mirror of https://github.com/axmolengine/axmol.git
627 lines
16 KiB
C++
627 lines
16 KiB
C++
/*
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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/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* bA, b2Body* bB, const b2Vec2& anchor, const b2Vec2& axis)
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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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localAxisA = 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_localAnchorA = def->localAnchorA;
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m_localAnchorB = def->localAnchorB;
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m_localXAxisA = def->localAxisA;
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m_localXAxisA.Normalize();
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m_localYAxisA = b2Cross(1.0f, m_localXAxisA);
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m_referenceAngle = def->referenceAngle;
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m_impulse.SetZero();
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m_motorMass = 0.0f;
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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 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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b2Vec2 cA = data.positions[m_indexA].c;
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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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b2Vec2 cB = data.positions[m_indexB].c;
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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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// Compute the effective masses.
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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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b2Vec2 d = (cB - cA) + rB - rA;
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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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// Compute motor Jacobian and effective mass.
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{
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m_axis = b2Mul(qA, m_localXAxisA);
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m_a1 = b2Cross(d + rA, m_axis);
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m_a2 = b2Cross(rB, m_axis);
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m_motorMass = mA + mB + iA * m_a1 * m_a1 + iB * m_a2 * m_a2;
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if (m_motorMass > 0.0f)
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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(qA, m_localYAxisA);
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m_s1 = b2Cross(d + rA, m_perp);
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m_s2 = b2Cross(rB, m_perp);
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float32 k11 = mA + mB + iA * m_s1 * m_s1 + iB * m_s2 * m_s2;
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float32 k12 = iA * m_s1 + iB * m_s2;
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float32 k13 = iA * m_s1 * m_a1 + iB * m_s2 * m_a2;
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float32 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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float32 k23 = iA * m_a1 + iB * m_a2;
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float32 k33 = mA + mB + iA * m_a1 * m_a1 + iB * m_a2 * m_a2;
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m_K.ex.Set(k11, k12, k13);
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m_K.ey.Set(k12, k22, k23);
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m_K.ez.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 (data.step.warmStarting)
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{
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// Account for variable time step.
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m_impulse *= data.step.dtRatio;
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m_motorImpulse *= data.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 LA = m_impulse.x * m_s1 + m_impulse.y + (m_motorImpulse + m_impulse.z) * m_a1;
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float32 LB = m_impulse.x * m_s2 + m_impulse.y + (m_motorImpulse + m_impulse.z) * m_a2;
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vA -= mA * P;
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wA -= iA * LA;
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vB += mB * P;
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wB += iB * LB;
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}
