namespace FarseerPhysics.Common.Decomposition.Seidel
+{
+    internal class Point
+    {
+        // Pointers to next and previous points in Monontone Mountain
+        public Point Next, Prev;
+        public float X, Y;
+
+        public Point(float x, float y)
+        {
+            X = x;
+            Y = y;
+            Next = null;
+            Prev = null;
+        }
+
+        public static Point operator -(Point p1, Point p2)
+        {
+            return new Point(p1.X - p2.X, p1.Y - p2.Y);
+        }
+
+        public static Point operator +(Point p1, Point p2)
+        {
+            return new Point(p1.X + p2.X, p1.Y + p2.Y);
+        }
+
+        public static Point operator -(Point p1, float f)
+        {
+            return new Point(p1.X - f, p1.Y - f);
+        }
+
+        public static Point operator +(Point p1, float f)
+        {
+            return new Point(p1.X + f, p1.Y + f);
+        }
+
+        public float Cross(Point p)
+        {
+            return X * p.Y - Y * p.X;
+        }
+
+        public float Dot(Point p)
+        {
+            return X * p.X + Y * p.Y;
+        }
+
+        public bool Neq(Point p)
+        {
+            return p.X != X || p.Y != Y;
+        }
+
+        public float Orient2D(Point pb, Point pc)
+        {
+            float acx = X - pc.X;
+            float bcx = pb.X - pc.X;
+            float acy = Y - pc.Y;
+            float bcy = pb.Y - pc.Y;
+            return acx * bcy - acy * bcx;
+        }
+    }
+}

Farseer Physics Engine 3.5/Common/Decomposition/Seidel/QueryGraph.cs

@@ -0,0 +1,78 @@
+using System.Collections.Generic;
+
+namespace FarseerPhysics.Common.Decomposition.Seidel
+{
+    // Directed Acyclic graph (DAG)
+    // See "Computational Geometry", 3rd edition, by Mark de Berg et al, Chapter 6.2
+    internal class QueryGraph
+    {
+        private Node _head;
+
+        public QueryGraph(Node head)
+        {
+            _head = head;
+        }
+
+        private Trapezoid Locate(Edge edge)
+        {
+            return _head.Locate(edge).Trapezoid;
+        }
+
+        public List<Trapezoid> FollowEdge(Edge edge)
+        {
+            List<Trapezoid> trapezoids = new List<Trapezoid>();
+            trapezoids.Add(Locate(edge));
+            int j = 0;
+
+            while (edge.Q.X > trapezoids[j].RightPoint.X)
+            {
+                if (edge.IsAbove(trapezoids[j].RightPoint))
+                {
+                    trapezoids.Add(trapezoids[j].UpperRight);
+                }
+                else
+                {
+                    trapezoids.Add(trapezoids[j].LowerRight);
+                }
+                j += 1;
+            }
+            return trapezoids;
+        }
+
+        private void Replace(Sink sink, Node node)
+        {
+            if (sink.ParentList.Count == 0)
+                _head = node;
+            else
+                node.Replace(sink);
+        }
+
+        public void Case1(Sink sink, Edge edge, Trapezoid[] tList)
+        {
+            YNode yNode = new YNode(edge, Sink.Isink(tList[1]), Sink.Isink(tList[2]));
+            XNode qNode = new XNode(edge.Q, yNode, Sink.Isink(tList[3]));
+            XNode pNode = new XNode(edge.P, Sink.Isink(tList[0]), qNode);
+            Replace(sink, pNode);
+        }
+
+        public void Case2(Sink sink, Edge edge, Trapezoid[] tList)
+        {
+            YNode yNode = new YNode(edge, Sink.Isink(tList[1]), Sink.Isink(tList[2]));
+            XNode pNode = new XNode(edge.P, Sink.Isink(tList[0]), yNode);
+            Replace(sink, pNode);
+        }
+
+        public void Case3(Sink sink, Edge edge, Trapezoid[] tList)
+        {
+            YNode yNode = new YNode(edge, Sink.Isink(tList[0]), Sink.Isink(tList[1]));
+            Replace(sink, yNode);
+        }
+
+        public void Case4(Sink sink, Edge edge, Trapezoid[] tList)
+        {
+            YNode yNode = new YNode(edge, Sink.Isink(tList[0]), Sink.Isink(tList[1]));
+            XNode qNode = new XNode(edge.Q, yNode, Sink.Isink(tList[2]));
+            Replace(sink, qNode);
+        }
+    }
+}

Farseer Physics Engine 3.5/Common/Decomposition/Seidel/Sink.cs

@@ -0,0 +1,27 @@
+namespace FarseerPhysics.Common.Decomposition.Seidel
+{
+    internal class Sink : Node
+    {
+        public Trapezoid Trapezoid;
+
+        private Sink(Trapezoid trapezoid)
+            : base(null, null)
+        {
+            Trapezoid = trapezoid;
+            trapezoid.Sink = this;
+        }
+
+        public static Sink Isink(Trapezoid trapezoid)
+        {
+            if (trapezoid.Sink == null)
+                return new Sink(trapezoid);
+
+            return trapezoid.Sink;
+        }
+
+        public override Sink Locate(Edge edge)
+        {
+            return this;
+        }
+    }
+}

Farseer Physics Engine 3.5/Common/Decomposition/Seidel/Trapezoid.cs

@@ -0,0 +1,123 @@
+using System.Collections.Generic;
+
+namespace FarseerPhysics.Common.Decomposition.Seidel
+{
+    internal class Trapezoid
+    {
+        public Edge Bottom;
+        public bool Inside;
+        public Point LeftPoint;
+
+        // Neighbor pointers
+        public Trapezoid LowerLeft;
+        public Trapezoid LowerRight;
+
+        public Point RightPoint;
+        public Sink Sink;
+
+        public Edge Top;
+        public Trapezoid UpperLeft;
+        public Trapezoid UpperRight;
+
+        public Trapezoid(Point leftPoint, Point rightPoint, Edge top, Edge bottom)
+        {
+            LeftPoint = leftPoint;
+            RightPoint = rightPoint;
+            Top = top;
+            Bottom = bottom;
+            UpperLeft = null;
+            UpperRight = null;
+            LowerLeft = null;
+            LowerRight = null;
+            Inside = true;
+            Sink = null;
+        }
+
+        // Update neighbors to the left
+        public void UpdateLeft(Trapezoid ul, Trapezoid ll)
+        {
+            UpperLeft = ul;
+            if (ul != null) ul.UpperRight = this;
+            LowerLeft = ll;
+            if (ll != null) ll.LowerRight = this;
+        }
+
+        // Update neighbors to the right
+        public void UpdateRight(Trapezoid ur, Trapezoid lr)
+        {
+            UpperRight = ur;
+            if (ur != null) ur.UpperLeft = this;
+            LowerRight = lr;
+            if (lr != null) lr.LowerLeft = this;
+        }
+
+        // Update neighbors on both sides
+        public void UpdateLeftRight(Trapezoid ul, Trapezoid ll, Trapezoid ur, Trapezoid lr)
+        {
+            UpperLeft = ul;
+            if (ul != null) ul.UpperRight = this;
+            LowerLeft = ll;
+            if (ll != null) ll.LowerRight = this;
+            UpperRight = ur;
+            if (ur != null) ur.UpperLeft = this;
+            LowerRight = lr;
+            if (lr != null) lr.LowerLeft = this;
+        }
+
+        // Recursively trim outside neighbors
+        public void TrimNeighbors()
+        {
+            if (Inside)
+            {
+                Inside = false;
+                if (UpperLeft != null) UpperLeft.TrimNeighbors();
+                if (LowerLeft != null) LowerLeft.TrimNeighbors();
+                if (UpperRight != null) UpperRight.TrimNeighbors();
+                if (LowerRight != null) LowerRight.TrimNeighbors();
+            }
+        }
+
+        // Determines if this point lies inside the trapezoid
+        public bool Contains(Point point)
+        {
+            return (point.X > LeftPoint.X && point.X < RightPoint.X && Top.IsAbove(point) && Bottom.IsBelow(point));
+        }
+
+        public List<Point> GetVertices()
+        {
+            List<Point> verts = new List<Point>(4);
+            verts.Add(LineIntersect(Top, LeftPoint.X));
+            verts.Add(LineIntersect(Bottom, LeftPoint.X));
+            verts.Add(LineIntersect(Bottom, RightPoint.X));
+            verts.Add(LineIntersect(Top, RightPoint.X));
+            return verts;
+        }
+
+        private Point LineIntersect(Edge edge, float x)
+        {
+            float y = edge.Slope * x + edge.B;
+            return new Point(x, y);
+        }
+
+        // Add points to monotone mountain
+        public void AddPoints()
+        {
+            if (LeftPoint != Bottom.P)
+            {
+                Bottom.AddMpoint(LeftPoint);
+            }
+            if (RightPoint != Bottom.Q)
+            {
+                Bottom.AddMpoint(RightPoint);
+            }
+            if (LeftPoint != Top.P)
+            {
+                Top.AddMpoint(LeftPoint);
+            }
+            if (RightPoint != Top.Q)
+            {
+                Top.AddMpoint(RightPoint);
+            }
+        }
+    }
+}

Farseer Physics Engine 3.5/Common/Decomposition/Seidel/TrapezoidalMap.cs

@@ -0,0 +1,195 @@
+using System.Collections.Generic;
+
+namespace FarseerPhysics.Common.Decomposition.Seidel
+{
+    internal class TrapezoidalMap
+    {
+        // Trapezoid container
+        public HashSet<Trapezoid> Map;
+
+        // Bottom segment that spans multiple trapezoids
+        private Edge _bCross;
+
+        // Top segment that spans multiple trapezoids
+        private Edge _cross;
+
+        // AABB margin
+        private float _margin;
+
+        public TrapezoidalMap()
+        {
+            Map = new HashSet<Trapezoid>();
+            _margin = 50.0f;
+            _bCross = null;
+            _cross = null;
+        }
+
+        public void Clear()
+        {
+            _bCross = null;
+            _cross = null;
+        }
+
+        // Case 1: segment completely enclosed by trapezoid
+        //         break trapezoid into 4 smaller trapezoids
+        public Trapezoid[] Case1(Trapezoid t, Edge e)
+        {
+            Trapezoid[] trapezoids = new Trapezoid[4];
+            trapezoids[0] = new Trapezoid(t.LeftPoint, e.P, t.Top, t.Bottom);
+            trapezoids[1] = new Trapezoid(e.P, e.Q, t.Top, e);
+            trapezoids[2] = new Trapezoid(e.P, e.Q, e, t.Bottom);
+            trapezoids[3] = new Trapezoid(e.Q, t.RightPoint, t.Top, t.Bottom);
+
+            trapezoids[0].UpdateLeft(t.UpperLeft, t.LowerLeft);
+            trapezoids[1].UpdateLeftRight(trapezoids[0], null, trapezoids[3], null);
+            trapezoids[2].UpdateLeftRight(null, trapezoids[0], null, trapezoids[3]);
+            trapezoids[3].UpdateRight(t.UpperRight, t.LowerRight);
+
+            return trapezoids;
+        }
+
+        // Case 2: Trapezoid contains point p, q lies outside
+        //         break trapezoid into 3 smaller trapezoids
+        public Trapezoid[] Case2(Trapezoid t, Edge e)
+        {
+            Point rp;
+            if (e.Q.X == t.RightPoint.X)
+                rp = e.Q;
+            else
+                rp = t.RightPoint;
+
+            Trapezoid[] trapezoids = new Trapezoid[3];
+            trapezoids[0] = new Trapezoid(t.LeftPoint, e.P, t.Top, t.Bottom);
+            trapezoids[1] = new Trapezoid(e.P, rp, t.Top, e);
+            trapezoids[2] = new Trapezoid(e.P, rp, e, t.Bottom);
+
+            trapezoids[0].UpdateLeft(t.UpperLeft, t.LowerLeft);
+            trapezoids[1].UpdateLeftRight(trapezoids[0], null, t.UpperRight, null);
+            trapezoids[2].UpdateLeftRight(null, trapezoids[0], null, t.LowerRight);
+
+            _bCross = t.Bottom;
+            _cross = t.Top;
+
+            e.Above = trapezoids[1];
+            e.Below = trapezoids[2];
+
+            return trapezoids;
+        }
+
+        // Case 3: Trapezoid is bisected
+        public Trapezoid[] Case3(Trapezoid t, Edge e)
+        {
+            Point lp;
+            if (e.P.X == t.LeftPoint.X)
+                lp = e.P;
+            else
+                lp = t.LeftPoint;
+
+            Point rp;
+            if (e.Q.X == t.RightPoint.X)
+                rp = e.Q;
+            else
+                rp = t.RightPoint;
+
+            Trapezoid[] trapezoids = new Trapezoid[2];
+
+            if (_cross == t.Top)
+            {
+                trapezoids[0] = t.UpperLeft;
+                trapezoids[0].UpdateRight(t.UpperRight, null);
+                trapezoids[0].RightPoint = rp;
+            }
+            else
+            {
+                trapezoids[0] = new Trapezoid(lp, rp, t.Top, e);
+                trapezoids[0].UpdateLeftRight(t.UpperLeft, e.Above, t.UpperRight, null);
+            }
+
+            if (_bCross == t.Bottom)
+            {
+                trapezoids[1] = t.LowerLeft;
+                trapezoids[1].UpdateRight(null, t.LowerRight);
+                trapezoids[1].RightPoint = rp;
+            }
+            else
+            {
+                trapezoids[1] = new Trapezoid(lp, rp, e, t.Bottom);
+                trapezoids[1].UpdateLeftRight(e.Below, t.LowerLeft, null, t.LowerRight);
+            }
+
+            _bCross = t.Bottom;
+            _cross = t.Top;
+
+            e.Above = trapezoids[0];
+            e.Below = trapezoids[1];
+
+            return trapezoids;
+        }
+
+        // Case 4: Trapezoid contains point q, p lies outside
+        //         break trapezoid into 3 smaller trapezoids
+        public Trapezoid[] Case4(Trapezoid t, Edge e)
+        {
+            Point lp;
+            if (e.P.X == t.LeftPoint.X)
+                lp = e.P;
+            else
+                lp = t.LeftPoint;
+
+            Trapezoid[] trapezoids = new Trapezoid[3];
+
+            if (_cross == t.Top)
+            {
+                trapezoids[0] = t.UpperLeft;
+                trapezoids[0].RightPoint = e.Q;
+            }
+            else
+            {
+                trapezoids[0] = new Trapezoid(lp, e.Q, t.Top, e);
+                trapezoids[0].UpdateLeft(t.UpperLeft, e.Above);
+            }
+
+            if (_bCross == t.Bottom)
+            {
+                trapezoids[1] = t.LowerLeft;
+                trapezoids[1].RightPoint = e.Q;
+            }
+            else
+            {
+                trapezoids[1] = new Trapezoid(lp, e.Q, e, t.Bottom);
+                trapezoids[1].UpdateLeft(e.Below, t.LowerLeft);
+            }
+
+            trapezoids[2] = new Trapezoid(e.Q, t.RightPoint, t.Top, t.Bottom);
+            trapezoids[2].UpdateLeftRight(trapezoids[0], trapezoids[1], t.UpperRight, t.LowerRight);
+
+            return trapezoids;
+        }
+
+        // Create an AABB around segments
+        public Trapezoid BoundingBox(List<Edge> edges)
+        {
+            Point max = edges[0].P + _margin;
+            Point min = edges[0].Q - _margin;
+
+            foreach (Edge e in edges)
+            {
+                if (e.P.X > max.X) max = new Point(e.P.X + _margin, max.Y);
+                if (e.P.Y > max.Y) max = new Point(max.X, e.P.Y + _margin);
+                if (e.Q.X > max.X) max = new Point(e.Q.X + _margin, max.Y);
+                if (e.Q.Y > max.Y) max = new Point(max.X, e.Q.Y + _margin);
+                if (e.P.X < min.X) min = new Point(e.P.X - _margin, min.Y);
+                if (e.P.Y < min.Y) min = new Point(min.X, e.P.Y - _margin);
+                if (e.Q.X < min.X) min = new Point(e.Q.X - _margin, min.Y);
+                if (e.Q.Y < min.Y) min = new Point(min.X, e.Q.Y - _margin);
+            }
+
+            Edge top = new Edge(new Point(min.X, max.Y), new Point(max.X, max.Y));
+            Edge bottom = new Edge(new Point(min.X, min.Y), new Point(max.X, min.Y));
+            Point left = bottom.P;
+            Point right = top.Q;
+
+            return new Trapezoid(left, right, top, bottom);
+        }
+    }
+}

Farseer Physics Engine 3.5/Common/Decomposition/Seidel/Triangulator.cs

@@ -0,0 +1,203 @@
+using System;
+using System.Collections.Generic;
+
+namespace FarseerPhysics.Common.Decomposition.Seidel
+{
+    internal class Triangulator
+    {
+        // Trapezoid decomposition list
+        public List<Trapezoid> Trapezoids;
+        public List<List<Point>> Triangles;
+
+        // Initialize trapezoidal map and query structure
+        private Trapezoid _boundingBox;
+        private List<Edge> _edgeList;
+        private QueryGraph _queryGraph;
+        private float _sheer = 0.001f;
+        private TrapezoidalMap _trapezoidalMap;
+        private List<MonotoneMountain> _xMonoPoly;
+
+        public Triangulator(List<Point> polyLine, float sheer)
+        {
+            _sheer = sheer;
+            Triangles = new List<List<Point>>();
+            Trapezoids = new List<Trapezoid>();
+            _xMonoPoly = new List<MonotoneMountain>();
+            _edgeList = InitEdges(polyLine);
+            _trapezoidalMap = new TrapezoidalMap();
+            _boundingBox = _trapezoidalMap.BoundingBox(_edgeList);
+            _queryGraph = new QueryGraph(Sink.Isink(_boundingBox));
+
+            Process();
+        }
+
+        // Build the trapezoidal map and query graph
+        private void Process()
+        {
+            foreach (Edge edge in _edgeList)
+            {
+                List<Trapezoid> traps = _queryGraph.FollowEdge(edge);
+
+                // Remove trapezoids from trapezoidal Map
+                foreach (Trapezoid t in traps)
+                {
+                    _trapezoidalMap.Map.Remove(t);
+
+                    bool cp = t.Contains(edge.P);
+                    bool cq = t.Contains(edge.Q);
+                    Trapezoid[] tList;
+
+                    if (cp && cq)
+                    {
+                        tList = _trapezoidalMap.Case1(t, edge);
+                        _queryGraph.Case1(t.Sink, edge, tList);
+                    }
+                    else if (cp && !cq)
+                    {
+                        tList = _trapezoidalMap.Case2(t, edge);
+                        _queryGraph.Case2(t.Sink, edge, tList);
+                    }
+                    else if (!cp && !cq)
+                    {
+                        tList = _trapezoidalMap.Case3(t, edge);
+                        _queryGraph.Case3(t.Sink, edge, tList);
+                    }
+                    else
+                    {
+                        tList = _trapezoidalMap.Case4(t, edge);
+                        _queryGraph.Case4(t.Sink, edge, tList);
+                    }
+                    // Add new trapezoids to map
+                    foreach (Trapezoid y in tList)
+                    {
+                        _trapezoidalMap.Map.Add(y);
+                    }
+                }
+                _trapezoidalMap.Clear();
+            }
+
+            // Mark outside trapezoids
+            foreach (Trapezoid t in _trapezoidalMap.Map)
+            {
+                MarkOutside(t);
+            }
+
+            // Collect interior trapezoids
+            foreach (Trapezoid t in _trapezoidalMap.Map)
+            {
+                if (t.Inside)
+                {
+                    Trapezoids.Add(t);
+                    t.AddPoints();
+                }
+            }
+
+            // Generate the triangles
+            CreateMountains();
+        }
+
+        // Build a list of x-monotone mountains
+        private void CreateMountains()
+        {
+            foreach (Edge edge in _edgeList)
+            {
+                if (edge.MPoints.Count > 2)
+                {
+                    MonotoneMountain mountain = new MonotoneMountain();
+
+                    // Sorting is a perfromance hit. Literature says this can be accomplised in
+                    // linear time, although I don't see a way around using traditional methods
+                    // when using a randomized incremental algorithm
+
+                    // Insertion sort is one of the fastest algorithms for sorting arrays containing 
+                    // fewer than ten elements, or for lists that are already mostly sorted.
+
+                    List<Point> points = new List<Point>(edge.MPoints);
+                    points.Sort((p1, p2) => p1.X.CompareTo(p2.X));
+
+                    foreach (Point p in points)
+                        mountain.Add(p);
+
+                    // Triangulate monotone mountain
+                    mountain.Process();
+
+                    // Extract the triangles into a single list
+                    foreach (List<Point> t in mountain.Triangles)
+                    {
+                        Triangles.Add(t);
+                    }
+
+                    _xMonoPoly.Add(mountain);
+                }
+            }
+        }
+
+        // Mark the outside trapezoids surrounding the polygon
+        private void MarkOutside(Trapezoid t)
+        {
+            if (t.Top == _boundingBox.Top || t.Bottom == _boundingBox.Bottom)
+                t.TrimNeighbors();
+        }
+
+        // Create segments and connect end points; update edge event pointer
+        private List<Edge> InitEdges(List<Point> points)
+        {
+            List<Edge> edges = new List<Edge>();
+
+            for (int i = 0; i < points.Count - 1; i++)
+            {
+                edges.Add(new Edge(points[i], points[i + 1]));
+            }
+            edges.Add(new Edge(points[0], points[points.Count - 1]));
+            return OrderSegments(edges);
+        }
+
+        private List<Edge> OrderSegments(List<Edge> edgeInput)
+        {
+            // Ignore vertical segments!
+            List<Edge> edges = new List<Edge>();
+
+            foreach (Edge e in edgeInput)
+            {
+                Point p = ShearTransform(e.P);
+                Point q = ShearTransform(e.Q);
+
+                // Point p must be to the left of point q
+                if (p.X > q.X)
+                {
+                    edges.Add(new Edge(q, p));
+                }
+                else if (p.X < q.X)
+                {
+                    edges.Add(new Edge(p, q));
+                }
+            }
+
+            // Randomized triangulation improves performance
+            // See Seidel's paper, or O'Rourke's book, p. 57 
+            Shuffle(edges);
+            return edges;
+        }
+
+        private static void Shuffle<T>(IList<T> list)
+        {
+            Random rng = new Random();
+            int n = list.Count;
+            while (n > 1)
+            {
+                n--;
+                int k = rng.Next(n + 1);
+                T value = list[k];
+                list[k] = list[n];
+                list[n] = value;
+            }
+        }
+
+        // Prevents any two distinct endpoints from lying on a common vertical line, and avoiding
+        // the degenerate case. See Mark de Berg et al, Chapter 6.3
+        private Point ShearTransform(Point point)
+        {
+            return new Point(point.X + _sheer * point.Y, point.Y);
+        }
+    }
+}

Farseer Physics Engine 3.5/Common/Decomposition/Seidel/XNode.cs

@@ -0,0 +1,21 @@
+namespace FarseerPhysics.Common.Decomposition.Seidel
+{
+    internal class XNode : Node
+    {
+        private Point _point;
+
+        public XNode(Point point, Node lChild, Node rChild)
+            : base(lChild, rChild)
+        {
+            _point = point;
+        }
+
+        public override Sink Locate(Edge edge)
+        {
+            if (edge.P.X >= _point.X)
+                return RightChild.Locate(edge); // Move to the right in the graph
+
+            return LeftChild.Locate(edge); // Move to the left in the graph
+        }
+    }
+}

Farseer Physics Engine 3.5/Common/Decomposition/Seidel/YNode.cs

@@ -0,0 +1,29 @@
+namespace FarseerPhysics.Common.Decomposition.Seidel
+{
+    internal class YNode : Node
+    {
+        private Edge _edge;
+
+        public YNode(Edge edge, Node lChild, Node rChild)
+            : base(lChild, rChild)
+        {
+            _edge = edge;
+        }
+
+        public override Sink Locate(Edge edge)
+        {
+            if (_edge.IsAbove(edge.P))
+                return RightChild.Locate(edge); // Move down the graph
+
+            if (_edge.IsBelow(edge.P))
+                return LeftChild.Locate(edge); // Move up the graph
+
+            // s and segment share the same endpoint, p
+            if (edge.Slope < _edge.Slope)
+                return RightChild.Locate(edge); // Move down the graph
+
+            // Move up the graph
+            return LeftChild.Locate(edge);
+        }
+    }
+}

Farseer Physics Engine 3.5/Common/Decomposition/SeidelDecomposer.cs

@@ -0,0 +1,109 @@
+/*
+* Farseer Physics Engine:
+* Copyright (c) 2012 Ian Qvist
+*/
+
+using System.Collections.Generic;
+using System.Diagnostics;
+using FarseerPhysics.Common.Decomposition.Seidel;
+using Microsoft.Xna.Framework;
+using Point = FarseerPhysics.Common.Decomposition.Seidel.Point;
+
+namespace FarseerPhysics.Common.Decomposition
+{
+    /// <summary>
+    /// Convex decomposition algorithm created by Raimund Seidel
+    /// 
+    /// Properties:
+    /// - Decompose the polygon into trapezoids, then triangulate.
+    /// - To use the trapezoid data, use ConvexPartitionTrapezoid()
+    /// - Generate a lot of garbage due to incapsulation of the Poly2Tri library.
+    /// - Running time is O(n log n), n = number of vertices.
+    /// - Running time is almost linear for most simple polygons.
+    /// - Does not care about winding order. 
+    /// 
+    /// For more information, see Raimund Seidel's paper "A simple and fast incremental randomized
+    /// algorithm for computing trapezoidal decompositions and for triangulating polygons"
+    /// 
+    /// See also: "Computational Geometry", 3rd edition, by Mark de Berg et al, Chapter 6.2
+    ///           "Computational Geometry in C", 2nd edition, by Joseph O'Rourke
+    /// 
+    /// Original code from the Poly2Tri project by Mason Green.
+    /// http://code.google.com/p/poly2tri/source/browse?repo=archive#hg/scala/src/org/poly2tri/seidel
+    /// 
+    /// This implementation is from Dec 14, 2010
+    /// </summary>
+    internal static class SeidelDecomposer
+    {
+        /// <summary>
+        /// Decompose the polygon into several smaller non-concave polygons.
+        /// </summary>
+        /// <param name="vertices">The polygon to decompose.</param>
+        /// <param name="sheer">The sheer to use if you get bad results, try using a higher value.</param>
+        /// <returns>A list of triangles</returns>
+        public static List<Vertices> ConvexPartition(Vertices vertices, float sheer = 0.001f)
+        {
+            Debug.Assert(vertices.Count > 3);
+
+            List<Point> compatList = new List<Point>(vertices.Count);
+
+            foreach (Vector2 vertex in vertices)
+            {
+                compatList.Add(new Point(vertex.X, vertex.Y));
+            }
+
+            Triangulator t = new Triangulator(compatList, sheer);
+
+            List<Vertices> list = new List<Vertices>();
+
+            foreach (List<Point> triangle in t.Triangles)
+            {
+                Vertices outTriangles = new Vertices(triangle.Count);
+
+                foreach (Point outTriangle in triangle)
+                {
+                    outTriangles.Add(new Vector2(outTriangle.X, outTriangle.Y));
+                }
+
+                list.Add(outTriangles);
+            }
+
+            return list;
+        }
+
+        /// <summary>
+        /// Decompose the polygon into several smaller non-concave polygons.
+        /// </summary>
+        /// <param name="vertices">The polygon to decompose.</param>
+        /// <param name="sheer">The sheer to use if you get bad results, try using a higher value.</param>
+        /// <returns>A list of trapezoids</returns>
+        public static List<Vertices> ConvexPartitionTrapezoid(Vertices vertices, float sheer = 0.001f)
+        {
+            List<Point> compatList = new List<Point>(vertices.Count);
+
+            foreach (Vector2 vertex in vertices)
+            {
+                compatList.Add(new Point(vertex.X, vertex.Y));
+            }
+
+            Triangulator t = new Triangulator(compatList, sheer);
+
+            List<Vertices> list = new List<Vertices>();
+
+            foreach (Trapezoid trapezoid in t.Trapezoids)
+            {
+                Vertices verts = new Vertices();
+
+                List<Point> points = trapezoid.GetVertices();
+                foreach (Point point in points)
+                {
+                    verts.Add(new Vector2(point.X, point.Y));
+                }
+
+                list.Add(verts);
+            }
+
+            return list;
+        }
+    }
+}

Farseer Physics Engine 3.5/Common/Decomposition/Triangulate.cs

@@ -0,0 +1,172 @@
+using System;
+using System.Collections.Generic;
+using System.Diagnostics;
+using FarseerPhysics.Common.ConvexHull;
+
+namespace FarseerPhysics.Common.Decomposition
+{
+    public enum TriangulationAlgorithm
+    {
+        /// <summary>
+        /// Convex decomposition algorithm using ear clipping
+        /// 
+        /// Properties:
+        /// - Only works on simple polygons.
+        /// - Does not support holes.
+        /// - Running time is O(n^2), n = number of vertices.
+        /// </summary>
+        Earclip,
+
+        /// <summary>
+        /// Convex decomposition algorithm created by Mark Bayazit (http://mnbayazit.com/)
+        /// 
+        /// Properties:
+        /// - Tries to decompose using polygons instead of triangles.
+        /// - Tends to produce optimal results with low processing time.
+        /// - Running time is O(nr), n = number of vertices, r = reflex vertices.
+        /// - Does not support holes.
+        /// </summary>
+        Bayazit,
+
+        /// <summary>
+        /// Convex decomposition algorithm created by unknown
+        /// 
+        /// Properties:
+        /// - No support for holes
+        /// - Very fast
+        /// - Only works on simple polygons
+        /// - Only works on counter clockwise polygons
+        /// </summary>
+        Flipcode,
+
+        /// <summary>
+        /// Convex decomposition algorithm created by Raimund Seidel
+        /// 
+        /// Properties:
+        /// - Decompose the polygon into trapezoids, then triangulate.
+        /// - To use the trapezoid data, use ConvexPartitionTrapezoid()
+        /// - Generate a lot of garbage due to incapsulation of the Poly2Tri library.
+        /// - Running time is O(n log n), n = number of vertices.
+        /// - Running time is almost linear for most simple polygons.
+        /// - Does not care about winding order. 
+        /// </summary>
+        Seidel,
+        SeidelTrapezoids,
+
+        /// <summary>
+        /// 2D constrained Delaunay triangulation algorithm.
+        /// Based on the paper "Sweep-line algorithm for constrained Delaunay triangulation" by V. Domiter and and B. Zalik
+        /// 
+        /// Properties:
+        /// - Creates triangles with a large interior angle.
+        /// - Supports holes
+        /// - Generate a lot of garbage due to incapsulation of the Poly2Tri library.
+        /// - Running time is O(n^2), n = number of vertices.
+        /// - Does not care about winding order.
+        /// </summary>
+        Delauny
+    }
+
+    public static class Triangulate
+    {
+        public static List<Vertices> ConvexPartition(Vertices vertices, TriangulationAlgorithm algorithm, bool discardAndFixInvalid = true, float tolerance = 0.001f)
+        {
+            if (vertices.Count <= 3)
+                return new List<Vertices> { vertices };
+
+            List<Vertices> results;
+
+            switch (algorithm)
+            {
+                case TriangulationAlgorithm.Earclip:
+                    if (Settings.SkipSanityChecks)
+                        Debug.Assert(!vertices.IsCounterClockWise(), "The Earclip algorithm expects the polygon to be clockwise.");
+                    else
+                    {
+                        if (vertices.IsCounterClockWise())
+                        {
+                            Vertices temp = new Vertices(vertices);
+                            temp.Reverse();
+                            results = EarclipDecomposer.ConvexPartition(temp, tolerance);
+                        }
+                        else
+                            results = EarclipDecomposer.ConvexPartition(vertices, tolerance);
+                    }
+                    break;
+                case TriangulationAlgorithm.Bayazit:
+                    if (Settings.SkipSanityChecks)
+                        Debug.Assert(vertices.IsCounterClockWise(), "The polygon is not counter clockwise. This is needed for Bayazit to work correctly.");
+                    else
+                    {
+                        if (!vertices.IsCounterClockWise())
+                        {
+                            Vertices temp = new Vertices(vertices);
+                            temp.Reverse();
+                            results = BayazitDecomposer.ConvexPartition(temp);
+                        }
+                        else
+                            results = BayazitDecomposer.ConvexPartition(vertices);
+                    }
+                    break;
+                case TriangulationAlgorithm.Flipcode:
+                    if (Settings.SkipSanityChecks)
+                        Debug.Assert(vertices.IsCounterClockWise(), "The polygon is not counter clockwise. This is needed for Bayazit to work correctly.");
+                    else
+                    {
+                        if (!vertices.IsCounterClockWise())
+                        {
+                            Vertices temp = new Vertices(vertices);
+                            temp.Reverse();
+                            results = FlipcodeDecomposer.ConvexPartition(temp);
+                        }
+                        else
+                            results = FlipcodeDecomposer.ConvexPartition(vertices);
+                    }
+                    break;
+                case TriangulationAlgorithm.Seidel:
+                    results = SeidelDecomposer.ConvexPartition(vertices, tolerance);
+                    break;
+                case TriangulationAlgorithm.SeidelTrapezoids:
+                    results = SeidelDecomposer.ConvexPartitionTrapezoid(vertices, tolerance);
+                    break;
+                case TriangulationAlgorithm.Delauny:
+                    results = CDTDecomposer.ConvexPartition(vertices);
+                    break;
+                default:
+                    throw new ArgumentOutOfRangeException("algorithm");
+            }
+
+            if (discardAndFixInvalid)
+            {
+                for (int i = results.Count - 1; i >= 0; i--)
+                {
+                    Vertices polygon = results[i];
+
+                    if (!ValidatePolygon(polygon))
+                        results.RemoveAt(i);
+                }
+            }
+
+            return results;
+        }
+
+        private static bool ValidatePolygon(Vertices polygon)
+        {
+            PolygonError errorCode = polygon.CheckPolygon();
+
+            if (errorCode == PolygonError.InvalidAmountOfVertices || errorCode == PolygonError.AreaTooSmall || errorCode == PolygonError.SideTooSmall || errorCode == PolygonError.NotSimple)
+                return false;
+
+            if (errorCode == PolygonError.NotCounterClockWise) //NotCounterCloseWise is the last check in CheckPolygon(), thus we don't need to call ValidatePolygon again.
+                polygon.Reverse();
+
+            if (errorCode == PolygonError.NotConvex)
+            {
+                polygon = GiftWrap.GetConvexHull(polygon);
+                return ValidatePolygon(polygon);
+            }
+
+            return true;
+        }
+    }
+}

