Regalis
768 lines
26 KiB
C#
768 lines
26 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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// 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 bodyA. 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 PrismaticJoint : Joint
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{
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private Vector2 _localYAxisA;
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private Vector3 _impulse;
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private float _lowerTranslation;
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private float _upperTranslation;
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private float _maxMotorForce;
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private float _motorSpeed;
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private bool _enableLimit;
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private bool _enableMotor;
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private LimitState _limitState;
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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 _axis, _perp;
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private float _s1, _s2;
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private float _a1, _a2;
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private Mat33 _K;
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private float _motorMass;
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private Vector2 _axis1;
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internal PrismaticJoint()
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{
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JointType = JointType.Prismatic;
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}
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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="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="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 PrismaticJoint(Body bodyA, Body bodyB, Vector2 anchorA, Vector2 anchorB, Vector2 axis, bool useWorldCoordinates = false)
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: base(bodyA, bodyB)
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{
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Initialize(anchorA, anchorB, axis, useWorldCoordinates);
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}
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public PrismaticJoint(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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Initialize(anchor, anchor, axis, useWorldCoordinates);
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}
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private void Initialize(Vector2 localAnchorA, Vector2 localAnchorB, Vector2 axis, bool useWorldCoordinates)
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{
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JointType = JointType.Prismatic;
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if (useWorldCoordinates)
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{
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LocalAnchorA = BodyA.GetLocalPoint(localAnchorA);
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LocalAnchorB = BodyB.GetLocalPoint(localAnchorB);
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}
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else
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{
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LocalAnchorA = localAnchorA;
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LocalAnchorB = localAnchorB;
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}
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Axis = axis; //FPE only: store the orignal value for use in Serialization
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ReferenceAngle = BodyB.Rotation - BodyA.Rotation;
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_limitState = LimitState.Inactive;
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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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/// 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) - BodyA.GetWorldPoint(LocalAnchorA);
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Vector2 axis = BodyA.GetWorldVector(LocalXAxis);
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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 xf1, xf2;
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BodyA.GetTransform(out xf1);
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BodyB.GetTransform(out xf2);
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Vector2 r1 = MathUtils.Mul(ref xf1.q, LocalAnchorA - BodyA.LocalCenter);
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Vector2 r2 = MathUtils.Mul(ref xf2.q, LocalAnchorB - BodyB.LocalCenter);
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Vector2 p1 = BodyA._sweep.C + 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 = BodyA.GetWorldVector(LocalXAxis);
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Vector2 v1 = BodyA._linearVelocity;
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Vector2 v2 = BodyB._linearVelocity;
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float w1 = BodyA._angularVelocity;
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float w2 = BodyB._angularVelocity;
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float speed = Vector2.Dot(d, MathUtils.Cross(w1, axis)) + 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 || BodyB.FixedRotation == false, "Warning: limits does currently not work with fixed rotation");
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if (value != _enableLimit)
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{
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WakeBodies();
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_enableLimit = value;
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_impulse.Z = 0;
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}
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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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if (value != _lowerTranslation)
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{
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WakeBodies();
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_lowerTranslation = value;
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_impulse.Z = 0.0f;
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}
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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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if (value != _upperTranslation)
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{
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WakeBodies();
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_upperTranslation = value;
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_impulse.Z = 0.0f;
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}
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}
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}
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/// <summary>
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/// Set the joint limits, usually in meters.
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/// </summary>
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/// <param name="lower">The lower limit</param>
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/// <param name="upper">The upper limit</param>
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public void SetLimits(float lower, float upper)
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{
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if (upper != _upperTranslation || lower != _lowerTranslation)
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{
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WakeBodies();
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_upperTranslation = upper;
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_lowerTranslation = lower;
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_impulse.Z = 0.0f;
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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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get { return _maxMotorForce; }
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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 impulse, usually in N.
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/// </summary>
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/// <value></value>
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public float MotorImpulse { get; set; }
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/// <summary>
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/// Gets the motor force.
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/// </summary>
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/// <param name="invDt">The inverse delta time</param>
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public float GetMotorForce(float invDt)
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{
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return invDt * MotorImpulse;
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}
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/// <summary>
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/// The axis at which the joint moves.
