636 lines
22 KiB
C#
636 lines
22 KiB
C#
/*
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* Farseer Physics Engine based on Box2D.XNA port:
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* Copyright (c) 2010 Ian Qvist
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*
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* Box2D.XNA port of Box2D:
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* Copyright (c) 2009 Brandon Furtwangler, Nathan Furtwangler
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*
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* Original source Box2D:
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* Copyright (c) 2006-2009 Erin Catto http://www.gphysics.com
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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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// Linear constraint (point-to-line)
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// d = p2 - p1 = x2 + r2 - x1 - r1
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// C = dot(perp, d)
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// Cdot = dot(d, cross(w1, perp)) + dot(perp, v2 + cross(w2, r2) - v1 - cross(w1, r1))
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// = -dot(perp, v1) - dot(cross(d + r1, perp), w1) + dot(perp, v2) + dot(cross(r2, perp), v2)
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// J = [-perp, -cross(d + r1, perp), perp, cross(r2,perp)]
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//
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// Angular constraint
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// C = a2 - a1 + a_initial
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// Cdot = w2 - w1
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// J = [0 0 -1 0 0 1]
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//
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// K = J * invM * JT
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//
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// J = [-a -s1 a s2]
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// [0 -1 0 1]
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// a = perp
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// s1 = cross(d + r1, a) = cross(p2 - x1, a)
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// s2 = cross(r2, a) = cross(p2 - x2, a)
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// Motor/Limit linear constraint
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// C = dot(ax1, d)
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// Cdot = = -dot(ax1, v1) - dot(cross(d + r1, ax1), w1) + dot(ax1, v2) + dot(cross(r2, ax1), v2)
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// J = [-ax1 -cross(d+r1,ax1) ax1 cross(r2,ax1)]
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// Block Solver
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// We develop a block solver that includes the joint limit. This makes the limit stiff (inelastic) even
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// when the mass has poor distribution (leading to large torques about the joint anchor points).
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//
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// The Jacobian has 3 rows:
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// J = [-uT -s1 uT s2] // linear
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// [0 -1 0 1] // angular
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// [-vT -a1 vT a2] // limit
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//
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// u = perp
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// v = axis
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// s1 = cross(d + r1, u), s2 = cross(r2, u)
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// a1 = cross(d + r1, v), a2 = cross(r2, v)
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// M * (v2 - v1) = JT * df
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// J * v2 = bias
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//
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// v2 = v1 + invM * JT * df
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// J * (v1 + invM * JT * df) = bias
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// K * df = bias - J * v1 = -Cdot
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// K = J * invM * JT
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// Cdot = J * v1 - bias
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//
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// Now solve for f2.
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// df = f2 - f1
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// K * (f2 - f1) = -Cdot
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// f2 = invK * (-Cdot) + f1
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//
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// Clamp accumulated limit impulse.
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// lower: f2(3) = max(f2(3), 0)
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// upper: f2(3) = min(f2(3), 0)
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//
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// Solve for correct f2(1:2)
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// K(1:2, 1:2) * f2(1:2) = -Cdot(1:2) - K(1:2,3) * f2(3) + K(1:2,1:3) * f1
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// = -Cdot(1:2) - K(1:2,3) * f2(3) + K(1:2,1:2) * f1(1:2) + K(1:2,3) * f1(3)
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// K(1:2, 1:2) * f2(1:2) = -Cdot(1:2) - K(1:2,3) * (f2(3) - f1(3)) + K(1:2,1:2) * f1(1:2)
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// f2(1:2) = invK(1:2,1:2) * (-Cdot(1:2) - K(1:2,3) * (f2(3) - f1(3))) + f1(1:2)
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//
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// Now compute impulse to be applied:
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// df = f2 - f1
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/// <summary>
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/// A prismatic joint. This joint provides one degree of freedom: translation
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/// along an axis fixed in body1. Relative rotation is prevented. You can
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/// use a joint limit to restrict the range of motion and a joint motor to
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/// drive the motion or to model joint friction.
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/// </summary>
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public class FixedPrismaticJoint : Joint
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{
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private Mat33 _K;
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private float _a1, _a2;
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private Vector2 _axis;
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private bool _enableLimit;
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private bool _enableMotor;
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private Vector3 _impulse;
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private LimitState _limitState;
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private Vector2 _localXAxis1;
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private Vector2 _localYAxis1;
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private float _lowerTranslation;
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private float _maxMotorForce;
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private float _motorMass; // effective mass for motor/limit translational constraint.
