/* 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.
 */

/*
 * Sweep-line, Constrained Delauney Triangulation (CDT) See: Domiter, V. and
 * Zalik, B.(2008)'Sweep-line algorithm for constrained Delaunay triangulation',
 * International Journal of Geographical Information Science
 * 
 * "FlipScan" Constrained Edge Algorithm invented by author of this code.
 * 
 * Author: Thomas Åhlén, thahlen@gmail.com 
 */

// Changes from the Java version
//   Turned DTSweep into a static class
//   Lots of deindentation via early bailout
// Future possibilities
//   Comments!

using System;
using System.Collections.Generic;
using System.Diagnostics;

namespace FarseerPhysics.Common.Decomposition.CDT.Delaunay.Sweep
{
    internal static class DTSweep
    {
        private const double PI_div2 = Math.PI / 2;
        private const double PI_3div4 = 3 * Math.PI / 4;

        /// <summary>
        /// Triangulate simple polygon with holes
        /// </summary>
        public static void Triangulate(DTSweepContext tcx)
        {
            tcx.CreateAdvancingFront();

            Sweep(tcx);

            // Finalize triangulation
            if (tcx.TriangulationMode == TriangulationMode.Polygon)
            {
                FinalizationPolygon(tcx);
            }
            else
            {
                FinalizationConvexHull(tcx);
            }

            tcx.Done();
        }

        /// <summary>
        /// Start sweeping the Y-sorted point set from bottom to top
        /// </summary>
        private static void Sweep(DTSweepContext tcx)
        {
            List<TriangulationPoint> points = tcx.Points;

            for (int i = 1; i < points.Count; i++)
            {
                TriangulationPoint point = points[i];

                AdvancingFrontNode node = PointEvent(tcx, point);

                if (point.HasEdges)
                {
                    foreach (DTSweepConstraint e in point.Edges)
                    {
                        EdgeEvent(tcx, e, node);
                    }
                }
                tcx.Update(null);
            }
        }

        /// <summary>
        /// If this is a Delaunay Triangulation of a pointset we need to fill so the triangle mesh gets a ConvexHull 
        /// </summary>
        private static void FinalizationConvexHull(DTSweepContext tcx)
        {
            DelaunayTriangle t1, t2;

            AdvancingFrontNode n1 = tcx.aFront.Head.Next;
            AdvancingFrontNode n2 = n1.Next;

            TurnAdvancingFrontConvex(tcx, n1, n2);

            // TODO: implement ConvexHull for lower right and left boundary

            // Lets remove triangles connected to the two "algorithm" points

            // XXX: When the first the nodes are points in a triangle we need to do a flip before 
            //      removing triangles or we will lose a valid triangle.
            //      Same for last three nodes!
            // !!! If I implement ConvexHull for lower right and left boundary this fix should not be 
            //     needed and the removed triangles will be added again by default
            n1 = tcx.aFront.Tail.Prev;
            if (n1.Triangle.Contains(n1.Next.Point) && n1.Triangle.Contains(n1.Prev.Point))
            {
                t1 = n1.Triangle.NeighborAcross(n1.Point);
                RotateTrianglePair(n1.Triangle, n1.Point, t1, t1.OppositePoint(n1.Triangle, n1.Point));
                tcx.MapTriangleToNodes(n1.Triangle);
                tcx.MapTriangleToNodes(t1);
            }
            n1 = tcx.aFront.Head.Next;
            if (n1.Triangle.Contains(n1.Prev.Point) && n1.Triangle.Contains(n1.Next.Point))
            {
                t1 = n1.Triangle.NeighborAcross(n1.Point);
                RotateTrianglePair(n1.Triangle, n1.Point, t1, t1.OppositePoint(n1.Triangle, n1.Point));
                tcx.MapTriangleToNodes(n1.Triangle);
                tcx.MapTriangleToNodes(t1);
            }

            // Lower right boundary 
            TriangulationPoint first = tcx.aFront.Head.Point;
            n2 = tcx.aFront.Tail.Prev;
            t1 = n2.Triangle;
            TriangulationPoint p1 = n2.Point;
            n2.Triangle = null;
            do
            {
                tcx.RemoveFromList(t1);
                p1 = t1.PointCCW(p1);
                if (p1 == first) break;
                t2 = t1.NeighborCCW(p1);
                t1.Clear();
                t1 = t2;
            } while (true);

            // Lower left boundary
            first = tcx.aFront.Head.Next.Point;
            p1 = t1.PointCW(tcx.aFront.Head.Point);
            t2 = t1.NeighborCW(tcx.aFront.Head.Point);
            t1.Clear();
            t1 = t2;
            while (p1 != first) //TODO: Port note. This was do while before.
            {
                tcx.RemoveFromList(t1);
                p1 = t1.PointCCW(p1);
                t2 = t1.NeighborCCW(p1);
                t1.Clear();
                t1 = t2;
            }

