mirror of https://github.com/axmolengine/axmol.git
587 lines
16 KiB
C++
587 lines
16 KiB
C++
/*
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* Copyright (c) 2006-2007 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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#include <Box2D/Dynamics/Joints/b2PrismaticJoint.h>
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#include <Box2D/Dynamics/b2Body.h>
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#include <Box2D/Dynamics/b2TimeStep.h>
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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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void b2PrismaticJointDef::Initialize(b2Body* b1, b2Body* b2, const b2Vec2& anchor, const b2Vec2& axis)
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{
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bodyA = b1;
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bodyB = b2;
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localAnchorA = bodyA->GetLocalPoint(anchor);
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localAnchorB = bodyB->GetLocalPoint(anchor);
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localAxis1 = bodyA->GetLocalVector(axis);
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referenceAngle = bodyB->GetAngle() - bodyA->GetAngle();
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}
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b2PrismaticJoint::b2PrismaticJoint(const b2PrismaticJointDef* def)
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: b2Joint(def)
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{
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m_localAnchor1 = def->localAnchorA;
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m_localAnchor2 = def->localAnchorB;
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m_localXAxis1 = def->localAxis1;
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m_localYAxis1 = b2Cross(1.0f, m_localXAxis1);
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m_refAngle = def->referenceAngle;
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m_impulse.SetZero();
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m_motorMass = 0.0;
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m_motorImpulse = 0.0f;
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m_lowerTranslation = def->lowerTranslation;
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m_upperTranslation = def->upperTranslation;
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m_maxMotorForce = def->maxMotorForce;
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m_motorSpeed = def->motorSpeed;
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m_enableLimit = def->enableLimit;
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m_enableMotor = def->enableMotor;
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m_limitState = e_inactiveLimit;
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m_axis.SetZero();
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m_perp.SetZero();
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}
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void b2PrismaticJoint::InitVelocityConstraints(const b2TimeStep& step)
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{
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b2Body* b1 = m_bodyA;
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b2Body* b2 = m_bodyB;
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m_localCenterA = b1->GetLocalCenter();
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m_localCenterB = b2->GetLocalCenter();
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b2Transform xf1 = b1->GetTransform();
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b2Transform xf2 = b2->GetTransform();
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// Compute the effective masses.
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b2Vec2 r1 = b2Mul(xf1.R, m_localAnchor1 - m_localCenterA);
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b2Vec2 r2 = b2Mul(xf2.R, m_localAnchor2 - m_localCenterB);
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b2Vec2 d = b2->m_sweep.c + r2 - b1->m_sweep.c - r1;
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m_invMassA = b1->m_invMass;
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m_invIA = b1->m_invI;
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m_invMassB = b2->m_invMass;
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m_invIB = b2->m_invI;
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// Compute motor Jacobian and effective mass.
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{
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m_axis = b2Mul(xf1.R, m_localXAxis1);
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m_a1 = b2Cross(d + r1, m_axis);
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m_a2 = b2Cross(r2, m_axis);
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m_motorMass = m_invMassA + m_invMassB + m_invIA * m_a1 * m_a1 + m_invIB * m_a2 * m_a2;
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if (m_motorMass > b2_epsilon)
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{
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m_motorMass = 1.0f / m_motorMass;
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}
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}
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// Prismatic constraint.
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{
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m_perp = b2Mul(xf1.R, m_localYAxis1);
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m_s1 = b2Cross(d + r1, m_perp);
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m_s2 = b2Cross(r2, m_perp);
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float32 m1 = m_invMassA, m2 = m_invMassB;
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float32 i1 = m_invIA, i2 = m_invIB;
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float32 k11 = m1 + m2 + i1 * m_s1 * m_s1 + i2 * m_s2 * m_s2;
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float32 k12 = i1 * m_s1 + i2 * m_s2;
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float32 k13 = i1 * m_s1 * m_a1 + i2 * m_s2 * m_a2;
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float32 k22 = i1 + i2;
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float32 k23 = i1 * m_a1 + i2 * m_a2;
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float32 k33 = m1 + m2 + i1 * m_a1 * m_a1 + i2 * m_a2 * m_a2;
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m_K.col1.Set(k11, k12, k13);
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m_K.col2.Set(k12, k22, k23);
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m_K.col3.Set(k13, k23, k33);
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}
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// Compute motor and limit terms.