Farseer Physics Engine 3.5/Common/FixedArray.cs

@@ -0,0 +1,224 @@
+/*
+* Farseer Physics Engine:
+* Copyright (c) 2012 Ian Qvist
+* 
+* Original source Box2D:
+* Copyright (c) 2006-2011 Erin Catto http://www.box2d.org 
+* 
+* This software is provided 'as-is', without any express or implied 
+* warranty.  In no event will the authors be held liable for any damages 
+* arising from the use of this software. 
+* Permission is granted to anyone to use this software for any purpose, 
+* including commercial applications, and to alter it and redistribute it 
+* freely, subject to the following restrictions: 
+* 1. The origin of this software must not be misrepresented; you must not 
+* claim that you wrote the original software. If you use this software 
+* in a product, an acknowledgment in the product documentation would be 
+* appreciated but is not required. 
+* 2. Altered source versions must be plainly marked as such, and must not be 
+* misrepresented as being the original software. 
+* 3. This notice may not be removed or altered from any source distribution. 
+*/
+
+using System;
+
+namespace FarseerPhysics.Common
+{
+    public struct FixedArray2<T>
+    {
+        private T _value0;
+        private T _value1;
+
+        public T this[int index]
+        {
+            get
+            {
+                switch (index)
+                {
+                    case 0:
+                        return _value0;
+                    case 1:
+                        return _value1;
+                    default:
+                        throw new IndexOutOfRangeException();
+                }
+            }
+            set
+            {
+                switch (index)
+                {
+                    case 0:
+                        _value0 = value;
+                        break;
+                    case 1:
+                        _value1 = value;
+                        break;
+                    default:
+                        throw new IndexOutOfRangeException();
+                }
+            }
+        }
+    }
+
+    public struct FixedArray3<T>
+    {
+        private T _value0;
+        private T _value1;
+        private T _value2;
+
+        public T this[int index]
+        {
+            get
+            {
+                switch (index)
+                {
+                    case 0:
+                        return _value0;
+                    case 1:
+                        return _value1;
+                    case 2:
+                        return _value2;
+                    default:
+                        throw new IndexOutOfRangeException();
+                }
+            }
+            set
+            {
+                switch (index)
+                {
+                    case 0:
+                        _value0 = value;
+                        break;
+                    case 1:
+                        _value1 = value;
+                        break;
+                    case 2:
+                        _value2 = value;
+                        break;
+                    default:
+                        throw new IndexOutOfRangeException();
+                }
+            }
+        }
+    }
+
+    public struct FixedArray4<T>
+    {
+        private T _value0;
+        private T _value1;
+        private T _value2;
+        private T _value3;
+
+        public T this[int index]
+        {
+            get
+            {
+                switch (index)
+                {
+                    case 0:
+                        return _value0;
+                    case 1:
+                        return _value1;
+                    case 2:
+                        return _value2;
+                    case 3:
+                        return _value3;
+                    default:
+                        throw new IndexOutOfRangeException();
+                }
+            }
+            set
+            {
+                switch (index)
+                {
+                    case 0:
+                        _value0 = value;
+                        break;
+                    case 1:
+                        _value1 = value;
+                        break;
+                    case 2:
+                        _value2 = value;
+                        break;
+                    case 3:
+                        _value3 = value;
+                        break;
+                    default:
+                        throw new IndexOutOfRangeException();
+                }
+            }
+        }
+    }
+
+    public struct FixedArray8<T>
+    {
+        private T _value0;
+        private T _value1;
+        private T _value2;
+        private T _value3;
+        private T _value4;
+        private T _value5;
+        private T _value6;
+        private T _value7;
+
+        public T this[int index]
+        {
+            get
+            {
+                switch (index)
+                {
+                    case 0:
+                        return _value0;
+                    case 1:
+                        return _value1;
+                    case 2:
+                        return _value2;
+                    case 3:
+                        return _value3;
+                    case 4:
+                        return _value4;
+                    case 5:
+                        return _value5;
+                    case 6:
+                        return _value6;
+                    case 7:
+                        return _value7;
+                    default:
+                        throw new IndexOutOfRangeException();
+                }
+            }
+            set
+            {
+                switch (index)
+                {
+                    case 0:
+                        _value0 = value;
+                        break;
+                    case 1:
+                        _value1 = value;
+                        break;
+                    case 2:
+                        _value2 = value;
+                        break;
+                    case 3:
+                        _value3 = value;
+                        break;
+                    case 4:
+                        _value4 = value;
+                        break;
+                    case 5:
+                        _value5 = value;
+                        break;
+                    case 6:
+                        _value6 = value;
+                        break;
+                    case 7:
+                        _value7 = value;
+                        break;
+                    default:
+                        throw new IndexOutOfRangeException();
+                }
+            }
+        }
+    }
+}

Farseer Physics Engine 3.5/Common/HashSet.cs

@@ -0,0 +1,78 @@
+#if WINDOWS_PHONE || XBOX
+
+using System.Collections;
+using System.Collections.Generic;
+
+namespace FarseerPhysics.Common
+{
+    public class HashSet<T> : ICollection<T>
+    {
+        private Dictionary<T, byte> _dict;
+
+        public HashSet(int capacity)
+        {
+            _dict = new Dictionary<T, byte>(capacity);
+        }
+
+        public HashSet()
+        {
+            _dict = new Dictionary<T, byte>();
+        }
+
+        #region ICollection<T> Members
+
+        public void Add(T item)
+        {
+            // We don't care for the value in dictionary, only keys matter.
+            if (!_dict.ContainsKey(item))
+                _dict.Add(item, 0);
+        }
+
+        public void Clear()
+        {
+            _dict.Clear();
+        }
+
+        public bool Contains(T item)
+        {
+            return _dict.ContainsKey(item);
+        }
+
+        public void CopyTo(T[] array, int arrayIndex)
+        {
+            foreach (var item in _dict.Keys)
+            {
+                array[arrayIndex++] = item;
+            }
+        }
+
+        public bool Remove(T item)
+        {
+            return _dict.Remove(item);
+        }
+
+        public IEnumerator<T> GetEnumerator()
+        {
+            return _dict.Keys.GetEnumerator();
+        }
+
+        IEnumerator IEnumerable.GetEnumerator()
+        {
+            return _dict.Keys.GetEnumerator();
+        }
+
+        // Properties
+        public int Count
+        {
+            get { return _dict.Keys.Count; }
+        }
+
+        public bool IsReadOnly
+        {
+            get { return false; }
+        }
+
+        #endregion
+    }
+}
+#endif

Farseer Physics Engine 3.5/Common/LineTools.cs

@@ -0,0 +1,287 @@
+using System;
+using FarseerPhysics.Collision;
+using Microsoft.Xna.Framework;
+
+namespace FarseerPhysics.Common
+{
+    /// <summary>
+    /// Collection of helper methods for misc collisions.
+    /// Does float tolerance and line collisions with lines and AABBs.
+    /// </summary>
+    public static class LineTools
+    {
+        public static float DistanceBetweenPointAndLineSegment(ref Vector2 point, ref Vector2 start, ref Vector2 end)
+        {
+            if (start == end)
+                return Vector2.Distance(point, start);
+
+            Vector2 v = Vector2.Subtract(end, start);
+            Vector2 w = Vector2.Subtract(point, start);
+
+            float c1 = Vector2.Dot(w, v);
+            if (c1 <= 0) return Vector2.Distance(point, start);
+
+            float c2 = Vector2.Dot(v, v);
+            if (c2 <= c1) return Vector2.Distance(point, end);
+
+            float b = c1 / c2;
+            Vector2 pointOnLine = Vector2.Add(start, Vector2.Multiply(v, b));
+            return Vector2.Distance(point, pointOnLine);
+        }
+
+        // From Eric Jordan's convex decomposition library
+        /// <summary>
+        ///Check if the lines a0->a1 and b0->b1 cross.
+        ///If they do, intersectionPoint will be filled
+        ///with the point of crossing.
+        ///
+        ///Grazing lines should not return true.
+        /// 
+        /// </summary>
+        public static bool LineIntersect2(ref Vector2 a0, ref Vector2 a1, ref Vector2 b0, ref  Vector2 b1, out Vector2 intersectionPoint)
+        {
+            intersectionPoint = Vector2.Zero;
+
+            if (a0 == b0 || a0 == b1 || a1 == b0 || a1 == b1)
+                return false;
+
+            float x1 = a0.X;
+            float y1 = a0.Y;
+            float x2 = a1.X;
+            float y2 = a1.Y;
+            float x3 = b0.X;
+            float y3 = b0.Y;
+            float x4 = b1.X;
+            float y4 = b1.Y;
+
+            //AABB early exit
+            if (Math.Max(x1, x2) < Math.Min(x3, x4) || Math.Max(x3, x4) < Math.Min(x1, x2))
+                return false;
+
+            if (Math.Max(y1, y2) < Math.Min(y3, y4) || Math.Max(y3, y4) < Math.Min(y1, y2))
+                return false;
+
+            float ua = ((x4 - x3) * (y1 - y3) - (y4 - y3) * (x1 - x3));
+            float ub = ((x2 - x1) * (y1 - y3) - (y2 - y1) * (x1 - x3));
+            float denom = (y4 - y3) * (x2 - x1) - (x4 - x3) * (y2 - y1);
+            if (Math.Abs(denom) < Settings.Epsilon)
+            {
+                //Lines are too close to parallel to call
+                return false;
+            }
+            ua /= denom;
+            ub /= denom;
+
+            if ((0 < ua) && (ua < 1) && (0 < ub) && (ub < 1))
+            {
+                intersectionPoint.X = (x1 + ua * (x2 - x1));
+                intersectionPoint.Y = (y1 + ua * (y2 - y1));
+                return true;
+            }
+
+            return false;
+        }
+
+        //From Mark Bayazit's convex decomposition algorithm
+        public static Vector2 LineIntersect(Vector2 p1, Vector2 p2, Vector2 q1, Vector2 q2)
+        {
+            Vector2 i = Vector2.Zero;
+            float a1 = p2.Y - p1.Y;
+            float b1 = p1.X - p2.X;
+            float c1 = a1 * p1.X + b1 * p1.Y;
+            float a2 = q2.Y - q1.Y;
+            float b2 = q1.X - q2.X;
+            float c2 = a2 * q1.X + b2 * q1.Y;
+            float det = a1 * b2 - a2 * b1;
+
+            if (!MathUtils.FloatEquals(det, 0))
+            {
+                // lines are not parallel
+                i.X = (b2 * c1 - b1 * c2) / det;
+                i.Y = (a1 * c2 - a2 * c1) / det;
+            }
+            return i;
+        }
+
+        /// <summary>
+        /// This method detects if two line segments (or lines) intersect,
+        /// and, if so, the point of intersection. Use the <paramref name="firstIsSegment"/> and
+        /// <paramref name="secondIsSegment"/> parameters to set whether the intersection point
+        /// must be on the first and second line segments. Setting these
+        /// both to true means you are doing a line-segment to line-segment
+        /// intersection. Setting one of them to true means you are doing a
+        /// line to line-segment intersection test, and so on.
+        /// Note: If two line segments are coincident, then 
+        /// no intersection is detected (there are actually
+        /// infinite intersection points).
+        /// Author: Jeremy Bell
+        /// </summary>
+        /// <param name="point1">The first point of the first line segment.</param>
+        /// <param name="point2">The second point of the first line segment.</param>
+        /// <param name="point3">The first point of the second line segment.</param>
+        /// <param name="point4">The second point of the second line segment.</param>
+        /// <param name="point">This is set to the intersection
+        /// point if an intersection is detected.</param>
+        /// <param name="firstIsSegment">Set this to true to require that the 
+        /// intersection point be on the first line segment.</param>
+        /// <param name="secondIsSegment">Set this to true to require that the
+        /// intersection point be on the second line segment.</param>
+        /// <returns>True if an intersection is detected, false otherwise.</returns>
+        public static bool LineIntersect(ref Vector2 point1, ref Vector2 point2, ref Vector2 point3, ref Vector2 point4, bool firstIsSegment, bool secondIsSegment, out Vector2 point)
+        {
+            point = new Vector2();
+
+            // these are reused later.
+            // each lettered sub-calculation is used twice, except
+            // for b and d, which are used 3 times
+            float a = point4.Y - point3.Y;
+            float b = point2.X - point1.X;
+            float c = point4.X - point3.X;
+            float d = point2.Y - point1.Y;
+
+            // denominator to solution of linear system
+            float denom = (a * b) - (c * d);
+
+            // if denominator is 0, then lines are parallel
+            if (!(denom >= -Settings.Epsilon && denom <= Settings.Epsilon))
+            {
+                float e = point1.Y - point3.Y;
+                float f = point1.X - point3.X;
+                float oneOverDenom = 1.0f / denom;
+
+                // numerator of first equation
+                float ua = (c * e) - (a * f);
+                ua *= oneOverDenom;
+
+                // check if intersection point of the two lines is on line segment 1
+                if (!firstIsSegment || ua >= 0.0f && ua <= 1.0f)
+                {
+                    // numerator of second equation
+                    float ub = (b * e) - (d * f);
+                    ub *= oneOverDenom;
+
+                    // check if intersection point of the two lines is on line segment 2
+                    // means the line segments intersect, since we know it is on
+                    // segment 1 as well.
+                    if (!secondIsSegment || ub >= 0.0f && ub <= 1.0f)
+                    {
+                        // check if they are coincident (no collision in this case)
+                        if (ua != 0f || ub != 0f)
+                        {
+                            //There is an intersection
+                            point.X = point1.X + ua * b;
+                            point.Y = point1.Y + ua * d;
+                            return true;
+                        }
+                    }
+                }
+            }
+
+            return false;
+        }
+
+        /// <summary>
+        /// This method detects if two line segments (or lines) intersect,
+        /// and, if so, the point of intersection. Use the <paramref name="firstIsSegment"/> and
+        /// <paramref name="secondIsSegment"/> parameters to set whether the intersection point
+        /// must be on the first and second line segments. Setting these
+        /// both to true means you are doing a line-segment to line-segment
+        /// intersection. Setting one of them to true means you are doing a
+        /// line to line-segment intersection test, and so on.
+        /// Note: If two line segments are coincident, then 
+        /// no intersection is detected (there are actually
+        /// infinite intersection points).
+        /// Author: Jeremy Bell
+        /// </summary>
+        /// <param name="point1">The first point of the first line segment.</param>
+        /// <param name="point2">The second point of the first line segment.</param>
+        /// <param name="point3">The first point of the second line segment.</param>
+        /// <param name="point4">The second point of the second line segment.</param>
+        /// <param name="intersectionPoint">This is set to the intersection
+        /// point if an intersection is detected.</param>
+        /// <param name="firstIsSegment">Set this to true to require that the 
+        /// intersection point be on the first line segment.</param>
+        /// <param name="secondIsSegment">Set this to true to require that the
+        /// intersection point be on the second line segment.</param>
+        /// <returns>True if an intersection is detected, false otherwise.</returns>
+        public static bool LineIntersect(Vector2 point1, Vector2 point2, Vector2 point3, Vector2 point4, bool firstIsSegment, bool secondIsSegment, out Vector2 intersectionPoint)
+        {
+            return LineIntersect(ref point1, ref point2, ref point3, ref point4, firstIsSegment, secondIsSegment, out intersectionPoint);
+        }
+
+        /// <summary>
+        /// This method detects if two line segments intersect,
+        /// and, if so, the point of intersection. 
+        /// Note: If two line segments are coincident, then 
+        /// no intersection is detected (there are actually
+        /// infinite intersection points).
+        /// </summary>
+        /// <param name="point1">The first point of the first line segment.</param>
+        /// <param name="point2">The second point of the first line segment.</param>
+        /// <param name="point3">The first point of the second line segment.</param>
+        /// <param name="point4">The second point of the second line segment.</param>
+        /// <param name="intersectionPoint">This is set to the intersection
+        /// point if an intersection is detected.</param>
+        /// <returns>True if an intersection is detected, false otherwise.</returns>
+        public static bool LineIntersect(ref Vector2 point1, ref Vector2 point2, ref Vector2 point3, ref Vector2 point4, out Vector2 intersectionPoint)
+        {
+            return LineIntersect(ref point1, ref point2, ref point3, ref point4, true, true, out intersectionPoint);
+        }
+
+        /// <summary>
+        /// This method detects if two line segments intersect,
+        /// and, if so, the point of intersection. 
+        /// Note: If two line segments are coincident, then 
+        /// no intersection is detected (there are actually
+        /// infinite intersection points).
+        /// </summary>
+        /// <param name="point1">The first point of the first line segment.</param>
+        /// <param name="point2">The second point of the first line segment.</param>
+        /// <param name="point3">The first point of the second line segment.</param>
+        /// <param name="point4">The second point of the second line segment.</param>
+        /// <param name="intersectionPoint">This is set to the intersection
+        /// point if an intersection is detected.</param>
+        /// <returns>True if an intersection is detected, false otherwise.</returns>
+        public static bool LineIntersect(Vector2 point1, Vector2 point2, Vector2 point3, Vector2 point4, out Vector2 intersectionPoint)
+        {
+            return LineIntersect(ref point1, ref point2, ref point3, ref point4, true, true, out intersectionPoint);
+        }
+
+        /// <summary>
+        /// Get all intersections between a line segment and a list of vertices
+        /// representing a polygon. The vertices reuse adjacent points, so for example
+        /// edges one and two are between the first and second vertices and between the
+        /// second and third vertices. The last edge is between vertex vertices.Count - 1
+        /// and verts0. (ie, vertices from a Geometry or AABB)
+        /// </summary>
+        /// <param name="point1">The first point of the line segment to test</param>
+        /// <param name="point2">The second point of the line segment to test.</param>
+        /// <param name="vertices">The vertices, as described above</param>
+        public static Vertices LineSegmentVerticesIntersect(ref Vector2 point1, ref Vector2 point2, Vertices vertices)
+        {
+            Vertices intersectionPoints = new Vertices();
+
+            for (int i = 0; i < vertices.Count; i++)
+            {
+                Vector2 point;
+                if (LineIntersect(vertices[i], vertices[vertices.NextIndex(i)], point1, point2, true, true, out point))
+                {
+                    intersectionPoints.Add(point);
+                }
+            }
+
+            return intersectionPoints;
+        }
+
+        /// <summary>
+        /// Get all intersections between a line segment and an AABB. 
+        /// </summary>
+        /// <param name="point1">The first point of the line segment to test</param>
+        /// <param name="point2">The second point of the line segment to test.</param>
+        /// <param name="aabb">The AABB that is used for testing intersection.</param>
+        public static Vertices LineSegmentAABBIntersect(ref Vector2 point1, ref Vector2 point2, AABB aabb)
+        {
+            return LineSegmentVerticesIntersect(ref point1, ref point2, aabb.Vertices);
+        }
+    }
+}

Farseer Physics Engine 3.5/Common/Math.cs

@@ -0,0 +1,806 @@
+/*
+* Farseer Physics Engine:
+* Copyright (c) 2012 Ian Qvist
+* 
+* Original source Box2D:
+* Copyright (c) 2006-2011 Erin Catto http://www.box2d.org 
+* 
+* This software is provided 'as-is', without any express or implied 
+* warranty.  In no event will the authors be held liable for any damages 
+* arising from the use of this software. 
+* Permission is granted to anyone to use this software for any purpose, 
+* including commercial applications, and to alter it and redistribute it 
+* freely, subject to the following restrictions: 
+* 1. The origin of this software must not be misrepresented; you must not 
+* claim that you wrote the original software. If you use this software 
+* in a product, an acknowledgment in the product documentation would be 
+* appreciated but is not required. 
+* 2. Altered source versions must be plainly marked as such, and must not be 
+* misrepresented as being the original software. 
+* 3. This notice may not be removed or altered from any source distribution. 
+*/
+
+using System;
+using System.Diagnostics;
+using System.Runtime.InteropServices;
+using Microsoft.Xna.Framework;
+
+namespace FarseerPhysics.Common
+{
+    public static class MathUtils
+    {
+        public static float Cross(ref Vector2 a, ref Vector2 b)
+        {
+            return a.X * b.Y - a.Y * b.X;
+        }
+
+        public static float Cross(Vector2 a, Vector2 b)
+        {
+            return Cross(ref a, ref b);
+        }
+
+        /// Perform the cross product on two vectors.
+        public static Vector3 Cross(Vector3 a, Vector3 b)
+        {
+            return new Vector3(a.Y * b.Z - a.Z * b.Y, a.Z * b.X - a.X * b.Z, a.X * b.Y - a.Y * b.X);
+        }
+
+        public static Vector2 Cross(Vector2 a, float s)
+        {
+            return new Vector2(s * a.Y, -s * a.X);
+        }
+
+        public static Vector2 Cross(float s, Vector2 a)
+        {
+            return new Vector2(-s * a.Y, s * a.X);
+        }
+
+        public static Vector2 Abs(Vector2 v)
+        {
+            return new Vector2(Math.Abs(v.X), Math.Abs(v.Y));
+        }
+
+        public static Vector2 Mul(ref Mat22 A, Vector2 v)
+        {
+            return Mul(ref A, ref v);
+        }
+
+        public static Vector2 Mul(ref Mat22 A, ref Vector2 v)
+        {
+            return new Vector2(A.ex.X * v.X + A.ey.X * v.Y, A.ex.Y * v.X + A.ey.Y * v.Y);
+        }
+
+        public static Vector2 Mul(ref Transform T, Vector2 v)
+        {
+            return Mul(ref T, ref v);
+        }
+
+        public static Vector2 Mul(ref Transform T, ref Vector2 v)
+        {
+            float x = (T.q.c * v.X - T.q.s * v.Y) + T.p.X;
+            float y = (T.q.s * v.X + T.q.c * v.Y) + T.p.Y;
+
+            return new Vector2(x, y);
+        }
+
+        public static Vector2 MulT(ref Mat22 A, Vector2 v)
+        {
+            return MulT(ref A, ref v);
+        }
+
+        public static Vector2 MulT(ref Mat22 A, ref Vector2 v)
+        {
+            return new Vector2(v.X * A.ex.X + v.Y * A.ex.Y, v.X * A.ey.X + v.Y * A.ey.Y);
+        }
+
+        public static Vector2 MulT(ref Transform T, Vector2 v)
+        {
+            return MulT(ref T, ref v);
+        }
+
+        public static Vector2 MulT(ref Transform T, ref Vector2 v)
+        {
+            float px = v.X - T.p.X;
+            float py = v.Y - T.p.Y;
+            float x = (T.q.c * px + T.q.s * py);
+            float y = (-T.q.s * px + T.q.c * py);
+
+            return new Vector2(x, y);
+        }
+
+        // A^T * B
+        public static void MulT(ref Mat22 A, ref Mat22 B, out Mat22 C)
+        {
+            C = new Mat22();
+            C.ex.X = A.ex.X * B.ex.X + A.ex.Y * B.ex.Y;
+            C.ex.Y = A.ey.X * B.ex.X + A.ey.Y * B.ex.Y;
+            C.ey.X = A.ex.X * B.ey.X + A.ex.Y * B.ey.Y;
+            C.ey.Y = A.ey.X * B.ey.X + A.ey.Y * B.ey.Y;
+        }
+
+        /// Multiply a matrix times a vector.
+        public static Vector3 Mul(Mat33 A, Vector3 v)
+        {
+            return v.X * A.ex + v.Y * A.ey + v.Z * A.ez;
+        }
+
+        // v2 = A.q.Rot(B.q.Rot(v1) + B.p) + A.p
+        //    = (A.q * B.q).Rot(v1) + A.q.Rot(B.p) + A.p
+        public static Transform Mul(Transform A, Transform B)
+        {
+            Transform C = new Transform();
+            C.q = Mul(A.q, B.q);
+            C.p = Mul(A.q, B.p) + A.p;
+            return C;
+        }
+
+        // v2 = A.q' * (B.q * v1 + B.p - A.p)
+        //    = A.q' * B.q * v1 + A.q' * (B.p - A.p)
+        public static void MulT(ref Transform A, ref Transform B, out Transform C)
+        {
+            C = new Transform();
+            C.q = MulT(A.q, B.q);
+            C.p = MulT(A.q, B.p - A.p);
+        }
+
+        public static void Swap<T>(ref T a, ref T b)
+        {
+            T tmp = a;
+            a = b;
+            b = tmp;
+        }
+
+        /// Multiply a matrix times a vector.
+        public static Vector2 Mul22(Mat33 A, Vector2 v)
+        {
+            return new Vector2(A.ex.X * v.X + A.ey.X * v.Y, A.ex.Y * v.X + A.ey.Y * v.Y);
+        }
+
+        /// Multiply two rotations: q * r
+        public static Rot Mul(Rot q, Rot r)
+        {
+            // [qc -qs] * [rc -rs] = [qc*rc-qs*rs -qc*rs-qs*rc]
+            // [qs  qc]   [rs  rc]   [qs*rc+qc*rs -qs*rs+qc*rc]
+            // s = qs * rc + qc * rs
+            // c = qc * rc - qs * rs
+            Rot qr;
+            qr.s = q.s * r.c + q.c * r.s;
+            qr.c = q.c * r.c - q.s * r.s;
+            return qr;
+        }
+
+        public static Vector2 MulT(Transform T, Vector2 v)
+        {
+            float px = v.X - T.p.X;
+            float py = v.Y - T.p.Y;
+            float x = (T.q.c * px + T.q.s * py);
+            float y = (-T.q.s * px + T.q.c * py);
+
+            return new Vector2(x, y);
+        }
+
+        /// Transpose multiply two rotations: qT * r
+        public static Rot MulT(Rot q, Rot r)
+        {
+            // [ qc qs] * [rc -rs] = [qc*rc+qs*rs -qc*rs+qs*rc]
+            // [-qs qc]   [rs  rc]   [-qs*rc+qc*rs qs*rs+qc*rc]
+            // s = qc * rs - qs * rc
+            // c = qc * rc + qs * rs
+            Rot qr;
+            qr.s = q.c * r.s - q.s * r.c;
+            qr.c = q.c * r.c + q.s * r.s;
+            return qr;
+        }
+
+        // v2 = A.q' * (B.q * v1 + B.p - A.p)
+        //    = A.q' * B.q * v1 + A.q' * (B.p - A.p)
+        public static Transform MulT(Transform A, Transform B)
+        {
+            Transform C = new Transform();
+            C.q = MulT(A.q, B.q);
+            C.p = MulT(A.q, B.p - A.p);
+            return C;
+        }
+
+        /// Rotate a vector
+        public static Vector2 Mul(Rot q, Vector2 v)
+        {
+            return new Vector2(q.c * v.X - q.s * v.Y, q.s * v.X + q.c * v.Y);
+        }
+
+        /// Inverse rotate a vector
+        public static Vector2 MulT(Rot q, Vector2 v)
+        {
+            return new Vector2(q.c * v.X + q.s * v.Y, -q.s * v.X + q.c * v.Y);
+        }
+
+        /// Get the skew vector such that dot(skew_vec, other) == cross(vec, other)
+        public static Vector2 Skew(Vector2 input)
+        {
+            return new Vector2(-input.Y, input.X);
+        }
+
+        /// <summary>
+        /// This function is used to ensure that a floating point number is
+        /// not a NaN or infinity.
+        /// </summary>
+        /// <param name="x">The x.</param>
+        /// <returns>
+        /// 	<c>true</c> if the specified x is valid; otherwise, <c>false</c>.
+        /// </returns>
+        public static bool IsValid(float x)
+        {
+            if (float.IsNaN(x))
+            {
+                // NaN.
+                return false;
+            }
+
+            return !float.IsInfinity(x);
+        }
+
+        public static bool IsValid(this Vector2 x)
+        {
+            return IsValid(x.X) && IsValid(x.Y);
+        }
+
+        /// <summary>
+        /// This is a approximate yet fast inverse square-root.
+        /// </summary>
+        /// <param name="x">The x.</param>
+        /// <returns></returns>
+        public static float InvSqrt(float x)
+        {
+            FloatConverter convert = new FloatConverter();
+            convert.x = x;
+            float xhalf = 0.5f * x;
+            convert.i = 0x5f3759df - (convert.i >> 1);
+            x = convert.x;
+            x = x * (1.5f - xhalf * x * x);
+            return x;
+        }
+
+        public static int Clamp(int a, int low, int high)
+        {
+            return Math.Max(low, Math.Min(a, high));
+        }
+
+        public static float Clamp(float a, float low, float high)
+        {
+            return Math.Max(low, Math.Min(a, high));
+        }
+
+        public static Vector2 Clamp(Vector2 a, Vector2 low, Vector2 high)
+        {
+            return Vector2.Max(low, Vector2.Min(a, high));
+        }
+
+        public static void Cross(ref Vector2 a, ref Vector2 b, out float c)
+        {
+            c = a.X * b.Y - a.Y * b.X;
+        }
+
+        /// <summary>
+        /// Return the angle between two vectors on a plane
+        /// The angle is from vector 1 to vector 2, positive anticlockwise
+        /// The result is between -pi -> pi
+        /// </summary>
+        public static double VectorAngle(ref Vector2 p1, ref Vector2 p2)
+        {
+            double theta1 = Math.Atan2(p1.Y, p1.X);
+            double theta2 = Math.Atan2(p2.Y, p2.X);
+            double dtheta = theta2 - theta1;
+            while (dtheta > Math.PI)
+                dtheta -= (2 * Math.PI);
+            while (dtheta < -Math.PI)
+                dtheta += (2 * Math.PI);
+
+            return (dtheta);
+        }
+
+        /// Perform the dot product on two vectors.
+        public static float Dot(Vector3 a, Vector3 b)
+        {
+            return a.X * b.X + a.Y * b.Y + a.Z * b.Z;
+        }
+
+        public static double VectorAngle(Vector2 p1, Vector2 p2)
+        {
+            return VectorAngle(ref p1, ref p2);
+        }
+
+        /// <summary>
+        /// Returns a positive number if c is to the left of the line going from a to b.
+        /// </summary>
+        /// <returns>Positive number if point is left, negative if point is right, 
+        /// and 0 if points are collinear.</returns>
+        public static float Area(Vector2 a, Vector2 b, Vector2 c)
+        {
+            return Area(ref a, ref b, ref c);
+        }
+
+        /// <summary>
+        /// Returns a positive number if c is to the left of the line going from a to b.
+        /// </summary>
+        /// <returns>Positive number if point is left, negative if point is right, 
+        /// and 0 if points are collinear.</returns>
+        public static float Area(ref Vector2 a, ref Vector2 b, ref Vector2 c)
+        {
+            return a.X * (b.Y - c.Y) + b.X * (c.Y - a.Y) + c.X * (a.Y - b.Y);
+        }
+
+        /// <summary>
+        /// Determines if three vertices are collinear (ie. on a straight line)
+        /// </summary>
+        /// <param name="a">First vertex</param>
+        /// <param name="b">Second vertex</param>
+        /// <param name="c">Third vertex</param>
+        /// <param name="tolerance">The tolerance</param>
+        /// <returns></returns>
+        public static bool IsCollinear(ref Vector2 a, ref Vector2 b, ref Vector2 c, float tolerance = 0)
+        {
+            return FloatInRange(Area(ref a, ref b, ref c), -tolerance, tolerance);
+        }
+
+        public static void Cross(float s, ref Vector2 a, out Vector2 b)
+        {
+            b = new Vector2(-s * a.Y, s * a.X);
+        }
+
+        public static bool FloatEquals(float value1, float value2)
+        {
+            return Math.Abs(value1 - value2) <= Settings.Epsilon;
+        }
+
+        /// <summary>
+        /// Checks if a floating point Value is equal to another,
+        /// within a certain tolerance.
+        /// </summary>
+        /// <param name="value1">The first floating point Value.</param>
+        /// <param name="value2">The second floating point Value.</param>
+        /// <param name="delta">The floating point tolerance.</param>
+        /// <returns>True if the values are "equal", false otherwise.</returns>
+        public static bool FloatEquals(float value1, float value2, float delta)
+        {
+            return FloatInRange(value1, value2 - delta, value2 + delta);
+        }
+
+        /// <summary>
+        /// Checks if a floating point Value is within a specified
+        /// range of values (inclusive).
+        /// </summary>
+        /// <param name="value">The Value to check.</param>
+        /// <param name="min">The minimum Value.</param>
+        /// <param name="max">The maximum Value.</param>
+        /// <returns>True if the Value is within the range specified,
+        /// false otherwise.</returns>
+        public static bool FloatInRange(float value, float min, float max)
+        {
+            return (value >= min && value <= max);
+        }
+
+        #region Nested type: FloatConverter
+
+        [StructLayout(LayoutKind.Explicit)]
+        private struct FloatConverter
+        {
+            [FieldOffset(0)]
+            public float x;
+            [FieldOffset(0)]
+            public int i;
+        }
+
+        #endregion
+
+        public static Vector2 Mul(ref Rot rot, Vector2 axis)
+        {
+            return Mul(rot, axis);
+        }
+
+        public static Vector2 MulT(ref Rot rot, Vector2 axis)
+        {
+            return MulT(rot, axis);
+        }
+    }
+
+    /// <summary>
+    /// A 2-by-2 matrix. Stored in column-major order.
+    /// </summary>
+    public struct Mat22
+    {
+        public Vector2 ex, ey;
+
+        /// <summary>
+        /// Construct this matrix using columns.
+        /// </summary>
+        /// <param name="c1">The c1.</param>
+        /// <param name="c2">The c2.</param>
+        public Mat22(Vector2 c1, Vector2 c2)
+        {
+            ex = c1;
+            ey = c2;
+        }
+
+        /// <summary>
+        /// Construct this matrix using scalars.
+        /// </summary>
+        /// <param name="a11">The a11.</param>
+        /// <param name="a12">The a12.</param>
+        /// <param name="a21">The a21.</param>
+        /// <param name="a22">The a22.</param>
+        public Mat22(float a11, float a12, float a21, float a22)
+        {
+            ex = new Vector2(a11, a21);
+            ey = new Vector2(a12, a22);
+        }
+
+        public Mat22 Inverse
+        {
+            get
+            {
+                float a = ex.X, b = ey.X, c = ex.Y, d = ey.Y;
+                float det = a * d - b * c;
+                if (det != 0.0f)
+                {
+                    det = 1.0f / det;
+                }
+
+                Mat22 result = new Mat22();
+                result.ex.X = det * d;
+                result.ex.Y = -det * c;
+
+                result.ey.X = -det * b;
+                result.ey.Y = det * a;
+
+                return result;
+            }
+        }
+
+        /// <summary>
+        /// Initialize this matrix using columns.
+        /// </summary>
+        /// <param name="c1">The c1.</param>
+        /// <param name="c2">The c2.</param>
+        public void Set(Vector2 c1, Vector2 c2)
+        {
+            ex = c1;
+            ey = c2;
+        }
+
+        /// <summary>
+        /// Set this to the identity matrix.
+        /// </summary>
+        public void SetIdentity()
+        {
+            ex.X = 1.0f;
+            ey.X = 0.0f;
+            ex.Y = 0.0f;
+            ey.Y = 1.0f;
+        }
+
+        /// <summary>
+        /// Set this matrix to all zeros.
+        /// </summary>
+        public void SetZero()
+        {
+            ex.X = 0.0f;
+            ey.X = 0.0f;
+            ex.Y = 0.0f;
+            ey.Y = 0.0f;
+        }
+
+        /// <summary>
+        /// Solve A * x = b, where b is a column vector. This is more efficient
+        /// than computing the inverse in one-shot cases.
+        /// </summary>
+        /// <param name="b">The b.</param>
+        /// <returns></returns>
+        public Vector2 Solve(Vector2 b)
+        {
+            float a11 = ex.X, a12 = ey.X, a21 = ex.Y, a22 = ey.Y;
+            float det = a11 * a22 - a12 * a21;
+            if (det != 0.0f)
+            {
+                det = 1.0f / det;
+            }
+
+            return new Vector2(det * (a22 * b.X - a12 * b.Y), det * (a11 * b.Y - a21 * b.X));
+        }
+
+        public static void Add(ref Mat22 A, ref Mat22 B, out Mat22 R)
+        {
+            R.ex = A.ex + B.ex;
+            R.ey = A.ey + B.ey;
+        }
+    }
+
+    /// <summary>
+    /// A 3-by-3 matrix. Stored in column-major order.
+    /// </summary>
+    public struct Mat33
+    {
+        public Vector3 ex, ey, ez;
+
+        /// <summary>
+        /// Construct this matrix using columns.
+        /// </summary>
+        /// <param name="c1">The c1.</param>
+        /// <param name="c2">The c2.</param>
+        /// <param name="c3">The c3.</param>
+        public Mat33(Vector3 c1, Vector3 c2, Vector3 c3)
+        {
+            ex = c1;
+            ey = c2;
+            ez = c3;
+        }
+
+        /// <summary>
+        /// Set this matrix to all zeros.
+        /// </summary>
+        public void SetZero()
+        {
+            ex = Vector3.Zero;
+            ey = Vector3.Zero;
+            ez = Vector3.Zero;
+        }
+
+        /// <summary>
+        /// Solve A * x = b, where b is a column vector. This is more efficient
+        /// than computing the inverse in one-shot cases.
+        /// </summary>
+        /// <param name="b">The b.</param>
+        /// <returns></returns>
+        public Vector3 Solve33(Vector3 b)
+        {
+            float det = Vector3.Dot(ex, Vector3.Cross(ey, ez));
+            if (det != 0.0f)
+            {
+                det = 1.0f / det;
+            }
+
+            return new Vector3(det * Vector3.Dot(b, Vector3.Cross(ey, ez)), det * Vector3.Dot(ex, Vector3.Cross(b, ez)), det * Vector3.Dot(ex, Vector3.Cross(ey, b)));
+        }
+
+        /// <summary>
+        /// Solve A * x = b, where b is a column vector. This is more efficient
+        /// than computing the inverse in one-shot cases. Solve only the upper
+        /// 2-by-2 matrix equation.
+        /// </summary>
+        /// <param name="b">The b.</param>
+        /// <returns></returns>
+        public Vector2 Solve22(Vector2 b)
+        {
+            float a11 = ex.X, a12 = ey.X, a21 = ex.Y, a22 = ey.Y;
+            float det = a11 * a22 - a12 * a21;
+
+            if (det != 0.0f)
+            {
+                det = 1.0f / det;
+            }
+
+            return new Vector2(det * (a22 * b.X - a12 * b.Y), det * (a11 * b.Y - a21 * b.X));
+        }
+
+        /// Get the inverse of this matrix as a 2-by-2.
+        /// Returns the zero matrix if singular.
+        public void GetInverse22(ref Mat33 M)
+        {
+            float a = ex.X, b = ey.X, c = ex.Y, d = ey.Y;
+            float det = a * d - b * c;
+            if (det != 0.0f)
+            {
+                det = 1.0f / det;
+            }
+
+            M.ex.X = det * d; M.ey.X = -det * b; M.ex.Z = 0.0f;
+            M.ex.Y = -det * c; M.ey.Y = det * a; M.ey.Z = 0.0f;
+            M.ez.X = 0.0f; M.ez.Y = 0.0f; M.ez.Z = 0.0f;
+        }
+
+        /// Get the symmetric inverse of this matrix as a 3-by-3.
+        /// Returns the zero matrix if singular.
+        public void GetSymInverse33(ref Mat33 M)
+        {
+            float det = MathUtils.Dot(ex, MathUtils.Cross(ey, ez));
+            if (det != 0.0f)
+            {
+                det = 1.0f / det;
+            }
+
+            float a11 = ex.X, a12 = ey.X, a13 = ez.X;
+            float a22 = ey.Y, a23 = ez.Y;
+            float a33 = ez.Z;
+
+            M.ex.X = det * (a22 * a33 - a23 * a23);
+            M.ex.Y = det * (a13 * a23 - a12 * a33);
+            M.ex.Z = det * (a12 * a23 - a13 * a22);
+
+            M.ey.X = M.ex.Y;
+            M.ey.Y = det * (a11 * a33 - a13 * a13);
+            M.ey.Z = det * (a13 * a12 - a11 * a23);
+
+            M.ez.X = M.ex.Z;
+            M.ez.Y = M.ey.Z;
+            M.ez.Z = det * (a11 * a22 - a12 * a12);
+        }
+    }
+
+    /// <summary>
+    /// Rotation
+    /// </summary>
+    public struct Rot
+    {
+        /// Sine and cosine
+        public float s, c;
+
+        /// <summary>
+        /// Initialize from an angle in radians
+        /// </summary>
+        /// <param name="angle">Angle in radians</param>
+        public Rot(float angle)
+        {
+            // TODO_ERIN optimize
+            s = (float)Math.Sin(angle);
+            c = (float)Math.Cos(angle);
+        }
+
+        /// <summary>
+        /// Set using an angle in radians.
+        /// </summary>
+        /// <param name="angle"></param>
+        public void Set(float angle)
+        {
+            // TODO_ERIN optimize
+            s = (float)Math.Sin(angle);
+            c = (float)Math.Cos(angle);
+        }
+
+        /// <summary>
+        /// Set to the identity rotation
+        /// </summary>
+        public void SetIdentity()
+        {
+            s = 0.0f;
+            c = 1.0f;
+        }
+
+        /// <summary>
+        /// Get the angle in radians
+        /// </summary>
+        public float GetAngle()
+        {
+            return (float)Math.Atan2(s, c);
+        }
+
+        /// <summary>
+        /// Get the x-axis
+        /// </summary>
+        public Vector2 GetXAxis()
+        {
+            return new Vector2(c, s);
+        }
+
+        /// <summary>
+        /// Get the y-axis
+        /// </summary>
+        public Vector2 GetYAxis()
+        {
+            return new Vector2(-s, c);
+        }
+    }
+
+    /// <summary>
+    /// A transform contains translation and rotation. It is used to represent
+    /// the position and orientation of rigid frames.
+    /// </summary>
+    public struct Transform
+    {
+        public Vector2 p;
+        public Rot q;
+
+        /// <summary>
+        /// Initialize using a position vector and a rotation matrix.
+        /// </summary>
+        /// <param name="position">The position.</param>
+        /// <param name="rotation">The r.</param>
+        public Transform(ref Vector2 position, ref Rot rotation)
+        {
+            p = position;
+            q = rotation;
+        }
+
+        /// <summary>
+        /// Set this to the identity transform.
+        /// </summary>
+        public void SetIdentity()
+        {
+            p = Vector2.Zero;
+            q.SetIdentity();
+        }
+
+        /// <summary>
+        /// Set this based on the position and angle.
+        /// </summary>
+        /// <param name="position">The position.</param>
+        /// <param name="angle">The angle.</param>
+        public void Set(Vector2 position, float angle)
+        {
+            p = position;
+            q.Set(angle);
+        }
+    }
+
+    /// <summary>
+    /// This describes the motion of a body/shape for TOI computation.
+    /// Shapes are defined with respect to the body origin, which may
+    /// no coincide with the center of mass. However, to support dynamics
+    /// we must interpolate the center of mass position.
+    /// </summary>
+    public struct Sweep
+    {
+        /// <summary>
+        /// World angles
+        /// </summary>
+        public float A;
+
+        public float A0;
+
+        /// <summary>
+        /// Fraction of the current time step in the range [0,1]
+        /// c0 and a0 are the positions at alpha0.
+        /// </summary>
+        public float Alpha0;
+
+        /// <summary>
+        /// Center world positions
+        /// </summary>
+        public Vector2 C;
+
+        public Vector2 C0;
+
+        /// <summary>
+        /// Local center of mass position
+        /// </summary>
+        public Vector2 LocalCenter;
+
+        /// <summary>
+        /// Get the interpolated transform at a specific time.
+        /// </summary>
+        /// <param name="xfb">The transform.</param>
+        /// <param name="beta">beta is a factor in [0,1], where 0 indicates alpha0.</param>
+        public void GetTransform(out Transform xfb, float beta)
+        {
+            xfb = new Transform();
+            xfb.p.X = (1.0f - beta) * C0.X + beta * C.X;
+            xfb.p.Y = (1.0f - beta) * C0.Y + beta * C.Y;
+            float angle = (1.0f - beta) * A0 + beta * A;
+            xfb.q.Set(angle);
+
+            // Shift to origin
+            xfb.p -= MathUtils.Mul(xfb.q, LocalCenter);
+        }
+
+        /// <summary>
+        /// Advance the sweep forward, yielding a new initial state.
+        /// </summary>
+        /// <param name="alpha">new initial time..</param>
+        public void Advance(float alpha)
+        {
+            Debug.Assert(Alpha0 < 1.0f);
+            float beta = (alpha - Alpha0) / (1.0f - Alpha0);
+            C0 += beta * (C - C0);
+            A0 += beta * (A - A0);
+            Alpha0 = alpha;
+        }
+
+        /// <summary>
+        /// Normalize the angles.
+        /// </summary>
+        public void Normalize()
+        {
+            float d = MathHelper.TwoPi * (float)Math.Floor(A0 / MathHelper.TwoPi);
+            A0 -= d;
+            A -= d;
+        }
+    }
+}

