345 lines
8.7 KiB
C++
345 lines
8.7 KiB
C++
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/*
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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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#include "Box2D/Dynamics/Joints/b2WeldJoint.h"
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#include "Box2D/Dynamics/b2Body.h"
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#include "Box2D/Dynamics/b2TimeStep.h"
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// Point-to-point constraint
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// C = p2 - p1
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// Cdot = v2 - v1
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// = v2 + cross(w2, r2) - v1 - cross(w1, r1)
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// J = [-I -r1_skew I r2_skew ]
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// Identity used:
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// w k % (rx i + ry j) = w * (-ry i + rx j)
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// Angle constraint
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// C = angle2 - angle1 - referenceAngle
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// Cdot = w2 - w1
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// J = [0 0 -1 0 0 1]
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// K = invI1 + invI2
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void b2WeldJointDef::Initialize(b2Body* bA, b2Body* bB, const b2Vec2& anchor)
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{
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bodyA = bA;
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bodyB = bB;
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localAnchorA = bodyA->GetLocalPoint(anchor);
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localAnchorB = bodyB->GetLocalPoint(anchor);
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referenceAngle = bodyB->GetAngle() - bodyA->GetAngle();
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}
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b2WeldJoint::b2WeldJoint(const b2WeldJointDef* def)
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: b2Joint(def)
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{
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m_localAnchorA = def->localAnchorA;
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m_localAnchorB = def->localAnchorB;
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m_referenceAngle = def->referenceAngle;
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m_frequencyHz = def->frequencyHz;
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m_dampingRatio = def->dampingRatio;
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m_impulse.SetZero();
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}
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void b2WeldJoint::InitVelocityConstraints(const b2SolverData& data)
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{
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m_indexA = m_bodyA->m_islandIndex;
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m_indexB = m_bodyB->m_islandIndex;
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m_localCenterA = m_bodyA->m_sweep.localCenter;
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m_localCenterB = m_bodyB->m_sweep.localCenter;
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m_invMassA = m_bodyA->m_invMass;
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m_invMassB = m_bodyB->m_invMass;
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m_invIA = m_bodyA->m_invI;
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m_invIB = m_bodyB->m_invI;
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float32 aA = data.positions[m_indexA].a;
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b2Vec2 vA = data.velocities[m_indexA].v;
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float32 wA = data.velocities[m_indexA].w;
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float32 aB = data.positions[m_indexB].a;
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b2Vec2 vB = data.velocities[m_indexB].v;
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float32 wB = data.velocities[m_indexB].w;
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b2Rot qA(aA), qB(aB);
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m_rA = b2Mul(qA, m_localAnchorA - m_localCenterA);
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m_rB = b2Mul(qB, m_localAnchorB - m_localCenterB);
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// J = [-I -r1_skew I r2_skew]
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// [ 0 -1 0 1]
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// r_skew = [-ry; rx]
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// Matlab
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// K = [ mA+r1y^2*iA+mB+r2y^2*iB, -r1y*iA*r1x-r2y*iB*r2x, -r1y*iA-r2y*iB]
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// [ -r1y*iA*r1x-r2y*iB*r2x, mA+r1x^2*iA+mB+r2x^2*iB, r1x*iA+r2x*iB]
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// [ -r1y*iA-r2y*iB, r1x*iA+r2x*iB, iA+iB]
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float32 mA = m_invMassA, mB = m_invMassB;
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float32 iA = m_invIA, iB = m_invIB;
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b2Mat33 K;
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K.ex.x = mA + mB + m_rA.y * m_rA.y * iA + m_rB.y * m_rB.y * iB;
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K.ey.x = -m_rA.y * m_rA.x * iA - m_rB.y * m_rB.x * iB;
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K.ez.x = -m_rA.y * iA - m_rB.y * iB;
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K.ex.y = K.ey.x;
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K.ey.y = mA + mB + m_rA.x * m_rA.x * iA + m_rB.x * m_rB.x * iB;
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K.ez.y = m_rA.x * iA + m_rB.x * iB;
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K.ex.z = K.ez.x;
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K.ey.z = K.ez.y;
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K.ez.z = iA + iB;
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if (m_frequencyHz > 0.0f)
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{
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K.GetInverse22(&m_mass);
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float32 invM = iA + iB;
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float32 m = invM > 0.0f ? 1.0f / invM : 0.0f;
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float32 C = aB - aA - m_referenceAngle;
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// Frequency
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float32 omega = 2.0f * b2_pi * m_frequencyHz;
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// Damping coefficient
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float32 d = 2.0f * m * m_dampingRatio * omega;
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// Spring stiffness
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float32 k = m * omega * omega;
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// magic formulas
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float32 h = data.step.dt;
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m_gamma = h * (d + h * k);
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m_gamma = m_gamma != 0.0f ? 1.0f / m_gamma : 0.0f;
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m_bias = C * h * k * m_gamma;
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invM += m_gamma;
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m_mass.ez.z = invM != 0.0f ? 1.0f / invM : 0.0f;
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}
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else if (K.ez.z == 0.0f)
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{
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K.GetInverse22(&m_mass);
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m_gamma = 0.0f;
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m_bias = 0.0f;
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}
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else
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{
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K.GetSymInverse33(&m_mass);
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m_gamma = 0.0f;
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m_bias = 0.0f;
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}
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if (data.step.warmStarting)
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{
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// Scale impulses to support a variable time step.