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if (m_enableLimit)
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{
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float32 jointTranslation = b2Dot(m_axis, d);
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if (b2Abs(m_upperTranslation - m_lowerTranslation) < 2.0f * b2_linearSlop)
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{
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m_limitState = e_equalLimits;
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}
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else if (jointTranslation <= m_lowerTranslation)
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{
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if (m_limitState != e_atLowerLimit)
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{
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m_limitState = e_atLowerLimit;
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m_impulse.z = 0.0f;
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}
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}
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else if (jointTranslation >= m_upperTranslation)
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{
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if (m_limitState != e_atUpperLimit)
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{
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m_limitState = e_atUpperLimit;
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m_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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m_limitState = e_inactiveLimit;
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m_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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m_limitState = e_inactiveLimit;
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m_impulse.z = 0.0f;
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}
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if (m_enableMotor == false)
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{
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m_motorImpulse = 0.0f;
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}
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if (step.warmStarting)
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{
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// Account for variable time step.
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m_impulse *= step.dtRatio;
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m_motorImpulse *= step.dtRatio;
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b2Vec2 P = m_impulse.x * m_perp + (m_motorImpulse + m_impulse.z) * m_axis;
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float32 L1 = m_impulse.x * m_s1 + m_impulse.y + (m_motorImpulse + m_impulse.z) * m_a1;
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float32 L2 = m_impulse.x * m_s2 + m_impulse.y + (m_motorImpulse + m_impulse.z) * m_a2;
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b1->m_linearVelocity -= m_invMassA * P;
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b1->m_angularVelocity -= m_invIA * L1;
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b2->m_linearVelocity += m_invMassB * P;
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b2->m_angularVelocity += m_invIB * L2;
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}
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else
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{
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m_impulse.SetZero();
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m_motorImpulse = 0.0f;
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}
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}
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void b2PrismaticJoint::SolveVelocityConstraints(const b2TimeStep& step)
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{
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b2Body* b1 = m_bodyA;
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b2Body* b2 = m_bodyB;
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b2Vec2 v1 = b1->m_linearVelocity;
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float32 w1 = b1->m_angularVelocity;
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b2Vec2 v2 = b2->m_linearVelocity;
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float32 w2 = b2->m_angularVelocity;
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// Solve linear motor constraint.
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if (m_enableMotor && m_limitState != e_equalLimits)
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{
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float32 Cdot = b2Dot(m_axis, v2 - v1) + m_a2 * w2 - m_a1 * w1;
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float32 impulse = m_motorMass * (m_motorSpeed - Cdot);
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float32 oldImpulse = m_motorImpulse;
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float32 maxImpulse = step.dt * m_maxMotorForce;
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m_motorImpulse = b2Clamp(m_motorImpulse + impulse, -maxImpulse, maxImpulse);
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impulse = m_motorImpulse - oldImpulse;
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b2Vec2 P = impulse * m_axis;
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float32 L1 = impulse * m_a1;
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float32 L2 = impulse * m_a2;
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v1 -= m_invMassA * P;
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w1 -= m_invIA * L1;
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v2 += m_invMassB * P;
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w2 += m_invIB * L2;
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}
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b2Vec2 Cdot1;
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Cdot1.x = b2Dot(m_perp, v2 - v1) + m_s2 * w2 - m_s1 * w1;
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Cdot1.y = w2 - w1;
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if (m_enableLimit && m_limitState != e_inactiveLimit)
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{
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// Solve prismatic and limit constraint in block form.
