331 lines
11 KiB
C#
331 lines
11 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 System.Diagnostics;
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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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// 1-D rained system
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// m (v2 - v1) = lambda
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// v2 + (beta/h) * x1 + gamma * lambda = 0, gamma has units of inverse mass.
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// x2 = x1 + h * v2
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// 1-D mass-damper-spring system
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// m (v2 - v1) + h * d * v2 + h * k *
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// C = norm(p2 - p1) - L
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// u = (p2 - p1) / norm(p2 - p1)
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// Cdot = dot(u, v2 + cross(w2, r2) - v1 - cross(w1, r1))
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// J = [-u -cross(r1, u) u cross(r2, u)]
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// K = J * invM * JT
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// = invMass1 + invI1 * cross(r1, u)^2 + invMass2 + invI2 * cross(r2, u)^2
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/// <summary>
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/// A distance joint rains two points on two bodies
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/// to remain at a fixed distance from each other. You can view
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/// this as a massless, rigid rod.
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/// </summary>
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public class DistanceJoint : Joint
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{
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// Solver shared
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private float _bias;
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private float _gamma;
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private float _impulse;
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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 _u;
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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 float _mass;
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internal DistanceJoint()
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{
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JointType = JointType.Distance;
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}
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/// <summary>
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/// This requires defining an
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/// anchor point on both bodies and the non-zero length of the
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/// distance joint. If you don't supply a length, the local anchor points
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/// is used so that the initial configuration can violate the constraint
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/// slightly. This helps when saving and loading a game.
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/// Warning Do not use a zero or short length.
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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 DistanceJoint(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.Distance;
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if (useWorldCoordinates)
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{
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LocalAnchorA = bodyA.GetLocalPoint(ref anchorA);
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LocalAnchorB = bodyB.GetLocalPoint(ref anchorB);
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Length = (anchorB - anchorA).Length();
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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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Length = (BodyB.GetWorldPoint(ref anchorB) - BodyA.GetWorldPoint(ref anchorA)).Length();
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}
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}
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/// <summary>
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/// The local anchor point relative to bodyA's origin.
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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 relative to bodyB's origin.
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/// </summary>
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public Vector2 LocalAnchorB { get; set; }
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public override sealed Vector2 WorldAnchorA
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{
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get { return BodyA.GetWorldPoint(LocalAnchorA); }
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set { Debug.Assert(false, "You can't set the world anchor on this joint type."); }
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}
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public override sealed Vector2 WorldAnchorB
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{
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get { return BodyB.GetWorldPoint(LocalAnchorB); }
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set { Debug.Assert(false, "You can't set the world anchor on this joint type."); }
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}
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/// <summary>
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/// The natural length between the anchor points.
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/// Manipulating the length can lead to non-physical behavior when the frequency is zero.
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/// </summary>
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public float Length { get; set; }
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/// <summary>
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/// The mass-spring-damper frequency in Hertz. A value of 0
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/// disables softness.
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/// </summary>
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public float Frequency { get; set; }
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/// <summary>
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/// The damping ratio. 0 = no damping, 1 = critical damping.
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/// </summary>
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public float DampingRatio { get; set; }
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/// <summary>
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/// Get the reaction force given the inverse time step. Unit is N.
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/// </summary>
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/// <param name="invDt"></param>
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/// <returns></returns>
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public override Vector2 GetReactionForce(float invDt)
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{
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Vector2 F = (invDt * _impulse) * _u;
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return F;
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}
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/// <summary>
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/// Get the reaction torque given the inverse time step.
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/// Unit is N*m. This is always zero for a distance joint.
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/// </summary>
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/// <param name="invDt"></param>
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/// <returns></returns>
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public override float GetReactionTorque(float invDt)
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{
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return 0.0f;
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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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Vector2 cA = data.positions[_indexA].c;
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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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Vector2 cB = data.positions[_indexB].c;
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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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_u = cB + _rB - cA - _rA;
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// Handle singularity.
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float length = _u.Length();
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if (length > Settings.LinearSlop)
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{
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_u *= 1.0f / length;
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}
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else
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{
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_u = Vector2.Zero;
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}
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float crAu = MathUtils.Cross(_rA, _u);
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float crBu = MathUtils.Cross(_rB, _u);
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float invMass = _invMassA + _invIA * crAu * crAu + _invMassB + _invIB * crBu * crBu;
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// Compute the effective mass matrix.
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_mass = invMass != 0.0f ? 1.0f / invMass : 0.0f;
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if (Frequency > 0.0f)
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{
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float C = length - Length;
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// Frequency
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float omega = 2.0f * Settings.Pi * Frequency;
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// Damping coefficient
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float d = 2.0f * _mass * DampingRatio * omega;
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// Spring stiffness
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float k = _mass * 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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invMass += _gamma;
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_mass = invMass != 0.0f ? 1.0f / invMass : 0.0f;
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}
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else
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{
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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 the impulse to support a variable time step.
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_impulse *= data.step.dtRatio;
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Vector2 P = _impulse * _u;
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vA -= _invMassA * P;
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wA -= _invIA * MathUtils.Cross(_rA, P);
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vB += _invMassB * P;
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wB += _invIB * MathUtils.Cross(_rB, P);
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}
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else
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{
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_impulse = 0.0f;
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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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// Cdot = dot(u, v + cross(w, r))
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Vector2 vpA = vA + MathUtils.Cross(wA, _rA);
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Vector2 vpB = vB + MathUtils.Cross(wB, _rB);
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float Cdot = Vector2.Dot(_u, vpB - vpA);
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float impulse = -_mass * (Cdot + _bias + _gamma * _impulse);
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_impulse += impulse;
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Vector2 P = impulse * _u;
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vA -= _invMassA * P;
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wA -= _invIA * MathUtils.Cross(_rA, P);
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vB += _invMassB * P;
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wB += _invIB * MathUtils.Cross(_rB, P);
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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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if (Frequency > 0.0f)
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{
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// There is no position correction for soft distance constraints.
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return true;
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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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Vector2 rA = MathUtils.Mul(qA, LocalAnchorA - _localCenterA);
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Vector2 rB = MathUtils.Mul(qB, LocalAnchorB - _localCenterB);
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Vector2 u = cB + rB - cA - rA;
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float length = u.Length(); u.Normalize();
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float C = length - Length;
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C = MathUtils.Clamp(C, -Settings.MaxLinearCorrection, Settings.MaxLinearCorrection);
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float impulse = -_mass * C;
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Vector2 P = impulse * u;
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cA -= _invMassA * P;
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aA -= _invIA * MathUtils.Cross(rA, P);
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cB += _invMassB * P;
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aB += _invIB * MathUtils.Cross(rB, P);
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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 Math.Abs(C) < Settings.LinearSlop;
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}
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}
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} |