            // Remove current head and tail node now that we have removed all triangles attached
            // to them. Then set new head and tail node points
            tcx.aFront.Head = tcx.aFront.Head.Next;
            tcx.aFront.Head.Prev = null;
            tcx.aFront.Tail = tcx.aFront.Tail.Prev;
            tcx.aFront.Tail.Next = null;

            tcx.FinalizeTriangulation();
        }

        /// <summary>
        /// We will traverse the entire advancing front and fill it to form a convex hull.
        /// </summary>
        private static void TurnAdvancingFrontConvex(DTSweepContext tcx, AdvancingFrontNode b, AdvancingFrontNode c)
        {
            AdvancingFrontNode first = b;
            while (c != tcx.aFront.Tail)
            {
                if (TriangulationUtil.Orient2d(b.Point, c.Point, c.Next.Point) == Orientation.CCW)
                {
                    // [b,c,d] Concave - fill around c
                    Fill(tcx, c);
                    c = c.Next;
                }
                else
                {
                    // [b,c,d] Convex
                    if (b != first && TriangulationUtil.Orient2d(b.Prev.Point, b.Point, c.Point) == Orientation.CCW)
                    {
                        // [a,b,c] Concave - fill around b
                        Fill(tcx, b);
                        b = b.Prev;
                    }
                    else
                    {
                        // [a,b,c] Convex - nothing to fill
                        b = c;
                        c = c.Next;
                    }
                }
            }
        }

        private static void FinalizationPolygon(DTSweepContext tcx)
        {
            // Get an Internal triangle to start with
            DelaunayTriangle t = tcx.aFront.Head.Next.Triangle;
            TriangulationPoint p = tcx.aFront.Head.Next.Point;
            while (!t.GetConstrainedEdgeCW(p))
            {
                t = t.NeighborCCW(p);
            }

            // Collect interior triangles constrained by edges
            tcx.MeshClean(t);
        }

        /// <summary>
        /// Find closes node to the left of the new point and
        /// create a new triangle. If needed new holes and basins
        /// will be filled to.
        /// </summary>
        private static AdvancingFrontNode PointEvent(DTSweepContext tcx, TriangulationPoint point)
        {
            AdvancingFrontNode node = tcx.LocateNode(point);
            AdvancingFrontNode newNode = NewFrontTriangle(tcx, point, node);

            // Only need to check +epsilon since point never have smaller 
            // x value than node due to how we fetch nodes from the front
            if (point.X <= node.Point.X + TriangulationUtil.EPSILON)
            {
                Fill(tcx, node);
            }

            tcx.AddNode(newNode);

            FillAdvancingFront(tcx, newNode);
            return newNode;
        }

        /// <summary>
        /// Creates a new front triangle and legalize it
        /// </summary>
        private static AdvancingFrontNode NewFrontTriangle(DTSweepContext tcx, TriangulationPoint point, AdvancingFrontNode node)
        {
            DelaunayTriangle triangle = new DelaunayTriangle(point, node.Point, node.Next.Point);
            triangle.MarkNeighbor(node.Triangle);
            tcx.Triangles.Add(triangle);

            AdvancingFrontNode newNode = new AdvancingFrontNode(point);
            newNode.Next = node.Next;
            newNode.Prev = node;
            node.Next.Prev = newNode;
            node.Next = newNode;

            tcx.AddNode(newNode); // XXX: BST

            if (!Legalize(tcx, triangle))
            {
                tcx.MapTriangleToNodes(triangle);
            }

            return newNode;
        }

        private static void EdgeEvent(DTSweepContext tcx, DTSweepConstraint edge, AdvancingFrontNode node)
        {
            try
            {
                tcx.EdgeEvent.ConstrainedEdge = edge;
                tcx.EdgeEvent.Right = edge.P.X > edge.Q.X;

                if (IsEdgeSideOfTriangle(node.Triangle, edge.P, edge.Q))
                {
                    return;
                }

                // For now we will do all needed filling
                // TODO: integrate with flip process might give some better performance 
                //       but for now this avoid the issue with cases that needs both flips and fills
                FillEdgeEvent(tcx, edge, node);

                EdgeEvent(tcx, edge.P, edge.Q, node.Triangle, edge.Q);
            }
            catch (PointOnEdgeException e)
            {
                Debug.WriteLine("Skipping Edge: {0}", e.Message);
            }
        }

        private static void FillEdgeEvent(DTSweepContext tcx, DTSweepConstraint edge, AdvancingFrontNode node)
        {
            if (tcx.EdgeEvent.Right)
            {
                FillRightAboveEdgeEvent(tcx, edge, node);
            }
            else
            {
                FillLeftAboveEdgeEvent(tcx, edge, node);
            }
        }