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private float _motorSpeed;
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private Vector2 _perp;
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private float _refAngle;
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private float _s1, _s2;
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private float _upperTranslation;
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/// <summary>
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/// This requires defining a line of
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/// motion using an axis and an anchor point. The definition uses local
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/// anchor points and a local axis so that the initial configuration
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/// can violate the constraint slightly. The joint translation is zero
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/// when the local anchor points coincide in world space. Using local
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/// anchors and a local axis helps when saving and loading a game.
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/// </summary>
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/// <param name="body">The body.</param>
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/// <param name="worldAnchor">The anchor.</param>
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/// <param name="axis">The axis.</param>
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public FixedPrismaticJoint(Body body, Vector2 worldAnchor, Vector2 axis)
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: base(body)
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{
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JointType = JointType.FixedPrismatic;
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BodyB = BodyA;
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LocalAnchorA = worldAnchor;
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LocalAnchorB = BodyB.GetLocalPoint(worldAnchor);
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_localXAxis1 = axis;
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_localYAxis1 = MathUtils.Cross(1.0f, _localXAxis1);
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_refAngle = BodyB.Rotation;
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_limitState = LimitState.Inactive;
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}
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public Vector2 LocalAnchorA { get; set; }
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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 LocalAnchorA; }
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}
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public override Vector2 WorldAnchorB
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{
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get { return BodyA.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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/// Get the current joint translation, usually in meters.
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/// </summary>
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/// <value></value>
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public float JointTranslation
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{
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get
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{
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Vector2 d = BodyB.GetWorldPoint(LocalAnchorB) - LocalAnchorA;
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Vector2 axis = _localXAxis1;
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return Vector2.Dot(d, axis);
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}
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}
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/// <summary>
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/// Get the current joint translation speed, usually in meters per second.
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/// </summary>
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/// <value></value>
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public float JointSpeed
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{
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get
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{
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Transform xf2;
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BodyB.GetTransform(out xf2);
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Vector2 r1 = LocalAnchorA;
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Vector2 r2 = MathUtils.Multiply(ref xf2.R, LocalAnchorB - BodyB.LocalCenter);
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Vector2 p1 = r1;
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Vector2 p2 = BodyB.Sweep.C + r2;
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Vector2 d = p2 - p1;
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Vector2 axis = _localXAxis1;
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Vector2 v1 = Vector2.Zero;
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Vector2 v2 = BodyB.LinearVelocityInternal;
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const float w1 = 0.0f;
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float w2 = BodyB.AngularVelocityInternal;
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float speed = Vector2.Dot(d, MathUtils.Cross(w1, axis)) +
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Vector2.Dot(axis, v2 + MathUtils.Cross(w2, r2) - v1 - MathUtils.Cross(w1, r1));
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return speed;
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}
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}
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/// <summary>
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/// Is the joint limit enabled?
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/// </summary>
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/// <value><c>true</c> if [limit enabled]; otherwise, <c>false</c>.</value>
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public bool LimitEnabled
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{
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get { return _enableLimit; }
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set
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{
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Debug.Assert(BodyA.FixedRotation == false, "Warning: limits does currently not work with fixed rotation");
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WakeBodies();
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_enableLimit = value;
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}
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}
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/// <summary>
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/// Get the lower joint limit, usually in meters.
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/// </summary>
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/// <value></value>
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public float LowerLimit
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{
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get { return _lowerTranslation; }
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set
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{
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WakeBodies();
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_lowerTranslation = value;
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}
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}
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/// <summary>
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/// Get the upper joint limit, usually in meters.
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/// </summary>
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/// <value></value>
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public float UpperLimit
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{
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get { return _upperTranslation; }
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set
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{
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WakeBodies();
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_upperTranslation = value;
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}
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}
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/// <summary>
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/// Is the joint motor enabled?
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/// </summary>
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/// <value><c>true</c> if [motor enabled]; otherwise, <c>false</c>.</value>
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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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/// Set the motor speed, usually in meters per second.
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/// </summary>
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/// <value>The speed.</value>
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public float MotorSpeed
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{
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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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get { return _motorSpeed; }
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}
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/// <summary>
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/// Set the maximum motor force, usually in N.
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/// </summary>
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/// <value>The force.</value>
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public float MaxMotorForce
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{
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set
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{
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WakeBodies();
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_maxMotorForce = value;
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}
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}
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/// <summary>
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/// Get the current motor force, usually in N.