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float32 Cdot2;
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Cdot2 = b2Dot(m_axis, v2 - v1) + m_a2 * w2 - m_a1 * w1;
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b2Vec3 Cdot(Cdot1.x, Cdot1.y, Cdot2);
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b2Vec3 f1 = m_impulse;
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b2Vec3 df = m_K.Solve33(-Cdot);
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m_impulse += df;
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if (m_limitState == e_atLowerLimit)
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{
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m_impulse.z = b2Max(m_impulse.z, 0.0f);
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}
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else if (m_limitState == e_atUpperLimit)
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{
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m_impulse.z = b2Min(m_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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b2Vec2 b = -Cdot1 - (m_impulse.z - f1.z) * b2Vec2(m_K.col3.x, m_K.col3.y);
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b2Vec2 f2r = m_K.Solve22(b) + b2Vec2(f1.x, f1.y);
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m_impulse.x = f2r.x;
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m_impulse.y = f2r.y;
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df = m_impulse - f1;
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b2Vec2 P = df.x * m_perp + df.z * m_axis;
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float32 L1 = df.x * m_s1 + df.y + df.z * m_a1;
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float32 L2 = df.x * m_s2 + df.y + df.z * m_a2;
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v1 -= m_invMassA * P;
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w1 -= m_invIA * L1;
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v2 += m_invMassB * P;
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w2 += m_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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b2Vec2 df = m_K.Solve22(-Cdot1);
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m_impulse.x += df.x;
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m_impulse.y += df.y;
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b2Vec2 P = df.x * m_perp;
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float32 L1 = df.x * m_s1 + df.y;
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float32 L2 = df.x * m_s2 + df.y;
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v1 -= m_invMassA * P;
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w1 -= m_invIA * L1;
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v2 += m_invMassB * P;
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w2 += m_invIB * L2;
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}
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b1->m_linearVelocity = v1;
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b1->m_angularVelocity = w1;
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b2->m_linearVelocity = v2;
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b2->m_angularVelocity = w2;
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}
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bool b2PrismaticJoint::SolvePositionConstraints(float32 baumgarte)
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{
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B2_NOT_USED(baumgarte);
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b2Body* b1 = m_bodyA;
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b2Body* b2 = m_bodyB;
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b2Vec2 c1 = b1->m_sweep.c;
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float32 a1 = b1->m_sweep.a;
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b2Vec2 c2 = b2->m_sweep.c;
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float32 a2 = b2->m_sweep.a;
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// Solve linear limit constraint.
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float32 linearError = 0.0f, angularError = 0.0f;
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bool active = false;
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float32 C2 = 0.0f;
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b2Mat22 R1(a1), R2(a2);
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b2Vec2 r1 = b2Mul(R1, m_localAnchor1 - m_localCenterA);
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b2Vec2 r2 = b2Mul(R2, m_localAnchor2 - m_localCenterB);
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b2Vec2 d = c2 + r2 - c1 - r1;
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if (m_enableLimit)
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{
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m_axis = b2Mul(R1, m_localXAxis1);
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m_a1 = b2Cross(d + r1, m_axis);
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m_a2 = b2Cross(r2, m_axis);
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float32 translation = b2Dot(m_axis, d);
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if (b2Abs(m_upperTranslation - m_lowerTranslation) < 2.0f * b2_linearSlop)
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{
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// Prevent large angular corrections
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C2 = b2Clamp(translation, -b2_maxLinearCorrection, b2_maxLinearCorrection);
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linearError = b2Abs(translation);
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active = true;
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}
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else if (translation <= m_lowerTranslation)
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{
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// Prevent large linear corrections and allow some slop.
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C2 = b2Clamp(translation - m_lowerTranslation + b2_linearSlop, -b2_maxLinearCorrection, 0.0f);
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linearError = m_lowerTranslation - translation;
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active = true;
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}
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else if (translation >= m_upperTranslation)
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{
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// Prevent large linear corrections and allow some slop.