        private static void FillRightConcaveEdgeEvent(DTSweepContext tcx, DTSweepConstraint edge,
                                                      AdvancingFrontNode node)
        {
            Fill(tcx, node.Next);
            if (node.Next.Point != edge.P)
            {
                // Next above or below edge?
                if (TriangulationUtil.Orient2d(edge.Q, node.Next.Point, edge.P) == Orientation.CCW)
                {
                    // Below
                    if (TriangulationUtil.Orient2d(node.Point, node.Next.Point, node.Next.Next.Point) == Orientation.CCW)
                    {
                        // Next is concave
                        FillRightConcaveEdgeEvent(tcx, edge, node);
                    }
                    else
                    {
                        // Next is convex
                    }
                }
            }
        }

        private static void FillRightConvexEdgeEvent(DTSweepContext tcx, DTSweepConstraint edge, AdvancingFrontNode node)
        {
            // Next concave or convex?
            if (TriangulationUtil.Orient2d(node.Next.Point, node.Next.Next.Point, node.Next.Next.Next.Point) ==
                Orientation.CCW)
            {
                // Concave
                FillRightConcaveEdgeEvent(tcx, edge, node.Next);
            }
            else
            {
                // Convex
                // Next above or below edge?
                if (TriangulationUtil.Orient2d(edge.Q, node.Next.Next.Point, edge.P) == Orientation.CCW)
                {
                    // Below
                    FillRightConvexEdgeEvent(tcx, edge, node.Next);
                }
                else
                {
                    // Above
                }
            }
        }

        private static void FillRightBelowEdgeEvent(DTSweepContext tcx, DTSweepConstraint edge, AdvancingFrontNode node)
        {
            if (node.Point.X < edge.P.X) // needed?
            {
                if (TriangulationUtil.Orient2d(node.Point, node.Next.Point, node.Next.Next.Point) == Orientation.CCW)
                {
                    // Concave 
                    FillRightConcaveEdgeEvent(tcx, edge, node);
                }
                else
                {
                    // Convex
                    FillRightConvexEdgeEvent(tcx, edge, node);
                    // Retry this one
                    FillRightBelowEdgeEvent(tcx, edge, node);
                }
            }
        }

        private static void FillRightAboveEdgeEvent(DTSweepContext tcx, DTSweepConstraint edge, AdvancingFrontNode node)
        {
            while (node.Next.Point.X < edge.P.X)
            {
                // Check if next node is below the edge
                Orientation o1 = TriangulationUtil.Orient2d(edge.Q, node.Next.Point, edge.P);
                if (o1 == Orientation.CCW)
                {
                    FillRightBelowEdgeEvent(tcx, edge, node);
                }
                else
                {
                    node = node.Next;
                }
            }
        }

        private static void FillLeftConvexEdgeEvent(DTSweepContext tcx, DTSweepConstraint edge, AdvancingFrontNode node)
        {
            // Next concave or convex?
            if (TriangulationUtil.Orient2d(node.Prev.Point, node.Prev.Prev.Point, node.Prev.Prev.Prev.Point) ==
                Orientation.CW)
            {
                // Concave
                FillLeftConcaveEdgeEvent(tcx, edge, node.Prev);
            }
            else
            {
                // Convex
                // Next above or below edge?
                if (TriangulationUtil.Orient2d(edge.Q, node.Prev.Prev.Point, edge.P) == Orientation.CW)
                {
                    // Below
                    FillLeftConvexEdgeEvent(tcx, edge, node.Prev);
                }
                else
                {
                    // Above
                }
            }
        }

        private static void FillLeftConcaveEdgeEvent(DTSweepContext tcx, DTSweepConstraint edge, AdvancingFrontNode node)
        {
            Fill(tcx, node.Prev);
            if (node.Prev.Point != edge.P)
            {
                // Next above or below edge?
                if (TriangulationUtil.Orient2d(edge.Q, node.Prev.Point, edge.P) == Orientation.CW)
                {
                    // Below
                    if (TriangulationUtil.Orient2d(node.Point, node.Prev.Point, node.Prev.Prev.Point) == Orientation.CW)
                    {
                        // Next is concave
                        FillLeftConcaveEdgeEvent(tcx, edge, node);
                    }
                    else
                    {
                        // Next is convex
                    }
                }
            }
        }

        private static void FillLeftBelowEdgeEvent(DTSweepContext tcx, DTSweepConstraint edge, AdvancingFrontNode node)
        {
            if (node.Point.X > edge.P.X)
            {
                if (TriangulationUtil.Orient2d(node.Point, node.Prev.Point, node.Prev.Prev.Point) == Orientation.CW)
                {
                    // Concave 
                    FillLeftConcaveEdgeEvent(tcx, edge, node);
                }
                else
                {
                    // Convex
                    FillLeftConvexEdgeEvent(tcx, edge, node);
                    // Retry this one
                    FillLeftBelowEdgeEvent(tcx, edge, node);
                }
            }
        }

        private static void FillLeftAboveEdgeEvent(DTSweepContext tcx, DTSweepConstraint edge, AdvancingFrontNode node)
        {
            while (node.Prev.Point.X > edge.P.X)
            {
                // Check if next node is below the edge
                Orientation o1 = TriangulationUtil.Orient2d(edge.Q, node.Prev.Point, edge.P);
                if (o1 == Orientation.CW)
                {
                    FillLeftBelowEdgeEvent(tcx, edge, node);
                }
                else
                {
                    node = node.Prev;
                }
            }
        }