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/// </summary>
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/// <value></value>
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public float MotorForce { get; set; }
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public Vector2 LocalXAxis1
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{
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get { return _localXAxis1; }
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set
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{
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_localXAxis1 = value;
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_localYAxis1 = MathUtils.Cross(1.0f, _localXAxis1);
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}
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}
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public override Vector2 GetReactionForce(float inv_dt)
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{
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return inv_dt * (_impulse.X * _perp + (MotorForce + _impulse.Z) * _axis);
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}
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public override float GetReactionTorque(float inv_dt)
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{
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return inv_dt * _impulse.Y;
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}
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internal override void InitVelocityConstraints(ref TimeStep step)
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{
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Body bB = BodyB;
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LocalCenterA = Vector2.Zero;
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LocalCenterB = bB.LocalCenter;
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Transform xf2;
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bB.GetTransform(out xf2);
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// Compute the effective masses.
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Vector2 r1 = LocalAnchorA;
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Vector2 r2 = MathUtils.Multiply(ref xf2.R, LocalAnchorB - LocalCenterB);
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Vector2 d = bB.Sweep.C + r2 - /* b1._sweep.Center - */ r1;
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InvMassA = 0.0f;
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InvIA = 0.0f;
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InvMassB = bB.InvMass;
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InvIB = bB.InvI;
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// Compute motor Jacobian and effective mass.
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{
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_axis = _localXAxis1;
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_a1 = MathUtils.Cross(d + r1, _axis);
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_a2 = MathUtils.Cross(r2, _axis);
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_motorMass = InvMassA + InvMassB + InvIA * _a1 * _a1 + InvIB * _a2 * _a2;
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if (_motorMass > Settings.Epsilon)
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{
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_motorMass = 1.0f / _motorMass;
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}
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}
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// Prismatic constraint.
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{
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_perp = _localYAxis1;
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_s1 = MathUtils.Cross(d + r1, _perp);
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_s2 = MathUtils.Cross(r2, _perp);
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float m1 = InvMassA, m2 = InvMassB;
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float i1 = InvIA, i2 = InvIB;
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float k11 = m1 + m2 + i1 * _s1 * _s1 + i2 * _s2 * _s2;
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float k12 = i1 * _s1 + i2 * _s2;
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float k13 = i1 * _s1 * _a1 + i2 * _s2 * _a2;
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float k22 = i1 + i2;
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float k23 = i1 * _a1 + i2 * _a2;
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float k33 = m1 + m2 + i1 * _a1 * _a1 + i2 * _a2 * _a2;
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_K.Col1 = new Vector3(k11, k12, k13);
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_K.Col2 = new Vector3(k12, k22, k23);
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_K.Col3 = new Vector3(k13, k23, k33);
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}
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// Compute motor and limit terms.
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if (_enableLimit)
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{
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float jointTranslation = Vector2.Dot(_axis, d);
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if (Math.Abs(_upperTranslation - _lowerTranslation) < 2.0f * Settings.LinearSlop)
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{
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_limitState = LimitState.Equal;
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}
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else if (jointTranslation <= _lowerTranslation)
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{
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if (_limitState != LimitState.AtLower)
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{
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_limitState = LimitState.AtLower;
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_impulse.Z = 0.0f;
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}
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}
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else if (jointTranslation >= _upperTranslation)
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{
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if (_limitState != LimitState.AtUpper)
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{
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_limitState = LimitState.AtUpper;
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_impulse.Z = 0.0f;
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}
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}
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else
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{
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_limitState = LimitState.Inactive;
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_impulse.Z = 0.0f;
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}
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}
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else
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{
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_limitState = LimitState.Inactive;
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}
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if (_enableMotor == false)
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{
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MotorForce = 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 *= step.dtRatio;
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MotorForce *= step.dtRatio;
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Vector2 P = _impulse.X * _perp + (MotorForce + _impulse.Z) * _axis;
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float L2 = _impulse.X * _s2 + _impulse.Y + (MotorForce + _impulse.Z) * _a2;
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bB.LinearVelocityInternal += InvMassB * P;
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bB.AngularVelocityInternal += InvIB * L2;
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}
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else
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{
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_impulse = Vector3.Zero;
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MotorForce = 0.0f;
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}
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}
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internal override void SolveVelocityConstraints(ref TimeStep step)
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{
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Body bB = BodyB;
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Vector2 v1 = Vector2.Zero;
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float w1 = 0.0f;
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Vector2 v2 = bB.LinearVelocityInternal;
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float w2 = bB.AngularVelocityInternal;
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// Solve linear motor constraint.
