388 lines
13 KiB
C#
388 lines
13 KiB
C#
/*
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* Farseer Physics Engine:
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* Copyright (c) 2012 Ian Qvist
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*
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* Original source Box2D:
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* Copyright (c) 2006-2011 Erin Catto http://www.box2d.org
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*
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* This software is provided 'as-is', without any express or implied
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* warranty. In no event will the authors be held liable for any damages
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* arising from the use of this software.
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* Permission is granted to anyone to use this software for any purpose,
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* including commercial applications, and to alter it and redistribute it
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* freely, subject to the following restrictions:
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* 1. The origin of this software must not be misrepresented; you must not
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* claim that you wrote the original software. If you use this software
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* in a product, an acknowledgment in the product documentation would be
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* appreciated but is not required.
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* 2. Altered source versions must be plainly marked as such, and must not be
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* misrepresented as being the original software.
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* 3. This notice may not be removed or altered from any source distribution.
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*/
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using System;
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using FarseerPhysics.Common;
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using Microsoft.Xna.Framework;
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namespace FarseerPhysics.Dynamics.Joints
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{
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// Point-to-point constraint
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// C = p2 - p1
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// Cdot = v2 - v1
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// = v2 + cross(w2, r2) - v1 - cross(w1, r1)
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// J = [-I -r1_skew I r2_skew ]
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// Identity used:
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// w k % (rx i + ry j) = w * (-ry i + rx j)
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// Angle constraint
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// C = angle2 - angle1 - referenceAngle
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// Cdot = w2 - w1
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// J = [0 0 -1 0 0 1]
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// K = invI1 + invI2
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/// <summary>
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/// A weld joint essentially glues two bodies together. A weld joint may
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/// distort somewhat because the island constraint solver is approximate.
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///
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/// The joint is soft constraint based, which means the two bodies will move
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/// relative to each other, when a force is applied. To combine two bodies
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/// in a rigid fashion, combine the fixtures to a single body instead.
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/// </summary>
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public class WeldJoint : Joint
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{
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// Solver shared
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private Vector3 _impulse;
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private float _gamma;
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private float _bias;
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// Solver temp
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private int _indexA;
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private int _indexB;
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private Vector2 _rA;
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private Vector2 _rB;
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private Vector2 _localCenterA;
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private Vector2 _localCenterB;
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private float _invMassA;
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private float _invMassB;
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private float _invIA;
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private float _invIB;
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private Mat33 _mass;
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internal WeldJoint()
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{
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JointType = JointType.Weld;
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}
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/// <summary>
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/// You need to specify an anchor point where they are attached.
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/// The position of the anchor point is important for computing the reaction torque.
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/// </summary>
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/// <param name="bodyA">The first body</param>
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/// <param name="bodyB">The second body</param>
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/// <param name="anchorA">The first body anchor.</param>
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/// <param name="anchorB">The second body anchor.</param>
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/// <param name="useWorldCoordinates">Set to true if you are using world coordinates as anchors.</param>
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public WeldJoint(Body bodyA, Body bodyB, Vector2 anchorA, Vector2 anchorB, bool useWorldCoordinates = false)
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: base(bodyA, bodyB)
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{
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JointType = JointType.Weld;
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if (useWorldCoordinates)
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{
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LocalAnchorA = bodyA.GetLocalPoint(anchorA);
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LocalAnchorB = bodyB.GetLocalPoint(anchorB);
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}
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else
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{
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LocalAnchorA = anchorA;
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LocalAnchorB = anchorB;
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}
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ReferenceAngle = BodyB.Rotation - BodyA.Rotation;
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}
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/// <summary>
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/// The local anchor point on BodyA
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/// </summary>
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public Vector2 LocalAnchorA { get; set; }
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/// <summary>
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/// The local anchor point on BodyB
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/// </summary>
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public Vector2 LocalAnchorB { get; set; }
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public override Vector2 WorldAnchorA
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{
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get { return BodyA.GetWorldPoint(LocalAnchorA); }
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set { LocalAnchorA = BodyA.GetLocalPoint(value); }
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}
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public override Vector2 WorldAnchorB
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{
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get { return BodyB.GetWorldPoint(LocalAnchorB); }
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set { LocalAnchorB = BodyB.GetLocalPoint(value); }
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}
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/// <summary>
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/// The bodyB angle minus bodyA angle in the reference state (radians).
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/// </summary>
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public float ReferenceAngle { get; set; }
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/// <summary>
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/// The frequency of the joint. A higher frequency means a stiffer joint, but
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/// a too high value can cause the joint to oscillate.
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/// Default is 0, which means the joint does no spring calculations.