        private static bool IsEdgeSideOfTriangle(DelaunayTriangle triangle, TriangulationPoint ep, TriangulationPoint eq)
        {
            int index = triangle.EdgeIndex(ep, eq);
            if (index != -1)
            {
                triangle.MarkConstrainedEdge(index);
                triangle = triangle.Neighbors[index];
                if (triangle != null)
                {
                    triangle.MarkConstrainedEdge(ep, eq);
                }
                return true;
            }
            return false;
        }

        private static void EdgeEvent(DTSweepContext tcx, TriangulationPoint ep, TriangulationPoint eq, DelaunayTriangle triangle, TriangulationPoint point)
        {
            if (IsEdgeSideOfTriangle(triangle, ep, eq))
                return;

            TriangulationPoint p1 = triangle.PointCCW(point);
            Orientation o1 = TriangulationUtil.Orient2d(eq, p1, ep);
            if (o1 == Orientation.Collinear)
            {
                if (triangle.Contains(eq, p1))
                {
                    triangle.MarkConstrainedEdge(eq, p1);
                    // We are modifying the constraint maybe it would be better to 
                    // not change the given constraint and just keep a variable for the new constraint
                    tcx.EdgeEvent.ConstrainedEdge.Q = p1;
                    triangle = triangle.NeighborAcross(point);
                    EdgeEvent(tcx, ep, p1, triangle, p1);
                }
                else
                {
                    throw new PointOnEdgeException("EdgeEvent - Point on constrained edge not supported yet");
                }
                if (tcx.IsDebugEnabled)
                {
                    Debug.WriteLine("EdgeEvent - Point on constrained edge");
                }
                return;
            }

            TriangulationPoint p2 = triangle.PointCW(point);
            Orientation o2 = TriangulationUtil.Orient2d(eq, p2, ep);
            if (o2 == Orientation.Collinear)
            {
                if (triangle.Contains(eq, p2))
                {
                    triangle.MarkConstrainedEdge(eq, p2);
                    // We are modifying the constraint maybe it would be better to 
                    // not change the given constraint and just keep a variable for the new constraint
                    tcx.EdgeEvent.ConstrainedEdge.Q = p2;
                    triangle = triangle.NeighborAcross(point);
                    EdgeEvent(tcx, ep, p2, triangle, p2);
                }
                else
                {
                    throw new PointOnEdgeException("EdgeEvent - Point on constrained edge not supported yet");
                }
                if (tcx.IsDebugEnabled)
                {
                    Debug.WriteLine("EdgeEvent - Point on constrained edge");
                }
                return;
            }

            if (o1 == o2)
            {
                // Need to decide if we are rotating CW or CCW to get to a triangle
                // that will cross edge
                if (o1 == Orientation.CW)
                {
                    triangle = triangle.NeighborCCW(point);
                }
                else
                {
                    triangle = triangle.NeighborCW(point);
                }
                EdgeEvent(tcx, ep, eq, triangle, point);
            }
            else
            {
                // This triangle crosses constraint so lets flippin start!
                FlipEdgeEvent(tcx, ep, eq, triangle, point);
            }
        }

        private static void FlipEdgeEvent(DTSweepContext tcx, TriangulationPoint ep, TriangulationPoint eq, DelaunayTriangle t, TriangulationPoint p)
        {
            DelaunayTriangle ot = t.NeighborAcross(p);
            TriangulationPoint op = ot.OppositePoint(t, p);

            if (ot == null)
            {
                // If we want to integrate the fillEdgeEvent do it here
                // With current implementation we should never get here
                throw new InvalidOperationException("[BUG:FIXME] FLIP failed due to missing triangle");
            }

            if (t.GetConstrainedEdgeAcross(p))
            {
                throw new Exception("Intersecting Constraints");
            }

            bool inScanArea = TriangulationUtil.InScanArea(p, t.PointCCW(p), t.PointCW(p), op);
            if (inScanArea)
            {
                // Lets rotate shared edge one vertex CW
                RotateTrianglePair(t, p, ot, op);
                tcx.MapTriangleToNodes(t);
                tcx.MapTriangleToNodes(ot);