Farseer Physics Engine 3.5/Common/MathHelper.cs

@@ -0,0 +1,158 @@
+#if !XNA && !WINDOWS_PHONE && !XBOX && !ANDROID
+
+#region License
+
+/*
+MIT License
+Copyright © 2006 The Mono.Xna Team
+
+All rights reserved.
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
+*/
+
+#endregion License
+
+using System;
+
+namespace Microsoft.Xna.Framework
+{
+    public static class MathHelper
+    {
+        public const float E = (float) Math.E;
+        public const float Log10E = 0.4342945f;
+        public const float Log2E = 1.442695f;
+        public const float Pi = (float) Math.PI;
+        public const float PiOver2 = (float) (Math.PI/2.0);
+        public const float PiOver4 = (float) (Math.PI/4.0);
+        public const float TwoPi = (float) (Math.PI*2.0);
+
+        public static float Barycentric(float value1, float value2, float value3, float amount1, float amount2)
+        {
+            return value1 + (value2 - value1)*amount1 + (value3 - value1)*amount2;
+        }
+
+        public static float CatmullRom(float value1, float value2, float value3, float value4, float amount)
+        {
+            // Using formula from http://www.mvps.org/directx/articles/catmull/
+            // Internally using doubles not to lose precission
+            double amountSquared = amount*amount;
+            double amountCubed = amountSquared*amount;
+            return (float) (0.5*(2.0*value2 +
+                                 (value3 - value1)*amount +
+                                 (2.0*value1 - 5.0*value2 + 4.0*value3 - value4)*amountSquared +
+                                 (3.0*value2 - value1 - 3.0*value3 + value4)*amountCubed));
+        }
+
+        public static float Clamp(float value, float min, float max)
+        {
+            // First we check to see if we're greater than the max
+            value = (value > max) ? max : value;
+
+            // Then we check to see if we're less than the min.
+            value = (value < min) ? min : value;
+
+            // There's no check to see if min > max.
+            return value;
+        }
+
+        public static float Distance(float value1, float value2)
+        {
+            return Math.Abs(value1 - value2);
+        }
+
+        public static float Hermite(float value1, float tangent1, float value2, float tangent2, float amount)
+        {
+            // All transformed to double not to lose precission
+            // Otherwise, for high numbers of param:amount the result is NaN instead of Infinity
+            double v1 = value1, v2 = value2, t1 = tangent1, t2 = tangent2, s = amount, result;
+            double sCubed = s*s*s;
+            double sSquared = s*s;
+
+            if (amount == 0f)
+                result = value1;
+            else if (amount == 1f)
+                result = value2;
+            else
+                result = (2*v1 - 2*v2 + t2 + t1)*sCubed +
+                         (3*v2 - 3*v1 - 2*t1 - t2)*sSquared +
+                         t1*s +
+                         v1;
+            return (float) result;
+        }
+
+        public static float Lerp(float value1, float value2, float amount)
+        {
+            return value1 + (value2 - value1)*amount;
+        }
+
+        public static float Max(float value1, float value2)
+        {
+            return Math.Max(value1, value2);
+        }
+
+        public static float Min(float value1, float value2)
+        {
+            return Math.Min(value1, value2);
+        }
+
+        public static float SmoothStep(float value1, float value2, float amount)
+        {
+            // It is expected that 0 < amount < 1
+            // If amount < 0, return value1
+            // If amount > 1, return value2
+            float result = Clamp(amount, 0f, 1f);
+            result = Hermite(value1, 0f, value2, 0f, result);
+            return result;
+        }
+
+        public static float ToDegrees(float radians)
+        {
+            // This method uses double precission internally,
+            // though it returns single float
+            // Factor = 180 / pi
+            return (float) (radians*57.295779513082320876798154814105);
+        }
+
+        public static float ToRadians(float degrees)
+        {
+            // This method uses double precission internally,
+            // though it returns single float
+            // Factor = pi / 180
+            return (float) (degrees*0.017453292519943295769236907684886);
+        }
+
+        public static float WrapAngle(float angle)
+        {
+            angle = (float) Math.IEEERemainder((double) angle, 6.2831854820251465); //2xPi precission is double
+            if (angle <= -3.141593f)
+            {
+                angle += 6.283185f;
+                return angle;
+            }
+            if (angle > 3.141593f)
+            {
+                angle -= 6.283185f;
+            }
+            return angle;
+        }
+    }
+}
+
+#endif

Farseer Physics Engine 3.5/Common/Path.cs

@@ -0,0 +1,337 @@
+using System;
+using System.Collections.Generic;
+using System.Text;
+using Microsoft.Xna.Framework;
+
+namespace FarseerPhysics.Common
+{
+    //Contributed by Matthew Bettcher
+
+    /// <summary>
+    /// Path:
+    /// Very similar to Vertices, but this
+    /// class contains vectors describing
+    /// control points on a Catmull-Rom
+    /// curve.
+    /// </summary>
+    public class Path
+    {
+        /// <summary>
+        /// All the points that makes up the curve
+        /// </summary>
+        public List<Vector2> ControlPoints;
+
+        private float _deltaT;
+
+        /// <summary>
+        /// Initializes a new instance of the <see cref="Path"/> class.
+        /// </summary>
+        public Path()
+        {
+            ControlPoints = new List<Vector2>();
+        }
+
+        /// <summary>
+        /// Initializes a new instance of the <see cref="Path"/> class.
+        /// </summary>
+        /// <param name="vertices">The vertices to created the path from.</param>
+        public Path(Vector2[] vertices)
+        {
+            ControlPoints = new List<Vector2>(vertices.Length);
+
+            for (int i = 0; i < vertices.Length; i++)
+            {
+                Add(vertices[i]);
+            }
+        }
+
+        /// <summary>
+        /// Initializes a new instance of the <see cref="Path"/> class.
+        /// </summary>
+        /// <param name="vertices">The vertices to created the path from.</param>
+        public Path(IList<Vector2> vertices)
+        {
+            ControlPoints = new List<Vector2>(vertices.Count);
+            for (int i = 0; i < vertices.Count; i++)
+            {
+                Add(vertices[i]);
+            }
+        }
+
+        /// <summary>
+        /// True if the curve is closed.
+        /// </summary>
+        /// <value><c>true</c> if closed; otherwise, <c>false</c>.</value>
+        public bool Closed { get; set; }
+
+        /// <summary>
+        /// Gets the next index of a controlpoint
+        /// </summary>
+        /// <param name="index">The index.</param>
+        /// <returns></returns>
+        public int NextIndex(int index)
+        {
+            if (index == ControlPoints.Count - 1)
+            {
+                return 0;
+            }
+            return index + 1;
+        }
+
+        /// <summary>
+        /// Gets the previous index of a controlpoint
+        /// </summary>
+        /// <param name="index">The index.</param>
+        /// <returns></returns>
+        public int PreviousIndex(int index)
+        {
+            if (index == 0)
+            {
+                return ControlPoints.Count - 1;
+            }
+            return index - 1;
+        }
+
+        /// <summary>
+        /// Translates the control points by the specified vector.
+        /// </summary>
+        /// <param name="vector">The vector.</param>
+        public void Translate(ref Vector2 vector)
+        {
+            for (int i = 0; i < ControlPoints.Count; i++)
+                ControlPoints[i] = Vector2.Add(ControlPoints[i], vector);
+        }
+
+        /// <summary>
+        /// Scales the control points by the specified vector.
+        /// </summary>
+        /// <param name="value">The Value.</param>
+        public void Scale(ref Vector2 value)
+        {
+            for (int i = 0; i < ControlPoints.Count; i++)
+                ControlPoints[i] = Vector2.Multiply(ControlPoints[i], value);
+        }
+
+        /// <summary>
+        /// Rotate the control points by the defined value in radians.
+        /// </summary>
+        /// <param name="value">The amount to rotate by in radians.</param>
+        public void Rotate(float value)
+        {
+            Matrix rotationMatrix;
+            Matrix.CreateRotationZ(value, out rotationMatrix);
+
+            for (int i = 0; i < ControlPoints.Count; i++)
+                ControlPoints[i] = Vector2.Transform(ControlPoints[i], rotationMatrix);
+        }
+
+        public override string ToString()
+        {
+            StringBuilder builder = new StringBuilder();
+            for (int i = 0; i < ControlPoints.Count; i++)
+            {
+                builder.Append(ControlPoints[i].ToString());
+                if (i < ControlPoints.Count - 1)
+                {
+                    builder.Append(" ");
+                }
+            }
+            return builder.ToString();
+        }
+
+        /// <summary>
+        /// Returns a set of points defining the
+        /// curve with the specifed number of divisions
+        /// between each control point.
+        /// </summary>
+        /// <param name="divisions">Number of divisions between each control point.</param>
+        /// <returns></returns>
+        public Vertices GetVertices(int divisions)
+        {
+            Vertices verts = new Vertices();
+
+            float timeStep = 1f / divisions;
+
+            for (float i = 0; i < 1f; i += timeStep)
+            {
+                verts.Add(GetPosition(i));
+            }
+
+            return verts;
+        }
+
+        public Vector2 GetPosition(float time)
+        {
+            Vector2 temp;
+
+            if (ControlPoints.Count < 2)
+                throw new Exception("You need at least 2 control points to calculate a position.");
+
+            if (Closed)
+            {
+                Add(ControlPoints[0]);
+
+                _deltaT = 1f / (ControlPoints.Count - 1);
+
+                int p = (int)(time / _deltaT);
+
+                // use a circular indexing system
+                int p0 = p - 1;
+                if (p0 < 0) p0 = p0 + (ControlPoints.Count - 1);
+                else if (p0 >= ControlPoints.Count - 1) p0 = p0 - (ControlPoints.Count - 1);
+                int p1 = p;
+                if (p1 < 0) p1 = p1 + (ControlPoints.Count - 1);
+                else if (p1 >= ControlPoints.Count - 1) p1 = p1 - (ControlPoints.Count - 1);
+                int p2 = p + 1;
+                if (p2 < 0) p2 = p2 + (ControlPoints.Count - 1);
+                else if (p2 >= ControlPoints.Count - 1) p2 = p2 - (ControlPoints.Count - 1);
+                int p3 = p + 2;
+                if (p3 < 0) p3 = p3 + (ControlPoints.Count - 1);
+                else if (p3 >= ControlPoints.Count - 1) p3 = p3 - (ControlPoints.Count - 1);
+
+                // relative time
+                float lt = (time - _deltaT * p) / _deltaT;
+
+                temp = Vector2.CatmullRom(ControlPoints[p0], ControlPoints[p1], ControlPoints[p2], ControlPoints[p3], lt);
+
+                RemoveAt(ControlPoints.Count - 1);
+            }
+            else
+            {
+                int p = (int)(time / _deltaT);
+
+                // 
+                int p0 = p - 1;
+                if (p0 < 0) p0 = 0;
+                else if (p0 >= ControlPoints.Count - 1) p0 = ControlPoints.Count - 1;
+                int p1 = p;
+                if (p1 < 0) p1 = 0;
+                else if (p1 >= ControlPoints.Count - 1) p1 = ControlPoints.Count - 1;
+                int p2 = p + 1;
+                if (p2 < 0) p2 = 0;
+                else if (p2 >= ControlPoints.Count - 1) p2 = ControlPoints.Count - 1;
+                int p3 = p + 2;
+                if (p3 < 0) p3 = 0;
+                else if (p3 >= ControlPoints.Count - 1) p3 = ControlPoints.Count - 1;
+
+                // relative time
+                float lt = (time - _deltaT * p) / _deltaT;
+
+                temp = Vector2.CatmullRom(ControlPoints[p0], ControlPoints[p1], ControlPoints[p2], ControlPoints[p3], lt);
+            }
+
+            return temp;
+        }
+
+        /// <summary>
+        /// Gets the normal for the given time.
+        /// </summary>
+        /// <param name="time">The time</param>
+        /// <returns>The normal.</returns>
+        public Vector2 GetPositionNormal(float time)
+        {
+            float offsetTime = time + 0.0001f;
+
+            Vector2 a = GetPosition(time);
+            Vector2 b = GetPosition(offsetTime);
+
+            Vector2 output, temp;
+
+            Vector2.Subtract(ref a, ref b, out temp);
+
+#if (XBOX360 || WINDOWS_PHONE)
+output = new Vector2();
+#endif
+            output.X = -temp.Y;
+            output.Y = temp.X;
+
+            Vector2.Normalize(ref output, out output);
+
+            return output;
+        }
+
+        public void Add(Vector2 point)
+        {
+            ControlPoints.Add(point);
+            _deltaT = 1f / (ControlPoints.Count - 1);
+        }
+
+        public void Remove(Vector2 point)
+        {
+            ControlPoints.Remove(point);
+            _deltaT = 1f / (ControlPoints.Count - 1);
+        }
+
+        public void RemoveAt(int index)
+        {
+            ControlPoints.RemoveAt(index);
+            _deltaT = 1f / (ControlPoints.Count - 1);
+        }
+
+        public float GetLength()
+        {
+            List<Vector2> verts = GetVertices(ControlPoints.Count * 25);
+            float length = 0;
+
+            for (int i = 1; i < verts.Count; i++)
+            {
+                length += Vector2.Distance(verts[i - 1], verts[i]);
+            }
+
+            if (Closed)
+                length += Vector2.Distance(verts[ControlPoints.Count - 1], verts[0]);
+
+            return length;
+        }
+
+        public List<Vector3> SubdivideEvenly(int divisions)
+        {
+            List<Vector3> verts = new List<Vector3>();
+
+            float length = GetLength();
+
+            float deltaLength = length / divisions + 0.001f;
+            float t = 0.000f;
+
+            // we always start at the first control point
+            Vector2 start = ControlPoints[0];
+            Vector2 end = GetPosition(t);
+
+            // increment t until we are at half the distance
+            while (deltaLength * 0.5f >= Vector2.Distance(start, end))
+            {
+                end = GetPosition(t);
+                t += 0.0001f;
+
+                if (t >= 1f)
+                    break;
+            }
+
+            start = end;
+
+            // for each box
+            for (int i = 1; i < divisions; i++)
+            {
+                Vector2 normal = GetPositionNormal(t);
+                float angle = (float)Math.Atan2(normal.Y, normal.X);
+
+                verts.Add(new Vector3(end, angle));
+
+                // until we reach the correct distance down the curve
+                while (deltaLength >= Vector2.Distance(start, end))
+                {
+                    end = GetPosition(t);
+                    t += 0.00001f;
+
+                    if (t >= 1f)
+                        break;
+                }
+                if (t >= 1f)
+                    break;
+
+                start = end;
+            }
+            return verts;
+        }
+    }
+}

Farseer Physics Engine 3.5/Common/PathManager.cs

@@ -0,0 +1,186 @@
+using System;
+using System.Collections.Generic;
+using FarseerPhysics.Collision.Shapes;
+using FarseerPhysics.Common.Decomposition;
+using FarseerPhysics.Dynamics;
+using FarseerPhysics.Dynamics.Joints;
+using Microsoft.Xna.Framework;
+
+namespace FarseerPhysics.Common
+{
+    /// <summary>
+    /// An easy to use manager for creating paths.
+    /// </summary>
+    public static class PathManager
+    {
+        #region LinkType enum
+
+        public enum LinkType
+        {
+            Revolute,
+            Slider
+        }
+
+        #endregion
+
+        //Contributed by Matthew Bettcher
+
+        /// <summary>
+        /// Convert a path into a set of edges and attaches them to the specified body.
+        /// Note: use only for static edges.
+        /// </summary>
+        /// <param name="path">The path.</param>
+        /// <param name="body">The body.</param>
+        /// <param name="subdivisions">The subdivisions.</param>
+        public static void ConvertPathToEdges(Path path, Body body, int subdivisions)
+        {
+            Vertices verts = path.GetVertices(subdivisions);
+
+            if (path.Closed)
+            {
+                ChainShape chain = new ChainShape(verts, true);
+                body.CreateFixture(chain);
+            }
+            else
+            {
+                for (int i = 1; i < verts.Count; i++)
+                {
+                    body.CreateFixture(new EdgeShape(verts[i], verts[i - 1]));
+                }
+            }
+        }
+
+        /// <summary>
+        /// Convert a closed path into a polygon.
+        /// Convex decomposition is automatically performed.
+        /// </summary>
+        /// <param name="path">The path.</param>
+        /// <param name="body">The body.</param>
+        /// <param name="density">The density.</param>
+        /// <param name="subdivisions">The subdivisions.</param>
+        public static void ConvertPathToPolygon(Path path, Body body, float density, int subdivisions)
+        {
+            if (!path.Closed)
+                throw new Exception("The path must be closed to convert to a polygon.");
+
+            List<Vector2> verts = path.GetVertices(subdivisions);
+
+            List<Vertices> decomposedVerts = Triangulate.ConvexPartition(new Vertices(verts), TriangulationAlgorithm.Bayazit);
+
+            foreach (Vertices item in decomposedVerts)
+            {
+                body.CreateFixture(new PolygonShape(item, density));
+            }
+        }
+
+        /// <summary>
+        /// Duplicates the given Body along the given path for approximatly the given copies.
+        /// </summary>
+        /// <param name="world">The world.</param>
+        /// <param name="path">The path.</param>
+        /// <param name="shapes">The shapes.</param>
+        /// <param name="type">The type.</param>
+        /// <param name="copies">The copies.</param>
+        /// <param name="userData"></param>
+        /// <returns></returns>
+        public static List<Body> EvenlyDistributeShapesAlongPath(World world, Path path, IEnumerable<Shape> shapes, BodyType type, int copies, object userData = null)
+        {
+            List<Vector3> centers = path.SubdivideEvenly(copies);
+            List<Body> bodyList = new List<Body>();
+
+            for (int i = 0; i < centers.Count; i++)
+            {
+                Body b = new Body(world);
+
+                // copy the type from original body
+                b.BodyType = type;
+                b.Position = new Vector2(centers[i].X, centers[i].Y);
+                b.Rotation = centers[i].Z;
+                b.UserData = userData;
+
+                foreach (Shape shape in shapes)
+                {
+                    b.CreateFixture(shape);
+                }
+
+                bodyList.Add(b);
+            }
+
+            return bodyList;
+        }
+
+
+        /// <summary>
+        /// Duplicates the given Body along the given path for approximatly the given copies.
+        /// </summary>
+        /// <param name="world">The world.</param>
+        /// <param name="path">The path.</param>
+        /// <param name="shape">The shape.</param>
+        /// <param name="type">The type.</param>
+        /// <param name="copies">The copies.</param>
+        /// <param name="userData">The user data.</param>
+        /// <returns></returns>
+        public static List<Body> EvenlyDistributeShapesAlongPath(World world, Path path, Shape shape, BodyType type,
+                                                                 int copies, object userData)
+        {
+            List<Shape> shapes = new List<Shape>(1);
+            shapes.Add(shape);
+
+            return EvenlyDistributeShapesAlongPath(world, path, shapes, type, copies, userData);
+        }
+
+        public static List<Body> EvenlyDistributeShapesAlongPath(World world, Path path, Shape shape, BodyType type, int copies)
+        {
+            return EvenlyDistributeShapesAlongPath(world, path, shape, type, copies, null);
+        }
+
+        /// <summary>
+        /// Moves the given body along the defined path.
+        /// </summary>
+        /// <param name="path">The path.</param>
+        /// <param name="body">The body.</param>
+        /// <param name="time">The time.</param>
+        /// <param name="strength">The strength.</param>
+        /// <param name="timeStep">The time step.</param>
+        public static void MoveBodyOnPath(Path path, Body body, float time, float strength, float timeStep)
+        {
+            Vector2 destination = path.GetPosition(time);
+            Vector2 positionDelta = body.Position - destination;
+            Vector2 velocity = (positionDelta / timeStep) * strength;
+
+            body.LinearVelocity = -velocity;
+        }
+
+        /// <summary>
+        /// Attaches the bodies with revolute joints.
+        /// </summary>
+        /// <param name="world">The world.</param>
+        /// <param name="bodies">The bodies.</param>
+        /// <param name="localAnchorA">The local anchor A.</param>
+        /// <param name="localAnchorB">The local anchor B.</param>
+        /// <param name="connectFirstAndLast">if set to <c>true</c> [connect first and last].</param>
+        /// <param name="collideConnected">if set to <c>true</c> [collide connected].</param>
+        public static List<RevoluteJoint> AttachBodiesWithRevoluteJoint(World world, List<Body> bodies, Vector2 localAnchorA, Vector2 localAnchorB, bool connectFirstAndLast, bool collideConnected)
+        {
+            List<RevoluteJoint> joints = new List<RevoluteJoint>(bodies.Count + 1);
+
+            for (int i = 1; i < bodies.Count; i++)
+            {
+                RevoluteJoint joint = new RevoluteJoint(bodies[i], bodies[i - 1], localAnchorA, localAnchorB);
+                joint.CollideConnected = collideConnected;
+                world.AddJoint(joint);
+                joints.Add(joint);
+            }
+
+            if (connectFirstAndLast)
+            {
+                RevoluteJoint lastjoint = new RevoluteJoint(bodies[0], bodies[bodies.Count - 1], localAnchorA, localAnchorB);
+                lastjoint.CollideConnected = collideConnected;
+                world.AddJoint(lastjoint);
+                joints.Add(lastjoint);
+            }
+
+            return joints;
+        }
+    }
+}