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/// </summary>
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public Vector2 Axis
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{
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get { return _axis1; }
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set
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{
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_axis1 = value;
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LocalXAxis = BodyA.GetLocalVector(_axis1);
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LocalXAxis.Normalize();
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_localYAxisA = 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 reference angle.
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/// </summary>
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public float ReferenceAngle { get; set; }
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public override Vector2 GetReactionForce(float invDt)
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{
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return invDt * (_impulse.X * _perp + (MotorImpulse + _impulse.Z) * _axis);
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}
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public override float GetReactionTorque(float invDt)
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{
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return invDt * _impulse.Y;
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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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// 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 d = (cB - cA) + rB - rA;
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float mA = _invMassA, mB = _invMassB;
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float iA = _invIA, iB = _invIB;
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// Compute motor Jacobian and effective mass.
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{
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_axis = MathUtils.Mul(qA, LocalXAxis);
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_a1 = MathUtils.Cross(d + rA, _axis);
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_a2 = MathUtils.Cross(rB, _axis);
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_motorMass = mA + mB + iA * _a1 * _a1 + iB * _a2 * _a2;
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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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// Prismatic constraint.
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{
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_perp = MathUtils.Mul(qA, _localYAxisA);
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_s1 = MathUtils.Cross(d + rA, _perp);
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_s2 = MathUtils.Cross(rB, _perp);
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float k11 = mA + mB + iA * _s1 * _s1 + iB * _s2 * _s2;
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float k12 = iA * _s1 + iB * _s2;
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float k13 = iA * _s1 * _a1 + iB * _s2 * _a2;
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float k22 = iA + iB;
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if (k22 == 0.0f)
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{
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// For bodies with fixed rotation.
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k22 = 1.0f;
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}
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float k23 = iA * _a1 + iB * _a2;
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float k33 = mA + mB + iA * _a1 * _a1 + iB * _a2 * _a2;
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_K.ex = new Vector3(k11, k12, k13);
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_K.ey = new Vector3(k12, k22, k23);
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_K.ez = 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;
|
|
_impulse.Z = 0.0f;
|
|
}
|
|
|
|
if (_enableMotor == false)
|
|
{
|
|
MotorImpulse = 0.0f;
|
|
}
|
|
|
|
if (Settings.EnableWarmstarting)
|
|
{
|
|
// Account for variable time step.
|
|
_impulse *= data.step.dtRatio;
|
|
MotorImpulse *= data.step.dtRatio;
|
|
|
|
Vector2 P = _impulse.X * _perp + (MotorImpulse + _impulse.Z) * _axis;
|
|
float LA = _impulse.X * _s1 + _impulse.Y + (MotorImpulse + _impulse.Z) * _a1;
|
|
float LB = _impulse.X * _s2 + _impulse.Y + (MotorImpulse + _impulse.Z) * _a2;
|
|
|
|
vA -= mA * P;
|
|
wA -= iA * LA;
|
|
|
|
vB += mB * P;
|
|
wB += iB * LB;
|
|
}
|
|
else
|
|
{
|
|
_impulse = Vector3.Zero;
|
|
MotorImpulse = 0.0f;
|
|
}
|
|
|
|
data.velocities[_indexA].v = vA;
|
|
data.velocities[_indexA].w = wA;
|
|
data.velocities[_indexB].v = vB;
|
|
data.velocities[_indexB].w = wB;
|
|
}
|
|
|
|
internal override void SolveVelocityConstraints(ref SolverData data)
|
|
{
|
|
Vector2 vA = data.velocities[_indexA].v;
|
|
float wA = data.velocities[_indexA].w;
|
|
Vector2 vB = data.velocities[_indexB].v;
|
|
float wB = data.velocities[_indexB].w;
|
|
|
|
float mA = _invMassA, mB = _invMassB;
|
|
float iA = _invIA, iB = _invIB;
|
|
|
|
// Solve linear motor constraint.