                if (p == eq && op == ep)
                {
                    if (eq == tcx.EdgeEvent.ConstrainedEdge.Q
                        && ep == tcx.EdgeEvent.ConstrainedEdge.P)
                    {
                        if (tcx.IsDebugEnabled) Console.WriteLine("[FLIP] - constrained edge done"); // TODO: remove
                        t.MarkConstrainedEdge(ep, eq);
                        ot.MarkConstrainedEdge(ep, eq);
                        Legalize(tcx, t);
                        Legalize(tcx, ot);
                    }
                    else
                    {
                        if (tcx.IsDebugEnabled) Console.WriteLine("[FLIP] - subedge done"); // TODO: remove
                        // XXX: I think one of the triangles should be legalized here?
                    }
                }
                else
                {
                    if (tcx.IsDebugEnabled)
                        Console.WriteLine("[FLIP] - flipping and continuing with triangle still crossing edge");
                    // TODO: remove
                    Orientation o = TriangulationUtil.Orient2d(eq, op, ep);
                    t = NextFlipTriangle(tcx, o, t, ot, p, op);
                    FlipEdgeEvent(tcx, ep, eq, t, p);
                }
            }
            else
            {
                TriangulationPoint newP = NextFlipPoint(ep, eq, ot, op);
                FlipScanEdgeEvent(tcx, ep, eq, t, ot, newP);
                EdgeEvent(tcx, ep, eq, t, p);
            }
        }

        /// <summary>
        /// When we need to traverse from one triangle to the next we need 
        /// the point in current triangle that is the opposite point to the next
        /// triangle. 
        /// </summary>
        private static TriangulationPoint NextFlipPoint(TriangulationPoint ep, TriangulationPoint eq, DelaunayTriangle ot, TriangulationPoint op)
        {
            Orientation o2d = TriangulationUtil.Orient2d(eq, op, ep);
            if (o2d == Orientation.CW)
            {
                // Right
                return ot.PointCCW(op);
            }
            else if (o2d == Orientation.CCW)
            {
                // Left
                return ot.PointCW(op);
            }
            else
            {
                // TODO: implement support for point on constraint edge
                throw new PointOnEdgeException("Point on constrained edge not supported yet");
            }
        }

        /// <summary>
        /// After a flip we have two triangles and know that only one will still be
        /// intersecting the edge. So decide which to contiune with and legalize the other
        /// </summary>
        /// <param name="tcx"></param>
        /// <param name="o">should be the result of an TriangulationUtil.orient2d( eq, op, ep )</param>
        /// <param name="t">triangle 1</param>
        /// <param name="ot">triangle 2</param>
        /// <param name="p">a point shared by both triangles</param>
        /// <param name="op">another point shared by both triangles</param>
        /// <returns>returns the triangle still intersecting the edge</returns>
        private static DelaunayTriangle NextFlipTriangle(DTSweepContext tcx, Orientation o, DelaunayTriangle t, DelaunayTriangle ot, TriangulationPoint p, TriangulationPoint op)
        {
            int edgeIndex;
            if (o == Orientation.CCW)
            {
                // ot is not crossing edge after flip
                edgeIndex = ot.EdgeIndex(p, op);
                ot.EdgeIsDelaunay[edgeIndex] = true;
                Legalize(tcx, ot);
                ot.EdgeIsDelaunay.Clear();
                return t;
            }
            // t is not crossing edge after flip
            edgeIndex = t.EdgeIndex(p, op);
            t.EdgeIsDelaunay[edgeIndex] = true;
            Legalize(tcx, t);
            t.EdgeIsDelaunay.Clear();
            return ot;
        }

        /// <summary>
        /// Scan part of the FlipScan algorithm<br>
        /// When a triangle pair isn't flippable we will scan for the next 
        /// point that is inside the flip triangle scan area. When found 
        /// we generate a new flipEdgeEvent
        /// </summary>
        /// <param name="tcx"></param>
        /// <param name="ep">last point on the edge we are traversing</param>
        /// <param name="eq">first point on the edge we are traversing</param>
        /// <param name="flipTriangle">the current triangle sharing the point eq with edge</param>
        /// <param name="t"></param>
        /// <param name="p"></param>
        private static void FlipScanEdgeEvent(DTSweepContext tcx, TriangulationPoint ep, TriangulationPoint eq, DelaunayTriangle flipTriangle, DelaunayTriangle t, TriangulationPoint p)
        {
            DelaunayTriangle ot = t.NeighborAcross(p);
            TriangulationPoint op = ot.OppositePoint(t, p);

            if (ot == null)
            {
                // If we want to integrate the fillEdgeEvent do it here
                // With current implementation we should never get here
                throw new Exception("[BUG:FIXME] FLIP failed due to missing triangle");
            }

            bool inScanArea = TriangulationUtil.InScanArea(eq, flipTriangle.PointCCW(eq), flipTriangle.PointCW(eq), op);
            if (inScanArea)
            {
                // flip with new edge op->eq
                FlipEdgeEvent(tcx, eq, op, ot, op);
                // TODO: Actually I just figured out that it should be possible to 
                //       improve this by getting the next ot and op before the the above 
                //       flip and continue the flipScanEdgeEvent here
                // set new ot and op here and loop back to inScanArea test
                // also need to set a new flipTriangle first
                // Turns out at first glance that this is somewhat complicated
                // so it will have to wait.
            }
            else
            {
                TriangulationPoint newP = NextFlipPoint(ep, eq, ot, op);
                FlipScanEdgeEvent(tcx, ep, eq, flipTriangle, ot, newP);
            }
        }