Farseer Physics Engine 3.5/Common/PhysicsLogic/FilterData.cs

@@ -0,0 +1,133 @@
+using FarseerPhysics.Dynamics;
+
+namespace FarseerPhysics.Common.PhysicsLogic
+{
+    /// <summary>
+    /// Contains filter data that can determine whether an object should be processed or not.
+    /// </summary>
+    public abstract class FilterData
+    {
+        /// <summary>
+        /// Disable the logic on specific categories.
+        /// Category.None by default.
+        /// </summary>
+        public Category DisabledOnCategories = Category.None;
+
+        /// <summary>
+        /// Disable the logic on specific groups
+        /// </summary>
+        public int DisabledOnGroup;
+
+        /// <summary>
+        /// Enable the logic on specific categories
+        /// Category.All by default.
+        /// </summary>
+        public Category EnabledOnCategories = Category.All;
+
+        /// <summary>
+        /// Enable the logic on specific groups.
+        /// </summary>
+        public int EnabledOnGroup;
+
+        /// <summary>
+        /// 
+        /// </summary>
+        /// <param name="body"></param>
+        /// <returns></returns>
+        public virtual bool IsActiveOn(Body body)
+        {
+            if (body == null || !body.Enabled || body.IsStatic)
+                return false;
+
+            if (body.FixtureList == null)
+                return false;
+
+            foreach (Fixture fixture in body.FixtureList)
+            {
+                //Disable
+                if ((fixture.CollisionGroup == DisabledOnGroup) && fixture.CollisionGroup != 0 && DisabledOnGroup != 0)
+                    return false;
+
+                if ((fixture.CollisionCategories & DisabledOnCategories) != Category.None)
+                    return false;
+
+                if (EnabledOnGroup != 0 || EnabledOnCategories != Category.All)
+                {
+                    //Enable
+                    if ((fixture.CollisionGroup == EnabledOnGroup) && fixture.CollisionGroup != 0 && EnabledOnGroup != 0)
+                        return true;
+
+                    if ((fixture.CollisionCategories & EnabledOnCategories) != Category.None &&
+                        EnabledOnCategories != Category.All)
+                        return true;
+                }
+                else
+                {
+                    return true;
+                }
+            }
+
+            return false;
+        }
+
+        /// <summary>
+        /// Adds the category.
+        /// </summary>
+        /// <param name="category">The category.</param>
+        public void AddDisabledCategory(Category category)
+        {
+            DisabledOnCategories |= category;
+        }
+
+        /// <summary>
+        /// Removes the category.
+        /// </summary>
+        /// <param name="category">The category.</param>
+        public void RemoveDisabledCategory(Category category)
+        {
+            DisabledOnCategories &= ~category;
+        }
+
+        /// <summary>
+        /// Determines whether this body ignores the the specified controller.
+        /// </summary>
+        /// <param name="category">The category.</param>
+        /// <returns>
+        /// 	<c>true</c> if the object has the specified category; otherwise, <c>false</c>.
+        /// </returns>
+        public bool IsInDisabledCategory(Category category)
+        {
+            return (DisabledOnCategories & category) == category;
+        }
+
+        /// <summary>
+        /// Adds the category.
+        /// </summary>
+        /// <param name="category">The category.</param>
+        public void AddEnabledCategory(Category category)
+        {
+            EnabledOnCategories |= category;
+        }
+
+        /// <summary>
+        /// Removes the category.
+        /// </summary>
+        /// <param name="category">The category.</param>
+        public void RemoveEnabledCategory(Category category)
+        {
+            EnabledOnCategories &= ~category;
+        }
+
+        /// <summary>
+        /// Determines whether this body ignores the the specified controller.
+        /// </summary>
+        /// <param name="category">The category.</param>
+        /// <returns>
+        /// 	<c>true</c> if the object has the specified category; otherwise, <c>false</c>.
+        /// </returns>
+        public bool IsInEnabledInCategory(Category category)
+        {
+            return (EnabledOnCategories & category) == category;
+        }
+    }
+}

Farseer Physics Engine 3.5/Common/PhysicsLogic/PhysicsLogic.cs

@@ -0,0 +1,66 @@
+using System;
+using FarseerPhysics.Dynamics;
+
+namespace FarseerPhysics.Common.PhysicsLogic
+{
+    [Flags]
+    public enum PhysicsLogicType
+    {
+        Explosion = (1 << 0)
+    }
+
+    public struct PhysicsLogicFilter
+    {
+        public PhysicsLogicType ControllerIgnores;
+
+        /// <summary>
+        /// Ignores the controller. The controller has no effect on this body.
+        /// </summary>
+        /// <param name="type">The logic type.</param>
+        public void IgnorePhysicsLogic(PhysicsLogicType type)
+        {
+            ControllerIgnores |= type;
+        }
+
+        /// <summary>
+        /// Restore the controller. The controller affects this body.
+        /// </summary>
+        /// <param name="type">The logic type.</param>
+        public void RestorePhysicsLogic(PhysicsLogicType type)
+        {
+            ControllerIgnores &= ~type;
+        }
+
+        /// <summary>
+        /// Determines whether this body ignores the the specified controller.
+        /// </summary>
+        /// <param name="type">The logic type.</param>
+        /// <returns>
+        /// 	<c>true</c> if the body has the specified flag; otherwise, <c>false</c>.
+        /// </returns>
+        public bool IsPhysicsLogicIgnored(PhysicsLogicType type)
+        {
+            return (ControllerIgnores & type) == type;
+        }
+    }
+
+    public abstract class PhysicsLogic : FilterData
+    {
+        private PhysicsLogicType _type;
+        public World World;
+
+        public override bool IsActiveOn(Body body)
+        {
+            if (body.PhysicsLogicFilter.IsPhysicsLogicIgnored(_type))
+                return false;
+
+            return base.IsActiveOn(body);
+        }
+
+        public PhysicsLogic(World world, PhysicsLogicType type)
+        {
+            _type = type;
+            World = world;
+        }
+    }
+}

Farseer Physics Engine 3.5/Common/PhysicsLogic/RealExplosion.cs

@@ -0,0 +1,418 @@
+using System;
+using System.Collections.Generic;
+using System.Linq;
+using FarseerPhysics.Collision;
+using FarseerPhysics.Collision.Shapes;
+using FarseerPhysics.Dynamics;
+using Microsoft.Xna.Framework;
+
+namespace FarseerPhysics.Common.PhysicsLogic
+{
+    // Original Code by Steven Lu - see http://www.box2d.org/forum/viewtopic.php?f=3&t=1688
+    // Ported to Farseer 3.0 by Nicolás Hormazábal
+
+    internal struct ShapeData
+    {
+        public Body Body;
+        public float Max;
+        public float Min; // absolute angles
+    }
+
+    /// <summary>
+    /// This is a comprarer used for 
+    /// detecting angle difference between rays
+    /// </summary>
+    internal class RayDataComparer : IComparer<float>
+    {
+        #region IComparer<float> Members
+
+        int IComparer<float>.Compare(float a, float b)
+        {
+            float diff = (a - b);
+            if (diff > 0)
+                return 1;
+            if (diff < 0)
+                return -1;
+            return 0;
+        }
+
+        #endregion
+    }
+
+    /* Methodology:
+     * Force applied at a ray is inversely proportional to the square of distance from source
+     * AABB is used to query for shapes that may be affected
+     * For each RIGID BODY (not shape -- this is an optimization) that is matched, loop through its vertices to determine
+     *		the extreme points -- if there is structure that contains outlining polygon, use that as an additional optimization
+     * Evenly cast a number of rays against the shape - number roughly proportional to the arc coverage
+     *		- Something like every 3 degrees should do the trick although this can be altered depending on the distance (if really close don't need such a high density of rays)
+     *		- There should be a minimum number of rays (3-5?) applied to each body so that small bodies far away are still accurately modeled
+     *		- Be sure to have the forces of each ray be proportional to the average arc length covered by each.
+     * For each ray that actually intersects with the shape (non intersections indicate something blocking the path of explosion):
+     *		- Apply the appropriate force dotted with the negative of the collision normal at the collision point
+     *		- Optionally apply linear interpolation between aforementioned Normal force and the original explosion force in the direction of ray to simulate "surface friction" of sorts
+     */
+
+    /// <summary>
+    /// Creates a realistic explosion based on raycasting. Objects in the open will be affected, but objects behind
+    /// static bodies will not. A body that is half in cover, half in the open will get half the force applied to the end in
+    /// the open.
+    /// </summary>
+    public sealed class RealExplosion : PhysicsLogic
+    {
+        /// <summary>
+        /// Two degrees: maximum angle from edges to first ray tested
+        /// </summary>
+        private const float MaxEdgeOffset = MathHelper.Pi / 90;
+
+        /// <summary>
+        /// Ratio of arc length to angle from edges to first ray tested.
+        /// Defaults to 1/40.
+        /// </summary>
+        public float EdgeRatio = 1.0f / 40.0f;
+
+        /// <summary>
+        /// Ignore Explosion if it happens inside a shape.
+        /// Default value is false.
+        /// </summary>
+        public bool IgnoreWhenInsideShape = false;
+
+        /// <summary>
+        /// Max angle between rays (used when segment is large).
+        /// Defaults to 15 degrees
+        /// </summary>
+        public float MaxAngle = MathHelper.Pi / 15;
+
+        /// <summary>
+        /// Maximum number of shapes involved in the explosion.
+        /// Defaults to 100
+        /// </summary>
+        public int MaxShapes = 100;
+
+        /// <summary>
+        /// How many rays per shape/body/segment.
+        /// Defaults to 5
+        /// </summary>
+        public int MinRays = 5;
+
+        private List<ShapeData> _data = new List<ShapeData>();
+        private RayDataComparer _rdc;
+
+        public RealExplosion(World world)
+            : base(world, PhysicsLogicType.Explosion)
+        {
+            _rdc = new RayDataComparer();
+            _data = new List<ShapeData>();
+        }
+
+        /// <summary>
+        /// Activate the explosion at the specified position.
+        /// </summary>
+        /// <param name="pos">The position where the explosion happens </param>
+        /// <param name="radius">The explosion radius </param>
+        /// <param name="maxForce">The explosion force at the explosion point (then is inversely proportional to the square of the distance)</param>
+        /// <returns>A list of bodies and the amount of force that was applied to them.</returns>
+        public Dictionary<Fixture, Vector2> Activate(Vector2 pos, float radius, float maxForce)
+        {
+            AABB aabb;
+            aabb.LowerBound = pos + new Vector2(-radius, -radius);
+            aabb.UpperBound = pos + new Vector2(radius, radius);
+            Fixture[] shapes = new Fixture[MaxShapes];
+
+            // More than 5 shapes in an explosion could be possible, but still strange.
+            Fixture[] containedShapes = new Fixture[5];
+            bool exit = false;
+
+            int shapeCount = 0;
+            int containedShapeCount = 0;
+
+            // Query the world for overlapping shapes.
+            World.QueryAABB(
+                fixture =>
+                {
+                    if (fixture.TestPoint(ref pos))
+                    {
+                        if (IgnoreWhenInsideShape)
+                        {
+                            exit = true;
+                            return false;
+                        }
+
+                        containedShapes[containedShapeCount++] = fixture;
+                    }
+                    else
+                    {
+                        shapes[shapeCount++] = fixture;
+                    }
+
+                    // Continue the query.
+                    return true;
+                }, ref aabb);
+
+            if (exit)
+                return new Dictionary<Fixture, Vector2>();
+
+            Dictionary<Fixture, Vector2> exploded = new Dictionary<Fixture, Vector2>(shapeCount + containedShapeCount);
+
+            // Per shape max/min angles for now.
+            float[] vals = new float[shapeCount * 2];
+            int valIndex = 0;
+            for (int i = 0; i < shapeCount; ++i)
+            {
+                PolygonShape ps;
+                CircleShape cs = shapes[i].Shape as CircleShape;
+                if (cs != null)
+                {
+                    // We create a "diamond" approximation of the circle
+                    Vertices v = new Vertices();
+                    Vector2 vec = Vector2.Zero + new Vector2(cs.Radius, 0);
+                    v.Add(vec);
+                    vec = Vector2.Zero + new Vector2(0, cs.Radius);
+                    v.Add(vec);
+                    vec = Vector2.Zero + new Vector2(-cs.Radius, cs.Radius);
+                    v.Add(vec);
+                    vec = Vector2.Zero + new Vector2(0, -cs.Radius);
+                    v.Add(vec);
+                    ps = new PolygonShape(v, 0);
+                }
+                else
+                    ps = shapes[i].Shape as PolygonShape;
+
+                if ((shapes[i].Body.BodyType == BodyType.Dynamic) && ps != null)
+                {
+                    Vector2 toCentroid = shapes[i].Body.GetWorldPoint(ps.MassData.Centroid) - pos;
+                    float angleToCentroid = (float)Math.Atan2(toCentroid.Y, toCentroid.X);
+                    float min = float.MaxValue;
+                    float max = float.MinValue;
+                    float minAbsolute = 0.0f;
+                    float maxAbsolute = 0.0f;
+
+                    for (int j = 0; j < ps.Vertices.Count; ++j)
+                    {
+                        Vector2 toVertex = (shapes[i].Body.GetWorldPoint(ps.Vertices[j]) - pos);
+                        float newAngle = (float)Math.Atan2(toVertex.Y, toVertex.X);
+                        float diff = (newAngle - angleToCentroid);
+
+                        diff = (diff - MathHelper.Pi) % (2 * MathHelper.Pi);
+                        // the minus pi is important. It means cutoff for going other direction is at 180 deg where it needs to be
+
+                        if (diff < 0.0f)
+                            diff += 2 * MathHelper.Pi; // correction for not handling negs
+
+                        diff -= MathHelper.Pi;
+
+                        if (Math.Abs(diff) > MathHelper.Pi)
+                            continue; // Something's wrong, point not in shape but exists angle diff > 180
+
+                        if (diff > max)
+                        {
+                            max = diff;
+                            maxAbsolute = newAngle;
+                        }
+                        if (diff < min)
+                        {
+                            min = diff;
+                            minAbsolute = newAngle;
+                        }
+                    }
+
+                    vals[valIndex] = minAbsolute;
+                    ++valIndex;
+                    vals[valIndex] = maxAbsolute;
+                    ++valIndex;
+                }
+            }
+
+            Array.Sort(vals, 0, valIndex, _rdc);
+            _data.Clear();
+            bool rayMissed = true;
+
+            for (int i = 0; i < valIndex; ++i)
+            {
+                Fixture fixture = null;
+                float midpt;
+
+                int iplus = (i == valIndex - 1 ? 0 : i + 1);
+                if (vals[i] == vals[iplus])
+                    continue;
+
+                if (i == valIndex - 1)
+                {
+                    // the single edgecase
+                    midpt = (vals[0] + MathHelper.Pi * 2 + vals[i]);
+                }
+                else
+                {
+                    midpt = (vals[i + 1] + vals[i]);
+                }
+
+                midpt = midpt / 2;
+
+                Vector2 p1 = pos;
+                Vector2 p2 = radius * new Vector2((float)Math.Cos(midpt), (float)Math.Sin(midpt)) + pos;
+
+                // RaycastOne
+                bool hitClosest = false;
+                World.RayCast((f, p, n, fr) =>
+                                  {
+                                      Body body = f.Body;
+
+                                      if (!IsActiveOn(body))
+                                          return 0;
+
+                                      hitClosest = true;
+                                      fixture = f;
+                                      return fr;
+                                  }, p1, p2);
+
+                //draws radius points
+                if ((hitClosest) && (fixture.Body.BodyType == BodyType.Dynamic))
+                {
+                    if ((_data.Any()) && (_data.Last().Body == fixture.Body) && (!rayMissed))
+                    {
+                        int laPos = _data.Count - 1;
+                        ShapeData la = _data[laPos];
+                        la.Max = vals[iplus];
+                        _data[laPos] = la;
+                    }
+                    else
+                    {
+                        // make new
+                        ShapeData d;
+                        d.Body = fixture.Body;
+                        d.Min = vals[i];
+                        d.Max = vals[iplus];
+                        _data.Add(d);
+                    }
+
+                    if ((_data.Count > 1)
+                        && (i == valIndex - 1)
+                        && (_data.Last().Body == _data.First().Body)
+                        && (_data.Last().Max == _data.First().Min))
+                    {
+                        ShapeData fi = _data[0];
+                        fi.Min = _data.Last().Min;
+                        _data.RemoveAt(_data.Count - 1);
+                        _data[0] = fi;
+                        while (_data.First().Min >= _data.First().Max)
+                        {
+                            fi.Min -= MathHelper.Pi * 2;
+                            _data[0] = fi;
+                        }
+                    }
+
+                    int lastPos = _data.Count - 1;
+                    ShapeData last = _data[lastPos];
+                    while ((_data.Count > 0)
+                           && (_data.Last().Min >= _data.Last().Max)) // just making sure min<max
+                    {
+                        last.Min = _data.Last().Min - 2 * MathHelper.Pi;
+                        _data[lastPos] = last;
+                    }
+                    rayMissed = false;
+                }
+                else
+                {
+                    rayMissed = true; // raycast did not find a shape
+                }
+            }
+
+            for (int i = 0; i < _data.Count; ++i)
+            {
+                if (!IsActiveOn(_data[i].Body))
+                    continue;
+
+                float arclen = _data[i].Max - _data[i].Min;
+
+                float first = MathHelper.Min(MaxEdgeOffset, EdgeRatio * arclen);
+                int insertedRays = (int)Math.Ceiling(((arclen - 2.0f * first) - (MinRays - 1) * MaxAngle) / MaxAngle);
+
+                if (insertedRays < 0)
+                    insertedRays = 0;
+
+                float offset = (arclen - first * 2.0f) / ((float)MinRays + insertedRays - 1);
+
+                //Note: This loop can go into infinite as it operates on floats.
+                //Added FloatEquals with a large epsilon.
+                for (float j = _data[i].Min + first;
+                     j < _data[i].Max || MathUtils.FloatEquals(j, _data[i].Max, 0.0001f);
+                     j += offset)
+                {
+                    Vector2 p1 = pos;
+                    Vector2 p2 = pos + radius * new Vector2((float)Math.Cos(j), (float)Math.Sin(j));
+                    Vector2 hitpoint = Vector2.Zero;
+                    float minlambda = float.MaxValue;
+
+                    List<Fixture> fl = _data[i].Body.FixtureList;
+                    for (int x = 0; x < fl.Count; x++)
+                    {
+                        Fixture f = fl[x];
+                        RayCastInput ri;
+                        ri.Point1 = p1;
+                        ri.Point2 = p2;
+                        ri.MaxFraction = 50f;
+
+                        RayCastOutput ro;
+                        if (f.RayCast(out ro, ref ri, 0))
+                        {
+                            if (minlambda > ro.Fraction)
+                            {
+                                minlambda = ro.Fraction;
+                                hitpoint = ro.Fraction * p2 + (1 - ro.Fraction) * p1;
+                            }
+                        }
+
+                        // the force that is to be applied for this particular ray.
+                        // offset is angular coverage. lambda*length of segment is distance.
+                        float impulse = (arclen / (MinRays + insertedRays)) * maxForce * 180.0f / MathHelper.Pi * (1.0f - Math.Min(1.0f, minlambda));
+
+                        // We Apply the impulse!!!
+                        Vector2 vectImp = Vector2.Dot(impulse * new Vector2((float)Math.Cos(j), (float)Math.Sin(j)), -ro.Normal) * new Vector2((float)Math.Cos(j), (float)Math.Sin(j));
+                        _data[i].Body.ApplyLinearImpulse(ref vectImp, ref hitpoint);
+
+                        // We gather the fixtures for returning them
+                        if (exploded.ContainsKey(f))
+                            exploded[f] += vectImp;
+                        else
+                            exploded.Add(f, vectImp);
+
+                        if (minlambda > 1.0f)
+                            hitpoint = p2;
+                    }
+                }
+            }
+
+            // We check contained shapes
+            for (int i = 0; i < containedShapeCount; ++i)
+            {
+                Fixture fix = containedShapes[i];
+
+                if (!IsActiveOn(fix.Body))
+                    continue;
+
+                float impulse = MinRays * maxForce * 180.0f / MathHelper.Pi;
+                Vector2 hitPoint;
+
+                CircleShape circShape = fix.Shape as CircleShape;
+                if (circShape != null)
+                {
+                    hitPoint = fix.Body.GetWorldPoint(circShape.Position);
+                }
+                else
+                {
+                    PolygonShape shape = fix.Shape as PolygonShape;
+                    hitPoint = fix.Body.GetWorldPoint(shape.MassData.Centroid);
+                }
+
+                Vector2 vectImp = impulse * (hitPoint - pos);
+
+                fix.Body.ApplyLinearImpulse(ref vectImp, ref hitPoint);
+
+                if (!exploded.ContainsKey(fix))
+                    exploded.Add(fix, vectImp);
+            }
+
+            return exploded;
+        }
+    }
+}

Farseer Physics Engine 3.5/Common/PhysicsLogic/SimpleExplosion.cs

@@ -0,0 +1,92 @@
+using System;
+using System.Collections.Generic;
+using FarseerPhysics.Collision;
+using FarseerPhysics.Dynamics;
+using Microsoft.Xna.Framework;
+
+namespace FarseerPhysics.Common.PhysicsLogic
+{
+    /// <summary>
+    /// Creates a simple explosion that ignores other bodies hiding behind static bodies.
+    /// </summary>
+    public sealed class SimpleExplosion : PhysicsLogic
+    {
+        public SimpleExplosion(World world)
+            : base(world, PhysicsLogicType.Explosion)
+        {
+            Power = 1; //linear
+        }
+
+        /// <summary>
+        /// This is the power used in the power function. A value of 1 means the force
+        /// applied to bodies in the explosion is linear. A value of 2 means it is exponential.
+        /// </summary>
+        public float Power { get; set; }
+
+        /// <summary>
+        /// Activate the explosion at the specified position.
+        /// </summary>
+        /// <param name="pos">The position (center) of the explosion.</param>
+        /// <param name="radius">The radius of the explosion.</param>
+        /// <param name="force">The force applied</param>
+        /// <param name="maxForce">A maximum amount of force. When force gets over this value, it will be equal to maxForce</param>
+        /// <returns>A list of bodies and the amount of force that was applied to them.</returns>
+        public Dictionary<Body, Vector2> Activate(Vector2 pos, float radius, float force, float maxForce = float.MaxValue)
+        {
+            HashSet<Body> affectedBodies = new HashSet<Body>();
+
+            AABB aabb;
+            aabb.LowerBound = pos - new Vector2(radius);
+            aabb.UpperBound = pos + new Vector2(radius);
+
+            // Query the world for bodies within the radius.
+            World.QueryAABB(fixture =>
+            {
+                if (Vector2.Distance(fixture.Body.Position, pos) <= radius)
+                {
+                    if (!affectedBodies.Contains(fixture.Body))
+                        affectedBodies.Add(fixture.Body);
+                }
+
+                return true;
+            }, ref aabb);
+
+            return ApplyImpulse(pos, radius, force, maxForce, affectedBodies);
+        }
+
+        private Dictionary<Body, Vector2> ApplyImpulse(Vector2 pos, float radius, float force, float maxForce, HashSet<Body> overlappingBodies)
+        {
+            Dictionary<Body, Vector2> forces = new Dictionary<Body, Vector2>(overlappingBodies.Count);
+
+            foreach (Body overlappingBody in overlappingBodies)
+            {
+                if (IsActiveOn(overlappingBody))
+                {
+                    float distance = Vector2.Distance(pos, overlappingBody.Position);
+                    float forcePercent = GetPercent(distance, radius);
+
+                    Vector2 forceVector = pos - overlappingBody.Position;
+                    forceVector *= 1f / (float)Math.Sqrt(forceVector.X * forceVector.X + forceVector.Y * forceVector.Y);
+                    forceVector *= MathHelper.Min(force * forcePercent, maxForce);
+                    forceVector *= -1;
+
+                    overlappingBody.ApplyLinearImpulse(forceVector);
+                    forces.Add(overlappingBody, forceVector);
+                }
+            }
+
+            return forces;
+        }
+
+        private float GetPercent(float distance, float radius)
+        {
+            //(1-(distance/radius))^power-1
+            float percent = (float)Math.Pow(1 - ((distance - radius) / radius), Power) - 1;
+
+            if (float.IsNaN(percent))
+                return 0f;
+
+            return MathHelper.Clamp(percent, 0f, 1f);
+        }
+    }
+}

Farseer Physics Engine 3.5/Common/PolygonManipulation/CuttingTools.cs

@@ -0,0 +1,217 @@
+using System.Collections.Generic;
+using System.Diagnostics;
+using FarseerPhysics.Collision.Shapes;
+using FarseerPhysics.Dynamics;
+using FarseerPhysics.Factories;
+using Microsoft.Xna.Framework;
+
+namespace FarseerPhysics.Common.PolygonManipulation
+{
+    public static class CuttingTools
+    {
+        //Cutting a shape into two is based on the work of Daid and his prototype BoxCutter: http://www.box2d.org/forum/viewtopic.php?f=3&t=1473
+
+        /// <summary>
+        /// Split a fixture into 2 vertice collections using the given entry and exit-point.
+        /// </summary>
+        /// <param name="fixture">The Fixture to split</param>
+        /// <param name="entryPoint">The entry point - The start point</param>
+        /// <param name="exitPoint">The exit point - The end point</param>
+        /// <param name="first">The first collection of vertexes</param>
+        /// <param name="second">The second collection of vertexes</param>
+        public static void SplitShape(Fixture fixture, Vector2 entryPoint, Vector2 exitPoint, out Vertices first, out Vertices second)
+        {
+            Vector2 localEntryPoint = fixture.Body.GetLocalPoint(ref entryPoint);
+            Vector2 localExitPoint = fixture.Body.GetLocalPoint(ref exitPoint);
+
+            PolygonShape shape = fixture.Shape as PolygonShape;
+
+            //We can only cut polygons at the moment
+            if (shape == null)
+            {
+                first = new Vertices();
+                second = new Vertices();
+                return;
+            }
+
+            //Offset the entry and exit points if they are too close to the vertices
+            foreach (Vector2 vertex in shape.Vertices)
+            {
+                if (vertex.Equals(localEntryPoint))
+                    localEntryPoint -= new Vector2(0, Settings.Epsilon);
+
+                if (vertex.Equals(localExitPoint))
+                    localExitPoint += new Vector2(0, Settings.Epsilon);
+            }
+
+            Vertices vertices = new Vertices(shape.Vertices);
+            Vertices[] newPolygon = new Vertices[2];
+
+            for (int i = 0; i < newPolygon.Length; i++)
+            {
+                newPolygon[i] = new Vertices(vertices.Count);
+            }
+
+            int[] cutAdded = { -1, -1 };
+            int last = -1;
+            for (int i = 0; i < vertices.Count; i++)
+            {
+                int n;
+                //Find out if this vertex is on the old or new shape.
+                if (Vector2.Dot(MathUtils.Cross(localExitPoint - localEntryPoint, 1), vertices[i] - localEntryPoint) > Settings.Epsilon)
+                    n = 0;
+                else
+                    n = 1;
+
+                if (last != n)
+                {
+                    //If we switch from one shape to the other add the cut vertices.
+                    if (last == 0)
+                    {
+                        Debug.Assert(cutAdded[0] == -1);
+                        cutAdded[0] = newPolygon[last].Count;
+                        newPolygon[last].Add(localExitPoint);
+                        newPolygon[last].Add(localEntryPoint);
+                    }
+                    if (last == 1)
+                    {
+                        Debug.Assert(cutAdded[last] == -1);
+                        cutAdded[last] = newPolygon[last].Count;
+                        newPolygon[last].Add(localEntryPoint);
+                        newPolygon[last].Add(localExitPoint);
+                    }
+                }
+
+                newPolygon[n].Add(vertices[i]);
+                last = n;
+            }
+
+            //Add the cut in case it has not been added yet.
+            if (cutAdded[0] == -1)
+            {
+                cutAdded[0] = newPolygon[0].Count;
+                newPolygon[0].Add(localExitPoint);
+                newPolygon[0].Add(localEntryPoint);
+            }
+            if (cutAdded[1] == -1)
+            {
+                cutAdded[1] = newPolygon[1].Count;
+                newPolygon[1].Add(localEntryPoint);
+                newPolygon[1].Add(localExitPoint);
+            }
+
+            for (int n = 0; n < 2; n++)
+            {
+                Vector2 offset;
+                if (cutAdded[n] > 0)
+                {
+                    offset = (newPolygon[n][cutAdded[n] - 1] - newPolygon[n][cutAdded[n]]);
+                }
+                else
+                {
+                    offset = (newPolygon[n][newPolygon[n].Count - 1] - newPolygon[n][0]);
+                }
+                offset.Normalize();
+
+                if (!offset.IsValid())
+                    offset = Vector2.One;
+
+                newPolygon[n][cutAdded[n]] += Settings.Epsilon * offset;
+
+                if (cutAdded[n] < newPolygon[n].Count - 2)
+                {
+                    offset = (newPolygon[n][cutAdded[n] + 2] - newPolygon[n][cutAdded[n] + 1]);
+                }
+                else
+                {
+                    offset = (newPolygon[n][0] - newPolygon[n][newPolygon[n].Count - 1]);
+                }
+                offset.Normalize();
+
+                if (!offset.IsValid())
+                    offset = Vector2.One;
+
+                newPolygon[n][cutAdded[n] + 1] += Settings.Epsilon * offset;
+            }
+
+            first = newPolygon[0];
+            second = newPolygon[1];
+        }
+
+        /// <summary>
+        /// This is a high-level function to cuts fixtures inside the given world, using the start and end points.
+        /// Note: We don't support cutting when the start or end is inside a shape.
+        /// </summary>
+        /// <param name="world">The world.</param>
+        /// <param name="start">The startpoint.</param>
+        /// <param name="end">The endpoint.</param>
+        /// <returns>True if the cut was performed.</returns>
+        public static bool Cut(World world, Vector2 start, Vector2 end)
+        {
+            List<Fixture> fixtures = new List<Fixture>();
+            List<Vector2> entryPoints = new List<Vector2>();
+            List<Vector2> exitPoints = new List<Vector2>();
+
+            //We don't support cutting when the start or end is inside a shape.
+            if (world.TestPoint(start) != null || world.TestPoint(end) != null)
+                return false;
+
+            //Get the entry points
+            world.RayCast((f, p, n, fr) =>
+                              {
+                                  fixtures.Add(f);
+                                  entryPoints.Add(p);
+                                  return 1;
+                              }, start, end);
+
+            //Reverse the ray to get the exitpoints
+            world.RayCast((f, p, n, fr) =>
+                              {
+                                  exitPoints.Add(p);
+                                  return 1;
+                              }, end, start);
+
+            //We only have a single point. We need at least 2
+            if (entryPoints.Count + exitPoints.Count < 2)
+                return false;
+
+            for (int i = 0; i < fixtures.Count; i++)
+            {
+                // can't cut circles or edges yet !
+                if (fixtures[i].Shape.ShapeType != ShapeType.Polygon)
+                    continue;
+
+                if (fixtures[i].Body.BodyType != BodyType.Static)
+                {
+                    //Split the shape up into two shapes
+                    Vertices first;
+                    Vertices second;
+                    SplitShape(fixtures[i], entryPoints[i], exitPoints[i], out first, out second);
+
+                    //Delete the original shape and create two new. Retain the properties of the body.
+                    if (first.CheckPolygon() == PolygonError.NoError)
+                    {
+                        Body firstFixture = BodyFactory.CreatePolygon(world, first, fixtures[i].Shape.Density, fixtures[i].Body.Position);
+                        firstFixture.Rotation = fixtures[i].Body.Rotation;
+                        firstFixture.LinearVelocity = fixtures[i].Body.LinearVelocity;
+                        firstFixture.AngularVelocity = fixtures[i].Body.AngularVelocity;
+                        firstFixture.BodyType = BodyType.Dynamic;
+                    }
+
+                    if (second.CheckPolygon() == PolygonError.NoError)
+                    {
+                        Body secondFixture = BodyFactory.CreatePolygon(world, second, fixtures[i].Shape.Density, fixtures[i].Body.Position);
+                        secondFixture.Rotation = fixtures[i].Body.Rotation;
+                        secondFixture.LinearVelocity = fixtures[i].Body.LinearVelocity;
+                        secondFixture.AngularVelocity = fixtures[i].Body.AngularVelocity;
+                        secondFixture.BodyType = BodyType.Dynamic;
+                    }
+
+                    world.RemoveBody(fixtures[i].Body);
+                }
+            }
+
+            return true;
+        }
+    }
+}