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/// </summary>
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public float FrequencyHz { get; set; }
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/// <summary>
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/// The damping on the joint. The damping is only used when
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/// the joint has a frequency (> 0). A higher value means more damping.
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/// </summary>
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public float DampingRatio { get; set; }
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public override Vector2 GetReactionForce(float invDt)
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{
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return invDt * new Vector2(_impulse.X, _impulse.Y);
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}
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public override float GetReactionTorque(float invDt)
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{
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return invDt * _impulse.Z;
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}
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internal override void InitVelocityConstraints(ref SolverData data)
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{
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_indexA = BodyA.IslandIndex;
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_indexB = BodyB.IslandIndex;
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_localCenterA = BodyA._sweep.LocalCenter;
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_localCenterB = BodyB._sweep.LocalCenter;
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_invMassA = BodyA._invMass;
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_invMassB = BodyB._invMass;
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_invIA = BodyA._invI;
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_invIB = BodyB._invI;
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float aA = data.positions[_indexA].a;
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Vector2 vA = data.velocities[_indexA].v;
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float wA = data.velocities[_indexA].w;
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float aB = data.positions[_indexB].a;
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Vector2 vB = data.velocities[_indexB].v;
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float wB = data.velocities[_indexB].w;
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Rot qA = new Rot(aA), qB = new Rot(aB);
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_rA = MathUtils.Mul(qA, LocalAnchorA - _localCenterA);
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_rB = MathUtils.Mul(qB, LocalAnchorB - _localCenterB);
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// J = [-I -r1_skew I r2_skew]
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// [ 0 -1 0 1]
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// r_skew = [-ry; rx]
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// Matlab
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// K = [ mA+r1y^2*iA+mB+r2y^2*iB, -r1y*iA*r1x-r2y*iB*r2x, -r1y*iA-r2y*iB]
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// [ -r1y*iA*r1x-r2y*iB*r2x, mA+r1x^2*iA+mB+r2x^2*iB, r1x*iA+r2x*iB]
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// [ -r1y*iA-r2y*iB, r1x*iA+r2x*iB, iA+iB]
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float mA = _invMassA, mB = _invMassB;
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float iA = _invIA, iB = _invIB;
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Mat33 K = new Mat33();
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K.ex.X = mA + mB + _rA.Y * _rA.Y * iA + _rB.Y * _rB.Y * iB;
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K.ey.X = -_rA.Y * _rA.X * iA - _rB.Y * _rB.X * iB;
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K.ez.X = -_rA.Y * iA - _rB.Y * iB;
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K.ex.Y = K.ey.X;
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K.ey.Y = mA + mB + _rA.X * _rA.X * iA + _rB.X * _rB.X * iB;
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K.ez.Y = _rA.X * iA + _rB.X * iB;
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K.ex.Z = K.ez.X;
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K.ey.Z = K.ez.Y;
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K.ez.Z = iA + iB;
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if (FrequencyHz > 0.0f)
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{
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K.GetInverse22(ref _mass);
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float invM = iA + iB;
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float m = invM > 0.0f ? 1.0f / invM : 0.0f;
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float C = aB - aA - ReferenceAngle;
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// Frequency
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float omega = 2.0f * Settings.Pi * FrequencyHz;
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// Damping coefficient
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float d = 2.0f * m * DampingRatio * omega;
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// Spring stiffness
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float k = m * omega * omega;
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// magic formulas
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float h = data.step.dt;
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_gamma = h * (d + h * k);
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_gamma = _gamma != 0.0f ? 1.0f / _gamma : 0.0f;
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_bias = C * h * k * _gamma;
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invM += _gamma;
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_mass.ez.Z = invM != 0.0f ? 1.0f / invM : 0.0f;
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}
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else
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{
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K.GetSymInverse33(ref _mass);
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_gamma = 0.0f;
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_bias = 0.0f;
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}
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if (Settings.EnableWarmstarting)
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{
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// Scale impulses to support a variable time step.