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m_impulse *= data.step.dtRatio;
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b2Vec2 P(m_impulse.x, m_impulse.y);
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vA -= mA * P;
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wA -= iA * (b2Cross(m_rA, P) + m_impulse.z);
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vB += mB * P;
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wB += iB * (b2Cross(m_rB, P) + m_impulse.z);
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}
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else
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{
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m_impulse.SetZero();
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}
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data.velocities[m_indexA].v = vA;
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data.velocities[m_indexA].w = wA;
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data.velocities[m_indexB].v = vB;
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data.velocities[m_indexB].w = wB;
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}
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void b2WeldJoint::SolveVelocityConstraints(const b2SolverData& data)
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{
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b2Vec2 vA = data.velocities[m_indexA].v;
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float32 wA = data.velocities[m_indexA].w;
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b2Vec2 vB = data.velocities[m_indexB].v;
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float32 wB = data.velocities[m_indexB].w;
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float32 mA = m_invMassA, mB = m_invMassB;
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float32 iA = m_invIA, iB = m_invIB;
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if (m_frequencyHz > 0.0f)
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{
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float32 Cdot2 = wB - wA;
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float32 impulse2 = -m_mass.ez.z * (Cdot2 + m_bias + m_gamma * m_impulse.z);
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m_impulse.z += impulse2;
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wA -= iA * impulse2;
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wB += iB * impulse2;
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b2Vec2 Cdot1 = vB + b2Cross(wB, m_rB) - vA - b2Cross(wA, m_rA);
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b2Vec2 impulse1 = -b2Mul22(m_mass, Cdot1);
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m_impulse.x += impulse1.x;
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m_impulse.y += impulse1.y;
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b2Vec2 P = impulse1;
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vA -= mA * P;
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wA -= iA * b2Cross(m_rA, P);
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vB += mB * P;
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wB += iB * b2Cross(m_rB, P);
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}
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else
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{
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b2Vec2 Cdot1 = vB + b2Cross(wB, m_rB) - vA - b2Cross(wA, m_rA);
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float32 Cdot2 = wB - wA;
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b2Vec3 Cdot(Cdot1.x, Cdot1.y, Cdot2);
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b2Vec3 impulse = -b2Mul(m_mass, Cdot);
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m_impulse += impulse;
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b2Vec2 P(impulse.x, impulse.y);
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vA -= mA * P;
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wA -= iA * (b2Cross(m_rA, P) + impulse.z);
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vB += mB * P;
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wB += iB * (b2Cross(m_rB, P) + impulse.z);
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}
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data.velocities[m_indexA].v = vA;
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data.velocities[m_indexA].w = wA;
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data.velocities[m_indexB].v = vB;
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data.velocities[m_indexB].w = wB;
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}
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bool b2WeldJoint::SolvePositionConstraints(const b2SolverData& data)
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{
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b2Vec2 cA = data.positions[m_indexA].c;
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float32 aA = data.positions[m_indexA].a;
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b2Vec2 cB = data.positions[m_indexB].c;
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float32 aB = data.positions[m_indexB].a;
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b2Rot qA(aA), qB(aB);
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float32 mA = m_invMassA, mB = m_invMassB;
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float32 iA = m_invIA, iB = m_invIB;
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b2Vec2 rA = b2Mul(qA, m_localAnchorA - m_localCenterA);
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b2Vec2 rB = b2Mul(qB, m_localAnchorB - m_localCenterB);
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float32 positionError, angularError;
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b2Mat33 K;
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K.ex.x = mA + mB + rA.y * rA.y * iA + rB.y * rB.y * iB;
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K.ey.x = -rA.y * rA.x * iA - rB.y * rB.x * iB;