Farseer Physics Engine 3.5/Common/PolygonManipulation/SimpleCombiner.cs

@@ -0,0 +1,226 @@
+/*
+* C# Version Ported by Matt Bettcher and Ian Qvist 2009-2010
+* 
+* Original C++ Version Copyright (c) 2007 Eric Jordan
+*
+* This software is provided 'as-is', without any express or implied
+* warranty.  In no event will the authors be held liable for any damages
+* arising from the use of this software.
+* Permission is granted to anyone to use this software for any purpose,
+* including commercial applications, and to alter it and redistribute it
+* freely, subject to the following restrictions:
+* 1. The origin of this software must not be misrepresented; you must not
+* claim that you wrote the original software. If you use this software
+* in a product, an acknowledgment in the product documentation would be
+* appreciated but is not required.
+* 2. Altered source versions must be plainly marked as such, and must not be
+* misrepresented as being the original software.
+* 3. This notice may not be removed or altered from any source distribution.
+*/
+
+using System.Collections.Generic;
+using System.Diagnostics;
+using Microsoft.Xna.Framework;
+
+namespace FarseerPhysics.Common.PolygonManipulation
+{
+    /// <summary>
+    /// Combines a list of triangles into a list of convex polygons.
+    /// Starts with a seed triangle, keep adding triangles to it until you can't add any more without making the polygon non-convex.
+    /// </summary>
+    public static class SimpleCombiner
+    {
+        /// <summary>
+        /// Combine a list of triangles into a list of convex polygons.
+        /// 
+        /// Note: This only works on triangles.
+        /// </summary>
+        ///<param name="triangles">The triangles.</param>
+        ///<param name="maxPolys">The maximun number of polygons to return.</param>
+        ///<param name="tolerance">The tolerance</param>
+        public static List<Vertices> PolygonizeTriangles(List<Vertices> triangles, int maxPolys = int.MaxValue, float tolerance = 0.001f)
+        {
+            if (triangles.Count <= 0)
+                return triangles;
+
+            List<Vertices> polys = new List<Vertices>();
+
+            bool[] covered = new bool[triangles.Count];
+            for (int i = 0; i < triangles.Count; ++i)
+            {
+                covered[i] = false;
+
+                //Check here for degenerate triangles
+                Vertices triangle = triangles[i];
+                Vector2 a = triangle[0];
+                Vector2 b = triangle[1];
+                Vector2 c = triangle[2];
+
+                if ((a.X == b.X && a.Y == b.Y) || (b.X == c.X && b.Y == c.Y) || (a.X == c.X && a.Y == c.Y))
+                    covered[i] = true;
+            }
+
+            int polyIndex = 0;
+
+            bool notDone = true;
+            while (notDone)
+            {
+                int currTri = -1;
+                for (int i = 0; i < triangles.Count; ++i)
+                {
+                    if (covered[i])
+                        continue;
+
+                    currTri = i;
+                    break;
+                }
+
+                if (currTri == -1)
+                {
+                    notDone = false;
+                }
+                else
+                {
+                    Vertices poly = new Vertices(3);
+
+                    for (int i = 0; i < 3; i++)
+                    {
+                        poly.Add(triangles[currTri][i]);
+                    }
+
+                    covered[currTri] = true;
+                    int index = 0;
+                    for (int i = 0; i < 2 * triangles.Count; ++i, ++index)
+                    {
+                        while (index >= triangles.Count) index -= triangles.Count;
+                        if (covered[index])
+                        {
+                            continue;
+                        }
+                        Vertices newP = AddTriangle(triangles[index], poly);
+                        if (newP == null)
+                            continue; // is this right
+
+                        if (newP.Count > Settings.MaxPolygonVertices)
+                            continue;
+
+                        if (newP.IsConvex())
+                        {
+                            //Or should it be IsUsable?  Maybe re-write IsConvex to apply the angle threshold from Box2d
+                            poly = new Vertices(newP);
+                            covered[index] = true;
+                        }
+                    }
+
+                    //We have a maximum of polygons that we need to keep under.
+                    if (polyIndex < maxPolys)
+                    {
+                        SimplifyTools.MergeParallelEdges(poly, tolerance);
+
+                        //If identical points are present, a triangle gets
+                        //borked by the MergeParallelEdges function, hence
+                        //the vertex number check
+                        if (poly.Count >= 3)
+                            polys.Add(new Vertices(poly));
+                        else
+                            Debug.WriteLine("Skipping corrupt poly.");
+                    }
+
+                    if (poly.Count >= 3)
+                        polyIndex++; //Must be outside (polyIndex < polysLength) test
+                }
+            }
+
+            //TODO: Add sanity check
+            //Remove empty vertice collections
+            for (int i = polys.Count - 1; i >= 0; i--)
+            {
+                if (polys[i].Count == 0)
+                    polys.RemoveAt(i);
+            }
+
+            return polys;
+        }
+
+        private static Vertices AddTriangle(Vertices t, Vertices vertices)
+        {
+            // First, find vertices that connect
+            int firstP = -1;
+            int firstT = -1;
+            int secondP = -1;
+            int secondT = -1;
+            for (int i = 0; i < vertices.Count; i++)
+            {
+                if (t[0].X == vertices[i].X && t[0].Y == vertices[i].Y)
+                {
+                    if (firstP == -1)
+                    {
+                        firstP = i;
+                        firstT = 0;
+                    }
+                    else
+                    {
+                        secondP = i;
+                        secondT = 0;
+                    }
+                }
+                else if (t[1].X == vertices[i].X && t[1].Y == vertices[i].Y)
+                {
+                    if (firstP == -1)
+                    {
+                        firstP = i;
+                        firstT = 1;
+                    }
+                    else
+                    {
+                        secondP = i;
+                        secondT = 1;
+                    }
+                }
+                else if (t[2].X == vertices[i].X && t[2].Y == vertices[i].Y)
+                {
+                    if (firstP == -1)
+                    {
+                        firstP = i;
+                        firstT = 2;
+                    }
+                    else
+                    {
+                        secondP = i;
+                        secondT = 2;
+                    }
+                }
+            }
+            // Fix ordering if first should be last vertex of poly
+            if (firstP == 0 && secondP == vertices.Count - 1)
+            {
+                firstP = vertices.Count - 1;
+                secondP = 0;
+            }
+
+            // Didn't find it
+            if (secondP == -1)
+            {
+                return null;
+            }
+
+            // Find tip index on triangle
+            int tipT = 0;
+            if (tipT == firstT || tipT == secondT)
+                tipT = 1;
+            if (tipT == firstT || tipT == secondT)
+                tipT = 2;
+
+            Vertices result = new Vertices(vertices.Count + 1);
+            for (int i = 0; i < vertices.Count; i++)
+            {
+                result.Add(vertices[i]);
+
+                if (i == firstP)
+                    result.Add(t[tipT]);
+            }
+
+            return result;
+        }
+    }
+}

Farseer Physics Engine 3.5/Common/PolygonManipulation/SimplifyTools.cs

@@ -0,0 +1,302 @@
+using System;
+using System.Collections.Generic;
+using System.Diagnostics;
+using Microsoft.Xna.Framework;
+
+namespace FarseerPhysics.Common.PolygonManipulation
+{
+    /// <summary>
+    /// Provides a set of tools to simplify polygons in various ways.
+    /// </summary>
+    public static class SimplifyTools
+    {
+        /// <summary>
+        /// Removes all collinear points on the polygon.
+        /// </summary>
+        /// <param name="vertices">The polygon that needs simplification.</param>
+        /// <param name="collinearityTolerance">The collinearity tolerance.</param>
+        /// <returns>A simplified polygon.</returns>
+        public static Vertices CollinearSimplify(Vertices vertices, float collinearityTolerance = 0)
+        {
+            if (vertices.Count <= 3)
+                return vertices;
+
+            Vertices simplified = new Vertices(vertices.Count);
+
+            for (int i = 0; i < vertices.Count; i++)
+            {
+                Vector2 prev = vertices.PreviousVertex(i);
+                Vector2 current = vertices[i];
+                Vector2 next = vertices.NextVertex(i);
+
+                //If they collinear, continue
+                if (MathUtils.IsCollinear(ref prev, ref current, ref next, collinearityTolerance))
+                    continue;
+
+                simplified.Add(current);
+            }
+
+            return simplified;
+        }
+
+        /// <summary>
+        /// Ramer-Douglas-Peucker polygon simplification algorithm. This is the general recursive version that does not use the
+        /// speed-up technique by using the Melkman convex hull.
+        /// 
+        /// If you pass in 0, it will remove all collinear points.
+        /// </summary>
+        /// <returns>The simplified polygon</returns>
+        public static Vertices DouglasPeuckerSimplify(Vertices vertices, float distanceTolerance)
+        {
+            if (vertices.Count <= 3)
+                return vertices;
+
+            bool[] usePoint = new bool[vertices.Count];
+
+            for (int i = 0; i < vertices.Count; i++)
+                usePoint[i] = true;
+
+            SimplifySection(vertices, 0, vertices.Count - 1, usePoint, distanceTolerance);
+
+            Vertices simplified = new Vertices(vertices.Count);
+
+            for (int i = 0; i < vertices.Count; i++)
+            {
+                if (usePoint[i])
+                    simplified.Add(vertices[i]);
+            }
+
+            return simplified;
+        }
+
+        private static void SimplifySection(Vertices vertices, int i, int j, bool[] usePoint, float distanceTolerance)
+        {
+            if ((i + 1) == j)
+                return;
+
+            Vector2 a = vertices[i];
+            Vector2 b = vertices[j];
+
+            double maxDistance = -1.0;
+            int maxIndex = i;
+            for (int k = i + 1; k < j; k++)
+            {
+                Vector2 point = vertices[k];
+
+                double distance = LineTools.DistanceBetweenPointAndLineSegment(ref point, ref a, ref b);
+
+                if (distance > maxDistance)
+                {
+                    maxDistance = distance;
+                    maxIndex = k;
+                }
+            }
+
+            if (maxDistance <= distanceTolerance)
+            {
+                for (int k = i + 1; k < j; k++)
+                {
+                    usePoint[k] = false;
+                }
+            }
+            else
+            {
+                SimplifySection(vertices, i, maxIndex, usePoint, distanceTolerance);
+                SimplifySection(vertices, maxIndex, j, usePoint, distanceTolerance);
+            }
+        }
+
+        /// <summary>
+        /// Merges all parallel edges in the list of vertices
+        /// </summary>
+        /// <param name="vertices">The vertices.</param>
+        /// <param name="tolerance">The tolerance.</param>
+        public static Vertices MergeParallelEdges(Vertices vertices, float tolerance)
+        {
+            //From Eric Jordan's convex decomposition library
+
+            if (vertices.Count <= 3)
+                return vertices; //Can't do anything useful here to a triangle
+
+            bool[] mergeMe = new bool[vertices.Count];
+            int newNVertices = vertices.Count;
+
+            //Gather points to process
+            for (int i = 0; i < vertices.Count; ++i)
+            {
+                int lower = (i == 0) ? (vertices.Count - 1) : (i - 1);
+                int middle = i;
+                int upper = (i == vertices.Count - 1) ? (0) : (i + 1);
+
+                float dx0 = vertices[middle].X - vertices[lower].X;
+                float dy0 = vertices[middle].Y - vertices[lower].Y;
+                float dx1 = vertices[upper].Y - vertices[middle].X;
+                float dy1 = vertices[upper].Y - vertices[middle].Y;
+                float norm0 = (float)Math.Sqrt(dx0 * dx0 + dy0 * dy0);
+                float norm1 = (float)Math.Sqrt(dx1 * dx1 + dy1 * dy1);
+
+                if (!(norm0 > 0.0f && norm1 > 0.0f) && newNVertices > 3)
+                {
+                    //Merge identical points
+                    mergeMe[i] = true;
+                    --newNVertices;
+                }
+
+                dx0 /= norm0;
+                dy0 /= norm0;
+                dx1 /= norm1;
+                dy1 /= norm1;
+                float cross = dx0 * dy1 - dx1 * dy0;
+                float dot = dx0 * dx1 + dy0 * dy1;
+
+                if (Math.Abs(cross) < tolerance && dot > 0 && newNVertices > 3)
+                {
+                    mergeMe[i] = true;
+                    --newNVertices;
+                }
+                else
+                    mergeMe[i] = false;
+            }
+
+            if (newNVertices == vertices.Count || newNVertices == 0)
+                return vertices;
+
+            int currIndex = 0;
+
+            //Copy the vertices to a new list and clear the old
+            Vertices newVertices = new Vertices(newNVertices);
+
+            for (int i = 0; i < vertices.Count; ++i)
+            {
+                if (mergeMe[i] || newNVertices == 0 || currIndex == newNVertices)
+                    continue;
+
+                Debug.Assert(currIndex < newNVertices);
+
+                newVertices.Add(vertices[i]);
+                ++currIndex;
+            }
+
+            return newVertices;
+        }
+
+        /// <summary>
+        /// Merges the identical points in the polygon.
+        /// </summary>
+        /// <param name="vertices">The vertices.</param>
+        public static Vertices MergeIdenticalPoints(Vertices vertices)
+        {
+            HashSet<Vector2> unique = new HashSet<Vector2>();
+
+            foreach (Vector2 vertex in vertices)
+            {
+                unique.Add(vertex);
+            }
+
+            return new Vertices(unique);
+        }
+
+        /// <summary>
+        /// Reduces the polygon by distance.
+        /// </summary>
+        /// <param name="vertices">The vertices.</param>
+        /// <param name="distance">The distance between points. Points closer than this will be removed.</param>
+        public static Vertices ReduceByDistance(Vertices vertices, float distance)
+        {
+            if (vertices.Count <= 3)
+                return vertices;
+
+            float distance2 = distance * distance;
+
+            Vertices simplified = new Vertices(vertices.Count);
+
+            for (int i = 0; i < vertices.Count; i++)
+            {
+                Vector2 current = vertices[i];
+                Vector2 next = vertices.NextVertex(i);
+
+                //If they are closer than the distance, continue
+                if ((next - current).LengthSquared() <= distance2)
+                    continue;
+
+                simplified.Add(current);
+            }
+
+            return simplified;
+        }
+
+        /// <summary>
+        /// Reduces the polygon by removing the Nth vertex in the vertices list.
+        /// </summary>
+        /// <param name="vertices">The vertices.</param>
+        /// <param name="nth">The Nth point to remove. Example: 5.</param>
+        /// <returns></returns>
+        public static Vertices ReduceByNth(Vertices vertices, int nth)
+        {
+            if (vertices.Count <= 3)
+                return vertices;
+
+            if (nth == 0)
+                return vertices;
+
+            Vertices simplified = new Vertices(vertices.Count);
+
+            for (int i = 0; i < vertices.Count; i++)
+            {
+                if (i % nth == 0)
+                    continue;
+
+                simplified.Add(vertices[i]);
+            }
+
+            return simplified;
+        }
+
+        /// <summary>
+        /// Simplify the polygon by removing all points that in pairs of 3 have an area less than the tolerance.
+        /// 
+        /// Pass in 0 as tolerance, and it will only remove collinear points.
+        /// </summary>
+        /// <param name="vertices"></param>
+        /// <param name="areaTolerance"></param>
+        /// <returns></returns>
+        public static Vertices ReduceByArea(Vertices vertices, float areaTolerance)
+        {
+            //From physics2d.net
+
+            if (vertices.Count <= 3)
+                return vertices;
+
+            if (areaTolerance < 0)
+                throw new ArgumentOutOfRangeException("areaTolerance", "must be equal to or greater than zero.");
+
+            Vertices simplified = new Vertices(vertices.Count);
+            Vector2 v3;
+            Vector2 v1 = vertices[vertices.Count - 2];
+            Vector2 v2 = vertices[vertices.Count - 1];
+            areaTolerance *= 2;
+
+            for (int i = 0; i < vertices.Count; ++i, v2 = v3)
+            {
+                v3 = i == vertices.Count - 1 ? simplified[0] : vertices[i];
+
+                float old1;
+                MathUtils.Cross(ref v1, ref v2, out old1);
+
+                float old2;
+                MathUtils.Cross(ref v2, ref v3, out old2);
+
+                float new1;
+                MathUtils.Cross(ref v1, ref v3, out new1);
+
+                if (Math.Abs(new1 - (old1 + old2)) > areaTolerance)
+                {
+                    simplified.Add(v2);
+                    v1 = v2;
+                }
+            }
+
+            return simplified;
+        }
+    }
+}

Farseer Physics Engine 3.5/Common/PolygonManipulation/YuPengClipper.cs

@@ -0,0 +1,514 @@
+using System;
+using System.Collections.Generic;
+using System.Diagnostics;
+using Microsoft.Xna.Framework;
+
+namespace FarseerPhysics.Common.PolygonManipulation
+{
+  internal enum PolyClipType
+  {
+    Intersect,
+    Union,
+    Difference
+  }
+
+  public enum PolyClipError
+  {
+    None,
+    DegeneratedOutput,
+    NonSimpleInput,
+    BrokenResult
+  }
+
+  //Clipper contributed by Helge Backhaus
+
+  public static class YuPengClipper
+  {
+    private const float ClipperEpsilonSquared = 1.192092896e-07f;
+
+    public static List<Vertices> Union(Vertices polygon1, Vertices polygon2, out PolyClipError error)
+    {
+      return Execute(polygon1, polygon2, PolyClipType.Union, out error);
+    }
+
+    public static List<Vertices> Difference(Vertices polygon1, Vertices polygon2, out PolyClipError error)
+    {
+      return Execute(polygon1, polygon2, PolyClipType.Difference, out error);
+    }
+
+    public static List<Vertices> Intersect(Vertices polygon1, Vertices polygon2, out PolyClipError error)
+    {
+      return Execute(polygon1, polygon2, PolyClipType.Intersect, out error);
+    }
+
+    /// <summary>
+    /// Implements "A new algorithm for Boolean operations on general polygons" 
+    /// available here: http://liama.ia.ac.cn/wiki/_media/user:dong:dong_cg_05.pdf
+    /// Merges two polygons, a subject and a clip with the specified operation. Polygons may not be 
+    /// self-intersecting.
+    /// 
+    /// Warning: May yield incorrect results or even crash if polygons contain collinear points.
+    /// </summary>
+    /// <param name="subject">The subject polygon.</param>
+    /// <param name="clip">The clip polygon, which is added, 
+    /// substracted or intersected with the subject</param>
+    /// <param name="clipType">The operation to be performed. Either
+    /// Union, Difference or Intersection.</param>
+    /// <param name="error">The error generated (if any)</param>
+    /// <returns>A list of closed polygons, which make up the result of the clipping operation.
+    /// Outer contours are ordered counter clockwise, holes are ordered clockwise.</returns>
+    private static List<Vertices> Execute(Vertices subject, Vertices clip, PolyClipType clipType, out PolyClipError error)
+    {
+      Debug.Assert(subject.IsSimple() && clip.IsSimple(), "Non simple input!", "Input polygons must be simple (cannot intersect themselves).");
+
+      // Copy polygons
+      Vertices slicedSubject;
+      Vertices slicedClip;
+      // Calculate the intersection and touch points between
+      // subject and clip and add them to both
+      CalculateIntersections(subject, clip, out slicedSubject, out slicedClip);
+
+      // Translate polygons into upper right quadrant
+      // as the algorithm depends on it
+      Vector2 lbSubject = subject.GetAABB().LowerBound;
+      Vector2 lbClip = clip.GetAABB().LowerBound;
+      Vector2 translate;
+      Vector2.Min(ref lbSubject, ref lbClip, out translate);
+      translate = Vector2.One - translate;
+      if (translate != Vector2.Zero)
+      {
+        slicedSubject.Translate(ref translate);
+        slicedClip.Translate(ref translate);
+      }
+
+      // Enforce counterclockwise contours
+      slicedSubject.ForceCounterClockWise();
+      slicedClip.ForceCounterClockWise();
+
+      List<Edge> subjectSimplices;
+      List<float> subjectCoeff;
+      List<Edge> clipSimplices;
+      List<float> clipCoeff;
+      // Build simplical chains from the polygons and calculate the
+      // the corresponding coefficients
+      CalculateSimplicalChain(slicedSubject, out subjectCoeff, out subjectSimplices);
+      CalculateSimplicalChain(slicedClip, out clipCoeff, out clipSimplices);
+
+      List<Edge> resultSimplices;
+
+      // Determine the characteristics function for all non-original edges
+      // in subject and clip simplical chain and combine the edges contributing
+      // to the result, depending on the clipType
+      CalculateResultChain(subjectCoeff, subjectSimplices, clipCoeff, clipSimplices, clipType,
+                           out resultSimplices);
+
+      List<Vertices> result;
+      // Convert result chain back to polygon(s)
+      error = BuildPolygonsFromChain(resultSimplices, out result);
+
+      // Reverse the polygon translation from the beginning
+      // and remove collinear points from output
+      translate *= -1f;
+      for (int i = 0; i < result.Count; ++i)
+      {
+        result[i].Translate(ref translate);
+        SimplifyTools.CollinearSimplify(result[i]);
+      }
+      return result;
+    }
+
+    /// <summary>
+    /// Calculates all intersections between two polygons.
+    /// </summary>
+    /// <param name="polygon1">The first polygon.</param>
+    /// <param name="polygon2">The second polygon.</param>
+    /// <param name="slicedPoly1">Returns the first polygon with added intersection points.</param>
+    /// <param name="slicedPoly2">Returns the second polygon with added intersection points.</param>
+    private static void CalculateIntersections(Vertices polygon1, Vertices polygon2,
+                                               out Vertices slicedPoly1, out Vertices slicedPoly2)
+    {
+      slicedPoly1 = new Vertices(polygon1);
+      slicedPoly2 = new Vertices(polygon2);
+
+      // Iterate through polygon1's edges
+      for (int i = 0; i < polygon1.Count; i++)
+      {
+        // Get edge vertices
+        Vector2 a = polygon1[i];
+        Vector2 b = polygon1[polygon1.NextIndex(i)];
+
+        // Get intersections between this edge and polygon2
+        for (int j = 0; j < polygon2.Count; j++)
+        {
+          Vector2 c = polygon2[j];
+          Vector2 d = polygon2[polygon2.NextIndex(j)];
+
+          Vector2 intersectionPoint;
+          // Check if the edges intersect
+          if (LineTools.LineIntersect(a, b, c, d, out intersectionPoint))
+          {
+            // calculate alpha values for sorting multiple intersections points on a edge
+            float alpha;
+            // Insert intersection point into first polygon
+            alpha = GetAlpha(a, b, intersectionPoint);
+            if (alpha > 0f && alpha < 1f)
+            {
+              int index = slicedPoly1.IndexOf(a) + 1;
+              while (index < slicedPoly1.Count &&
+                     GetAlpha(a, b, slicedPoly1[index]) <= alpha)
+              {
+                ++index;
+              }
+              slicedPoly1.Insert(index, intersectionPoint);
+            }
+            // Insert intersection point into second polygon
+            alpha = GetAlpha(c, d, intersectionPoint);
+            if (alpha > 0f && alpha < 1f)
+            {
+              int index = slicedPoly2.IndexOf(c) + 1;
+              while (index < slicedPoly2.Count &&
+                     GetAlpha(c, d, slicedPoly2[index]) <= alpha)
+              {
+                ++index;
+              }
+              slicedPoly2.Insert(index, intersectionPoint);
+            }
+          }
+        }
+      }
+      // Check for very small edges
+      for (int i = 0; i < slicedPoly1.Count; ++i)
+      {
+        int iNext = slicedPoly1.NextIndex(i);
+        //If they are closer than the distance remove vertex
+        if ((slicedPoly1[iNext] - slicedPoly1[i]).LengthSquared() <= ClipperEpsilonSquared)
+        {
+          slicedPoly1.RemoveAt(i);
+          --i;
+        }
+      }
+      for (int i = 0; i < slicedPoly2.Count; ++i)
+      {
+        int iNext = slicedPoly2.NextIndex(i);
+        //If they are closer than the distance remove vertex
+        if ((slicedPoly2[iNext] - slicedPoly2[i]).LengthSquared() <= ClipperEpsilonSquared)
+        {
+          slicedPoly2.RemoveAt(i);
+          --i;
+        }
+      }
+    }
+
+    /// <summary>
+    /// Calculates the simplical chain corresponding to the input polygon.
+    /// </summary>
+    /// <remarks>Used by method <c>Execute()</c>.</remarks>
+    private static void CalculateSimplicalChain(Vertices poly, out List<float> coeff,
+                                                out List<Edge> simplicies)
+    {
+      simplicies = new List<Edge>();
+      coeff = new List<float>();
+      for (int i = 0; i < poly.Count; ++i)
+      {
+        simplicies.Add(new Edge(poly[i], poly[poly.NextIndex(i)]));
+        coeff.Add(CalculateSimplexCoefficient(Vector2.Zero, poly[i], poly[poly.NextIndex(i)]));
+      }
+    }
+
+    /// <summary>
+    /// Calculates the characteristics function for all edges of
+    /// the given simplical chains and builds the result chain.
+    /// </summary>
+    /// <remarks>Used by method <c>Execute()</c>.</remarks>
+    private static void CalculateResultChain(List<float> poly1Coeff, List<Edge> poly1Simplicies,
+                                               List<float> poly2Coeff, List<Edge> poly2Simplicies,
+                                               PolyClipType clipType, out List<Edge> resultSimplices)
+    {
+      resultSimplices = new List<Edge>();
+
+      for (int i = 0; i < poly1Simplicies.Count; ++i)
+      {
+        float edgeCharacter = 0;
+        if (poly2Simplicies.Contains(poly1Simplicies[i]))
+        {
+          edgeCharacter = 1f;
+        }
+        else if (poly2Simplicies.Contains(-poly1Simplicies[i]) && clipType == PolyClipType.Union)
+        {
+          edgeCharacter = 1f;
+        }
+        else
+        {
+          for (int j = 0; j < poly2Simplicies.Count; ++j)
+          {
+            if (!poly2Simplicies.Contains(-poly1Simplicies[i]))
+            {
+              edgeCharacter += CalculateBeta(poly1Simplicies[i].GetCenter(),
+                                             poly2Simplicies[j], poly2Coeff[j]);
+            }
+          }
+        }
+        if (clipType == PolyClipType.Intersect)
+        {
+          if (edgeCharacter == 1f)
+          {
+            resultSimplices.Add(poly1Simplicies[i]);
+          }
+        }
+        else
+        {
+          if (edgeCharacter == 0f)
+          {
+            resultSimplices.Add(poly1Simplicies[i]);
+          }
+        }
+      }
+      for (int i = 0; i < poly2Simplicies.Count; ++i)
+      {
+        float edgeCharacter = 0f;
+        if (!resultSimplices.Contains(poly2Simplicies[i]) &&
+            !resultSimplices.Contains(-poly2Simplicies[i]))
+        {
+          if (poly1Simplicies.Contains(-poly2Simplicies[i]) && clipType == PolyClipType.Union)
+          {
+            edgeCharacter = 1f;
+          }
+          else
+          {
+            edgeCharacter = 0f;
+            for (int j = 0; j < poly1Simplicies.Count; ++j)
+            {
+              if (!poly1Simplicies.Contains(poly2Simplicies[i]) && !poly1Simplicies.Contains(-poly2Simplicies[i]))
+              {
+                edgeCharacter += CalculateBeta(poly2Simplicies[i].GetCenter(),
+                                               poly1Simplicies[j], poly1Coeff[j]);
+              }
+            }
+            if (clipType == PolyClipType.Intersect || clipType == PolyClipType.Difference)
+            {
+              if (edgeCharacter == 1f)
+              {
+                resultSimplices.Add(-poly2Simplicies[i]);
+              }
+            }
+            else
+            {
+              if (edgeCharacter == 0f)
+              {
+                resultSimplices.Add(poly2Simplicies[i]);
+              }
+            }
+          }
+        }
+      }
+    }
+
+    /// <summary>
+    /// Calculates the polygon(s) from the result simplical chain.
+    /// </summary>
+    /// <remarks>Used by method <c>Execute()</c>.</remarks>
+    private static PolyClipError BuildPolygonsFromChain(List<Edge> simplicies, out List<Vertices> result)
+    {
+      result = new List<Vertices>();
+      PolyClipError errVal = PolyClipError.None;
+
+      while (simplicies.Count > 0)
+      {
+        Vertices output = new Vertices();
+        output.Add(simplicies[0].EdgeStart);
+        output.Add(simplicies[0].EdgeEnd);
+        simplicies.RemoveAt(0);
+        bool closed = false;
+        int index = 0;
+        int count = simplicies.Count; // Needed to catch infinite loops
+        while (!closed && simplicies.Count > 0)
+        {
+          if (VectorEqual(output[output.Count - 1], simplicies[index].EdgeStart))
+          {
+            if (VectorEqual(simplicies[index].EdgeEnd, output[0]))
+            {
+              closed = true;
+            }
+            else
+            {
+              output.Add(simplicies[index].EdgeEnd);
+            }
+            simplicies.RemoveAt(index);
+            --index;
+          }
+          else if (VectorEqual(output[output.Count - 1], simplicies[index].EdgeEnd))
+          {
+            if (VectorEqual(simplicies[index].EdgeStart, output[0]))
+            {
+              closed = true;
+            }
+            else
+            {
+              output.Add(simplicies[index].EdgeStart);
+            }
+            simplicies.RemoveAt(index);
+            --index;
+          }
+          if (!closed)
+          {
+            if (++index == simplicies.Count)
+            {
+              if (count == simplicies.Count)
+              {
+                result = new List<Vertices>();
+                Debug.WriteLine("Undefined error while building result polygon(s).");
+                return PolyClipError.BrokenResult;
+              }
+              index = 0;
+              count = simplicies.Count;
+            }
+          }
+        }
+        if (output.Count < 3)
+        {
+          errVal = PolyClipError.DegeneratedOutput;
+          Debug.WriteLine("Degenerated output polygon produced (vertices < 3).");
+        }
+        result.Add(output);
+      }
+      return errVal;
+    }
+
+    /// <summary>
+    /// Needed to calculate the characteristics function of a simplex.
+    /// </summary>
+    /// <remarks>Used by method <c>CalculateEdgeCharacter()</c>.</remarks>
+    private static float CalculateBeta(Vector2 point, Edge e, float coefficient)
+    {
+      float result = 0f;
+      if (PointInSimplex(point, e))
+      {
+        result = coefficient;
+      }
+      if (PointOnLineSegment(Vector2.Zero, e.EdgeStart, point) ||
+          PointOnLineSegment(Vector2.Zero, e.EdgeEnd, point))
+      {
+        result = .5f * coefficient;
+      }
+      return result;
+    }
+
+    /// <summary>
+    /// Needed for sorting multiple intersections points on the same edge.
+    /// </summary>
+    /// <remarks>Used by method <c>CalculateIntersections()</c>.</remarks>
+    private static float GetAlpha(Vector2 start, Vector2 end, Vector2 point)
+    {
+      return (point - start).LengthSquared() / (end - start).LengthSquared();
+    }
+
+    /// <summary>
+    /// Returns the coefficient of a simplex.
+    /// </summary>
+    /// <remarks>Used by method <c>CalculateSimplicalChain()</c>.</remarks>
+    private static float CalculateSimplexCoefficient(Vector2 a, Vector2 b, Vector2 c)
+    {
+      float isLeft = MathUtils.Area(ref a, ref b, ref c);
+      if (isLeft < 0f)
+      {
+        return -1f;
+      }
+
+      if (isLeft > 0f)
+      {
+        return 1f;
+      }
+
+      return 0f;
+    }
+
+    /// <summary>
+    /// Winding number test for a point in a simplex.
+    /// </summary>
+    /// <param name="point">The point to be tested.</param>
+    /// <param name="edge">The edge that the point is tested against.</param>
+    /// <returns>False if the winding number is even and the point is outside
+    /// the simplex and True otherwise.</returns>
+    private static bool PointInSimplex(Vector2 point, Edge edge)
+    {
+      Vertices polygon = new Vertices();
+      polygon.Add(Vector2.Zero);
+      polygon.Add(edge.EdgeStart);
+      polygon.Add(edge.EdgeEnd);
+      return (polygon.PointInPolygon(ref point) == 1);
+    }
+
+    /// <summary>
+    /// Tests if a point lies on a line segment.
+    /// </summary>
+    /// <remarks>Used by method <c>CalculateBeta()</c>.</remarks>
+    private static bool PointOnLineSegment(Vector2 start, Vector2 end, Vector2 point)
+    {
+      Vector2 segment = end - start;
+      return MathUtils.Area(ref start, ref end, ref point) == 0f &&
+             Vector2.Dot(point - start, segment) >= 0f &&
+             Vector2.Dot(point - end, segment) <= 0f;
+    }
+
+    private static bool VectorEqual(Vector2 vec1, Vector2 vec2)
+    {
+      return (vec2 - vec1).LengthSquared() <= ClipperEpsilonSquared;
+    }
+
+    #region Nested type: Edge
+
+    /// <summary>Specifies an Edge. Edges are used to represent simplicies in simplical chains</summary>
+    private sealed class Edge
+    {
+      public Edge(Vector2 edgeStart, Vector2 edgeEnd)
+      {
+        EdgeStart = edgeStart;
+        EdgeEnd = edgeEnd;
+      }
+
+      public Vector2 EdgeStart { get; private set; }
+      public Vector2 EdgeEnd { get; private set; }
+
+      public Vector2 GetCenter()
+      {
+        return (EdgeStart + EdgeEnd) / 2f;
+      }
+
+      public static Edge operator -(Edge e)
+      {
+        return new Edge(e.EdgeEnd, e.EdgeStart);
+      }
+
+      public override bool Equals(Object obj)
+      {
+        // If parameter is null return false.
+        if (obj == null)
+        {
+          return false;
+        }
+
+        // If parameter cannot be cast to Point return false.
+        return Equals(obj as Edge);
+      }
+
+      public bool Equals(Edge e)
+      {
+        // If parameter is null return false:
+        if (e == null)
+        {
+          return false;
+        }
+
+        // Return true if the fields match
+        return VectorEqual(EdgeStart, e.EdgeStart) && VectorEqual(EdgeEnd, e.EdgeEnd);
+      }
+
+      public override int GetHashCode()
+      {
+        return EdgeStart.GetHashCode() ^ EdgeEnd.GetHashCode();
+      }
+    }
+
+    #endregion
+  }
+}