|
|
if (_enableMotor && _limitState != LimitState.Equal)
|
|
{
|
|
float Cdot = Vector2.Dot(_axis, vB - vA) + _a2 * wB - _a1 * wA;
|
|
float impulse = _motorMass * (_motorSpeed - Cdot);
|
|
float oldImpulse = MotorImpulse;
|
|
float maxImpulse = data.step.dt * _maxMotorForce;
|
|
MotorImpulse = MathUtils.Clamp(MotorImpulse + impulse, -maxImpulse, maxImpulse);
|
|
impulse = MotorImpulse - oldImpulse;
|
|
|
|
Vector2 P = impulse * _axis;
|
|
float LA = impulse * _a1;
|
|
float LB = impulse * _a2;
|
|
|
|
vA -= mA * P;
|
|
wA -= iA * LA;
|
|
|
|
vB += mB * P;
|
|
wB += iB * LB;
|
|
}
|
|
|
|
Vector2 Cdot1 = new Vector2();
|
|
Cdot1.X = Vector2.Dot(_perp, vB - vA) + _s2 * wB - _s1 * wA;
|
|
Cdot1.Y = wB - wA;
|
|
|
|
if (_enableLimit && _limitState != LimitState.Inactive)
|
|
{
|
|
// Solve prismatic and limit constraint in block form.
|
|
float Cdot2;
|
|
Cdot2 = Vector2.Dot(_axis, vB - vA) + _a2 * wB - _a1 * wA;
|
|
Vector3 Cdot = new Vector3(Cdot1.X, Cdot1.Y, Cdot2);
|
|
|
|
Vector3 f1 = _impulse;
|
|
Vector3 df = _K.Solve33(-Cdot);
|
|
_impulse += df;
|
|
|
|
if (_limitState == LimitState.AtLower)
|
|
{
|
|
_impulse.Z = Math.Max(_impulse.Z, 0.0f);
|
|
}
|
|
else if (_limitState == LimitState.AtUpper)
|
|
{
|
|
_impulse.Z = Math.Min(_impulse.Z, 0.0f);
|
|
}
|
|
|
|
// f2(1:2) = invK(1:2,1:2) * (-Cdot(1:2) - K(1:2,3) * (f2(3) - f1(3))) + f1(1:2)
|
|
Vector2 b = -Cdot1 - (_impulse.Z - f1.Z) * new Vector2(_K.ez.X, _K.ez.Y);
|
|
Vector2 f2r = _K.Solve22(b) + new Vector2(f1.X, f1.Y);
|
|
_impulse.X = f2r.X;
|
|
_impulse.Y = f2r.Y;
|
|
|
|
df = _impulse - f1;
|
|
|
|
Vector2 P = df.X * _perp + df.Z * _axis;
|
|
float LA = df.X * _s1 + df.Y + df.Z * _a1;
|
|
float LB = df.X * _s2 + df.Y + df.Z * _a2;
|
|
|
|
vA -= mA * P;
|
|
wA -= iA * LA;
|
|
|
|
vB += mB * P;
|
|
wB += iB * LB;
|
|
}
|
|
else
|
|
{
|
|
// Limit is inactive, just solve the prismatic constraint in block form.