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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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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 b2PrismaticJoint::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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// 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, vB - vA) + m_a2 * wB - m_a1 * wA;
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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 = data.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 LA = impulse * m_a1;
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float32 LB = impulse * m_a2;
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vA -= mA * P;
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wA -= iA * LA;
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vB += mB * P;
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wB += iB * LB;
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}
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b2Vec2 Cdot1;
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Cdot1.x = b2Dot(m_perp, vB - vA) + m_s2 * wB - m_s1 * wA;
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Cdot1.y = wB - wA;
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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, vB - vA) + m_a2 * wB - m_a1 * wA;
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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.ez.x, m_K.ez.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 LA = df.x * m_s1 + df.y + df.z * m_a1;
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float32 LB = df.x * m_s2 + df.y + df.z * m_a2;
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vA -= mA * P;
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wA -= iA * LA;
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vB += mB * P;
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wB += iB * LB;
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}
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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 LA = df.x * m_s1 + df.y;
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float32 LB = df.x * m_s2 + df.y;
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vA -= mA * P;
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wA -= iA * LA;
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vB += mB * P;
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wB += iB * LB;
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}
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data.velocities[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 b2PrismaticJoint::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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// Compute fresh Jacobians
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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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b2Vec2 d = cB + rB - cA - rA;
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b2Vec2 axis = b2Mul(qA, m_localXAxisA);
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float32 a1 = b2Cross(d + rA, axis);
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float32 a2 = b2Cross(rB, axis);
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b2Vec2 perp = b2Mul(qA, m_localYAxisA);
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float32 s1 = b2Cross(d + rA, perp);
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float32 s2 = b2Cross(rB, perp);
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b2Vec3 impulse;
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b2Vec2 C1;
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C1.x = b2Dot(perp, d);
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C1.y = aB - aA - m_referenceAngle;
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float32 linearError = b2Abs(C1.x);
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float32 angularError = b2Abs(C1.y);
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bool active = false;
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float32 C2 = 0.0f;
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if (m_enableLimit)
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{
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float32 translation = b2Dot(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 = b2Max(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 = b2Max(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 = b2Max(linearError, translation - m_upperTranslation);
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active = true;
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}
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}
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if (active)
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{
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float32 k11 = mA + mB + iA * s1 * s1 + iB * s2 * s2;