Farseer Physics Engine 3.5/Common/PolygonTools.cs

@@ -0,0 +1,360 @@
+using System;
+using System.Collections.Generic;
+using System.Diagnostics;
+using FarseerPhysics.Common.TextureTools;
+using Microsoft.Xna.Framework;
+
+namespace FarseerPhysics.Common
+{
+    public static class PolygonTools
+    {
+        /// <summary>
+        /// Build vertices to represent an axis-aligned box.
+        /// </summary>
+        /// <param name="hx">the half-width.</param>
+        /// <param name="hy">the half-height.</param>
+        public static Vertices CreateRectangle(float hx, float hy)
+        {
+            Vertices vertices = new Vertices(4);
+            vertices.Add(new Vector2(-hx, -hy));
+            vertices.Add(new Vector2(hx, -hy));
+            vertices.Add(new Vector2(hx, hy));
+            vertices.Add(new Vector2(-hx, hy));
+
+            return vertices;
+        }
+
+        /// <summary>
+        /// Build vertices to represent an oriented box.
+        /// </summary>
+        /// <param name="hx">the half-width.</param>
+        /// <param name="hy">the half-height.</param>
+        /// <param name="center">the center of the box in local coordinates.</param>
+        /// <param name="angle">the rotation of the box in local coordinates.</param>
+        public static Vertices CreateRectangle(float hx, float hy, Vector2 center, float angle)
+        {
+            Vertices vertices = CreateRectangle(hx, hy);
+
+            Transform xf = new Transform();
+            xf.p = center;
+            xf.q.Set(angle);
+
+            // Transform vertices
+            for (int i = 0; i < 4; ++i)
+            {
+                vertices[i] = MathUtils.Mul(ref xf, vertices[i]);
+            }
+
+            return vertices;
+        }
+
+        //Rounded rectangle contributed by Jonathan Smars - jsmars@gmail.com
+
+        /// <summary>
+        /// Creates a rounded rectangle with the specified width and height.
+        /// </summary>
+        /// <param name="width">The width.</param>
+        /// <param name="height">The height.</param>
+        /// <param name="xRadius">The rounding X radius.</param>
+        /// <param name="yRadius">The rounding Y radius.</param>
+        /// <param name="segments">The number of segments to subdivide the edges.</param>
+        /// <returns></returns>
+        public static Vertices CreateRoundedRectangle(float width, float height, float xRadius, float yRadius,
+                                                      int segments)
+        {
+            if (yRadius > height / 2 || xRadius > width / 2)
+                throw new Exception("Rounding amount can't be more than half the height and width respectively.");
+            if (segments < 0)
+                throw new Exception("Segments must be zero or more.");
+
+            //We need at least 8 vertices to create a rounded rectangle
+            Debug.Assert(Settings.MaxPolygonVertices >= 8);
+
+            Vertices vertices = new Vertices();
+            if (segments == 0)
+            {
+                vertices.Add(new Vector2(width * .5f - xRadius, -height * .5f));
+                vertices.Add(new Vector2(width * .5f, -height * .5f + yRadius));
+
+                vertices.Add(new Vector2(width * .5f, height * .5f - yRadius));
+                vertices.Add(new Vector2(width * .5f - xRadius, height * .5f));
+
+                vertices.Add(new Vector2(-width * .5f + xRadius, height * .5f));
+                vertices.Add(new Vector2(-width * .5f, height * .5f - yRadius));
+
+                vertices.Add(new Vector2(-width * .5f, -height * .5f + yRadius));
+                vertices.Add(new Vector2(-width * .5f + xRadius, -height * .5f));
+            }
+            else
+            {
+                int numberOfEdges = (segments * 4 + 8);
+
+                float stepSize = MathHelper.TwoPi / (numberOfEdges - 4);
+                int perPhase = numberOfEdges / 4;
+
+                Vector2 posOffset = new Vector2(width / 2 - xRadius, height / 2 - yRadius);
+                vertices.Add(posOffset + new Vector2(xRadius, -yRadius + yRadius));
+                short phase = 0;
+                for (int i = 1; i < numberOfEdges; i++)
+                {
+                    if (i - perPhase == 0 || i - perPhase * 3 == 0)
+                    {
+                        posOffset.X *= -1;
+                        phase--;
+                    }
+                    else if (i - perPhase * 2 == 0)
+                    {
+                        posOffset.Y *= -1;
+                        phase--;
+                    }
+
+                    vertices.Add(posOffset + new Vector2(xRadius * (float)Math.Cos(stepSize * -(i + phase)),
+                                                         -yRadius * (float)Math.Sin(stepSize * -(i + phase))));
+                }
+            }
+
+            return vertices;
+        }
+
+        /// <summary>
+        /// Set this as a single edge.
+        /// </summary>
+        /// <param name="start">The first point.</param>
+        /// <param name="end">The second point.</param>
+        public static Vertices CreateLine(Vector2 start, Vector2 end)
+        {
+            Vertices vertices = new Vertices(2);
+            vertices.Add(start);
+            vertices.Add(end);
+
+            return vertices;
+        }
+
+        /// <summary>
+        /// Creates a circle with the specified radius and number of edges.
+        /// </summary>
+        /// <param name="radius">The radius.</param>
+        /// <param name="numberOfEdges">The number of edges. The more edges, the more it resembles a circle</param>
+        /// <returns></returns>
+        public static Vertices CreateCircle(float radius, int numberOfEdges)
+        {
+            return CreateEllipse(radius, radius, numberOfEdges);
+        }
+
+        /// <summary>
+        /// Creates a ellipse with the specified width, height and number of edges.
+        /// </summary>
+        /// <param name="xRadius">Width of the ellipse.</param>
+        /// <param name="yRadius">Height of the ellipse.</param>
+        /// <param name="numberOfEdges">The number of edges. The more edges, the more it resembles an ellipse</param>
+        /// <returns></returns>
+        public static Vertices CreateEllipse(float xRadius, float yRadius, int numberOfEdges)
+        {
+            Vertices vertices = new Vertices();
+
+            float stepSize = MathHelper.TwoPi / numberOfEdges;
+
+            vertices.Add(new Vector2(xRadius, 0));
+            for (int i = numberOfEdges - 1; i > 0; --i)
+                vertices.Add(new Vector2(xRadius * (float)Math.Cos(stepSize * i),
+                                         -yRadius * (float)Math.Sin(stepSize * i)));
+
+            return vertices;
+        }
+
+        public static Vertices CreateArc(float radians, int sides, float radius)
+        {
+            Debug.Assert(radians > 0, "The arc needs to be larger than 0");
+            Debug.Assert(sides > 1, "The arc needs to have more than 1 sides");
+            Debug.Assert(radius > 0, "The arc needs to have a radius larger than 0");
+
+            Vertices vertices = new Vertices();
+
+            float stepSize = radians / sides;
+            for (int i = sides - 1; i > 0; i--)
+            {
+                vertices.Add(new Vector2(radius * (float)Math.Cos(stepSize * i),
+                                         radius * (float)Math.Sin(stepSize * i)));
+            }
+
+            return vertices;
+        }
+
+        //Capsule contributed by Yobiv
+
+        /// <summary>
+        /// Creates an capsule with the specified height, radius and number of edges.
+        /// A capsule has the same form as a pill capsule.
+        /// </summary>
+        /// <param name="height">Height (inner height + 2 * radius) of the capsule.</param>
+        /// <param name="endRadius">Radius of the capsule ends.</param>
+        /// <param name="edges">The number of edges of the capsule ends. The more edges, the more it resembles an capsule</param>
+        /// <returns></returns>
+        public static Vertices CreateCapsule(float height, float endRadius, int edges)
+        {
+            if (endRadius >= height / 2)
+                throw new ArgumentException(
+                    "The radius must be lower than height / 2. Higher values of radius would create a circle, and not a half circle.",
+                    "endRadius");
+
+            return CreateCapsule(height, endRadius, edges, endRadius, edges);
+        }
+
+        /// <summary>
+        /// Creates an capsule with the specified  height, radius and number of edges.
+        /// A capsule has the same form as a pill capsule.
+        /// </summary>
+        /// <param name="height">Height (inner height + radii) of the capsule.</param>
+        /// <param name="topRadius">Radius of the top.</param>
+        /// <param name="topEdges">The number of edges of the top. The more edges, the more it resembles an capsule</param>
+        /// <param name="bottomRadius">Radius of bottom.</param>
+        /// <param name="bottomEdges">The number of edges of the bottom. The more edges, the more it resembles an capsule</param>
+        /// <returns></returns>
+        public static Vertices CreateCapsule(float height, float topRadius, int topEdges, float bottomRadius,
+                                             int bottomEdges)
+        {
+            if (height <= 0)
+                throw new ArgumentException("Height must be longer than 0", "height");
+
+            if (topRadius <= 0)
+                throw new ArgumentException("The top radius must be more than 0", "topRadius");
+
+            if (topEdges <= 0)
+                throw new ArgumentException("Top edges must be more than 0", "topEdges");
+
+            if (bottomRadius <= 0)
+                throw new ArgumentException("The bottom radius must be more than 0", "bottomRadius");
+
+            if (bottomEdges <= 0)
+                throw new ArgumentException("Bottom edges must be more than 0", "bottomEdges");
+
+            if (topRadius >= height / 2)
+                throw new ArgumentException(
+                    "The top radius must be lower than height / 2. Higher values of top radius would create a circle, and not a half circle.",
+                    "topRadius");
+
+            if (bottomRadius >= height / 2)
+                throw new ArgumentException(
+                    "The bottom radius must be lower than height / 2. Higher values of bottom radius would create a circle, and not a half circle.",
+                    "bottomRadius");
+
+            Vertices vertices = new Vertices();
+
+            float newHeight = (height - topRadius - bottomRadius) * 0.5f;
+
+            // top
+            vertices.Add(new Vector2(topRadius, newHeight));
+
+            float stepSize = MathHelper.Pi / topEdges;
+            for (int i = 1; i < topEdges; i++)
+            {
+                vertices.Add(new Vector2(topRadius * (float)Math.Cos(stepSize * i),
+                                         topRadius * (float)Math.Sin(stepSize * i) + newHeight));
+            }
+
+            vertices.Add(new Vector2(-topRadius, newHeight));
+
+            // bottom
+            vertices.Add(new Vector2(-bottomRadius, -newHeight));
+
+            stepSize = MathHelper.Pi / bottomEdges;
+            for (int i = 1; i < bottomEdges; i++)
+            {
+                vertices.Add(new Vector2(-bottomRadius * (float)Math.Cos(stepSize * i),
+                                         -bottomRadius * (float)Math.Sin(stepSize * i) - newHeight));
+            }
+
+            vertices.Add(new Vector2(bottomRadius, -newHeight));
+
+            return vertices;
+        }
+
+        /// <summary>
+        /// Creates a gear shape with the specified radius and number of teeth.
+        /// </summary>
+        /// <param name="radius">The radius.</param>
+        /// <param name="numberOfTeeth">The number of teeth.</param>
+        /// <param name="tipPercentage">The tip percentage.</param>
+        /// <param name="toothHeight">Height of the tooth.</param>
+        /// <returns></returns>
+        public static Vertices CreateGear(float radius, int numberOfTeeth, float tipPercentage, float toothHeight)
+        {
+            Vertices vertices = new Vertices();
+
+            float stepSize = MathHelper.TwoPi / numberOfTeeth;
+            tipPercentage /= 100f;
+            MathHelper.Clamp(tipPercentage, 0f, 1f);
+            float toothTipStepSize = (stepSize / 2f) * tipPercentage;
+
+            float toothAngleStepSize = (stepSize - (toothTipStepSize * 2f)) / 2f;
+
+            for (int i = numberOfTeeth - 1; i >= 0; --i)
+            {
+                if (toothTipStepSize > 0f)
+                {
+                    vertices.Add(
+                        new Vector2(radius *
+                                    (float)Math.Cos(stepSize * i + toothAngleStepSize * 2f + toothTipStepSize),
+                                    -radius *
+                                    (float)Math.Sin(stepSize * i + toothAngleStepSize * 2f + toothTipStepSize)));
+
+                    vertices.Add(
+                        new Vector2((radius + toothHeight) *
+                                    (float)Math.Cos(stepSize * i + toothAngleStepSize + toothTipStepSize),
+                                    -(radius + toothHeight) *
+                                    (float)Math.Sin(stepSize * i + toothAngleStepSize + toothTipStepSize)));
+                }
+
+                vertices.Add(new Vector2((radius + toothHeight) *
+                                         (float)Math.Cos(stepSize * i + toothAngleStepSize),
+                                         -(radius + toothHeight) *
+                                         (float)Math.Sin(stepSize * i + toothAngleStepSize)));
+
+                vertices.Add(new Vector2(radius * (float)Math.Cos(stepSize * i),
+                                         -radius * (float)Math.Sin(stepSize * i)));
+            }
+
+            return vertices;
+        }
+
+        /// <summary>
+        /// Detects the vertices by analyzing the texture data.
+        /// </summary>
+        /// <param name="data">The texture data.</param>
+        /// <param name="width">The texture width.</param>
+        /// <returns></returns>
+        public static Vertices CreatePolygon(uint[] data, int width)
+        {
+            return TextureConverter.DetectVertices(data, width);
+        }
+
+        /// <summary>
+        /// Detects the vertices by analyzing the texture data.
+        /// </summary>
+        /// <param name="data">The texture data.</param>
+        /// <param name="width">The texture width.</param>
+        /// <param name="holeDetection">if set to <c>true</c> it will perform hole detection.</param>
+        /// <returns></returns>
+        public static Vertices CreatePolygon(uint[] data, int width, bool holeDetection)
+        {
+            return TextureConverter.DetectVertices(data, width, holeDetection);
+        }
+
+        /// <summary>
+        /// Detects the vertices by analyzing the texture data.
+        /// </summary>
+        /// <param name="data">The texture data.</param>
+        /// <param name="width">The texture width.</param>
+        /// <param name="hullTolerance">The hull tolerance.</param>
+        /// <param name="alphaTolerance">The alpha tolerance.</param>
+        /// <param name="multiPartDetection">if set to <c>true</c> it will perform multi part detection.</param>
+        /// <param name="holeDetection">if set to <c>true</c> it will perform hole detection.</param>
+        /// <returns></returns>
+        public static List<Vertices> CreatePolygon(uint[] data, int width, float hullTolerance,
+                                                   byte alphaTolerance, bool multiPartDetection, bool holeDetection)
+        {
+            return TextureConverter.DetectVertices(data, width, hullTolerance, alphaTolerance,
+                                                   multiPartDetection, holeDetection);
+        }
+    }
+}

Farseer Physics Engine 3.5/Common/Stopwatch.cs

@@ -0,0 +1,112 @@
+#if SILVERLIGHT
+using System;
+
+namespace FarseerPhysics.Common
+{
+    // Source: http://www.wiredprairie.us/blog/index.php/archives/723
+
+    /// <summary>
+    /// An emulation for the Stopwatch class for Windows Phone and Silverlight.
+    /// </summary>
+    public sealed class Stopwatch
+    {
+        private long _startTick;
+        private long _elapsed;
+        private bool _isRunning;
+
+        /// <summary>
+        /// Creates a new instance of the class and starts the watch immediately.
+        /// </summary>
+        /// <returns>An instance of Stopwatch, running.</returns>
+        public static Stopwatch StartNew()
+        {
+            Stopwatch sw = new Stopwatch();
+            sw.Start();
+            return sw;
+        }
+
+        /// <summary>
+        /// Creates an instance of the Stopwatch class.
+        /// </summary>
+        public Stopwatch() { }
+
+        /// <summary>
+        /// Completely resets and deactivates the timer.
+        /// </summary>
+        public void Reset()
+        {
+            _elapsed = 0;
+            _isRunning = false;
+            _startTick = 0;
+        }
+
+        /// <summary>
+        /// Begins the timer.
+        /// </summary>
+        public void Start()
+        {
+            if (!_isRunning)
+            {
+                _startTick = GetCurrentTicks();
+                _isRunning = true;
+            }
+        }
+
+        /// <summary>
+        /// Stops the current timer.
+        /// </summary>
+        public void Stop()
+        {
+            if (_isRunning)
+            {
+                _elapsed += GetCurrentTicks() - _startTick;
+                _isRunning = false;
+            }
+        }
+
+        /// <summary>
+        /// Gets a value indicating whether the instance is currently recording.
+        /// </summary>
+        public bool IsRunning
+        {
+            get { return _isRunning; }
+        }
+
+        /// <summary>
+        /// Gets the Elapsed time as a Timespan.
+        /// </summary>
+        public TimeSpan Elapsed
+        {
+            get { return TimeSpan.FromMilliseconds(ElapsedMilliseconds); }
+        }
+
+        /// <summary>
+        /// Gets the Elapsed time as the total number of milliseconds.
+        /// </summary>
+        public long ElapsedMilliseconds
+        {
+            get { return GetCurrentElapsedTicks() / TimeSpan.TicksPerMillisecond; }
+        }
+
+        /// <summary>
+        /// Gets the Elapsed time as the total number of ticks (which is faked
+        /// as Silverlight doesn't have a way to get at the actual "Ticks")
+        /// </summary>
+        public long ElapsedTicks
+        {
+            get { return GetCurrentElapsedTicks(); }
+        }
+
+        private long GetCurrentElapsedTicks()
+        {
+            return _elapsed + (IsRunning ? (GetCurrentTicks() - _startTick) : 0);
+        }
+
+        private long GetCurrentTicks()
+        {
+            // TickCount: Gets the number of milliseconds elapsed since the system started.
+            return Environment.TickCount * TimeSpan.TicksPerMillisecond;
+        }
+    }
+}
+#endif

Farseer Physics Engine 3.5/Common/TextureTools/MarchingSquares.cs

@@ -0,0 +1,800 @@
+using System.Collections.Generic;
+using FarseerPhysics.Collision;
+using Microsoft.Xna.Framework;
+
+namespace FarseerPhysics.Common.TextureTools
+{
+    // Ported by Matthew Bettcher - Feb 2011
+
+    /*
+    Copyright (c) 2010, Luca Deltodesco
+    All rights reserved.
+
+    Redistribution and use in source and binary forms, with or without modification, are permitted
+    provided that the following conditions are met:
+
+        * Redistributions of source code must retain the above copyright notice, this list of conditions
+	      and the following disclaimer.
+        * Redistributions in binary form must reproduce the above copyright notice, this list of
+	      conditions and the following disclaimer in the documentation and/or other materials provided
+	      with the distribution.
+        * Neither the name of the nape project nor the names of its contributors may be used to endorse
+	     or promote products derived from this software without specific prior written permission.
+
+    THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR
+    IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND
+    FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR
+    CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+    DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+    DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER
+    IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
+    OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+    */
+
+    public static class MarchingSquares
+    {
+        /// <summary>
+        /// Marching squares over the given domain using the mesh defined via the dimensions
+        ///    (wid,hei) to build a set of polygons such that f(x,y) less than 0, using the given number
+        ///    'bin' for recursive linear inteprolation along cell boundaries.
+        ///
+        ///    if 'comb' is true, then the polygons will also be composited into larger possible concave
+        ///    polygons.
+        /// </summary>
+        /// <param name="domain"></param>
+        /// <param name="cellWidth"></param>
+        /// <param name="cellHeight"></param>
+        /// <param name="f"></param>
+        /// <param name="lerpCount"></param>
+        /// <param name="combine"></param>
+        /// <returns></returns>
+        public static List<Vertices> DetectSquares(AABB domain, float cellWidth, float cellHeight, sbyte[,] f,
+                                                   int lerpCount, bool combine)
+        {
+            CxFastList<GeomPoly> ret = new CxFastList<GeomPoly>();
+
+            List<Vertices> verticesList = new List<Vertices>();
+
+            //NOTE: removed assignments as they were not used.
+            List<GeomPoly> polyList;
+            GeomPoly gp;
+
+            int xn = (int)(domain.Extents.X * 2 / cellWidth);
+            bool xp = xn == (domain.Extents.X * 2 / cellWidth);
+            int yn = (int)(domain.Extents.Y * 2 / cellHeight);
+            bool yp = yn == (domain.Extents.Y * 2 / cellHeight);
+            if (!xp) xn++;
+            if (!yp) yn++;
+
+            sbyte[,] fs = new sbyte[xn + 1, yn + 1];
+            GeomPolyVal[,] ps = new GeomPolyVal[xn + 1, yn + 1];
+
+            //populate shared function lookups.
+            for (int x = 0; x < xn + 1; x++)
+            {
+                int x0;
+                if (x == xn) x0 = (int)domain.UpperBound.X;
+                else x0 = (int)(x * cellWidth + domain.LowerBound.X);
+                for (int y = 0; y < yn + 1; y++)
+                {
+                    int y0;
+                    if (y == yn) y0 = (int)domain.UpperBound.Y;
+                    else y0 = (int)(y * cellHeight + domain.LowerBound.Y);
+                    fs[x, y] = f[x0, y0];
+                }
+            }
+
+            //generate sub-polys and combine to scan lines
+            for (int y = 0; y < yn; y++)
+            {
+                float y0 = y * cellHeight + domain.LowerBound.Y;
+                float y1;
+                if (y == yn - 1) y1 = domain.UpperBound.Y;
+                else y1 = y0 + cellHeight;
+                GeomPoly pre = null;
+                for (int x = 0; x < xn; x++)
+                {
+                    float x0 = x * cellWidth + domain.LowerBound.X;
+                    float x1;
+                    if (x == xn - 1) x1 = domain.UpperBound.X;
+                    else x1 = x0 + cellWidth;
+
+                    gp = new GeomPoly();
+
+                    int key = MarchSquare(f, fs, ref gp, x, y, x0, y0, x1, y1, lerpCount);
+                    if (gp.Length != 0)
+                    {
+                        if (combine && pre != null && (key & 9) != 0)
+                        {
+                            combLeft(ref pre, ref gp);
+                            gp = pre;
+                        }
+                        else
+                            ret.Add(gp);
+                        ps[x, y] = new GeomPolyVal(gp, key);
+                    }
+                    else
+                        gp = null;
+                    pre = gp;
+                }
+            }
+            if (!combine)
+            {
+                polyList = ret.GetListOfElements();
+
+                foreach (GeomPoly poly in polyList)
+                {
+                    verticesList.Add(new Vertices(poly.Points.GetListOfElements()));
+                }
+
+                return verticesList;
+            }
+
+            //combine scan lines together
+            for (int y = 1; y < yn; y++)
+            {
+                int x = 0;
+                while (x < xn)
+                {
+                    GeomPolyVal p = ps[x, y];
+
+                    //skip along scan line if no polygon exists at this point
+                    if (p == null)
+                    {
+                        x++;
+                        continue;
+                    }
+
+                    //skip along if current polygon cannot be combined above.
+                    if ((p.Key & 12) == 0)
+                    {
+                        x++;
+                        continue;
+                    }
+
+                    //skip along if no polygon exists above.
+                    GeomPolyVal u = ps[x, y - 1];
+                    if (u == null)
+                    {
+                        x++;
+                        continue;
+                    }
+
+                    //skip along if polygon above cannot be combined with.
+                    if ((u.Key & 3) == 0)
+                    {
+                        x++;
+                        continue;
+                    }
+
+                    float ax = x * cellWidth + domain.LowerBound.X;
+                    float ay = y * cellHeight + domain.LowerBound.Y;
+
+                    CxFastList<Vector2> bp = p.GeomP.Points;
+                    CxFastList<Vector2> ap = u.GeomP.Points;
+
+                    //skip if it's already been combined with above polygon
+                    if (u.GeomP == p.GeomP)
+                    {
+                        x++;
+                        continue;
+                    }
+
+                    //combine above (but disallow the hole thingies
+                    CxFastListNode<Vector2> bi = bp.Begin();
+                    while (Square(bi.Elem().Y - ay) > Settings.Epsilon || bi.Elem().X < ax) bi = bi.Next();
+
+                    //NOTE: Unused
+                    //Vector2 b0 = bi.elem();
+                    Vector2 b1 = bi.Next().Elem();
+                    if (Square(b1.Y - ay) > Settings.Epsilon)
+                    {
+                        x++;
+                        continue;
+                    }
+
+                    bool brk = true;
+                    CxFastListNode<Vector2> ai = ap.Begin();
+                    while (ai != ap.End())
+                    {
+                        if (VecDsq(ai.Elem(), b1) < Settings.Epsilon)
+                        {
+                            brk = false;
+                            break;
+                        }
+                        ai = ai.Next();
+                    }
+                    if (brk)
+                    {
+                        x++;
+                        continue;
+                    }
+
+                    CxFastListNode<Vector2> bj = bi.Next().Next();
+                    if (bj == bp.End()) bj = bp.Begin();
+                    while (bj != bi)
+                    {
+                        ai = ap.Insert(ai, bj.Elem()); // .clone()
+                        bj = bj.Next();
+                        if (bj == bp.End()) bj = bp.Begin();
+                        u.GeomP.Length++;
+                    }
+                    //u.p.simplify(float.Epsilon,float.Epsilon);
+                    //
+                    ax = x + 1;
+                    while (ax < xn)
+                    {
+                        GeomPolyVal p2 = ps[(int)ax, y];
+                        if (p2 == null || p2.GeomP != p.GeomP)
+                        {
+                            ax++;
+                            continue;
+                        }
+                        p2.GeomP = u.GeomP;
+                        ax++;
+                    }
+                    ax = x - 1;
+                    while (ax >= 0)
+                    {
+                        GeomPolyVal p2 = ps[(int)ax, y];
+                        if (p2 == null || p2.GeomP != p.GeomP)
+                        {
+                            ax--;
+                            continue;
+                        }
+                        p2.GeomP = u.GeomP;
+                        ax--;
+                    }
+                    ret.Remove(p.GeomP);
+                    p.GeomP = u.GeomP;
+
+                    x = (int)((bi.Next().Elem().X - domain.LowerBound.X) / cellWidth) + 1;
+                    //x++; this was already commented out!
+                }
+            }
+
+            polyList = ret.GetListOfElements();
+
+            foreach (GeomPoly poly in polyList)
+            {
+                verticesList.Add(new Vertices(poly.Points.GetListOfElements()));
+            }
+
+            return verticesList;
+        }
+
+        #region Private Methods
+
+        //- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
+
+        /** Linearly interpolate between (x0 to x1) given a value at these coordinates (v0 and v1)
+            such as to approximate value(return) = 0
+        **/
+
+        private static int[] _lookMarch = {
+                                              0x00, 0xE0, 0x38, 0xD8, 0x0E, 0xEE, 0x36, 0xD6, 0x83, 0x63, 0xBB, 0x5B, 0x8D,
+                                              0x6D, 0xB5, 0x55
+                                          };
+
+        private static float Lerp(float x0, float x1, float v0, float v1)
+        {
+            float dv = v0 - v1;
+            float t;
+            if (dv * dv < Settings.Epsilon)
+                t = 0.5f;
+            else t = v0 / dv;
+            return x0 + t * (x1 - x0);
+        }
+
+        //- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
+
+        /** Recursive linear interpolation for use in marching squares **/
+
+        private static float Xlerp(float x0, float x1, float y, float v0, float v1, sbyte[,] f, int c)
+        {
+            float xm = Lerp(x0, x1, v0, v1);
+            if (c == 0)
+                return xm;
+
+            sbyte vm = f[(int)xm, (int)y];
+
+            if (v0 * vm < 0)
+                return Xlerp(x0, xm, y, v0, vm, f, c - 1);
+
+            return Xlerp(xm, x1, y, vm, v1, f, c - 1);
+        }
+
+        /** Recursive linear interpolation for use in marching squares **/
+
+        private static float Ylerp(float y0, float y1, float x, float v0, float v1, sbyte[,] f, int c)
+        {
+            float ym = Lerp(y0, y1, v0, v1);
+            if (c == 0)
+                return ym;
+
+            sbyte vm = f[(int)x, (int)ym];
+
+            if (v0 * vm < 0)
+                return Ylerp(y0, ym, x, v0, vm, f, c - 1);
+
+            return Ylerp(ym, y1, x, vm, v1, f, c - 1);
+        }
+
+        /** Square value for use in marching squares **/
+
+        private static float Square(float x)
+        {
+            return x * x;
+        }
+
+        private static float VecDsq(Vector2 a, Vector2 b)
+        {
+            Vector2 d = a - b;
+            return d.X * d.X + d.Y * d.Y;
+        }
+
+        private static float VecCross(Vector2 a, Vector2 b)
+        {
+            return a.X * b.Y - a.Y * b.X;
+        }
+
+        /** Look-up table to relate polygon key with the vertices that should be used for
+            the sub polygon in marching squares
+        **/
+
+        /** Perform a single celled marching square for for the given cell defined by (x0,y0) (x1,y1)
+            using the function f for recursive interpolation, given the look-up table 'fs' of
+            the values of 'f' at cell vertices with the result to be stored in 'poly' given the actual
+            coordinates of 'ax' 'ay' in the marching squares mesh.
+        **/
+
+        private static int MarchSquare(sbyte[,] f, sbyte[,] fs, ref GeomPoly poly, int ax, int ay, float x0, float y0,
+                                       float x1, float y1, int bin)
+        {
+            //key lookup
+            int key = 0;
+            sbyte v0 = fs[ax, ay];
+            if (v0 < 0) key |= 8;
+            sbyte v1 = fs[ax + 1, ay];
+            if (v1 < 0) key |= 4;
+            sbyte v2 = fs[ax + 1, ay + 1];
+            if (v2 < 0) key |= 2;
+            sbyte v3 = fs[ax, ay + 1];
+            if (v3 < 0) key |= 1;
+
+            int val = _lookMarch[key];
+            if (val != 0)
+            {
+                CxFastListNode<Vector2> pi = null;
+                for (int i = 0; i < 8; i++)
+                {
+                    Vector2 p;
+                    if ((val & (1 << i)) != 0)
+                    {
+                        if (i == 7 && (val & 1) == 0)
+                            poly.Points.Add(p = new Vector2(x0, Ylerp(y0, y1, x0, v0, v3, f, bin)));
+                        else
+                        {
+                            if (i == 0) p = new Vector2(x0, y0);
+                            else if (i == 2) p = new Vector2(x1, y0);
+                            else if (i == 4) p = new Vector2(x1, y1);
+                            else if (i == 6) p = new Vector2(x0, y1);
+
+                            else if (i == 1) p = new Vector2(Xlerp(x0, x1, y0, v0, v1, f, bin), y0);
+                            else if (i == 5) p = new Vector2(Xlerp(x0, x1, y1, v3, v2, f, bin), y1);
+
+                            else if (i == 3) p = new Vector2(x1, Ylerp(y0, y1, x1, v1, v2, f, bin));
+                            else p = new Vector2(x0, Ylerp(y0, y1, x0, v0, v3, f, bin));
+
+                            pi = poly.Points.Insert(pi, p);
+                        }
+                        poly.Length++;
+                    }
+                }
+                //poly.simplify(float.Epsilon,float.Epsilon);
+            }
+            return key;
+        }
+
+        /** Used in polygon composition to composit polygons into scan lines
+            Combining polya and polyb into one super-polygon stored in polya.
+        **/
+
+        private static void combLeft(ref GeomPoly polya, ref GeomPoly polyb)
+        {
+            CxFastList<Vector2> ap = polya.Points;
+            CxFastList<Vector2> bp = polyb.Points;
+            CxFastListNode<Vector2> ai = ap.Begin();
+            CxFastListNode<Vector2> bi = bp.Begin();
+
+            Vector2 b = bi.Elem();
+            CxFastListNode<Vector2> prea = null;
+            while (ai != ap.End())
+            {
+                Vector2 a = ai.Elem();
+                if (VecDsq(a, b) < Settings.Epsilon)
+                {
+                    //ignore shared vertex if parallel
+                    if (prea != null)
+                    {
+                        Vector2 a0 = prea.Elem();
+                        b = bi.Next().Elem();
+
+                        Vector2 u = a - a0;
+                        //vec_new(u); vec_sub(a.p.p, a0.p.p, u);
+                        Vector2 v = b - a;
+                        //vec_new(v); vec_sub(b.p.p, a.p.p, v);
+                        float dot = VecCross(u, v);
+                        if (dot * dot < Settings.Epsilon)
+                        {
+                            ap.Erase(prea, ai);
+                            polya.Length--;
+                            ai = prea;
+                        }
+                    }
+
+                    //insert polyb into polya
+                    bool fst = true;
+                    CxFastListNode<Vector2> preb = null;
+                    while (!bp.Empty())
+                    {
+                        Vector2 bb = bp.Front();
+                        bp.Pop();
+                        if (!fst && !bp.Empty())
+                        {
+                            ai = ap.Insert(ai, bb);
+                            polya.Length++;
+                            preb = ai;
+                        }
+                        fst = false;
+                    }
+
+                    //ignore shared vertex if parallel
+                    ai = ai.Next();
+                    Vector2 a1 = ai.Elem();
+                    ai = ai.Next();
+                    if (ai == ap.End()) ai = ap.Begin();
+                    Vector2 a2 = ai.Elem();
+                    Vector2 a00 = preb.Elem();
+                    Vector2 uu = a1 - a00;
+                    //vec_new(u); vec_sub(a1.p, a0.p, u);
+                    Vector2 vv = a2 - a1;
+                    //vec_new(v); vec_sub(a2.p, a1.p, v);
+                    float dot1 = VecCross(uu, vv);
+                    if (dot1 * dot1 < Settings.Epsilon)
+                    {
+                        ap.Erase(preb, preb.Next());
+                        polya.Length--;
+                    }
+
+                    return;
+                }
+                prea = ai;
+                ai = ai.Next();
+            }
+        }
+
+        #endregion
+
+        #region CxFastList from nape physics
+
+        #region Nested type: CxFastList
+
+        /// <summary>
+        /// Designed as a complete port of CxFastList from CxStd.
+        /// </summary>
+        internal class CxFastList<T>
+        {
+            // first node in the list
+            private CxFastListNode<T> _head;
+            private int _count;
+
+            /// <summary>
+            /// Iterator to start of list (O(1))
+            /// </summary>
+            public CxFastListNode<T> Begin()
+            {
+                return _head;
+            }
+
+            /// <summary>
+            /// Iterator to end of list (O(1))
+            /// </summary>
+            public CxFastListNode<T> End()
+            {
+                return null;
+            }
+
+            /// <summary>
+            /// Returns first element of list (O(1))
+            /// </summary>
+            public T Front()
+            {
+                return _head.Elem();
+            }
+
+            /// <summary>
+            /// add object to list (O(1))
+            /// </summary>
+            public CxFastListNode<T> Add(T value)
+            {
+                CxFastListNode<T> newNode = new CxFastListNode<T>(value);
+                if (_head == null)
+                {
+                    newNode._next = null;
+                    _head = newNode;
+                    _count++;
+                    return newNode;
+                }
+                newNode._next = _head;
+                _head = newNode;
+
+                _count++;
+
+                return newNode;
+            }
+
+            /// <summary>
+            /// remove object from list, returns true if an element was removed (O(n))
+            /// </summary>
+            public bool Remove(T value)
+            {
+                CxFastListNode<T> head = _head;
+                CxFastListNode<T> prev = _head;
+
+                EqualityComparer<T> comparer = EqualityComparer<T>.Default;
+
+                if (head != null)
+                {
+                    if (value != null)
+                    {
+                        do
+                        {
+                            // if we are on the value to be removed
+                            if (comparer.Equals(head._elt, value))
+                            {
+                                // then we need to patch the list
+                                // check to see if we are removing the _head
+                                if (head == _head)
+                                {
+                                    _head = head._next;
+                                    _count--;
+                                    return true;
+                                }
+                                else
+                                {
+                                    // were not at the head
+                                    prev._next = head._next;
+                                    _count--;
+                                    return true;
+                                }
+                            }
+                            // cache the current as the previous for the next go around
+                            prev = head;
+                            head = head._next;
+                        } while (head != null);
+                    }
+                }
+                return false;
+            }
+
+            /// <summary>
+            /// pop element from head of list (O(1)) Note: this does not return the object popped! 
+            /// There is good reason to this, and it regards the Alloc list variants which guarantee 
+            /// objects are released to the object pool. You do not want to retrieve an element 
+            /// through pop or else that object may suddenly be used by another piece of code which 
+            /// retrieves it from the object pool.
+            /// </summary>
+            public CxFastListNode<T> Pop()
+            {
+                return Erase(null, _head);
+            }
+
+            /// <summary>
+            /// insert object after 'node' returning an iterator to the inserted object.
+            /// </summary>
+            public CxFastListNode<T> Insert(CxFastListNode<T> node, T value)
+            {
+                if (node == null)
+                {
+                    return Add(value);
+                }
+                CxFastListNode<T> newNode = new CxFastListNode<T>(value);
+                CxFastListNode<T> nextNode = node._next;
+                newNode._next = nextNode;
+                node._next = newNode;
+
+                _count++;
+
+                return newNode;
+            }
+
+            /// <summary>
+            /// removes the element pointed to by 'node' with 'prev' being the previous iterator, 
+            /// returning an iterator to the element following that of 'node' (O(1))
+            /// </summary>
+            public CxFastListNode<T> Erase(CxFastListNode<T> prev, CxFastListNode<T> node)
+            {
+                // cache the node after the node to be removed
+                CxFastListNode<T> nextNode = node._next;
+                if (prev != null)
+                    prev._next = nextNode;
+                else if (_head != null)
+                    _head = _head._next;
+                else
+                    return null;
+
+                _count--;
+                return nextNode;
+            }
+
+            /// <summary>
+            /// whether the list is empty (O(1))
+            /// </summary>
+            public bool Empty()
+            {
+                if (_head == null)
+                    return true;
+                return false;
+            }
+
+            /// <summary>
+            /// computes size of list (O(n))
+            /// </summary>
+            public int Size()
+            {
+                CxFastListNode<T> i = Begin();
+                int count = 0;
+
+                do
+                {
+                    count++;
+                } while (i.Next() != null);
+
+                return count;
+            }
+
+            /// <summary>
+            /// empty the list (O(1) if CxMixList, O(n) otherwise)
+            /// </summary>
+            public void Clear()
+            {
+                CxFastListNode<T> head = _head;
+                while (head != null)
+                {
+                    CxFastListNode<T> node2 = head;
+                    head = head._next;
+                    node2._next = null;
+                }
+                _head = null;
+                _count = 0;
+            }
+
+            /// <summary>
+            /// returns true if 'value' is an element of the list (O(n))
+            /// </summary>
+            public bool Has(T value)
+            {
+                return (Find(value) != null);
+            }
+
+            // Non CxFastList Methods 
+            public CxFastListNode<T> Find(T value)
+            {
+                // start at head
+                CxFastListNode<T> head = _head;
+                EqualityComparer<T> comparer = EqualityComparer<T>.Default;
+                if (head != null)
+                {
+                    if (value != null)
+                    {
+                        do
+                        {
+                            if (comparer.Equals(head._elt, value))
+                            {
+                                return head;
+                            }
+                            head = head._next;
+                        } while (head != _head);
+                    }
+                    else
+                    {
+                        do
+                        {
+                            if (head._elt == null)
+                            {
+                                return head;
+                            }
+                            head = head._next;
+                        } while (head != _head);
+                    }
+                }
+                return null;
+            }
+
+            public List<T> GetListOfElements()
+            {
+                List<T> list = new List<T>();
+
+                CxFastListNode<T> iter = Begin();
+
+                if (iter != null)
+                {
+                    do
+                    {
+                        list.Add(iter._elt);
+                        iter = iter._next;
+                    } while (iter != null);
+                }
+                return list;
+            }
+        }
+
+        #endregion
+
+        #region Nested type: CxFastListNode
+
+        internal class CxFastListNode<T>
+        {
+            internal T _elt;
+            internal CxFastListNode<T> _next;
+
+            public CxFastListNode(T obj)
+            {
+                _elt = obj;
+            }
+
+            public T Elem()
+            {
+                return _elt;
+            }
+
+            public CxFastListNode<T> Next()
+            {
+                return _next;
+            }
+        }
+
+        #endregion
+
+        #endregion
+
+        #region Internal Stuff
+
+        #region Nested type: GeomPoly
+
+        internal class GeomPoly
+        {
+            public int Length;
+            public CxFastList<Vector2> Points;
+
+            public GeomPoly()
+            {
+                Points = new CxFastList<Vector2>();
+                Length = 0;
+            }
+        }
+
+        #endregion
+
+        #region Nested type: GeomPolyVal
+
+        private class GeomPolyVal
+        {
+            /** Associated polygon at coordinate **/
+            /** Key of original sub-polygon **/
+            public int Key;
+            public GeomPoly GeomP;
+
+            public GeomPolyVal(GeomPoly geomP, int K)
+            {
+                GeomP = geomP;
+                Key = K;
+            }
+        }
+
+        #endregion
+
+        #endregion
+    }
+}