        /// <summary>
        /// Fills holes in the Advancing Front
        /// </summary>
        private static void FillAdvancingFront(DTSweepContext tcx, AdvancingFrontNode n)
        {
            double angle;

            // Fill right holes
            AdvancingFrontNode node = n.Next;
            while (node.HasNext)
            {
                // if HoleAngle exceeds 90 degrees then break.
                if (LargeHole_DontFill(node))
                    break;

                Fill(tcx, node);
                node = node.Next;
            }

            // Fill left holes
            node = n.Prev;
            while (node.HasPrev)
            {
                // if HoleAngle exceeds 90 degrees then break.
                if (LargeHole_DontFill(node))
                    break;

                angle = HoleAngle(node);
                if (angle > PI_div2 || angle < -PI_div2)
                {
                    break;
                }
                Fill(tcx, node);
                node = node.Prev;
            }

            // Fill right basins
            if (n.HasNext && n.Next.HasNext)
            {
                angle = BasinAngle(n);
                if (angle < PI_3div4)
                {
                    FillBasin(tcx, n);
                }
            }
        }

        // True if HoleAngle exceeds 90 degrees.
        private static bool LargeHole_DontFill(AdvancingFrontNode node)
        {
            AdvancingFrontNode nextNode = node.Next;
            AdvancingFrontNode prevNode = node.Prev;
            if (!AngleExceeds90Degrees(node.Point, nextNode.Point, prevNode.Point))
                return false;

            // Check additional points on front.
            AdvancingFrontNode next2Node = nextNode.Next;
            // "..Plus.." because only want angles on same side as point being added.
            if ((next2Node != null) && !AngleExceedsPlus90DegreesOrIsNegative(node.Point, next2Node.Point, prevNode.Point))
                return false;

            AdvancingFrontNode prev2Node = prevNode.Prev;
            // "..Plus.." because only want angles on same side as point being added.
            if ((prev2Node != null) && !AngleExceedsPlus90DegreesOrIsNegative(node.Point, nextNode.Point, prev2Node.Point))
                return false;

            return true;
        }

        private static bool AngleExceeds90Degrees(TriangulationPoint origin, TriangulationPoint pa, TriangulationPoint pb)
        {
            double angle = Angle(origin, pa, pb);
            bool exceeds90Degrees = ((angle > PI_div2) || (angle < -PI_div2));
            return exceeds90Degrees;
        }

        private static bool AngleExceedsPlus90DegreesOrIsNegative(TriangulationPoint origin, TriangulationPoint pa, TriangulationPoint pb)
        {
            double angle = Angle(origin, pa, pb);
            bool exceedsPlus90DegreesOrIsNegative = (angle > PI_div2) || (angle < 0);
            return exceedsPlus90DegreesOrIsNegative;
        }

        private static double Angle(TriangulationPoint origin, TriangulationPoint pa, TriangulationPoint pb)
        {
            /* Complex plane
            * ab = cosA +i*sinA
            * ab = (ax + ay*i)(bx + by*i) = (ax*bx + ay*by) + i(ax*by-ay*bx)
            * atan2(y,x) computes the principal value of the argument function
            * applied to the complex number x+iy
            * Where x = ax*bx + ay*by
            * y = ax*by - ay*bx
            */
            double px = origin.X;
            double py = origin.Y;
            double ax = pa.X - px;
            double ay = pa.Y - py;
            double bx = pb.X - px;
            double by = pb.Y - py;
            double x = ax * by - ay * bx;
            double y = ax * bx + ay * by;
            double angle = Math.Atan2(x, y);
            return angle;
        }

        /// <summary>
        /// Fills a basin that has formed on the Advancing Front to the right
        /// of given node.
        /// First we decide a left,bottom and right node that forms the 
        /// boundaries of the basin. Then we do a reqursive fill.
        /// </summary>
        /// <param name="tcx"></param>
        /// <param name="node">starting node, this or next node will be left node</param>
        private static void FillBasin(DTSweepContext tcx, AdvancingFrontNode node)
        {
            if (TriangulationUtil.Orient2d(node.Point, node.Next.Point, node.Next.Next.Point) == Orientation.CCW)
            {
                // tcx.basin.leftNode = node.next.next;
                tcx.Basin.leftNode = node;
            }
            else
            {
                tcx.Basin.leftNode = node.Next;
            }

            // Find the bottom and right node
            tcx.Basin.bottomNode = tcx.Basin.leftNode;
            while (tcx.Basin.bottomNode.HasNext && tcx.Basin.bottomNode.Point.Y >= tcx.Basin.bottomNode.Next.Point.Y)
            {
                tcx.Basin.bottomNode = tcx.Basin.bottomNode.Next;
            }

            if (tcx.Basin.bottomNode == tcx.Basin.leftNode)
            {
                // No valid basins
                return;
            }

            tcx.Basin.rightNode = tcx.Basin.bottomNode;
            while (tcx.Basin.rightNode.HasNext && tcx.Basin.rightNode.Point.Y < tcx.Basin.rightNode.Next.Point.Y)
            {
                tcx.Basin.rightNode = tcx.Basin.rightNode.Next;
            }

            if (tcx.Basin.rightNode == tcx.Basin.bottomNode)
            {
                // No valid basins
                return;
            }

            tcx.Basin.width = tcx.Basin.rightNode.Point.X - tcx.Basin.leftNode.Point.X;
            tcx.Basin.leftHighest = tcx.Basin.leftNode.Point.Y > tcx.Basin.rightNode.Point.Y;