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float32 k12 = iA * s1 + iB * s2;
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float32 k13 = iA * s1 * a1 + iB * s2 * a2;
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float32 k22 = iA + iB;
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if (k22 == 0.0f)
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{
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// For fixed rotation
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k22 = 1.0f;
|
|
}
|
|
float32 k23 = iA * a1 + iB * a2;
|
|
float32 k33 = mA + mB + iA * a1 * a1 + iB * a2 * a2;
|
|
|
|
b2Mat33 K;
|
|
K.ex.Set(k11, k12, k13);
|
|
K.ey.Set(k12, k22, k23);
|
|
K.ez.Set(k13, k23, k33);
|
|
|
|
b2Vec3 C;
|
|
C.x = C1.x;
|
|
C.y = C1.y;
|
|
C.z = C2;
|
|
|
|
impulse = K.Solve33(-C);
|
|
}
|
|
else
|
|
{
|
|
float32 k11 = mA + mB + iA * s1 * s1 + iB * s2 * s2;
|
|
float32 k12 = iA * s1 + iB * s2;
|
|
float32 k22 = iA + iB;
|
|
if (k22 == 0.0f)
|
|
{
|
|
k22 = 1.0f;
|
|
}
|
|
|
|
b2Mat22 K;
|
|
K.ex.Set(k11, k12);
|
|
K.ey.Set(k12, k22);
|
|
|
|
b2Vec2 impulse1 = K.Solve(-C1);
|
|
impulse.x = impulse1.x;
|
|
impulse.y = impulse1.y;
|
|
impulse.z = 0.0f;
|
|
}
|
|
|
|
b2Vec2 P = impulse.x * perp + impulse.z * axis;
|
|
float32 LA = impulse.x * s1 + impulse.y + impulse.z * a1;
|
|
float32 LB = impulse.x * s2 + impulse.y + impulse.z * a2;
|
|
|
|
cA -= mA * P;
|
|
aA -= iA * LA;
|
|
cB += mB * P;
|
|
aB += iB * LB;
|
|
|
|
data.positions[m_indexA].c = cA;
|
|
data.positions[m_indexA].a = aA;
|
|
data.positions[m_indexB].c = cB;
|
|
data.positions[m_indexB].a = aB;
|
|
|
|
return linearError <= b2_linearSlop && angularError <= b2_angularSlop;
|
|
}
|
|
|
|
b2Vec2 b2PrismaticJoint::GetAnchorA() const
|
|
{
|
|
return m_bodyA->GetWorldPoint(m_localAnchorA);
|
|
}
|
|
|
|
b2Vec2 b2PrismaticJoint::GetAnchorB() const
|
|
{
|
|
return m_bodyB->GetWorldPoint(m_localAnchorB);
|
|
}
|
|
|
|
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
|
|
{
|
|
b2Vec2 pA = m_bodyA->GetWorldPoint(m_localAnchorA);
|
|
b2Vec2 pB = m_bodyB->GetWorldPoint(m_localAnchorB);
|
|
b2Vec2 d = pB - pA;
|
|
b2Vec2 axis = m_bodyA->GetWorldVector(m_localXAxisA);
|
|
|
|
float32 translation = b2Dot(d, axis);
|
|
return translation;
|
|
}
|
|
|
|
float32 b2PrismaticJoint::GetJointSpeed() const
|
|
{
|
|
b2Body* bA = m_bodyA;
|
|
b2Body* bB = m_bodyB;
|
|
|
|
b2Vec2 rA = b2Mul(bA->m_xf.q, m_localAnchorA - bA->m_sweep.localCenter);
|
|
b2Vec2 rB = b2Mul(bB->m_xf.q, m_localAnchorB - bB->m_sweep.localCenter);
|
|
b2Vec2 p1 = bA->m_sweep.c + rA;
|
|
b2Vec2 p2 = bB->m_sweep.c + rB;
|
|
b2Vec2 d = p2 - p1;
|
|
b2Vec2 axis = b2Mul(bA->m_xf.q, m_localXAxisA);
|
|
|
|
b2Vec2 vA = bA->m_linearVelocity;
|
|
b2Vec2 vB = bB->m_linearVelocity;
|
|
float32 wA = bA->m_angularVelocity;
|
|
float32 wB = bB->m_angularVelocity;
|
|
|
|
float32 speed = b2Dot(d, b2Cross(wA, axis)) + b2Dot(axis, vB + b2Cross(wB, rB) - vA - b2Cross(wA, rA));
|
|
return speed;
|
|
}
|
|
|
|
bool b2PrismaticJoint::IsLimitEnabled() const
|
|
{
|
|
return m_enableLimit;
|
|
}
|
|
|
|
void b2PrismaticJoint::EnableLimit(bool flag)
|
|
{
|
|
if (flag != m_enableLimit)
|
|
{
|
|
m_bodyA->SetAwake(true);
|
|
m_bodyB->SetAwake(true);
|
|
m_enableLimit = flag;
|
|
m_impulse.z = 0.0f;
|
|
}
|
|
}
|
|
|
|
float32 b2PrismaticJoint::GetLowerLimit() const
|
|
{
|
|
return m_lowerTranslation;
|
|
}
|
|
|
|
float32 b2PrismaticJoint::GetUpperLimit() const
|
|
{
|
|
return m_upperTranslation;
|
|
}
|
|
|
|
void b2PrismaticJoint::SetLimits(float32 lower, float32 upper)
|
|
{
|
|
b2Assert(lower <= upper);
|
|
if (lower != m_lowerTranslation || upper != m_upperTranslation)
|
|
{
|
|
m_bodyA->SetAwake(true);
|
|
m_bodyB->SetAwake(true);
|
|
m_lowerTranslation = lower;
|
|
m_upperTranslation = upper;
|
|
m_impulse.z = 0.0f;
|
|
}
|
|
}
|
|
|
|
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(float32 inv_dt) const
|
|
{
|
|
return inv_dt * m_motorImpulse;
|
|
}
|
|
|
|
void b2PrismaticJoint::Dump()
|
|
{
|
|
int32 indexA = m_bodyA->m_islandIndex;
|
|
int32 indexB = m_bodyB->m_islandIndex;
|
|
|
|
b2Log(" b2PrismaticJointDef jd;\n");
|
|
b2Log(" jd.bodyA = bodies[%d];\n", indexA);
|
|
b2Log(" jd.bodyB = bodies[%d];\n", indexB);
|
|
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.localAxisA.Set(%.15lef, %.15lef);\n", m_localXAxisA.x, m_localXAxisA.y);
|
|
b2Log(" jd.referenceAngle = %.15lef;\n", m_referenceAngle);
|
|
b2Log(" jd.enableLimit = bool(%d);\n", m_enableLimit);
|
|
b2Log(" jd.lowerTranslation = %.15lef;\n", m_lowerTranslation);
|
|
b2Log(" jd.upperTranslation = %.15lef;\n", m_upperTranslation);
|
|
b2Log(" jd.enableMotor = bool(%d);\n", m_enableMotor);
|
|
b2Log(" jd.motorSpeed = %.15lef;\n", m_motorSpeed);
|
|
b2Log(" jd.maxMotorForce = %.15lef;\n", m_maxMotorForce);
|
|
b2Log(" joints[%d] = m_world->CreateJoint(&jd);\n", m_index);
|
|
}
|