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C2 = b2Clamp(translation - m_upperTranslation - b2_linearSlop, 0.0f, b2_maxLinearCorrection);
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linearError = translation - m_upperTranslation;
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active = true;
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}
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}
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m_perp = b2Mul(R1, m_localYAxis1);
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m_s1 = b2Cross(d + r1, m_perp);
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m_s2 = b2Cross(r2, m_perp);
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b2Vec3 impulse;
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b2Vec2 C1;
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C1.x = b2Dot(m_perp, d);
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C1.y = a2 - a1 - m_refAngle;
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linearError = b2Max(linearError, b2Abs(C1.x));
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angularError = b2Abs(C1.y);
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if (active)
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{
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float32 m1 = m_invMassA, m2 = m_invMassB;
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float32 i1 = m_invIA, i2 = m_invIB;
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float32 k11 = m1 + m2 + i1 * m_s1 * m_s1 + i2 * m_s2 * m_s2;
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float32 k12 = i1 * m_s1 + i2 * m_s2;
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float32 k13 = i1 * m_s1 * m_a1 + i2 * m_s2 * m_a2;
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float32 k22 = i1 + i2;
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float32 k23 = i1 * m_a1 + i2 * m_a2;
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float32 k33 = m1 + m2 + i1 * m_a1 * m_a1 + i2 * m_a2 * m_a2;
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m_K.col1.Set(k11, k12, k13);
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m_K.col2.Set(k12, k22, k23);
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m_K.col3.Set(k13, k23, k33);
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b2Vec3 C;
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C.x = C1.x;
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C.y = C1.y;
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C.z = C2;
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impulse = m_K.Solve33(-C);
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}
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else
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|
{
|
|
float32 m1 = m_invMassA, m2 = m_invMassB;
|
|
float32 i1 = m_invIA, i2 = m_invIB;
|
|
|
|
float32 k11 = m1 + m2 + i1 * m_s1 * m_s1 + i2 * m_s2 * m_s2;
|
|
float32 k12 = i1 * m_s1 + i2 * m_s2;
|
|
float32 k22 = i1 + i2;
|
|
|
|
m_K.col1.Set(k11, k12, 0.0f);
|
|
m_K.col2.Set(k12, k22, 0.0f);
|
|
|
|
b2Vec2 impulse1 = m_K.Solve22(-C1);
|
|
impulse.x = impulse1.x;
|
|
impulse.y = impulse1.y;
|
|
impulse.z = 0.0f;
|
|
}
|
|
|
|
b2Vec2 P = impulse.x * m_perp + impulse.z * m_axis;
|
|
float32 L1 = impulse.x * m_s1 + impulse.y + impulse.z * m_a1;
|
|
float32 L2 = impulse.x * m_s2 + impulse.y + impulse.z * m_a2;