Farseer Physics Engine 3.5/Common/TextureTools/Terrain.cs

@@ -0,0 +1,264 @@
+using System.Collections.Generic;
+using FarseerPhysics.Collision;
+using FarseerPhysics.Common.Decomposition;
+using FarseerPhysics.Common.PolygonManipulation;
+using FarseerPhysics.Dynamics;
+using FarseerPhysics.Factories;
+using Microsoft.Xna.Framework;
+
+namespace FarseerPhysics.Common.TextureTools
+{
+    /// <summary>
+    /// Simple class to maintain a terrain. It can keep track
+    /// </summary>
+    public class Terrain
+    {
+        /// <summary>
+        /// World to manage terrain in.
+        /// </summary>
+        public World World;
+
+        /// <summary>
+        /// Center of terrain in world units.
+        /// </summary>
+        public Vector2 Center;
+
+        /// <summary>
+        /// Width of terrain in world units.
+        /// </summary>
+        public float Width;
+
+        /// <summary>
+        /// Height of terrain in world units.
+        /// </summary>
+        public float Height;
+
+        /// <summary>
+        /// Points per each world unit used to define the terrain in the point cloud.
+        /// </summary>
+        public int PointsPerUnit;
+
+        /// <summary>
+        /// Points per cell.
+        /// </summary>
+        public int CellSize;
+
+        /// <summary>
+        /// Points per sub cell.
+        /// </summary>
+        public int SubCellSize;
+
+        /// <summary>
+        /// Number of iterations to perform in the Marching Squares algorithm.
+        /// Note: More then 3 has almost no effect on quality.
+        /// </summary>
+        public int Iterations = 2;
+
+        /// <summary>
+        /// Decomposer to use when regenerating terrain. Can be changed on the fly without consequence.
+        /// Note: Some decomposerers are unstable.
+        /// </summary>
+        public TriangulationAlgorithm Decomposer;
+
+        /// <summary>
+        /// Point cloud defining the terrain.
+        /// </summary>
+        private sbyte[,] _terrainMap;
+
+        /// <summary>
+        /// Generated bodies.
+        /// </summary>
+        private List<Body>[,] _bodyMap;
+
+        private float _localWidth;
+        private float _localHeight;
+        private int _xnum;
+        private int _ynum;
+        private AABB _dirtyArea;
+        private Vector2 _topLeft;
+
+        /// <summary>
+        /// Creates a new terrain.
+        /// </summary>
+        /// <param name="world">The World</param>
+        /// <param name="area">The area of the terrain.</param>
+        public Terrain(World world, AABB area)
+        {
+            World = world;
+            Width = area.Width;
+            Height = area.Height;
+            Center = area.Center;
+        }
+
+        /// <summary>
+        /// Creates a new terrain
+        /// </summary>
+        /// <param name="world">The World</param>
+        /// <param name="position">The position (center) of the terrain.</param>
+        /// <param name="width">The width of the terrain.</param>
+        /// <param name="height">The height of the terrain.</param>
+        public Terrain(World world, Vector2 position, float width, float height)
+        {
+            World = world;
+            Width = width;
+            Height = height;
+            Center = position;
+        }
+
+        /// <summary>
+        /// Initialize the terrain for use.
+        /// </summary>
+        public void Initialize()
+        {
+            // find top left of terrain in world space
+            _topLeft = new Vector2(Center.X - (Width * 0.5f), Center.Y - (-Height * 0.5f));
+
+            // convert the terrains size to a point cloud size
+            _localWidth = Width * PointsPerUnit;
+            _localHeight = Height * PointsPerUnit;
+
+            _terrainMap = new sbyte[(int)_localWidth + 1, (int)_localHeight + 1];
+
+            for (int x = 0; x < _localWidth; x++)
+            {
+                for (int y = 0; y < _localHeight; y++)
+                {
+                    _terrainMap[x, y] = 1;
+                }
+            }
+
+            _xnum = (int)(_localWidth / CellSize);
+            _ynum = (int)(_localHeight / CellSize);
+            _bodyMap = new List<Body>[_xnum, _ynum];
+
+            // make sure to mark the dirty area to an infinitely small box
+            _dirtyArea = new AABB(new Vector2(float.MaxValue, float.MaxValue), new Vector2(float.MinValue, float.MinValue));
+        }
+
+        /// <summary>
+        /// Apply the specified texture data to the terrain.
+        /// </summary>
+        /// <param name="data"></param>
+        /// <param name="offset"></param>
+        public void ApplyData(sbyte[,] data, Vector2 offset = default(Vector2))
+        {
+            for (int x = 0; x < data.GetUpperBound(0); x++)
+            {
+                for (int y = 0; y < data.GetUpperBound(1); y++)
+                {
+                    if (x + offset.X >= 0 && x + offset.X < _localWidth && y + offset.Y >= 0 && y + offset.Y < _localHeight)
+                    {
+                        _terrainMap[(int)(x + offset.X), (int)(y + offset.Y)] = data[x, y];
+                    }
+                }
+            }
+
+            RemoveOldData(0, _xnum, 0, _ynum);
+        }
+
+        /// <summary>
+        /// Modify a single point in the terrain.
+        /// </summary>
+        /// <param name="location">World location to modify. Automatically clipped.</param>
+        /// <param name="value">-1 = inside terrain, 1 = outside terrain</param>
+        public void ModifyTerrain(Vector2 location, sbyte value)
+        {
+            // find local position
+            // make position local to map space
+            Vector2 p = location - _topLeft;
+
+            // find map position for each axis
+            p.X = p.X * _localWidth / Width;
+            p.Y = p.Y * -_localHeight / Height;
+
+            if (p.X >= 0 && p.X < _localWidth && p.Y >= 0 && p.Y < _localHeight)
+            {
+                _terrainMap[(int)p.X, (int)p.Y] = value;
+
+                // expand dirty area
+                if (p.X < _dirtyArea.LowerBound.X) _dirtyArea.LowerBound.X = p.X;
+                if (p.X > _dirtyArea.UpperBound.X) _dirtyArea.UpperBound.X = p.X;
+
+                if (p.Y < _dirtyArea.LowerBound.Y) _dirtyArea.LowerBound.Y = p.Y;
+                if (p.Y > _dirtyArea.UpperBound.Y) _dirtyArea.UpperBound.Y = p.Y;
+            }
+        }
+
+        /// <summary>
+        /// Regenerate the terrain.
+        /// </summary>
+        public void RegenerateTerrain()
+        {
+            //iterate effected cells
+            int xStart = (int)(_dirtyArea.LowerBound.X / CellSize);
+            if (xStart < 0) xStart = 0;
+
+            int xEnd = (int)(_dirtyArea.UpperBound.X / CellSize) + 1;
+            if (xEnd > _xnum) xEnd = _xnum;
+
+            int yStart = (int)(_dirtyArea.LowerBound.Y / CellSize);
+            if (yStart < 0) yStart = 0;
+
+            int yEnd = (int)(_dirtyArea.UpperBound.Y / CellSize) + 1;
+            if (yEnd > _ynum) yEnd = _ynum;
+
+            RemoveOldData(xStart, xEnd, yStart, yEnd);
+
+            _dirtyArea = new AABB(new Vector2(float.MaxValue, float.MaxValue), new Vector2(float.MinValue, float.MinValue));
+        }
+
+        private void RemoveOldData(int xStart, int xEnd, int yStart, int yEnd)
+        {
+            for (int x = xStart; x < xEnd; x++)
+            {
+                for (int y = yStart; y < yEnd; y++)
+                {
+                    //remove old terrain object at grid cell
+                    if (_bodyMap[x, y] != null)
+                    {
+                        for (int i = 0; i < _bodyMap[x, y].Count; i++)
+                        {
+                            World.RemoveBody(_bodyMap[x, y][i]);
+                        }
+                    }
+
+                    _bodyMap[x, y] = null;
+
+                    //generate new one
+                    GenerateTerrain(x, y);
+                }
+            }
+        }
+
+        private void GenerateTerrain(int gx, int gy)
+        {
+            float ax = gx * CellSize;
+            float ay = gy * CellSize;
+
+            List<Vertices> polys = MarchingSquares.DetectSquares(new AABB(new Vector2(ax, ay), new Vector2(ax + CellSize, ay + CellSize)), SubCellSize, SubCellSize, _terrainMap, Iterations, true);
+            if (polys.Count == 0) return;
+
+            _bodyMap[gx, gy] = new List<Body>();
+
+            // create the scale vector
+            Vector2 scale = new Vector2(1f / PointsPerUnit, 1f / -PointsPerUnit);
+
+            // create physics object for this grid cell
+            foreach (Vertices item in polys)
+            {
+                // does this need to be negative?
+                item.Scale(ref scale);
+                item.Translate(ref _topLeft);
+                Vertices simplified = SimplifyTools.CollinearSimplify(item);
+
+                List<Vertices> decompPolys = Triangulate.ConvexPartition(simplified, Decomposer);
+
+                foreach (Vertices poly in decompPolys)
+                {
+                    if (poly.Count > 2)
+                        _bodyMap[gx, gy].Add(BodyFactory.CreatePolygon(World, poly, 1));
+                }
+            }
+        }
+    }
+}

Farseer Physics Engine 3.5/Common/Vector2.cs

@@ -0,0 +1,588 @@
+#if !XNA && !WINDOWS_PHONE && !XBOX && !ANDROID
+
+#region License
+
+/*
+MIT License
+Copyright © 2006 The Mono.Xna Team
+
+All rights reserved.
+
+Authors
+ * Alan McGovern
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
+*/
+
+#endregion License
+
+using System;
+using System.Runtime.InteropServices;
+using System.Text;
+
+namespace Microsoft.Xna.Framework
+{
+    [StructLayout(LayoutKind.Sequential)]
+    public struct Vector2 : IEquatable<Vector2>
+    {
+#region Private Fields
+
+        private static Vector2 zeroVector = new Vector2(0f, 0f);
+        private static Vector2 unitVector = new Vector2(1f, 1f);
+        private static Vector2 unitXVector = new Vector2(1f, 0f);
+        private static Vector2 unitYVector = new Vector2(0f, 1f);
+
+        #endregion Private Fields
+
+#region Public Fields
+
+        public float X;
+        public float Y;
+
+        #endregion Public Fields
+
+#region Properties
+
+        public static Vector2 Zero
+        {
+            get { return zeroVector; }
+        }
+
+        public static Vector2 One
+        {
+            get { return unitVector; }
+        }
+
+        public static Vector2 UnitX
+        {
+            get { return unitXVector; }
+        }
+
+        public static Vector2 UnitY
+        {
+            get { return unitYVector; }
+        }
+
+        #endregion Properties
+
+#region Constructors
+
+        /// <summary>
+        /// Constructor foe standard 2D vector.
+        /// </summary>
+        /// <param name="x">
+        /// A <see cref="System.Single"/>
+        /// </param>
+        /// <param name="y">
+        /// A <see cref="System.Single"/>
+        /// </param>
+        public Vector2(float x, float y)
+        {
+            X = x;
+            Y = y;
+        }
+
+        /// <summary>
+        /// Constructor for "square" vector.
+        /// </summary>
+        /// <param name="value">
+        /// A <see cref="System.Single"/>
+        /// </param>
+        public Vector2(float value)
+        {
+            X = value;
+            Y = value;
+        }
+
+        #endregion Constructors
+
+#region Public Methods
+
+        public static void Reflect(ref Vector2 vector, ref Vector2 normal, out Vector2 result)
+        {
+            float dot = Dot(vector, normal);
+            result.X = vector.X - ((2f*dot)*normal.X);
+            result.Y = vector.Y - ((2f*dot)*normal.Y);
+        }
+
+        public static Vector2 Reflect(Vector2 vector, Vector2 normal)
+        {
+            Vector2 result;
+            Reflect(ref vector, ref normal, out result);
+            return result;
+        }
+
+        public static Vector2 Add(Vector2 value1, Vector2 value2)
+        {
+            value1.X += value2.X;
+            value1.Y += value2.Y;
+            return value1;
+        }
+
+        public static void Add(ref Vector2 value1, ref Vector2 value2, out Vector2 result)
+        {
+            result.X = value1.X + value2.X;
+            result.Y = value1.Y + value2.Y;
+        }
+
+        public static Vector2 Barycentric(Vector2 value1, Vector2 value2, Vector2 value3, float amount1, float amount2)
+        {
+            return new Vector2(
+                MathHelper.Barycentric(value1.X, value2.X, value3.X, amount1, amount2),
+                MathHelper.Barycentric(value1.Y, value2.Y, value3.Y, amount1, amount2));
+        }
+
+        public static void Barycentric(ref Vector2 value1, ref Vector2 value2, ref Vector2 value3, float amount1,
+                                       float amount2, out Vector2 result)
+        {
+            result = new Vector2(
+                MathHelper.Barycentric(value1.X, value2.X, value3.X, amount1, amount2),
+                MathHelper.Barycentric(value1.Y, value2.Y, value3.Y, amount1, amount2));
+        }
+
+        public static Vector2 CatmullRom(Vector2 value1, Vector2 value2, Vector2 value3, Vector2 value4, float amount)
+        {
+            return new Vector2(
+                MathHelper.CatmullRom(value1.X, value2.X, value3.X, value4.X, amount),
+                MathHelper.CatmullRom(value1.Y, value2.Y, value3.Y, value4.Y, amount));
+        }
+
+        public static void CatmullRom(ref Vector2 value1, ref Vector2 value2, ref Vector2 value3, ref Vector2 value4,
+                                      float amount, out Vector2 result)
+        {
+            result = new Vector2(
+                MathHelper.CatmullRom(value1.X, value2.X, value3.X, value4.X, amount),
+                MathHelper.CatmullRom(value1.Y, value2.Y, value3.Y, value4.Y, amount));
+        }
+
+        public static Vector2 Clamp(Vector2 value1, Vector2 min, Vector2 max)
+        {
+            return new Vector2(
+                MathHelper.Clamp(value1.X, min.X, max.X),
+                MathHelper.Clamp(value1.Y, min.Y, max.Y));
+        }
+
+        public static void Clamp(ref Vector2 value1, ref Vector2 min, ref Vector2 max, out Vector2 result)
+        {
+            result = new Vector2(
+                MathHelper.Clamp(value1.X, min.X, max.X),
+                MathHelper.Clamp(value1.Y, min.Y, max.Y));
+        }
+
+        /// <summary>
+        /// Returns float precison distanve between two vectors
+        /// </summary>
+        /// <param name="value1">
+        /// A <see cref="Vector2"/>
+        /// </param>
+        /// <param name="value2">
+        /// A <see cref="Vector2"/>
+        /// </param>
+        /// <returns>
+        /// A <see cref="System.Single"/>
+        /// </returns>
+        public static float Distance(Vector2 value1, Vector2 value2)
+        {
+            float result;
+            DistanceSquared(ref value1, ref value2, out result);
+            return (float) Math.Sqrt(result);
+        }
+
+
+        public static void Distance(ref Vector2 value1, ref Vector2 value2, out float result)
+        {
+            DistanceSquared(ref value1, ref value2, out result);
+            result = (float) Math.Sqrt(result);
+        }
+
+        public static float DistanceSquared(Vector2 value1, Vector2 value2)
+        {
+            float result;
+            DistanceSquared(ref value1, ref value2, out result);
+            return result;
+        }
+
+        public static void DistanceSquared(ref Vector2 value1, ref Vector2 value2, out float result)
+        {
+            result = (value1.X - value2.X)*(value1.X - value2.X) + (value1.Y - value2.Y)*(value1.Y - value2.Y);
+        }
+
+        /// <summary>
+        /// Devide first vector with the secund vector
+        /// </summary>
+        /// <param name="value1">
+        /// A <see cref="Vector2"/>
+        /// </param>
+        /// <param name="value2">
+        /// A <see cref="Vector2"/>
+        /// </param>
+        /// <returns>
+        /// A <see cref="Vector2"/>
+        /// </returns>
+        public static Vector2 Divide(Vector2 value1, Vector2 value2)
+        {
+            value1.X /= value2.X;
+            value1.Y /= value2.Y;
+            return value1;
+        }
+
+        public static void Divide(ref Vector2 value1, ref Vector2 value2, out Vector2 result)
+        {
+            result.X = value1.X/value2.X;
+            result.Y = value1.Y/value2.Y;
+        }
+
+        public static Vector2 Divide(Vector2 value1, float divider)
+        {
+            float factor = 1/divider;
+            value1.X *= factor;
+            value1.Y *= factor;
+            return value1;
+        }
+
+        public static void Divide(ref Vector2 value1, float divider, out Vector2 result)
+        {
+            float factor = 1/divider;
+            result.X = value1.X*factor;
+            result.Y = value1.Y*factor;
+        }
+
+        public static float Dot(Vector2 value1, Vector2 value2)
+        {
+            return value1.X*value2.X + value1.Y*value2.Y;
+        }
+
+        public static void Dot(ref Vector2 value1, ref Vector2 value2, out float result)
+        {
+            result = value1.X*value2.X + value1.Y*value2.Y;
+        }
+
+        public override bool Equals(object obj)
+        {
+            return (obj is Vector2) ? this == ((Vector2) obj) : false;
+        }
+
+        public bool Equals(Vector2 other)
+        {
+            return this == other;
+        }
+
+        public override int GetHashCode()
+        {
+            return (int) (X + Y);
+        }
+
+        public static Vector2 Hermite(Vector2 value1, Vector2 tangent1, Vector2 value2, Vector2 tangent2, float amount)
+        {
+            Vector2 result = new Vector2();
+            Hermite(ref value1, ref tangent1, ref value2, ref tangent2, amount, out result);
+            return result;
+        }
+
+        public static void Hermite(ref Vector2 value1, ref Vector2 tangent1, ref Vector2 value2, ref Vector2 tangent2,
+                                   float amount, out Vector2 result)
+        {
+            result.X = MathHelper.Hermite(value1.X, tangent1.X, value2.X, tangent2.X, amount);
+            result.Y = MathHelper.Hermite(value1.Y, tangent1.Y, value2.Y, tangent2.Y, amount);
+        }
+
+        public float Length()
+        {
+            float result;
+            DistanceSquared(ref this, ref zeroVector, out result);
+            return (float) Math.Sqrt(result);
+        }
+
+        public float LengthSquared()
+        {
+            float result;
+            DistanceSquared(ref this, ref zeroVector, out result);
+            return result;
+        }
+
+        public static Vector2 Lerp(Vector2 value1, Vector2 value2, float amount)
+        {
+            return new Vector2(
+                MathHelper.Lerp(value1.X, value2.X, amount),
+                MathHelper.Lerp(value1.Y, value2.Y, amount));
+        }
+
+        public static void Lerp(ref Vector2 value1, ref Vector2 value2, float amount, out Vector2 result)
+        {
+            result = new Vector2(
+                MathHelper.Lerp(value1.X, value2.X, amount),
+                MathHelper.Lerp(value1.Y, value2.Y, amount));
+        }
+
+        public static Vector2 Max(Vector2 value1, Vector2 value2)
+        {
+            return new Vector2(
+                MathHelper.Max(value1.X, value2.X),
+                MathHelper.Max(value1.Y, value2.Y));
+        }
+
+        public static void Max(ref Vector2 value1, ref Vector2 value2, out Vector2 result)
+        {
+            result = new Vector2(
+                MathHelper.Max(value1.X, value2.X),
+                MathHelper.Max(value1.Y, value2.Y));
+        }
+
+        public static Vector2 Min(Vector2 value1, Vector2 value2)
+        {
+            return new Vector2(
+                MathHelper.Min(value1.X, value2.X),
+                MathHelper.Min(value1.Y, value2.Y));
+        }
+
+        public static void Min(ref Vector2 value1, ref Vector2 value2, out Vector2 result)
+        {
+            result = new Vector2(
+                MathHelper.Min(value1.X, value2.X),
+                MathHelper.Min(value1.Y, value2.Y));
+        }
+
+        public static Vector2 Multiply(Vector2 value1, Vector2 value2)
+        {
+            value1.X *= value2.X;
+            value1.Y *= value2.Y;
+            return value1;
+        }
+
+        public static Vector2 Multiply(Vector2 value1, float scaleFactor)
+        {
+            value1.X *= scaleFactor;
+            value1.Y *= scaleFactor;
+            return value1;
+        }
+
+        public static void Multiply(ref Vector2 value1, float scaleFactor, out Vector2 result)
+        {
+            result.X = value1.X*scaleFactor;
+            result.Y = value1.Y*scaleFactor;
+        }
+
+        public static void Multiply(ref Vector2 value1, ref Vector2 value2, out Vector2 result)
+        {
+            result.X = value1.X*value2.X;
+            result.Y = value1.Y*value2.Y;
+        }
+
+        public static Vector2 Negate(Vector2 value)
+        {
+            value.X = -value.X;
+            value.Y = -value.Y;
+            return value;
+        }
+
+        public static void Negate(ref Vector2 value, out Vector2 result)
+        {
+            result.X = -value.X;
+            result.Y = -value.Y;
+        }
+
+        public void Normalize()
+        {
+            Normalize(ref this, out this);
+        }
+
+        public static Vector2 Normalize(Vector2 value)
+        {
+            Normalize(ref value, out value);
+            return value;
+        }
+
+        public static void Normalize(ref Vector2 value, out Vector2 result)
+        {
+            float factor;
+            DistanceSquared(ref value, ref zeroVector, out factor);
+            factor = 1f/(float) Math.Sqrt(factor);
+            result.X = value.X*factor;
+            result.Y = value.Y*factor;
+        }
+
+        public static Vector2 SmoothStep(Vector2 value1, Vector2 value2, float amount)
+        {
+            return new Vector2(
+                MathHelper.SmoothStep(value1.X, value2.X, amount),
+                MathHelper.SmoothStep(value1.Y, value2.Y, amount));
+        }
+
+        public static void SmoothStep(ref Vector2 value1, ref Vector2 value2, float amount, out Vector2 result)
+        {
+            result = new Vector2(
+                MathHelper.SmoothStep(value1.X, value2.X, amount),
+                MathHelper.SmoothStep(value1.Y, value2.Y, amount));
+        }
+
+        public static Vector2 Subtract(Vector2 value1, Vector2 value2)
+        {
+            value1.X -= value2.X;
+            value1.Y -= value2.Y;
+            return value1;
+        }
+
+        public static void Subtract(ref Vector2 value1, ref Vector2 value2, out Vector2 result)
+        {
+            result.X = value1.X - value2.X;
+            result.Y = value1.Y - value2.Y;
+        }
+
+        public static Vector2 Transform(Vector2 position, Matrix matrix)
+        {
+            Transform(ref position, ref matrix, out position);
+            return position;
+        }
+
+        public static void Transform(ref Vector2 position, ref Matrix matrix, out Vector2 result)
+        {
+            result = new Vector2((position.X*matrix.M11) + (position.Y*matrix.M21) + matrix.M41,
+                                 (position.X*matrix.M12) + (position.Y*matrix.M22) + matrix.M42);
+        }
+
+        public static void Transform(Vector2[] sourceArray, ref Matrix matrix, Vector2[] destinationArray)
+        {
+            throw new NotImplementedException();
+        }
+
+        public static void Transform(Vector2[] sourceArray, int sourceIndex, ref Matrix matrix,
+                                     Vector2[] destinationArray, int destinationIndex, int length)
+        {
+            throw new NotImplementedException();
+        }
+
+        public static Vector2 TransformNormal(Vector2 normal, Matrix matrix)
+        {
+            TransformNormal(ref normal, ref matrix, out normal);
+            return normal;
+        }
+
+        public static void TransformNormal(ref Vector2 normal, ref Matrix matrix, out Vector2 result)
+        {
+            result = new Vector2((normal.X*matrix.M11) + (normal.Y*matrix.M21),
+                                 (normal.X*matrix.M12) + (normal.Y*matrix.M22));
+        }
+
+        public static void TransformNormal(Vector2[] sourceArray, ref Matrix matrix, Vector2[] destinationArray)
+        {
+            throw new NotImplementedException();
+        }
+
+        public static void TransformNormal(Vector2[] sourceArray, int sourceIndex, ref Matrix matrix,
+                                           Vector2[] destinationArray, int destinationIndex, int length)
+        {
+            throw new NotImplementedException();
+        }
+
+        public override string ToString()
+        {
+            StringBuilder sb = new StringBuilder(24);
+            sb.Append("{X:");
+            sb.Append(X);
+            sb.Append(" Y:");
+            sb.Append(Y);
+            sb.Append("}");
+            return sb.ToString();
+        }
+
+        #endregion Public Methods
+
+#region Operators
+
+        public static Vector2 operator -(Vector2 value)
+        {
+            value.X = -value.X;
+            value.Y = -value.Y;
+            return value;
+        }
+
+
+        public static bool operator ==(Vector2 value1, Vector2 value2)
+        {
+            return value1.X == value2.X && value1.Y == value2.Y;
+        }
+
+
+        public static bool operator !=(Vector2 value1, Vector2 value2)
+        {
+            return value1.X != value2.X || value1.Y != value2.Y;
+        }
+
+
+        public static Vector2 operator +(Vector2 value1, Vector2 value2)
+        {
+            value1.X += value2.X;
+            value1.Y += value2.Y;
+            return value1;
+        }
+
+
+        public static Vector2 operator -(Vector2 value1, Vector2 value2)
+        {
+            value1.X -= value2.X;
+            value1.Y -= value2.Y;
+            return value1;
+        }
+
+
+        public static Vector2 operator *(Vector2 value1, Vector2 value2)
+        {
+            value1.X *= value2.X;
+            value1.Y *= value2.Y;
+            return value1;
+        }
+
+
+        public static Vector2 operator *(Vector2 value, float scaleFactor)
+        {
+            value.X *= scaleFactor;
+            value.Y *= scaleFactor;
+            return value;
+        }
+
+
+        public static Vector2 operator *(float scaleFactor, Vector2 value)
+        {
+            value.X *= scaleFactor;
+            value.Y *= scaleFactor;
+            return value;
+        }
+
+
+        public static Vector2 operator /(Vector2 value1, Vector2 value2)
+        {
+            value1.X /= value2.X;
+            value1.Y /= value2.Y;
+            return value1;
+        }
+
+
+        public static Vector2 operator /(Vector2 value1, float divider)
+        {
+            float factor = 1/divider;
+            value1.X *= factor;
+            value1.Y *= factor;
+            return value1;
+        }
+
+        #endregion Operators
+    }
+}
+
+#endif