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if (_enableMotor && _limitState != LimitState.Equal)
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{
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float Cdot = Vector2.Dot(_axis, v2 - v1) + _a2 * w2 - _a1 * w1;
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float impulse = _motorMass * (_motorSpeed - Cdot);
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float oldImpulse = MotorForce;
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float maxImpulse = step.dt * _maxMotorForce;
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MotorForce = MathUtils.Clamp(MotorForce + impulse, -maxImpulse, maxImpulse);
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impulse = MotorForce - oldImpulse;
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Vector2 P = impulse * _axis;
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float L1 = impulse * _a1;
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float L2 = impulse * _a2;
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v1 -= InvMassA * P;
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w1 -= InvIA * L1;
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v2 += InvMassB * P;
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w2 += InvIB * L2;
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}
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Vector2 Cdot1 = new Vector2(Vector2.Dot(_perp, v2 - v1) + _s2 * w2 - _s1 * w1, w2 - w1);
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if (_enableLimit && _limitState != LimitState.Inactive)
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{
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// Solve prismatic and limit constraint in block form.
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float Cdot2 = Vector2.Dot(_axis, v2 - v1) + _a2 * w2 - _a1 * w1;
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Vector3 Cdot = new Vector3(Cdot1.X, Cdot1.Y, Cdot2);
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Vector3 f1 = _impulse;
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Vector3 df = _K.Solve33(-Cdot);
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_impulse += df;
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if (_limitState == LimitState.AtLower)
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{
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_impulse.Z = Math.Max(_impulse.Z, 0.0f);
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}
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else if (_limitState == LimitState.AtUpper)
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{
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_impulse.Z = Math.Min(_impulse.Z, 0.0f);
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}
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// f2(1:2) = invK(1:2,1:2) * (-Cdot(1:2) - K(1:2,3) * (f2(3) - f1(3))) + f1(1:2)
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Vector2 b = -Cdot1 - (_impulse.Z - f1.Z) * new Vector2(_K.Col3.X, _K.Col3.Y);
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Vector2 f2r = _K.Solve22(b) + new Vector2(f1.X, f1.Y);
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_impulse.X = f2r.X;
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_impulse.Y = f2r.Y;
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df = _impulse - f1;
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Vector2 P = df.X * _perp + df.Z * _axis;
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float L2 = df.X * _s2 + df.Y + df.Z * _a2;
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v2 += InvMassB * P;
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w2 += InvIB * L2;
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}
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else
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{
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// Limit is inactive, just solve the prismatic constraint in block form.
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Vector2 df = _K.Solve22(-Cdot1);
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_impulse.X += df.X;
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_impulse.Y += df.Y;
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Vector2 P = df.X * _perp;
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float L2 = df.X * _s2 + df.Y;
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v2 += InvMassB * P;
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w2 += InvIB * L2;
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}
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bB.LinearVelocityInternal = v2;
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bB.AngularVelocityInternal = w2;
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}
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|
|
|
internal override bool SolvePositionConstraints()
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|
{
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//Body b1 = BodyA;
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Body b2 = BodyB;
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|
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Vector2 c1 = Vector2.Zero; // b1._sweep.Center;
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float a1 = 0.0f; // b1._sweep.Angle;
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|
|
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Vector2 c2 = b2.Sweep.C;
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float a2 = b2.Sweep.A;
|
|
|
|
// Solve linear limit constraint.
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|
float linearError = 0.0f;
|
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bool active = false;
|
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float C2 = 0.0f;
|
|
|
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Mat22 R1 = new Mat22(a1);
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Mat22 R2 = new Mat22(a2);
|
|
|
|
Vector2 r1 = MathUtils.Multiply(ref R1, LocalAnchorA - LocalCenterA);
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Vector2 r2 = MathUtils.Multiply(ref R2, LocalAnchorB - LocalCenterB);
|
|
Vector2 d = c2 + r2 - c1 - r1;
|
|
|
|
if (_enableLimit)
|
|
{
|
|
_axis = MathUtils.Multiply(ref R1, _localXAxis1);
|
|
|
|
_a1 = MathUtils.Cross(d + r1, _axis);
|
|
_a2 = MathUtils.Cross(r2, _axis);
|
|
|
|
float translation = Vector2.Dot(_axis, d);
|
|
if (Math.Abs(_upperTranslation - _lowerTranslation) < 2.0f * Settings.LinearSlop)
|
|
{
|
|
// Prevent large angular corrections
|
|
C2 = MathUtils.Clamp(translation, -Settings.MaxLinearCorrection, Settings.MaxLinearCorrection);
|
|
linearError = Math.Abs(translation);
|
|
active = true;
|
|
}
|
|
else if (translation <= _lowerTranslation)
|
|
{
|
|
// Prevent large linear corrections and allow some slop.
