// MIT License
// Copyright (c) 2019 Erin Catto
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to deal
// in the Software without restriction, including without limitation the rights
// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
// The above copyright notice and this permission notice shall be included in all
// copies or substantial portions of the Software.
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
// SOFTWARE.
#include "box2d/b2_body.h"
#include "box2d/b2_motor_joint.h"
#include "box2d/b2_time_step.h"
// Point-to-point constraint
// Cdot = v2 - v1
// = v2 + cross(w2, r2) - v1 - cross(w1, r1)
// J = [-I -r1_skew I r2_skew ]
// Identity used:
// w k % (rx i + ry j) = w * (-ry i + rx j)
//
// r1 = offset - c1
// r2 = -c2
// Angle constraint
// Cdot = w2 - w1
// J = [0 0 -1 0 0 1]
// K = invI1 + invI2
void b2MotorJointDef::Initialize(b2Body* bA, b2Body* bB)
{
bodyA = bA;
bodyB = bB;
b2Vec2 xB = bodyB->GetPosition();
linearOffset = bodyA->GetLocalPoint(xB);
float angleA = bodyA->GetAngle();
float angleB = bodyB->GetAngle();
angularOffset = angleB - angleA;
}
b2MotorJoint::b2MotorJoint(const b2MotorJointDef* def)
: b2Joint(def)
{
m_linearOffset = def->linearOffset;
m_angularOffset = def->angularOffset;
m_linearImpulse.SetZero();
m_angularImpulse = 0.0f;
m_maxForce = def->maxForce;
m_maxTorque = def->maxTorque;
m_correctionFactor = def->correctionFactor;
}
void b2MotorJoint::InitVelocityConstraints(const b2SolverData& data)
{
m_indexA = m_bodyA->m_islandIndex;
m_indexB = m_bodyB->m_islandIndex;
m_localCenterA = m_bodyA->m_sweep.localCenter;
m_localCenterB = m_bodyB->m_sweep.localCenter;
m_invMassA = m_bodyA->m_invMass;
m_invMassB = m_bodyB->m_invMass;
m_invIA = m_bodyA->m_invI;
m_invIB = m_bodyB->m_invI;
b2Vec2 cA = data.positions[m_indexA].c;
float aA = data.positions[m_indexA].a;
b2Vec2 vA = data.velocities[m_indexA].v;
float wA = data.velocities[m_indexA].w;
b2Vec2 cB = data.positions[m_indexB].c;
float aB = data.positions[m_indexB].a;
b2Vec2 vB = data.velocities[m_indexB].v;
float wB = data.velocities[m_indexB].w;
b2Rot qA(aA), qB(aB);
// Compute the effective mass matrix.
m_rA = b2Mul(qA, m_linearOffset - m_localCenterA);
m_rB = b2Mul(qB, -m_localCenterB);
// J = [-I -r1_skew I r2_skew]
// r_skew = [-ry; rx]
// Matlab
// K = [ mA+r1y^2*iA+mB+r2y^2*iB, -r1y*iA*r1x-r2y*iB*r2x, -r1y*iA-r2y*iB]
// [ -r1y*iA*r1x-r2y*iB*r2x, mA+r1x^2*iA+mB+r2x^2*iB, r1x*iA+r2x*iB]
// [ -r1y*iA-r2y*iB, r1x*iA+r2x*iB, iA+iB]
float mA = m_invMassA, mB = m_invMassB;
float iA = m_invIA, iB = m_invIB;
// Upper 2 by 2 of K for point to point
b2Mat22 K;
K.ex.x = mA + mB + iA * m_rA.y * m_rA.y + iB * m_rB.y * m_rB.y;
K.ex.y = -iA * m_rA.x * m_rA.y - iB * m_rB.x * m_rB.y;
K.ey.x = K.ex.y;
K.ey.y = mA + mB + iA * m_rA.x * m_rA.x + iB * m_rB.x * m_rB.x;
m_linearMass = K.GetInverse();
m_angularMass = iA + iB;
if (m_angularMass > 0.0f)
{
m_angularMass = 1.0f / m_angularMass;
}
m_linearError = cB + m_rB - cA - m_rA;
m_angularError = aB - aA - m_angularOffset;
if (data.step.warmStarting)
{
// Scale impulses to support a variable time step.