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_impulse *= data.step.dtRatio;
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Vector2 P = new Vector2(_impulse.X, _impulse.Y);
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vA -= mA * P;
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wA -= iA * (MathUtils.Cross(_rA, P) + _impulse.Z);
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vB += mB * P;
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wB += iB * (MathUtils.Cross(_rB, P) + _impulse.Z);
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}
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else
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{
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_impulse = Vector3.Zero;
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}
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data.velocities[_indexA].v = vA;
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data.velocities[_indexA].w = wA;
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data.velocities[_indexB].v = vB;
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data.velocities[_indexB].w = wB;
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}
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internal override void SolveVelocityConstraints(ref SolverData data)
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{
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Vector2 vA = data.velocities[_indexA].v;
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float wA = data.velocities[_indexA].w;
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Vector2 vB = data.velocities[_indexB].v;
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float wB = data.velocities[_indexB].w;
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float mA = _invMassA, mB = _invMassB;
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float iA = _invIA, iB = _invIB;
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if (FrequencyHz > 0.0f)
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{
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float Cdot2 = wB - wA;
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float impulse2 = -_mass.ez.Z * (Cdot2 + _bias + _gamma * _impulse.Z);
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_impulse.Z += impulse2;
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wA -= iA * impulse2;
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wB += iB * impulse2;
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Vector2 Cdot1 = vB + MathUtils.Cross(wB, _rB) - vA - MathUtils.Cross(wA, _rA);
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Vector2 impulse1 = -MathUtils.Mul22(_mass, Cdot1);
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_impulse.X += impulse1.X;
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_impulse.Y += impulse1.Y;
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Vector2 P = impulse1;
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vA -= mA * P;
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wA -= iA * MathUtils.Cross(_rA, P);
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vB += mB * P;
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wB += iB * MathUtils.Cross(_rB, P);
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}
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else
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{
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Vector2 Cdot1 = vB + MathUtils.Cross(wB, _rB) - vA - MathUtils.Cross(wA, _rA);
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float Cdot2 = wB - wA;
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Vector3 Cdot = new Vector3(Cdot1.X, Cdot1.Y, Cdot2);
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Vector3 impulse = -MathUtils.Mul(_mass, Cdot);
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_impulse += impulse;
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Vector2 P = new Vector2(impulse.X, impulse.Y);
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vA -= mA * P;
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wA -= iA * (MathUtils.Cross(_rA, P) + impulse.Z);
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vB += mB * P;
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wB += iB * (MathUtils.Cross(_rB, P) + impulse.Z);
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}
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data.velocities[_indexA].v = vA;
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data.velocities[_indexA].w = wA;
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data.velocities[_indexB].v = vB;
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data.velocities[_indexB].w = wB;
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}
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internal override bool SolvePositionConstraints(ref SolverData data)
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{
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Vector2 cA = data.positions[_indexA].c;
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float aA = data.positions[_indexA].a;
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Vector2 cB = data.positions[_indexB].c;
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float aB = data.positions[_indexB].a;
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Rot qA = new Rot(aA), qB = new Rot(aB);
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float mA = _invMassA, mB = _invMassB;
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float iA = _invIA, iB = _invIB;
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Vector2 rA = MathUtils.Mul(qA, LocalAnchorA - _localCenterA);
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Vector2 rB = MathUtils.Mul(qB, LocalAnchorB - _localCenterB);
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float positionError, angularError;
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Mat33 K = new Mat33();
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K.ex.X = mA + mB + rA.Y * rA.Y * iA + rB.Y * rB.Y * iB;
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K.ey.X = -rA.Y * rA.X * iA - rB.Y * rB.X * iB;
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K.ez.X = -rA.Y * iA - rB.Y * iB;
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K.ex.Y = K.ey.X;
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K.ey.Y = mA + mB + rA.X * rA.X * iA + rB.X * rB.X * iB;
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K.ez.Y = rA.X * iA + rB.X * iB;
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K.ex.Z = K.ez.X;
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K.ey.Z = K.ez.Y;
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K.ez.Z = iA + iB;
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if (FrequencyHz > 0.0f)
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{
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Vector2 C1 = cB + rB - cA - rA;
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positionError = C1.Length();
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angularError = 0.0f;
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Vector2 P = -K.Solve22(C1);
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cA -= mA * P;
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aA -= iA * MathUtils.Cross(rA, P);
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cB += mB * P;
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aB += iB * MathUtils.Cross(rB, P);
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}
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else
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{
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Vector2 C1 = cB + rB - cA - rA;
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float C2 = aB - aA - ReferenceAngle;
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positionError = C1.Length();
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angularError = Math.Abs(C2);
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Vector3 C = new Vector3(C1.X, C1.Y, C2);
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Vector3 impulse = -K.Solve33(C);
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Vector2 P = new Vector2(impulse.X, impulse.Y);
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cA -= mA * P;
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aA -= iA * (MathUtils.Cross(rA, P) + impulse.Z);
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cB += mB * P;
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aB += iB * (MathUtils.Cross(rB, P) + impulse.Z);
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}
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data.positions[_indexA].c = cA;
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data.positions[_indexA].a = aA;
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data.positions[_indexB].c = cB;
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data.positions[_indexB].a = aB;
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return positionError <= Settings.LinearSlop && angularError <= Settings.AngularSlop;
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}
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}
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} |