|
|
C2 = MathUtils.Clamp(translation - _lowerTranslation + Settings.LinearSlop,
|
|
-Settings.MaxLinearCorrection, 0.0f);
|
|
linearError = _lowerTranslation - translation;
|
|
active = true;
|
|
}
|
|
else if (translation >= _upperTranslation)
|
|
{
|
|
// Prevent large linear corrections and allow some slop.
|
|
C2 = MathUtils.Clamp(translation - _upperTranslation - Settings.LinearSlop, 0.0f,
|
|
Settings.MaxLinearCorrection);
|
|
linearError = translation - _upperTranslation;
|
|
active = true;
|
|
}
|
|
}
|
|
|
|
_perp = MathUtils.Multiply(ref R1, _localYAxis1);
|
|
|
|
_s1 = MathUtils.Cross(d + r1, _perp);
|
|
_s2 = MathUtils.Cross(r2, _perp);
|
|
|
|
Vector3 impulse;
|
|
Vector2 C1 = new Vector2(Vector2.Dot(_perp, d), a2 - a1 - _refAngle);
|
|
|
|
linearError = Math.Max(linearError, Math.Abs(C1.X));
|
|
float angularError = Math.Abs(C1.Y);
|
|
|
|
if (active)
|
|
{
|
|
float m1 = InvMassA, m2 = InvMassB;
|
|
float i1 = InvIA, i2 = InvIB;
|
|
|
|
float k11 = m1 + m2 + i1 * _s1 * _s1 + i2 * _s2 * _s2;
|
|
float k12 = i1 * _s1 + i2 * _s2;
|
|
float k13 = i1 * _s1 * _a1 + i2 * _s2 * _a2;
|
|
float k22 = i1 + i2;
|
|
float k23 = i1 * _a1 + i2 * _a2;
|
|
float k33 = m1 + m2 + i1 * _a1 * _a1 + i2 * _a2 * _a2;
|
|
|
|
_K.Col1 = new Vector3(k11, k12, k13);
|
|
_K.Col2 = new Vector3(k12, k22, k23);
|
|
_K.Col3 = new Vector3(k13, k23, k33);
|
|
|
|
Vector3 C = new Vector3(-C1.X, -C1.Y, -C2);
|
|
impulse = _K.Solve33(C); // negated above
|
|
}
|
|
else
|
|
{
|
|
float m1 = InvMassA, m2 = InvMassB;
|
|
float i1 = InvIA, i2 = InvIB;
|
|
|
|
float k11 = m1 + m2 + i1 * _s1 * _s1 + i2 * _s2 * _s2;
|
|
float k12 = i1 * _s1 + i2 * _s2;
|
|
float k22 = i1 + i2;
|
|
|
|
_K.Col1 = new Vector3(k11, k12, 0.0f);
|
|
_K.Col2 = new Vector3(k12, k22, 0.0f);
|
|
|
|
Vector2 impulse1 = _K.Solve22(-C1);
|
|
impulse.X = impulse1.X;
|
|
impulse.Y = impulse1.Y;
|
|
impulse.Z = 0.0f;
|
|
}
|
|
|
|
Vector2 P = impulse.X * _perp + impulse.Z * _axis;
|
|
float L2 = impulse.X * _s2 + impulse.Y + impulse.Z * _a2;
|
|
|
|
c2 += InvMassB * P;
|
|
a2 += InvIB * L2;
|
|
|
|
// TODO_ERIN remove need for this.
|
|
b2.Sweep.C = c2;
|
|
b2.Sweep.A = a2;
|
|
b2.SynchronizeTransform();
|
|
|
|
return linearError <= Settings.LinearSlop && angularError <= Settings.AngularSlop;
|
|
}
|
|
}
|
|
} |