|
|
Vector2 df = _K.Solve22(-Cdot1);
|
|
_impulse.X += df.X;
|
|
_impulse.Y += df.Y;
|
|
|
|
Vector2 P = df.X * _perp;
|
|
float LA = df.X * _s1 + df.Y;
|
|
float LB = df.X * _s2 + df.Y;
|
|
|
|
vA -= mA * P;
|
|
wA -= iA * LA;
|
|
|
|
vB += mB * P;
|
|
wB += iB * LB;
|
|
}
|
|
|
|
data.velocities[_indexA].v = vA;
|
|
data.velocities[_indexA].w = wA;
|
|
data.velocities[_indexB].v = vB;
|
|
data.velocities[_indexB].w = wB;
|
|
}
|
|
|
|
internal override bool SolvePositionConstraints(ref SolverData data)
|
|
{
|
|
Vector2 cA = data.positions[_indexA].c;
|
|
float aA = data.positions[_indexA].a;
|
|
Vector2 cB = data.positions[_indexB].c;
|
|
float aB = data.positions[_indexB].a;
|
|
|
|
Rot qA = new Rot(aA), qB = new Rot(aB);
|
|
|
|
float mA = _invMassA, mB = _invMassB;
|
|
float iA = _invIA, iB = _invIB;
|
|
|
|
// Compute fresh Jacobians
|
|
Vector2 rA = MathUtils.Mul(qA, LocalAnchorA - _localCenterA);
|
|
Vector2 rB = MathUtils.Mul(qB, LocalAnchorB - _localCenterB);
|
|
Vector2 d = cB + rB - cA - rA;
|
|
|
|
Vector2 axis = MathUtils.Mul(qA, LocalXAxis);
|
|
float a1 = MathUtils.Cross(d + rA, axis);
|
|
float a2 = MathUtils.Cross(rB, axis);
|
|
Vector2 perp = MathUtils.Mul(qA, _localYAxisA);
|
|
|
|
float s1 = MathUtils.Cross(d + rA, perp);
|
|
float s2 = MathUtils.Cross(rB, perp);
|
|
|
|
Vector3 impulse;
|
|
Vector2 C1 = new Vector2();
|
|
C1.X = Vector2.Dot(perp, d);
|
|
C1.Y = aB - aA - ReferenceAngle;
|
|
|
|
float linearError = Math.Abs(C1.X);
|
|
float angularError = Math.Abs(C1.Y);
|
|
|
|
bool active = false;
|
|
float C2 = 0.0f;
|
|
if (_enableLimit)
|
|
{
|
|
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.Max(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 = Math.Max(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 = Math.Max(linearError, translation - _upperTranslation);
|
|
active = true;
|
|
}
|
|
}
|
|
|
|
if (active)
|
|
{
|
|
float k11 = mA + mB + iA * s1 * s1 + iB * s2 * s2;
|
|
float k12 = iA * s1 + iB * s2;
|
|
float k13 = iA * s1 * a1 + iB * s2 * a2;
|
|
float k22 = iA + iB;
|
|
if (k22 == 0.0f)
|
|
{
|
|
// For fixed rotation
|
|
k22 = 1.0f;
|
|
}
|
|
float k23 = iA * a1 + iB * a2;
|
|
float k33 = mA + mB + iA * a1 * a1 + iB * a2 * a2;
|
|
|
|
Mat33 K = new Mat33();
|
|
K.ex = new Vector3(k11, k12, k13);
|
|
K.ey = new Vector3(k12, k22, k23);
|
|
K.ez = new Vector3(k13, k23, k33);
|
|
|
|
Vector3 C = new Vector3();
|
|
C.X = C1.X;
|
|
C.Y = C1.Y;
|
|
C.Z = C2;
|
|
|
|
impulse = K.Solve33(-C);
|
|
}
|
|
else
|
|
{
|
|
float k11 = mA + mB + iA * s1 * s1 + iB * s2 * s2;
|
|
float k12 = iA * s1 + iB * s2;
|
|
float k22 = iA + iB;
|
|
if (k22 == 0.0f)
|
|
{
|
|
k22 = 1.0f;
|
|
}
|
|
|
|
Mat22 K = new Mat22();
|
|
K.ex = new Vector2(k11, k12);
|
|
K.ey = new Vector2(k12, k22);
|
|
|
|
Vector2 impulse1 = K.Solve(-C1);
|
|
impulse = new Vector3();
|
|
impulse.X = impulse1.X;
|
|
impulse.Y = impulse1.Y;
|
|
impulse.Z = 0.0f;
|
|
}
|
|
|
|
Vector2 P = impulse.X * perp + impulse.Z * axis;
|
|
float LA = impulse.X * s1 + impulse.Y + impulse.Z * a1;
|
|
float LB = impulse.X * s2 + impulse.Y + impulse.Z * a2;
|
|
|
|
cA -= mA * P;
|
|
aA -= iA * LA;
|
|
cB += mB * P;
|
|
aB += iB * LB;
|
|
|
|
data.positions[_indexA].c = cA;
|
|
data.positions[_indexA].a = aA;
|
|
data.positions[_indexB].c = cB;
|
|
data.positions[_indexB].a = aB;
|
|
|
|
return linearError <= Settings.LinearSlop && angularError <= Settings.AngularSlop;
|
|
}
|
|
}
|
|
} |