            FillBasinReq(tcx, tcx.Basin.bottomNode);
        }

        /// <summary>
        /// Recursive algorithm to fill a Basin with triangles
        /// </summary>
        private static void FillBasinReq(DTSweepContext tcx, AdvancingFrontNode node)
        {
            // if shallow stop filling
            if (IsShallow(tcx, node))
            {
                return;
            }

            Fill(tcx, node);
            if (node.Prev == tcx.Basin.leftNode && node.Next == tcx.Basin.rightNode)
            {
                return;
            }
            else if (node.Prev == tcx.Basin.leftNode)
            {
                Orientation o = TriangulationUtil.Orient2d(node.Point, node.Next.Point, node.Next.Next.Point);
                if (o == Orientation.CW)
                {
                    return;
                }
                node = node.Next;
            }
            else if (node.Next == tcx.Basin.rightNode)
            {
                Orientation o = TriangulationUtil.Orient2d(node.Point, node.Prev.Point, node.Prev.Prev.Point);
                if (o == Orientation.CCW)
                {
                    return;
                }
                node = node.Prev;
            }
            else
            {
                // Continue with the neighbor node with lowest Y value
                if (node.Prev.Point.Y < node.Next.Point.Y)
                {
                    node = node.Prev;
                }
                else
                {
                    node = node.Next;
                }
            }
            FillBasinReq(tcx, node);
        }

        private static bool IsShallow(DTSweepContext tcx, AdvancingFrontNode node)
        {
            double height;

            if (tcx.Basin.leftHighest)
            {
                height = tcx.Basin.leftNode.Point.Y - node.Point.Y;
            }
            else
            {
                height = tcx.Basin.rightNode.Point.Y - node.Point.Y;
            }
            if (tcx.Basin.width > height)
            {
                return true;
            }
            return false;
        }

        /// <summary>
        /// ???
        /// </summary>
        /// <param name="node">middle node</param>
        /// <returns>the angle between 3 front nodes</returns>
        private static double HoleAngle(AdvancingFrontNode node)
        {
            // XXX: do we really need a signed angle for holeAngle?
            //      could possible save some cycles here
            /* Complex plane
             * ab = cosA +i*sinA
             * ab = (ax + ay*i)(bx + by*i) = (ax*bx + ay*by) + i(ax*by-ay*bx)
             * atan2(y,x) computes the principal value of the argument function
             * applied to the complex number x+iy
             * Where x = ax*bx + ay*by
             *       y = ax*by - ay*bx
             */
            double px = node.Point.X;
            double py = node.Point.Y;
            double ax = node.Next.Point.X - px;
            double ay = node.Next.Point.Y - py;
            double bx = node.Prev.Point.X - px;
            double by = node.Prev.Point.Y - py;
            return Math.Atan2(ax * by - ay * bx, ax * bx + ay * by);
        }

        /// <summary>
        /// The basin angle is decided against the horizontal line [1,0]
        /// </summary>
        private static double BasinAngle(AdvancingFrontNode node)
        {
            double ax = node.Point.X - node.Next.Next.Point.X;
            double ay = node.Point.Y - node.Next.Next.Point.Y;
            return Math.Atan2(ay, ax);
        }

        /// <summary>
        /// Adds a triangle to the advancing front to fill a hole.
        /// </summary>
        /// <param name="tcx"></param>
        /// <param name="node">middle node, that is the bottom of the hole</param>
        private static void Fill(DTSweepContext tcx, AdvancingFrontNode node)
        {
            DelaunayTriangle triangle = new DelaunayTriangle(node.Prev.Point, node.Point, node.Next.Point);
            // TODO: should copy the cEdge value from neighbor triangles
            //       for now cEdge values are copied during the legalize 
            triangle.MarkNeighbor(node.Prev.Triangle);
            triangle.MarkNeighbor(node.Triangle);
            tcx.Triangles.Add(triangle);

            // Update the advancing front
            node.Prev.Next = node.Next;
            node.Next.Prev = node.Prev;
            tcx.RemoveNode(node);

            // If it was legalized the triangle has already been mapped
            if (!Legalize(tcx, triangle))
            {
                tcx.MapTriangleToNodes(triangle);
            }
        }

        /// <summary>
        /// Returns true if triangle was legalized
        /// </summary>
        private static bool Legalize(DTSweepContext tcx, DelaunayTriangle t)
        {
            // To legalize a triangle we start by finding if any of the three edges
            // violate the Delaunay condition
            for (int i = 0; i < 3; i++)
            {
                // TODO: fix so that cEdge is always valid when creating new triangles then we can check it here
                //       instead of below with ot
                if (t.EdgeIsDelaunay[i])
                {
                    continue;
                }