Farseer Physics Engine 3.5/Common/Vector3.cs

@@ -0,0 +1,648 @@
+#if !XNA && !WINDOWS_PHONE && !XBOX && !ANDROID
+
+#region License
+
+/*
+MIT License
+Copyright © 2006 The Mono.Xna Team
+
+All rights reserved.
+
+Authors:
+ * Alan McGovern
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
+*/
+
+#endregion License
+
+using System;
+using System.Runtime.InteropServices;
+using System.Text;
+
+namespace Microsoft.Xna.Framework
+{
+    [StructLayout(LayoutKind.Sequential)]
+    public struct Vector3 : IEquatable<Vector3>
+    {
+#region Private Fields
+
+        private static Vector3 zero = new Vector3(0f, 0f, 0f);
+        private static Vector3 one = new Vector3(1f, 1f, 1f);
+        private static Vector3 unitX = new Vector3(1f, 0f, 0f);
+        private static Vector3 unitY = new Vector3(0f, 1f, 0f);
+        private static Vector3 unitZ = new Vector3(0f, 0f, 1f);
+        private static Vector3 up = new Vector3(0f, 1f, 0f);
+        private static Vector3 down = new Vector3(0f, -1f, 0f);
+        private static Vector3 right = new Vector3(1f, 0f, 0f);
+        private static Vector3 left = new Vector3(-1f, 0f, 0f);
+        private static Vector3 forward = new Vector3(0f, 0f, -1f);
+        private static Vector3 backward = new Vector3(0f, 0f, 1f);
+
+#endregion Private Fields
+
+#region Public Fields
+
+        public float X;
+        public float Y;
+        public float Z;
+
+#endregion Public Fields
+
+#region Properties
+
+        public static Vector3 Zero
+        {
+            get { return zero; }
+        }
+
+        public static Vector3 One
+        {
+            get { return one; }
+        }
+
+        public static Vector3 UnitX
+        {
+            get { return unitX; }
+        }
+
+        public static Vector3 UnitY
+        {
+            get { return unitY; }
+        }
+
+        public static Vector3 UnitZ
+        {
+            get { return unitZ; }
+        }
+
+        public static Vector3 Up
+        {
+            get { return up; }
+        }
+
+        public static Vector3 Down
+        {
+            get { return down; }
+        }
+
+        public static Vector3 Right
+        {
+            get { return right; }
+        }
+
+        public static Vector3 Left
+        {
+            get { return left; }
+        }
+
+        public static Vector3 Forward
+        {
+            get { return forward; }
+        }
+
+        public static Vector3 Backward
+        {
+            get { return backward; }
+        }
+
+#endregion Properties
+
+#region Constructors
+
+        public Vector3(float x, float y, float z)
+        {
+            X = x;
+            Y = y;
+            Z = z;
+        }
+
+
+        public Vector3(float value)
+        {
+            X = value;
+            Y = value;
+            Z = value;
+        }
+
+
+        public Vector3(Vector2 value, float z)
+        {
+            X = value.X;
+            Y = value.Y;
+            Z = z;
+        }
+
+#endregion Constructors
+
+#region Public Methods
+
+        public static Vector3 Add(Vector3 value1, Vector3 value2)
+        {
+            value1.X += value2.X;
+            value1.Y += value2.Y;
+            value1.Z += value2.Z;
+            return value1;
+        }
+
+        public static void Add(ref Vector3 value1, ref Vector3 value2, out Vector3 result)
+        {
+            result.X = value1.X + value2.X;
+            result.Y = value1.Y + value2.Y;
+            result.Z = value1.Z + value2.Z;
+        }
+
+        public static Vector3 Barycentric(Vector3 value1, Vector3 value2, Vector3 value3, float amount1, float amount2)
+        {
+            return new Vector3(
+                MathHelper.Barycentric(value1.X, value2.X, value3.X, amount1, amount2),
+                MathHelper.Barycentric(value1.Y, value2.Y, value3.Y, amount1, amount2),
+                MathHelper.Barycentric(value1.Z, value2.Z, value3.Z, amount1, amount2));
+        }
+
+        public static void Barycentric(ref Vector3 value1, ref Vector3 value2, ref Vector3 value3, float amount1,
+                                       float amount2, out Vector3 result)
+        {
+            result = new Vector3(
+                MathHelper.Barycentric(value1.X, value2.X, value3.X, amount1, amount2),
+                MathHelper.Barycentric(value1.Y, value2.Y, value3.Y, amount1, amount2),
+                MathHelper.Barycentric(value1.Z, value2.Z, value3.Z, amount1, amount2));
+        }
+
+        public static Vector3 CatmullRom(Vector3 value1, Vector3 value2, Vector3 value3, Vector3 value4, float amount)
+        {
+            return new Vector3(
+                MathHelper.CatmullRom(value1.X, value2.X, value3.X, value4.X, amount),
+                MathHelper.CatmullRom(value1.Y, value2.Y, value3.Y, value4.Y, amount),
+                MathHelper.CatmullRom(value1.Z, value2.Z, value3.Z, value4.Z, amount));
+        }
+
+        public static void CatmullRom(ref Vector3 value1, ref Vector3 value2, ref Vector3 value3, ref Vector3 value4,
+                                      float amount, out Vector3 result)
+        {
+            result = new Vector3(
+                MathHelper.CatmullRom(value1.X, value2.X, value3.X, value4.X, amount),
+                MathHelper.CatmullRom(value1.Y, value2.Y, value3.Y, value4.Y, amount),
+                MathHelper.CatmullRom(value1.Z, value2.Z, value3.Z, value4.Z, amount));
+        }
+
+        public static Vector3 Clamp(Vector3 value1, Vector3 min, Vector3 max)
+        {
+            return new Vector3(
+                MathHelper.Clamp(value1.X, min.X, max.X),
+                MathHelper.Clamp(value1.Y, min.Y, max.Y),
+                MathHelper.Clamp(value1.Z, min.Z, max.Z));
+        }
+
+        public static void Clamp(ref Vector3 value1, ref Vector3 min, ref Vector3 max, out Vector3 result)
+        {
+            result = new Vector3(
+                MathHelper.Clamp(value1.X, min.X, max.X),
+                MathHelper.Clamp(value1.Y, min.Y, max.Y),
+                MathHelper.Clamp(value1.Z, min.Z, max.Z));
+        }
+
+        public static Vector3 Cross(Vector3 vector1, Vector3 vector2)
+        {
+            Cross(ref vector1, ref vector2, out vector1);
+            return vector1;
+        }
+
+        public static void Cross(ref Vector3 vector1, ref Vector3 vector2, out Vector3 result)
+        {
+            result = new Vector3(vector1.Y*vector2.Z - vector2.Y*vector1.Z,
+                                 -(vector1.X*vector2.Z - vector2.X*vector1.Z),
+                                 vector1.X*vector2.Y - vector2.X*vector1.Y);
+        }
+
+        public static float Distance(Vector3 vector1, Vector3 vector2)
+        {
+            float result;
+            DistanceSquared(ref vector1, ref vector2, out result);
+            return (float) Math.Sqrt(result);
+        }
+
+        public static void Distance(ref Vector3 value1, ref Vector3 value2, out float result)
+        {
+            DistanceSquared(ref value1, ref value2, out result);
+            result = (float) Math.Sqrt(result);
+        }
+
+        public static float DistanceSquared(Vector3 value1, Vector3 value2)
+        {
+            float result;
+            DistanceSquared(ref value1, ref value2, out result);
+            return result;
+        }
+
+        public static void DistanceSquared(ref Vector3 value1, ref Vector3 value2, out float result)
+        {
+            result = (value1.X - value2.X)*(value1.X - value2.X) +
+                     (value1.Y - value2.Y)*(value1.Y - value2.Y) +
+                     (value1.Z - value2.Z)*(value1.Z - value2.Z);
+        }
+
+        public static Vector3 Divide(Vector3 value1, Vector3 value2)
+        {
+            value1.X /= value2.X;
+            value1.Y /= value2.Y;
+            value1.Z /= value2.Z;
+            return value1;
+        }
+
+        public static Vector3 Divide(Vector3 value1, float value2)
+        {
+            float factor = 1/value2;
+            value1.X *= factor;
+            value1.Y *= factor;
+            value1.Z *= factor;
+            return value1;
+        }
+
+        public static void Divide(ref Vector3 value1, float divisor, out Vector3 result)
+        {
+            float factor = 1/divisor;
+            result.X = value1.X*factor;
+            result.Y = value1.Y*factor;
+            result.Z = value1.Z*factor;
+        }
+
+        public static void Divide(ref Vector3 value1, ref Vector3 value2, out Vector3 result)
+        {
+            result.X = value1.X/value2.X;
+            result.Y = value1.Y/value2.Y;
+            result.Z = value1.Z/value2.Z;
+        }
+
+        public static float Dot(Vector3 vector1, Vector3 vector2)
+        {
+            return vector1.X*vector2.X + vector1.Y*vector2.Y + vector1.Z*vector2.Z;
+        }
+
+        public static void Dot(ref Vector3 vector1, ref Vector3 vector2, out float result)
+        {
+            result = vector1.X*vector2.X + vector1.Y*vector2.Y + vector1.Z*vector2.Z;
+        }
+
+        public override bool Equals(object obj)
+        {
+            return (obj is Vector3) ? this == (Vector3) obj : false;
+        }
+
+        public bool Equals(Vector3 other)
+        {
+            return this == other;
+        }
+
+        public override int GetHashCode()
+        {
+            return (int) (X + Y + Z);
+        }
+
+        public static Vector3 Hermite(Vector3 value1, Vector3 tangent1, Vector3 value2, Vector3 tangent2, float amount)
+        {
+            Vector3 result = new Vector3();
+            Hermite(ref value1, ref tangent1, ref value2, ref tangent2, amount, out result);
+            return result;
+        }
+
+        public static void Hermite(ref Vector3 value1, ref Vector3 tangent1, ref Vector3 value2, ref Vector3 tangent2,
+                                   float amount, out Vector3 result)
+        {
+            result.X = MathHelper.Hermite(value1.X, tangent1.X, value2.X, tangent2.X, amount);
+            result.Y = MathHelper.Hermite(value1.Y, tangent1.Y, value2.Y, tangent2.Y, amount);
+            result.Z = MathHelper.Hermite(value1.Z, tangent1.Z, value2.Z, tangent2.Z, amount);
+        }
+
+        public float Length()
+        {
+            float result;
+            DistanceSquared(ref this, ref zero, out result);
+            return (float) Math.Sqrt(result);
+        }
+
+        public float LengthSquared()
+        {
+            float result;
+            DistanceSquared(ref this, ref zero, out result);
+            return result;
+        }
+
+        public static Vector3 Lerp(Vector3 value1, Vector3 value2, float amount)
+        {
+            return new Vector3(
+                MathHelper.Lerp(value1.X, value2.X, amount),
+                MathHelper.Lerp(value1.Y, value2.Y, amount),
+                MathHelper.Lerp(value1.Z, value2.Z, amount));
+        }
+
+        public static void Lerp(ref Vector3 value1, ref Vector3 value2, float amount, out Vector3 result)
+        {
+            result = new Vector3(
+                MathHelper.Lerp(value1.X, value2.X, amount),
+                MathHelper.Lerp(value1.Y, value2.Y, amount),
+                MathHelper.Lerp(value1.Z, value2.Z, amount));
+        }
+
+        public static Vector3 Max(Vector3 value1, Vector3 value2)
+        {
+            return new Vector3(
+                MathHelper.Max(value1.X, value2.X),
+                MathHelper.Max(value1.Y, value2.Y),
+                MathHelper.Max(value1.Z, value2.Z));
+        }
+
+        public static void Max(ref Vector3 value1, ref Vector3 value2, out Vector3 result)
+        {
+            result = new Vector3(
+                MathHelper.Max(value1.X, value2.X),
+                MathHelper.Max(value1.Y, value2.Y),
+                MathHelper.Max(value1.Z, value2.Z));
+        }
+
+        public static Vector3 Min(Vector3 value1, Vector3 value2)
+        {
+            return new Vector3(
+                MathHelper.Min(value1.X, value2.X),
+                MathHelper.Min(value1.Y, value2.Y),
+                MathHelper.Min(value1.Z, value2.Z));
+        }
+
+        public static void Min(ref Vector3 value1, ref Vector3 value2, out Vector3 result)
+        {
+            result = new Vector3(
+                MathHelper.Min(value1.X, value2.X),
+                MathHelper.Min(value1.Y, value2.Y),
+                MathHelper.Min(value1.Z, value2.Z));
+        }
+
+        public static Vector3 Multiply(Vector3 value1, Vector3 value2)
+        {
+            value1.X *= value2.X;
+            value1.Y *= value2.Y;
+            value1.Z *= value2.Z;
+            return value1;
+        }
+
+        public static Vector3 Multiply(Vector3 value1, float scaleFactor)
+        {
+            value1.X *= scaleFactor;
+            value1.Y *= scaleFactor;
+            value1.Z *= scaleFactor;
+            return value1;
+        }
+
+        public static void Multiply(ref Vector3 value1, float scaleFactor, out Vector3 result)
+        {
+            result.X = value1.X*scaleFactor;
+            result.Y = value1.Y*scaleFactor;
+            result.Z = value1.Z*scaleFactor;
+        }
+
+        public static void Multiply(ref Vector3 value1, ref Vector3 value2, out Vector3 result)
+        {
+            result.X = value1.X*value2.X;
+            result.Y = value1.Y*value2.Y;
+            result.Z = value1.Z*value2.Z;
+        }
+
+        public static Vector3 Negate(Vector3 value)
+        {
+            value = new Vector3(-value.X, -value.Y, -value.Z);
+            return value;
+        }
+
+        public static void Negate(ref Vector3 value, out Vector3 result)
+        {
+            result = new Vector3(-value.X, -value.Y, -value.Z);
+        }
+
+        public void Normalize()
+        {
+            Normalize(ref this, out this);
+        }
+
+        public static Vector3 Normalize(Vector3 vector)
+        {
+            Normalize(ref vector, out vector);
+            return vector;
+        }
+
+        public static void Normalize(ref Vector3 value, out Vector3 result)
+        {
+            float factor;
+            Distance(ref value, ref zero, out factor);
+            factor = 1f/factor;
+            result.X = value.X*factor;
+            result.Y = value.Y*factor;
+            result.Z = value.Z*factor;
+        }
+
+        public static Vector3 Reflect(Vector3 vector, Vector3 normal)
+        {
+            Vector3 result;
+            Reflect(ref vector, ref normal, out result);
+            return result;
+        }
+
+        public static void Reflect(ref Vector3 vector, ref Vector3 normal, out Vector3 result)
+        {
+            float dot = Dot(vector, normal);
+            result.X = vector.X - ((2f*dot)*normal.X);
+            result.Y = vector.Y - ((2f*dot)*normal.Y);
+            result.Z = vector.Z - ((2f*dot)*normal.Z);
+        }
+
+        public static Vector3 SmoothStep(Vector3 value1, Vector3 value2, float amount)
+        {
+            return new Vector3(
+                MathHelper.SmoothStep(value1.X, value2.X, amount),
+                MathHelper.SmoothStep(value1.Y, value2.Y, amount),
+                MathHelper.SmoothStep(value1.Z, value2.Z, amount));
+        }
+
+        public static void SmoothStep(ref Vector3 value1, ref Vector3 value2, float amount, out Vector3 result)
+        {
+            result = new Vector3(
+                MathHelper.SmoothStep(value1.X, value2.X, amount),
+                MathHelper.SmoothStep(value1.Y, value2.Y, amount),
+                MathHelper.SmoothStep(value1.Z, value2.Z, amount));
+        }
+
+        public static Vector3 Subtract(Vector3 value1, Vector3 value2)
+        {
+            value1.X -= value2.X;
+            value1.Y -= value2.Y;
+            value1.Z -= value2.Z;
+            return value1;
+        }
+
+        public static void Subtract(ref Vector3 value1, ref Vector3 value2, out Vector3 result)
+        {
+            result.X = value1.X - value2.X;
+            result.Y = value1.Y - value2.Y;
+            result.Z = value1.Z - value2.Z;
+        }
+
+        public override string ToString()
+        {
+            StringBuilder sb = new StringBuilder(32);
+            sb.Append("{X:");
+            sb.Append(X);
+            sb.Append(" Y:");
+            sb.Append(Y);
+            sb.Append(" Z:");
+            sb.Append(Z);
+            sb.Append("}");
+            return sb.ToString();
+        }
+
+        public static Vector3 Transform(Vector3 position, Matrix matrix)
+        {
+            Transform(ref position, ref matrix, out position);
+            return position;
+        }
+
+        public static void Transform(ref Vector3 position, ref Matrix matrix, out Vector3 result)
+        {
+            result =
+                new Vector3((position.X*matrix.M11) + (position.Y*matrix.M21) + (position.Z*matrix.M31) + matrix.M41,
+                            (position.X*matrix.M12) + (position.Y*matrix.M22) + (position.Z*matrix.M32) + matrix.M42,
+                            (position.X*matrix.M13) + (position.Y*matrix.M23) + (position.Z*matrix.M33) + matrix.M43);
+        }
+
+        public static void Transform(Vector3[] sourceArray, ref Matrix matrix, Vector3[] destinationArray)
+        {
+            throw new NotImplementedException();
+        }
+
+        public static void Transform(Vector3[] sourceArray, int sourceIndex, ref Matrix matrix,
+                                     Vector3[] destinationArray, int destinationIndex, int length)
+        {
+            throw new NotImplementedException();
+        }
+
+        public static void TransformNormal(Vector3[] sourceArray, ref Matrix matrix, Vector3[] destinationArray)
+        {
+            throw new NotImplementedException();
+        }
+
+        public static void TransformNormal(Vector3[] sourceArray, int sourceIndex, ref Matrix matrix,
+                                           Vector3[] destinationArray, int destinationIndex, int length)
+        {
+            throw new NotImplementedException();
+        }
+
+        public static Vector3 TransformNormal(Vector3 normal, Matrix matrix)
+        {
+            TransformNormal(ref normal, ref matrix, out normal);
+            return normal;
+        }
+
+        public static void TransformNormal(ref Vector3 normal, ref Matrix matrix, out Vector3 result)
+        {
+            result = new Vector3((normal.X*matrix.M11) + (normal.Y*matrix.M21) + (normal.Z*matrix.M31),
+                                 (normal.X*matrix.M12) + (normal.Y*matrix.M22) + (normal.Z*matrix.M32),
+                                 (normal.X*matrix.M13) + (normal.Y*matrix.M23) + (normal.Z*matrix.M33));
+        }
+
+#endregion Public methods
+
+#region Operators
+
+        public static bool operator ==(Vector3 value1, Vector3 value2)
+        {
+            return value1.X == value2.X
+                   && value1.Y == value2.Y
+                   && value1.Z == value2.Z;
+        }
+
+        public static bool operator !=(Vector3 value1, Vector3 value2)
+        {
+            return !(value1 == value2);
+        }
+
+        public static Vector3 operator +(Vector3 value1, Vector3 value2)
+        {
+            value1.X += value2.X;
+            value1.Y += value2.Y;
+            value1.Z += value2.Z;
+            return value1;
+        }
+
+        public static Vector3 operator -(Vector3 value)
+        {
+            value = new Vector3(-value.X, -value.Y, -value.Z);
+            return value;
+        }
+
+        public static Vector3 operator -(Vector3 value1, Vector3 value2)
+        {
+            value1.X -= value2.X;
+            value1.Y -= value2.Y;
+            value1.Z -= value2.Z;
+            return value1;
+        }
+
+        public static Vector3 operator *(Vector3 value1, Vector3 value2)
+        {
+            value1.X *= value2.X;
+            value1.Y *= value2.Y;
+            value1.Z *= value2.Z;
+            return value1;
+        }
+
+        public static Vector3 operator *(Vector3 value, float scaleFactor)
+        {
+            value.X *= scaleFactor;
+            value.Y *= scaleFactor;
+            value.Z *= scaleFactor;
+            return value;
+        }
+
+        public static Vector3 operator *(float scaleFactor, Vector3 value)
+        {
+            value.X *= scaleFactor;
+            value.Y *= scaleFactor;
+            value.Z *= scaleFactor;
+            return value;
+        }
+
+        public static Vector3 operator /(Vector3 value1, Vector3 value2)
+        {
+            value1.X /= value2.X;
+            value1.Y /= value2.Y;
+            value1.Z /= value2.Z;
+            return value1;
+        }
+
+        public static Vector3 operator /(Vector3 value, float divider)
+        {
+            float factor = 1/divider;
+            value.X *= factor;
+            value.Y *= factor;
+            value.Z *= factor;
+            return value;
+        }
+
+#endregion
+    }
+}
+
+#endif

Farseer Physics Engine 3.5/Common/Vertices.cs

@@ -0,0 +1,582 @@
+/*
+* Farseer Physics Engine:
+* Copyright (c) 2012 Ian Qvist
+*/
+
+using System;
+using System.Collections.Generic;
+using System.Diagnostics;
+using System.Text;
+using FarseerPhysics.Collision;
+using Microsoft.Xna.Framework;
+
+namespace FarseerPhysics.Common
+{
+    public enum PolygonError
+    {
+        /// <summary>
+        /// There were no errors in the polygon
+        /// </summary>
+        NoError,
+
+        /// <summary>
+        /// Polygon must have between 3 and Settings.MaxPolygonVertices vertices.
+        /// </summary>
+        InvalidAmountOfVertices,
+
+        /// <summary>
+        /// Polygon must be simple. This means no overlapping edges.
+        /// </summary>
+        NotSimple,
+
+        /// <summary>
+        /// Polygon must have a counter clockwise winding.
+        /// </summary>
+        NotCounterClockWise,
+
+        /// <summary>
+        /// The polygon is concave, it needs to be convex.
+        /// </summary>
+        NotConvex,
+
+        /// <summary>
+        /// Polygon area is too small.
+        /// </summary>
+        AreaTooSmall,
+
+        /// <summary>
+        /// The polygon has a side that is too short.
+        /// </summary>
+        SideTooSmall
+    }
+
+#if !(XBOX360)
+    [DebuggerDisplay("Count = {Count} Vertices = {ToString()}")]
+#endif
+    public class Vertices : List<Vector2>
+    {
+        public Vertices() { }
+
+        public Vertices(int capacity) : base(capacity) { }
+
+        public Vertices(IEnumerable<Vector2> vertices)
+        {
+            AddRange(vertices);
+        }
+
+        internal bool AttachedToBody { get; set; }
+
+        /// <summary>
+        /// You can add holes to this collection.
+        /// It will get respected by some of the triangulation algoithms, but otherwise not used.
+        /// </summary>
+        public List<Vertices> Holes { get; set; }
+
+        /// <summary>
+        /// Gets the next index. Used for iterating all the edges with wrap-around.
+        /// </summary>
+        /// <param name="index">The current index</param>
+        public int NextIndex(int index)
+        {
+            return (index + 1 > Count - 1) ? 0 : index + 1;
+        }
+
+        /// <summary>
+        /// Gets the next vertex. Used for iterating all the edges with wrap-around.
+        /// </summary>
+        /// <param name="index">The current index</param>
+        public Vector2 NextVertex(int index)
+        {
+            return this[NextIndex(index)];
+        }
+
+        /// <summary>
+        /// Gets the previous index. Used for iterating all the edges with wrap-around.
+        /// </summary>
+        /// <param name="index">The current index</param>
+        public int PreviousIndex(int index)
+        {
+            return index - 1 < 0 ? Count - 1 : index - 1;
+        }
+
+        /// <summary>
+        /// Gets the previous vertex. Used for iterating all the edges with wrap-around.
+        /// </summary>
+        /// <param name="index">The current index</param>
+        public Vector2 PreviousVertex(int index)
+        {
+            return this[PreviousIndex(index)];
+        }
+
+        /// <summary>
+        /// Gets the signed area.
+        /// If the area is less than 0, it indicates that the polygon is clockwise winded.
+        /// </summary>
+        /// <returns>The signed area</returns>
+        public float GetSignedArea()
+        {
+            //The simplest polygon which can exist in the Euclidean plane has 3 sides.
+            if (Count < 3)
+                return 0;
+
+            int i;
+            float area = 0;
+
+            for (i = 0; i < Count; i++)
+            {
+                int j = (i + 1) % Count;
+
+                Vector2 vi = this[i];
+                Vector2 vj = this[j];
+
+                area += vi.X * vj.Y;
+                area -= vi.Y * vj.X;
+            }
+            area /= 2.0f;
+            return area;
+        }
+
+        /// <summary>
+        /// Gets the area.
+        /// </summary>
+        /// <returns></returns>
+        public float GetArea()
+        {
+            float area = GetSignedArea();
+            return (area < 0 ? -area : area);
+        }
+
+        /// <summary>
+        /// Gets the centroid.
+        /// </summary>
+        /// <returns></returns>
+        public Vector2 GetCentroid()
+        {
+            //The simplest polygon which can exist in the Euclidean plane has 3 sides.
+            if (Count < 3)
+                return new Vector2(float.NaN, float.NaN);
+
+            // Same algorithm is used by Box2D
+            Vector2 c = Vector2.Zero;
+            float area = 0.0f;
+            const float inv3 = 1.0f / 3.0f;
+
+            for (int i = 0; i < Count; ++i)
+            {
+                // Triangle vertices.
+                Vector2 current = this[i];
+                Vector2 next = (i + 1 < Count ? this[i + 1] : this[0]);
+
+                float triangleArea = 0.5f * (current.X * next.Y - current.Y * next.X);
+                area += triangleArea;
+
+                // Area weighted centroid
+                c += triangleArea * inv3 * (current + next);
+            }
+
+            // Centroid
+            c *= 1.0f / area;
+            return c;
+        }
+
+        /// <summary>
+        /// Returns an AABB that fully contains this polygon.
+        /// </summary>
+        public AABB GetAABB()
+        {
+            AABB aabb;
+            Vector2 lowerBound = new Vector2(float.MaxValue, float.MaxValue);
+            Vector2 upperBound = new Vector2(float.MinValue, float.MinValue);
+
+            for (int i = 0; i < Count; ++i)
+            {
+                if (this[i].X < lowerBound.X)
+                {
+                    lowerBound.X = this[i].X;
+                }
+                if (this[i].X > upperBound.X)
+                {
+                    upperBound.X = this[i].X;
+                }
+
+                if (this[i].Y < lowerBound.Y)
+                {
+                    lowerBound.Y = this[i].Y;
+                }
+                if (this[i].Y > upperBound.Y)
+                {
+                    upperBound.Y = this[i].Y;
+                }
+            }
+
+            aabb.LowerBound = lowerBound;
+            aabb.UpperBound = upperBound;
+
+            return aabb;
+        }
+
+        /// <summary>
+        /// Translates the vertices with the specified vector.
+        /// </summary>
+        /// <param name="value">The value.</param>
+        public void Translate(Vector2 value)
+        {
+            Translate(ref value);
+        }
+
+        /// <summary>
+        /// Translates the vertices with the specified vector.
+        /// </summary>
+        /// <param name="value">The vector.</param>
+        public void Translate(ref Vector2 value)
+        {
+            Debug.Assert(!AttachedToBody, "Translating vertices that are used by a Body can result in unstable behavior. Use Body.Position instead.");
+
+            for (int i = 0; i < Count; i++)
+                this[i] = Vector2.Add(this[i], value);
+
+            if (Holes != null && Holes.Count > 0)
+            {
+                foreach (Vertices hole in Holes)
+                {
+                    hole.Translate(ref value);
+                }
+            }
+        }
+
+        /// <summary>
+        /// Scales the vertices with the specified vector.
+        /// </summary>
+        /// <param name="value">The Value.</param>
+        public void Scale(Vector2 value)
+        {
+            Scale(ref value);
+        }
+
+        /// <summary>
+        /// Scales the vertices with the specified vector.
+        /// </summary>
+        /// <param name="value">The Value.</param>
+        public void Scale(ref Vector2 value)
+        {
+            Debug.Assert(!AttachedToBody, "Scaling vertices that are used by a Body can result in unstable behavior.");
+
+            for (int i = 0; i < Count; i++)
+                this[i] = Vector2.Multiply(this[i], value);
+
+            if (Holes != null && Holes.Count > 0)
+            {
+                foreach (Vertices hole in Holes)
+                {
+                    hole.Scale(ref value);
+                }
+            }
+        }
+
+        /// <summary>
+        /// Rotate the vertices with the defined value in radians.
+        /// 
+        /// Warning: Using this method on an active set of vertices of a Body,
+        /// will cause problems with collisions. Use Body.Rotation instead.
+        /// </summary>
+        /// <param name="value">The amount to rotate by in radians.</param>
+        public void Rotate(float value)
+        {
+            Debug.Assert(!AttachedToBody, "Rotating vertices that are used by a Body can result in unstable behavior.");
+
+            float num1 = (float)Math.Cos(value);
+            float num2 = (float)Math.Sin(value);
+
+            for (int i = 0; i < Count; i++)
+            {
+                Vector2 position = this[i];
+                this[i] = new Vector2((position.X * num1 + position.Y * -num2), (position.X * num2 + position.Y * num1));
+            }
+
+            if (Holes != null && Holes.Count > 0)
+            {
+                foreach (Vertices hole in Holes)
+                {
+                    hole.Rotate(value);
+                }
+            }
+        }
+
+        /// <summary>
+        /// Determines whether the polygon is convex.
+        /// O(n^2) running time.
+        /// 
+        /// Assumptions:
+        /// - The polygon is in counter clockwise order
+        /// - The polygon has no overlapping edges
+        /// </summary>
+        /// <returns>
+        /// 	<c>true</c> if it is convex; otherwise, <c>false</c>.
+        /// </returns>
+        public bool IsConvex()
+        {
+            //The simplest polygon which can exist in the Euclidean plane has 3 sides.
+            if (Count < 3)
+                return false;
+
+            //Triangles are always convex
+            if (Count == 3)
+                return true;
+
+            // Checks the polygon is convex and the interior is to the left of each edge.
+            for (int i = 0; i < Count; ++i)
+            {
+                int next = i + 1 < Count ? i + 1 : 0;
+                Vector2 edge = this[next] - this[i];
+
+                for (int j = 0; j < Count; ++j)
+                {
+                    // Don't check vertices on the current edge.
+                    if (j == i || j == next)
+                        continue;
+
+                    Vector2 r = this[j] - this[i];
+
+                    float s = edge.X * r.Y - edge.Y * r.X;
+
+                    if (s <= 0.0f)
+                        return false;
+                }
+            }
+            return true;
+        }
+
+        /// <summary>
+        /// Indicates if the vertices are in counter clockwise order.
+        /// Warning: If the area of the polygon is 0, it is unable to determine the winding.
+        /// </summary>
+        public bool IsCounterClockWise()
+        {
+            //The simplest polygon which can exist in the Euclidean plane has 3 sides.
+            if (Count < 3)
+                return false;
+
+            return (GetSignedArea() > 0.0f);
+        }
+
+        /// <summary>
+        /// Forces the vertices to be counter clock wise order.
+        /// </summary>
+        public void ForceCounterClockWise()
+        {
+            //The simplest polygon which can exist in the Euclidean plane has 3 sides.
+            if (Count < 3)
+                return;
+
+            if (!IsCounterClockWise())
+                Reverse();
+        }
+
+        /// <summary>
+        /// Checks if the vertices forms an simple polygon by checking for edge crossings.
+        /// </summary>
+        public bool IsSimple()
+        {
+            //The simplest polygon which can exist in the Euclidean plane has 3 sides.
+            if (Count < 3)
+                return false;
+
+            for (int i = 0; i < Count; ++i)
+            {
+                Vector2 a1 = this[i];
+                Vector2 a2 = NextVertex(i);
+                for (int j = i + 1; j < Count; ++j)
+                {
+                    Vector2 b1 = this[j];
+                    Vector2 b2 = NextVertex(j);
+
+                    Vector2 temp;
+
+                    if (LineTools.LineIntersect2(ref a1, ref a2, ref b1, ref b2, out temp))
+                        return false;
+                }
+            }
+            return true;
+        }
+
+        /// <summary>
+        /// Checks if the polygon is valid for use in the engine.
+        ///
+        /// Performs a full check, for simplicity, convexity,
+        /// orientation, minimum angle, and volume.
+        /// 
+        /// From Eric Jordan's convex decomposition library
+        /// </summary>
+        /// <returns>PolygonError.NoError if there were no error.</returns>
+        public PolygonError CheckPolygon()
+        {
+            if (Count < 3 || Count > Settings.MaxPolygonVertices)
+                return PolygonError.InvalidAmountOfVertices;
+
+            if (!IsSimple())
+                return PolygonError.NotSimple;
+
+            if (GetArea() <= Settings.Epsilon)
+                return PolygonError.AreaTooSmall;
+
+            if (!IsConvex())
+                return PolygonError.NotConvex;
+
+            //Check if the sides are of adequate length.
+            for (int i = 0; i < Count; ++i)
+            {
+                int next = i + 1 < Count ? i + 1 : 0;
+                Vector2 edge = this[next] - this[i];
+                if (edge.LengthSquared() <= Settings.Epsilon*Settings.Epsilon)
+                {
+                    return PolygonError.SideTooSmall;
+                }
+            }
+
+            if (!IsCounterClockWise())
+                return PolygonError.NotCounterClockWise;
+
+            return PolygonError.NoError;
+        }
+
+        /// <summary>
+        /// Projects to axis.
+        /// </summary>
+        /// <param name="axis">The axis.</param>
+        /// <param name="min">The min.</param>
+        /// <param name="max">The max.</param>
+        public void ProjectToAxis(ref Vector2 axis, out float min, out float max)
+        {
+            // To project a point on an axis use the dot product
+            float dotProduct = Vector2.Dot(axis, this[0]);
+            min = dotProduct;
+            max = dotProduct;
+
+            for (int i = 0; i < Count; i++)
+            {
+                dotProduct = Vector2.Dot(this[i], axis);
+                if (dotProduct < min)
+                {
+                    min = dotProduct;
+                }
+                else
+                {
+                    if (dotProduct > max)
+                    {
+                        max = dotProduct;
+                    }
+                }
+            }
+        }
+
+        /// <summary>
+        /// Winding number test for a point in a polygon.
+        /// </summary>
+        /// See more info about the algorithm here: http://softsurfer.com/Archive/algorithm_0103/algorithm_0103.htm
+        /// <param name="point">The point to be tested.</param>
+        /// <returns>-1 if the winding number is zero and the point is outside
+        /// the polygon, 1 if the point is inside the polygon, and 0 if the point
+        /// is on the polygons edge.</returns>
+        public int PointInPolygon(ref Vector2 point)
+        {
+            // Winding number
+            int wn = 0;
+
+            // Iterate through polygon's edges
+            for (int i = 0; i < Count; i++)
+            {
+                // Get points
+                Vector2 p1 = this[i];
+                Vector2 p2 = this[NextIndex(i)];
+
+                // Test if a point is directly on the edge
+                Vector2 edge = p2 - p1;
+                float area = MathUtils.Area(ref p1, ref p2, ref point);
+                if (area == 0f && Vector2.Dot(point - p1, edge) >= 0f && Vector2.Dot(point - p2, edge) <= 0f)
+                {
+                    return 0;
+                }
+                // Test edge for intersection with ray from point
+                if (p1.Y <= point.Y)
+                {
+                    if (p2.Y > point.Y && area > 0f)
+                    {
+                        ++wn;
+                    }
+                }
+                else
+                {
+                    if (p2.Y <= point.Y && area < 0f)
+                    {
+                        --wn;
+                    }
+                }
+            }
+            return (wn == 0 ? -1 : 1);
+        }
+
+        /// <summary>
+        /// Compute the sum of the angles made between the test point and each pair of points making up the polygon. 
+        /// If this sum is 2pi then the point is an interior point, if 0 then the point is an exterior point. 
+        /// ref: http://ozviz.wasp.uwa.edu.au/~pbourke/geometry/insidepoly/  - Solution 2 
+        /// </summary>
+        public bool PointInPolygonAngle(ref Vector2 point)
+        {
+            double angle = 0;
+
+            // Iterate through polygon's edges
+            for (int i = 0; i < Count; i++)
+            {
+                // Get points
+                Vector2 p1 = this[i] - point;
+                Vector2 p2 = this[NextIndex(i)] - point;
+
+                angle += MathUtils.VectorAngle(ref p1, ref p2);
+            }
+
+            if (Math.Abs(angle) < Math.PI)
+            {
+                return false;
+            }
+
+            return true;
+        }
+
+        /// <summary>
+        /// Transforms the polygon using the defined matrix.
+        /// </summary>
+        /// <param name="transform">The matrix to use as transformation.</param>
+        public void Transform(ref Matrix transform)
+        {
+            // Transform main polygon
+            for (int i = 0; i < Count; i++)
+                this[i] = Vector2.Transform(this[i], transform);
+
+            // Transform holes
+            if (Holes != null && Holes.Count > 0)
+            {
+                for (int i = 0; i < Holes.Count; i++)
+                {
+                    Vector2[] temp = Holes[i].ToArray();
+                    Vector2.Transform(temp, ref transform, temp);
+
+                    Holes[i] = new Vertices(temp);
+                }
+            }
+        }
+
+        public override string ToString()
+        {
+            StringBuilder builder = new StringBuilder();
+            for (int i = 0; i < Count; i++)
+            {
+                builder.Append(this[i].ToString());
+                if (i < Count - 1)
+                {
+                    builder.Append(" ");
+                }
+            }
+            return builder.ToString();
+        }
+    }
+}