513 lines
16 KiB
C#
513 lines
16 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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// Linear constraint (point-to-line)
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// d = pB - pA = xB + rB - xA - rA
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// C = dot(ay, d)
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// Cdot = dot(d, cross(wA, ay)) + dot(ay, vB + cross(wB, rB) - vA - cross(wA, rA))
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// = -dot(ay, vA) - dot(cross(d + rA, ay), wA) + dot(ay, vB) + dot(cross(rB, ay), vB)
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// J = [-ay, -cross(d + rA, ay), ay, cross(rB, ay)]
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// Spring linear constraint
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// C = dot(ax, d)
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// Cdot = = -dot(ax, vA) - dot(cross(d + rA, ax), wA) + dot(ax, vB) + dot(cross(rB, ax), vB)
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// J = [-ax -cross(d+rA, ax) ax cross(rB, ax)]
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// Motor rotational constraint
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// Cdot = wB - wA
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// J = [0 0 -1 0 0 1]
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/// <summary>
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/// A wheel joint. This joint provides two degrees of freedom: translation
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/// along an axis fixed in bodyA and rotation in the plane. You can use a
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/// joint limit to restrict the range of motion and a joint motor to drive
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/// the rotation or to model rotational friction.
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/// This joint is designed for vehicle suspensions.
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/// </summary>
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public class WheelJoint : Joint
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{
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// Solver shared
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private Vector2 _localYAxis;
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private float _impulse;
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private float _motorImpulse;
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private float _springImpulse;
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private float _maxMotorTorque;
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private float _motorSpeed;
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private bool _enableMotor;
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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 _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 Vector2 _ax, _ay;
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private float _sAx, _sBx;
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private float _sAy, _sBy;
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private float _mass;
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private float _motorMass;
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private float _springMass;
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private float _bias;
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private float _gamma;
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private Vector2 _axis;
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internal WheelJoint()
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{
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JointType = JointType.Wheel;
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}
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/// <summary>
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/// Constructor for WheelJoint
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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="anchor">The anchor point</param>
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/// <param name="axis">The axis</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 WheelJoint(Body bodyA, Body bodyB, Vector2 anchor, Vector2 axis, bool useWorldCoordinates = false)
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: base(bodyA, bodyB)
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{
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JointType = JointType.Wheel;
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if (useWorldCoordinates)
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{
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LocalAnchorA = bodyA.GetLocalPoint(anchor);
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LocalAnchorB = bodyB.GetLocalPoint(anchor);
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}
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else
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{
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LocalAnchorA = bodyA.GetLocalPoint(bodyB.GetWorldPoint(anchor));
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LocalAnchorB = anchor;
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}
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Axis = axis; //FPE only: We maintain the original value as it is supposed to.
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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 axis at which the suspension moves.
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/// </summary>
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public Vector2 Axis
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{
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get { return _axis; }
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set
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{
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_axis = value;
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LocalXAxis = BodyA.GetLocalVector(_axis);
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_localYAxis = MathUtils.Cross(1.0f, LocalXAxis);
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}
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}
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/// <summary>
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/// The axis in local coordinates relative to BodyA
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/// </summary>
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public Vector2 LocalXAxis { get; private set; }
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/// <summary>
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/// The desired motor speed in radians per second.
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/// </summary>
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public float MotorSpeed
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{
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get { return _motorSpeed; }
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set
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{
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WakeBodies();
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_motorSpeed = value;
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}
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}
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/// <summary>
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/// The maximum motor torque, usually in N-m.
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/// </summary>
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public float MaxMotorTorque
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{
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get { return _maxMotorTorque; }
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set
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{
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WakeBodies();
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_maxMotorTorque = value;
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}
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}
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/// <summary>
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/// Suspension frequency, zero indicates no suspension
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/// </summary>
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public float Frequency { get; set; }
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/// <summary>
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/// Suspension damping ratio, one indicates 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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/// Gets the translation along the axis
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/// </summary>
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public float JointTranslation
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{
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get
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{
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Body bA = BodyA;
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Body bB = BodyB;
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Vector2 pA = bA.GetWorldPoint(LocalAnchorA);
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Vector2 pB = bB.GetWorldPoint(LocalAnchorB);
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Vector2 d = pB - pA;
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Vector2 axis = bA.GetWorldVector(LocalXAxis);
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float translation = Vector2.Dot(d, axis);
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return translation;
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}
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}
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/// <summary>
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/// Gets the angular velocity of the joint
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/// </summary>
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public float JointSpeed
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{
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get
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{
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float wA = BodyA.AngularVelocity;
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float wB = BodyB.AngularVelocity;
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return wB - wA;
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}
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}
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/// <summary>
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/// Enable/disable the joint motor.
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/// </summary>
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public bool MotorEnabled
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{
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get { return _enableMotor; }
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set
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{
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WakeBodies();
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_enableMotor = value;
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}
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}
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/// <summary>
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/// Gets the torque of the motor
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/// </summary>
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/// <param name="invDt">inverse delta time</param>
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public float GetMotorTorque(float invDt)
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{
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return invDt * _motorImpulse;
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}
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public override Vector2 GetReactionForce(float invDt)
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{
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return invDt * (_impulse * _ay + _springImpulse * _ax);
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}
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public override float GetReactionTorque(float invDt)
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{
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return invDt * _motorImpulse;
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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 mA = _invMassA, mB = _invMassB;
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float iA = _invIA, iB = _invIB;
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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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// Compute the effective masses.