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K.ez.x = -rA.y * iA - rB.y * iB;
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K.ex.y = K.ey.x;
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K.ey.y = mA + mB + rA.x * rA.x * iA + rB.x * rB.x * iB;
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K.ez.y = rA.x * iA + rB.x * iB;
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K.ex.z = K.ez.x;
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K.ey.z = K.ez.y;
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K.ez.z = iA + iB;
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if (m_frequencyHz > 0.0f)
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{
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b2Vec2 C1 = cB + rB - cA - rA;
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positionError = C1.Length();
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angularError = 0.0f;
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b2Vec2 P = -K.Solve22(C1);
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cA -= mA * P;
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aA -= iA * b2Cross(rA, P);
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cB += mB * P;
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aB += iB * b2Cross(rB, P);
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}
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else
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{
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b2Vec2 C1 = cB + rB - cA - rA;
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float32 C2 = aB - aA - m_referenceAngle;
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positionError = C1.Length();
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angularError = b2Abs(C2);
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b2Vec3 C(C1.x, C1.y, C2);
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b2Vec3 impulse;
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if (K.ez.z > 0.0f)
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{
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impulse = -K.Solve33(C);
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}
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else
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{
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b2Vec2 impulse2 = -K.Solve22(C1);
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impulse.Set(impulse2.x, impulse2.y, 0.0f);
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}
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b2Vec2 P(impulse.x, impulse.y);
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cA -= mA * P;
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aA -= iA * (b2Cross(rA, P) + impulse.z);
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cB += mB * P;
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aB += iB * (b2Cross(rB, P) + impulse.z);
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}
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data.positions[m_indexA].c = cA;
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data.positions[m_indexA].a = aA;
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data.positions[m_indexB].c = cB;
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data.positions[m_indexB].a = aB;
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return positionError <= b2_linearSlop && angularError <= b2_angularSlop;
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}
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b2Vec2 b2WeldJoint::GetAnchorA() const
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{
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return m_bodyA->GetWorldPoint(m_localAnchorA);
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}
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b2Vec2 b2WeldJoint::GetAnchorB() const
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{
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return m_bodyB->GetWorldPoint(m_localAnchorB);
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}
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b2Vec2 b2WeldJoint::GetReactionForce(float32 inv_dt) const
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{
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b2Vec2 P(m_impulse.x, m_impulse.y);
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return inv_dt * P;
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}
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float32 b2WeldJoint::GetReactionTorque(float32 inv_dt) const
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{
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return inv_dt * m_impulse.z;
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}
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void b2WeldJoint::Dump()
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{
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int32 indexA = m_bodyA->m_islandIndex;
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int32 indexB = m_bodyB->m_islandIndex;
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b2Log(" b2WeldJointDef jd;\n");
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b2Log(" jd.bodyA = bodies[%d];\n", indexA);
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b2Log(" jd.bodyB = bodies[%d];\n", indexB);
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b2Log(" jd.collideConnected = bool(%d);\n", m_collideConnected);
|
||
|
|
b2Log(" jd.localAnchorA.Set(%.15lef, %.15lef);\n", m_localAnchorA.x, m_localAnchorA.y);
|
||
|
|
b2Log(" jd.localAnchorB.Set(%.15lef, %.15lef);\n", m_localAnchorB.x, m_localAnchorB.y);
|
||
|
|
b2Log(" jd.referenceAngle = %.15lef;\n", m_referenceAngle);
|
||
|
|
b2Log(" jd.frequencyHz = %.15lef;\n", m_frequencyHz);
|
||
|
|
b2Log(" jd.dampingRatio = %.15lef;\n", m_dampingRatio);
|
||
|
|
b2Log(" joints[%d] = m_world->CreateJoint(&jd);\n", m_index);
|
||
|
|
}
|