|
|
|
|
c1 -= m_invMassA * P;
|
|
a1 -= m_invIA * L1;
|
|
c2 += m_invMassB * P;
|
|
a2 += m_invIB * L2;
|
|
|
|
// TODO_ERIN remove need for this.
|
|
b1->m_sweep.c = c1;
|
|
b1->m_sweep.a = a1;
|
|
b2->m_sweep.c = c2;
|
|
b2->m_sweep.a = a2;
|
|
b1->SynchronizeTransform();
|
|
b2->SynchronizeTransform();
|
|
|
|
return linearError <= b2_linearSlop && angularError <= b2_angularSlop;
|
|
}
|
|
|
|
b2Vec2 b2PrismaticJoint::GetAnchorA() const
|
|
{
|
|
return m_bodyA->GetWorldPoint(m_localAnchor1);
|
|
}
|
|
|
|
b2Vec2 b2PrismaticJoint::GetAnchorB() const
|
|
{
|
|
return m_bodyB->GetWorldPoint(m_localAnchor2);
|
|
}
|
|
|
|
b2Vec2 b2PrismaticJoint::GetReactionForce(float32 inv_dt) const
|
|
{
|
|
return inv_dt * (m_impulse.x * m_perp + (m_motorImpulse + m_impulse.z) * m_axis);
|
|
}
|
|
|
|
float32 b2PrismaticJoint::GetReactionTorque(float32 inv_dt) const
|
|
{
|
|
return inv_dt * m_impulse.y;
|
|
}
|
|
|
|
float32 b2PrismaticJoint::GetJointTranslation() const
|
|
{
|
|
b2Body* b1 = m_bodyA;
|
|
b2Body* b2 = m_bodyB;
|
|
|
|
b2Vec2 p1 = b1->GetWorldPoint(m_localAnchor1);
|
|
b2Vec2 p2 = b2->GetWorldPoint(m_localAnchor2);
|
|
b2Vec2 d = p2 - p1;
|
|
b2Vec2 axis = b1->GetWorldVector(m_localXAxis1);
|
|
|
|
float32 translation = b2Dot(d, axis);
|
|
return translation;
|
|
}
|
|
|
|
float32 b2PrismaticJoint::GetJointSpeed() const
|
|
{
|
|
b2Body* b1 = m_bodyA;
|
|
b2Body* b2 = m_bodyB;
|
|
|
|
b2Vec2 r1 = b2Mul(b1->GetTransform().R, m_localAnchor1 - b1->GetLocalCenter());
|
|
b2Vec2 r2 = b2Mul(b2->GetTransform().R, m_localAnchor2 - b2->GetLocalCenter());
|
|
b2Vec2 p1 = b1->m_sweep.c + r1;
|
|
b2Vec2 p2 = b2->m_sweep.c + r2;
|
|
b2Vec2 d = p2 - p1;
|
|
b2Vec2 axis = b1->GetWorldVector(m_localXAxis1);
|
|
|
|
b2Vec2 v1 = b1->m_linearVelocity;
|
|
b2Vec2 v2 = b2->m_linearVelocity;
|
|
float32 w1 = b1->m_angularVelocity;
|
|
float32 w2 = b2->m_angularVelocity;
|
|
|
|
float32 speed = b2Dot(d, b2Cross(w1, axis)) + b2Dot(axis, v2 + b2Cross(w2, r2) - v1 - b2Cross(w1, r1));
|
|
return speed;
|
|
}
|
|
|
|
bool b2PrismaticJoint::IsLimitEnabled() const
|
|
{
|
|
return m_enableLimit;
|
|
}
|
|
|
|
void b2PrismaticJoint::EnableLimit(bool flag)
|
|
{
|
|
m_bodyA->SetAwake(true);
|
|
m_bodyB->SetAwake(true);
|
|
m_enableLimit = flag;
|
|
}
|
|
|
|
float32 b2PrismaticJoint::GetLowerLimit() const
|
|
{
|
|
return m_lowerTranslation;
|
|
}
|
|
|
|
float32 b2PrismaticJoint::GetUpperLimit() const
|
|
{
|
|
return m_upperTranslation;
|
|
}
|
|
|
|
void b2PrismaticJoint::SetLimits(float32 lower, float32 upper)
|
|
{
|
|
b2Assert(lower <= upper);
|
|
m_bodyA->SetAwake(true);
|
|
m_bodyB->SetAwake(true);
|
|
m_lowerTranslation = lower;
|
|
m_upperTranslation = upper;
|
|
}
|
|
|
|
bool b2PrismaticJoint::IsMotorEnabled() const
|
|
{
|
|
return m_enableMotor;
|
|
}
|
|
|
|
void b2PrismaticJoint::EnableMotor(bool flag)
|
|
{
|
|
m_bodyA->SetAwake(true);
|
|
m_bodyB->SetAwake(true);
|
|
m_enableMotor = flag;
|
|
}
|
|
|
|
void b2PrismaticJoint::SetMotorSpeed(float32 speed)
|
|
{
|
|
m_bodyA->SetAwake(true);
|
|
m_bodyB->SetAwake(true);
|
|
m_motorSpeed = speed;
|
|
}
|
|
|
|
void b2PrismaticJoint::SetMaxMotorForce(float32 force)
|
|
{
|
|
m_bodyA->SetAwake(true);
|
|
m_bodyB->SetAwake(true);
|
|
m_maxMotorForce = force;
|
|
}
|
|
|
|
float32 b2PrismaticJoint::GetMotorForce() const
|
|
{
|
|
return m_motorImpulse;
|
|
}
|