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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 d1 = cB + rB - cA - rA;
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// Point to line constraint
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{
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_ay = MathUtils.Mul(qA, _localYAxis);
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_sAy = MathUtils.Cross(d1 + rA, _ay);
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_sBy = MathUtils.Cross(rB, _ay);
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_mass = mA + mB + iA * _sAy * _sAy + iB * _sBy * _sBy;
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if (_mass > 0.0f)
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{
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_mass = 1.0f / _mass;
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}
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}
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// Spring constraint
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_springMass = 0.0f;
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_bias = 0.0f;
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_gamma = 0.0f;
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if (Frequency > 0.0f)
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{
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_ax = MathUtils.Mul(qA, LocalXAxis);
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_sAx = MathUtils.Cross(d1 + rA, _ax);
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_sBx = MathUtils.Cross(rB, _ax);
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float invMass = mA + mB + iA * _sAx * _sAx + iB * _sBx * _sBx;
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if (invMass > 0.0f)
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{
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_springMass = 1.0f / invMass;
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float C = Vector2.Dot(d1, _ax);
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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 * _springMass * DampingRatio * omega;
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// Spring stiffness
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float k = _springMass * 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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if (_gamma > 0.0f)
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{
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_gamma = 1.0f / _gamma;
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}
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_bias = C * h * k * _gamma;
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_springMass = invMass + _gamma;
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if (_springMass > 0.0f)
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{
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_springMass = 1.0f / _springMass;
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}
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}
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}
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else
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{
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_springImpulse = 0.0f;
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}
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// Rotational motor
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if (_enableMotor)
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{
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_motorMass = iA + iB;
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if (_motorMass > 0.0f)
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{
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_motorMass = 1.0f / _motorMass;
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}
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}
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else
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{
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_motorMass = 0.0f;
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_motorImpulse = 0.0f;
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}
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if (Settings.EnableWarmstarting)
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{
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// Account for variable time step.
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_impulse *= data.step.dtRatio;
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_springImpulse *= data.step.dtRatio;
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_motorImpulse *= data.step.dtRatio;
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Vector2 P = _impulse * _ay + _springImpulse * _ax;
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float LA = _impulse * _sAy + _springImpulse * _sAx + _motorImpulse;
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float LB = _impulse * _sBy + _springImpulse * _sBx + _motorImpulse;
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vA -= _invMassA * P;
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wA -= _invIA * LA;
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vB += _invMassB * P;
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wB += _invIB * LB;
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}
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else
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{
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_impulse = 0.0f;
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_springImpulse = 0.0f;
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_motorImpulse = 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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float mA = _invMassA, mB = _invMassB;
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float iA = _invIA, iB = _invIB;
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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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// Solve spring constraint
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{
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float Cdot = Vector2.Dot(_ax, vB - vA) + _sBx * wB - _sAx * wA;
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float impulse = -_springMass * (Cdot + _bias + _gamma * _springImpulse);
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_springImpulse += impulse;
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Vector2 P = impulse * _ax;
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float LA = impulse * _sAx;
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float LB = impulse * _sBx;
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vA -= mA * P;
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wA -= iA * LA;
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vB += mB * P;
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wB += iB * LB;
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}
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// Solve rotational motor constraint
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{
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float Cdot = wB - wA - _motorSpeed;
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float impulse = -_motorMass * Cdot;
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float oldImpulse = _motorImpulse;
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float maxImpulse = data.step.dt * _maxMotorTorque;
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_motorImpulse = MathUtils.Clamp(_motorImpulse + impulse, -maxImpulse, maxImpulse);
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impulse = _motorImpulse - oldImpulse;
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wA -= iA * impulse;
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wB += iB * impulse;
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}
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// Solve point to line constraint
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{
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float Cdot = Vector2.Dot(_ay, vB - vA) + _sBy * wB - _sAy * wA;
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float impulse = -_mass * Cdot;
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_impulse += impulse;
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Vector2 P = impulse * _ay;
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float LA = impulse * _sAy;
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float LB = impulse * _sBy;
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vA -= mA * P;
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wA -= iA * LA;
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vB += mB * P;
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wB += iB * LB;
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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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Vector2 rA = MathUtils.Mul(qA, LocalAnchorA - _localCenterA);
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Vector2 rB = MathUtils.Mul(qB, LocalAnchorB - _localCenterB);
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Vector2 d = (cB - cA) + rB - rA;
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Vector2 ay = MathUtils.Mul(qA, _localYAxis);
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float sAy = MathUtils.Cross(d + rA, ay);
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float sBy = MathUtils.Cross(rB, ay);
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float C = Vector2.Dot(d, ay);
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float k = _invMassA + _invMassB + _invIA * _sAy * _sAy + _invIB * _sBy * _sBy;
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float impulse;
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if (k != 0.0f)
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{
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impulse = -C / k;
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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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Vector2 P = impulse * ay;
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float LA = impulse * sAy;
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float LB = impulse * sBy;
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cA -= _invMassA * P;
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aA -= _invIA * LA;
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cB += _invMassB * P;
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aB += _invIB * LB;
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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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} |