                DelaunayTriangle ot = t.Neighbors[i];
                if (ot != null)
                {
                    TriangulationPoint p = t.Points[i];
                    TriangulationPoint op = ot.OppositePoint(t, p);
                    int oi = ot.IndexOf(op);
                    // If this is a Constrained Edge or a Delaunay Edge(only during recursive legalization)
                    // then we should not try to legalize
                    if (ot.EdgeIsConstrained[oi] || ot.EdgeIsDelaunay[oi])
                    {
                        t.EdgeIsConstrained[i] = ot.EdgeIsConstrained[oi];
                        // XXX: have no good way of setting this property when creating new triangles so lets set it here
                        continue;
                    }

                    bool inside = TriangulationUtil.SmartIncircle(p, t.PointCCW(p), t.PointCW(p), op);

                    if (inside)
                    {
                        // Lets mark this shared edge as Delaunay 
                        t.EdgeIsDelaunay[i] = true;
                        ot.EdgeIsDelaunay[oi] = true;

                        // Lets rotate shared edge one vertex CW to legalize it
                        RotateTrianglePair(t, p, ot, op);

                        // We now got one valid Delaunay Edge shared by two triangles
                        // This gives us 4 new edges to check for Delaunay

                        // Make sure that triangle to node mapping is done only one time for a specific triangle
                        bool notLegalized = !Legalize(tcx, t);

                        if (notLegalized)
                        {
                            tcx.MapTriangleToNodes(t);
                        }
                        notLegalized = !Legalize(tcx, ot);
                        if (notLegalized)
                        {
                            tcx.MapTriangleToNodes(ot);
                        }

                        // Reset the Delaunay edges, since they only are valid Delaunay edges
                        // until we add a new triangle or point.
                        // XXX: need to think about this. Can these edges be tried after we 
                        //      return to previous recursive level?
                        t.EdgeIsDelaunay[i] = false;
                        ot.EdgeIsDelaunay[oi] = false;

                        // If triangle have been legalized no need to check the other edges since
                        // the recursive legalization will handles those so we can end here.
                        return true;
                    }
                }
            }
            return false;
        }

        /// <summary>
        /// Rotates a triangle pair one vertex CW
        ///       n2                    n2
        ///  P +-----+             P +-----+
        ///    | t  /|               |\  t |  
        ///    |   / |               | \   |
        ///  n1|  /  |n3           n1|  \  |n3
        ///    | /   |    after CW   |   \ |
        ///    |/ oT |               | oT \|
        ///    +-----+ oP            +-----+
        ///       n4                    n4
        /// </summary>
        private static void RotateTrianglePair(DelaunayTriangle t, TriangulationPoint p, DelaunayTriangle ot, TriangulationPoint op)
        {
            DelaunayTriangle n1 = t.NeighborCCW(p);
            DelaunayTriangle n2 = t.NeighborCW(p);
            DelaunayTriangle n3 = ot.NeighborCCW(op);
            DelaunayTriangle n4 = ot.NeighborCW(op);

            bool ce1 = t.GetConstrainedEdgeCCW(p);
            bool ce2 = t.GetConstrainedEdgeCW(p);
            bool ce3 = ot.GetConstrainedEdgeCCW(op);
            bool ce4 = ot.GetConstrainedEdgeCW(op);

            bool de1 = t.GetDelaunayEdgeCCW(p);
            bool de2 = t.GetDelaunayEdgeCW(p);
            bool de3 = ot.GetDelaunayEdgeCCW(op);
            bool de4 = ot.GetDelaunayEdgeCW(op);

            t.Legalize(p, op);
            ot.Legalize(op, p);

            // Remap dEdge
            ot.SetDelaunayEdgeCCW(p, de1);
            t.SetDelaunayEdgeCW(p, de2);
            t.SetDelaunayEdgeCCW(op, de3);
            ot.SetDelaunayEdgeCW(op, de4);

            // Remap cEdge
            ot.SetConstrainedEdgeCCW(p, ce1);
            t.SetConstrainedEdgeCW(p, ce2);
            t.SetConstrainedEdgeCCW(op, ce3);
            ot.SetConstrainedEdgeCW(op, ce4);

            // Remap neighbors
            // XXX: might optimize the markNeighbor by keeping track of
            //      what side should be assigned to what neighbor after the 
            //      rotation. Now mark neighbor does lots of testing to find 
            //      the right side.
            t.Neighbors.Clear();
            ot.Neighbors.Clear();
            if (n1 != null) ot.MarkNeighbor(n1);
            if (n2 != null) t.MarkNeighbor(n2);
            if (n3 != null) t.MarkNeighbor(n3);
            if (n4 != null) ot.MarkNeighbor(n4);
            t.MarkNeighbor(ot);
        }
    }
}