m_linearImpulse *= data.step.dtRatio;
m_angularImpulse *= data.step.dtRatio;
b2Vec2 P(m_linearImpulse.x, m_linearImpulse.y);
vA -= mA * P;
wA -= iA * (b2Cross(m_rA, P) + m_angularImpulse);
vB += mB * P;
wB += iB * (b2Cross(m_rB, P) + m_angularImpulse);
}
else
{
m_linearImpulse.SetZero();
m_angularImpulse = 0.0f;
}
data.velocities[m_indexA].v = vA;
data.velocities[m_indexA].w = wA;
data.velocities[m_indexB].v = vB;
data.velocities[m_indexB].w = wB;
}
void b2MotorJoint::SolveVelocityConstraints(const b2SolverData& data)
{
b2Vec2 vA = data.velocities[m_indexA].v;
float wA = data.velocities[m_indexA].w;
b2Vec2 vB = data.velocities[m_indexB].v;
float wB = data.velocities[m_indexB].w;
float mA = m_invMassA, mB = m_invMassB;
float iA = m_invIA, iB = m_invIB;
float h = data.step.dt;
float inv_h = data.step.inv_dt;
// Solve angular friction
{
float Cdot = wB - wA + inv_h * m_correctionFactor * m_angularError;
float impulse = -m_angularMass * Cdot;
float oldImpulse = m_angularImpulse;
float maxImpulse = h * m_maxTorque;
m_angularImpulse = b2Clamp(m_angularImpulse + impulse, -maxImpulse, maxImpulse);
impulse = m_angularImpulse - oldImpulse;
wA -= iA * impulse;
wB += iB * impulse;
}
// Solve linear friction
{
b2Vec2 Cdot = vB + b2Cross(wB, m_rB) - vA - b2Cross(wA, m_rA) + inv_h * m_correctionFactor * m_linearError;
b2Vec2 impulse = -b2Mul(m_linearMass, Cdot);
b2Vec2 oldImpulse = m_linearImpulse;
m_linearImpulse += impulse;
float maxImpulse = h * m_maxForce;
if (m_linearImpulse.LengthSquared() > maxImpulse * maxImpulse)
{
m_linearImpulse.Normalize();
m_linearImpulse *= maxImpulse;
}
impulse = m_linearImpulse - oldImpulse;
vA -= mA * impulse;
wA -= iA * b2Cross(m_rA, impulse);
vB += mB * impulse;
wB += iB * b2Cross(m_rB, impulse);
}
data.velocities[m_indexA].v = vA;
data.velocities[m_indexA].w = wA;
data.velocities[m_indexB].v = vB;
data.velocities[m_indexB].w = wB;
}
bool b2MotorJoint::SolvePositionConstraints(const b2SolverData& data)
{
B2_NOT_USED(data);
return true;
}
b2Vec2 b2MotorJoint::GetAnchorA() const
{
return m_bodyA->GetPosition();
}
b2Vec2 b2MotorJoint::GetAnchorB() const
{
return m_bodyB->GetPosition();
}
b2Vec2 b2MotorJoint::GetReactionForce(float inv_dt) const
{
return inv_dt * m_linearImpulse;
}
float b2MotorJoint::GetReactionTorque(float inv_dt) const
{
return inv_dt * m_angularImpulse;
}
void b2MotorJoint::SetMaxForce(float force)
{
b2Assert(b2IsValid(force) && force >= 0.0f);
m_maxForce = force;
}
float b2MotorJoint::GetMaxForce() const
{
return m_maxForce;
}
void b2MotorJoint::SetMaxTorque(float torque)
{
b2Assert(b2IsValid(torque) && torque >= 0.0f);
m_maxTorque = torque;
}
float b2MotorJoint::GetMaxTorque() const
{
return m_maxTorque;
}
void b2MotorJoint::SetCorrectionFactor(float factor)
{
b2Assert(b2IsValid(factor) && 0.0f <= factor && factor <= 1.0f);
m_correctionFactor = factor;
}
float b2MotorJoint::GetCorrectionFactor() const
{
return m_correctionFactor;
}
void b2MotorJoint::SetLinearOffset(const b2Vec2& linearOffset)
{
if (linearOffset.x != m_linearOffset.x || linearOffset.y != m_linearOffset.y)
{
m_bodyA->SetAwake(true);
m_bodyB->SetAwake(true);
m_linearOffset = linearOffset;
}
}
const b2Vec2& b2MotorJoint::GetLinearOffset() const
{
return m_linearOffset;
}
void b2MotorJoint::SetAngularOffset(float angularOffset)
{
if (angularOffset != m_angularOffset)
{
m_bodyA->SetAwake(true);
m_bodyB->SetAwake(true);
m_angularOffset = angularOffset;
}
}
float b2MotorJoint::GetAngularOffset() const
{
return m_angularOffset;
}
void b2MotorJoint::Dump()
{
int32 indexA = m_bodyA->m_islandIndex;
int32 indexB = m_bodyB->m_islandIndex;
b2Dump(" b2MotorJointDef jd;\n");
b2Dump(" jd.bodyA = bodies[%d];\n", indexA);
b2Dump(" jd.bodyB = bodies[%d];\n", indexB);
b2Dump(" jd.collideConnected = bool(%d);\n", m_collideConnected);
b2Dump(" jd.linearOffset.Set(%.9g, %.9g);\n", m_linearOffset.x, m_linearOffset.y);
b2Dump(" jd.angularOffset = %.9g;\n", m_angularOffset);
b2Dump(" jd.maxForce = %.9g;\n", m_maxForce);
b2Dump(" jd.maxTorque = %.9g;\n", m_maxTorque);
b2Dump(" jd.correctionFactor = %.9g;\n", m_correctionFactor);
b2Dump(" joints[%d] = m_world->CreateJoint(&jd);\n", m_index);
}Useful References
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