b2_wheel_joint.cpp

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// 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_draw.h"
#include "box2d/b2_wheel_joint.h"
#include "box2d/b2_time_step.h"
 
// Linear constraint (point-to-line)
// d = pB - pA = xB + rB - xA - rA
// C = dot(ay, d)
// Cdot = dot(d, cross(wA, ay)) + dot(ay, vB + cross(wB, rB) - vA - cross(wA, rA))
//      = -dot(ay, vA) - dot(cross(d + rA, ay), wA) + dot(ay, vB) + dot(cross(rB, ay), vB)
// J = [-ay, -cross(d + rA, ay), ay, cross(rB, ay)]
 
// Spring linear constraint
// C = dot(ax, d)
// Cdot = = -dot(ax, vA) - dot(cross(d + rA, ax), wA) + dot(ax, vB) + dot(cross(rB, ax), vB)
// J = [-ax -cross(d+rA, ax) ax cross(rB, ax)]
 
// Motor rotational constraint
// Cdot = wB - wA
// J = [0 0 -1 0 0 1]
 
void b2WheelJointDef::Initialize(b2Body* bA, b2Body* bB, const b2Vec2& anchor, const b2Vec2& axis)
{
        bodyA = bA;
        bodyB = bB;
        localAnchorA = bodyA->GetLocalPoint(anchor);
        localAnchorB = bodyB->GetLocalPoint(anchor);
        localAxisA = bodyA->GetLocalVector(axis);
}
 
b2WheelJoint::b2WheelJoint(const b2WheelJointDef* def)
: b2Joint(def)
{
        m_localAnchorA = def->localAnchorA;
        m_localAnchorB = def->localAnchorB;
        m_localXAxisA = def->localAxisA;
        m_localYAxisA = b2Cross(1.0f, m_localXAxisA);
 
        m_mass = 0.0f;
        m_impulse = 0.0f;
        m_motorMass = 0.0f;
        m_motorImpulse = 0.0f;
        m_springMass = 0.0f;
        m_springImpulse = 0.0f;
 
        m_axialMass = 0.0f;
        m_lowerImpulse = 0.0f;
        m_upperImpulse = 0.0f;
        m_lowerTranslation = def->lowerTranslation;
        m_upperTranslation = def->upperTranslation;
        m_enableLimit = def->enableLimit;
 
        m_maxMotorTorque = def->maxMotorTorque;
        m_motorSpeed = def->motorSpeed;
        m_enableMotor = def->enableMotor;
 
        m_bias = 0.0f;
        m_gamma = 0.0f;
 
        m_ax.SetZero();
        m_ay.SetZero();
 
        m_stiffness = def->stiffness;
        m_damping = def->damping;
}
 
void b2WheelJoint::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;
 
        float mA = m_invMassA, mB = m_invMassB;
        float iA = m_invIA, iB = m_invIB;
 
        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 masses.
        b2Vec2 rA = b2Mul(qA, m_localAnchorA - m_localCenterA);
        b2Vec2 rB = b2Mul(qB, m_localAnchorB - m_localCenterB);
        b2Vec2 d = cB + rB - cA - rA;
 
        // Point to line constraint
        {
                m_ay = b2Mul(qA, m_localYAxisA);
                m_sAy = b2Cross(d + rA, m_ay);
                m_sBy = b2Cross(rB, m_ay);
 
                m_mass = mA + mB + iA * m_sAy * m_sAy + iB * m_sBy * m_sBy;
 
                if (m_mass > 0.0f)
                {
                        m_mass = 1.0f / m_mass;
                }
        }
 
        // Spring constraint
        m_ax = b2Mul(qA, m_localXAxisA);
        m_sAx = b2Cross(d + rA, m_ax);
        m_sBx = b2Cross(rB, m_ax);
 
        const float invMass = mA + mB + iA * m_sAx * m_sAx + iB * m_sBx * m_sBx;
        if (invMass > 0.0f)
        {
                m_axialMass = 1.0f / invMass;
        }
        else
        {
                m_axialMass = 0.0f;
        }
 
        m_springMass = 0.0f;
        m_bias = 0.0f;
        m_gamma = 0.0f;
 
        if (m_stiffness > 0.0f && invMass > 0.0f)
        {
                m_springMass = 1.0f / invMass;
 
                float C = b2Dot(d, m_ax);
 
                // magic formulas
                float h = data.step.dt;
                m_gamma = h * (m_damping + h * m_stiffness);
                if (m_gamma > 0.0f)
                {
                        m_gamma = 1.0f / m_gamma;
                }
 
                m_bias = C * h * m_stiffness * m_gamma;
 
                m_springMass = invMass + m_gamma;
                if (m_springMass > 0.0f)
                {
                        m_springMass = 1.0f / m_springMass;
                }
        }
        else
        {
                m_springImpulse = 0.0f;
        }
 
        if (m_enableLimit)
        {
                m_translation = b2Dot(m_ax, d);
        }
        else
        {
                m_lowerImpulse = 0.0f;
                m_upperImpulse = 0.0f;
        }
 
        if (m_enableMotor)
        {
                m_motorMass = iA + iB;
                if (m_motorMass > 0.0f)
                {
                        m_motorMass = 1.0f / m_motorMass;
                }
        }
        else
        {
                m_motorMass = 0.0f;
                m_motorImpulse = 0.0f;
        }
 
        if (data.step.warmStarting)
        {
                // Account for variable time step.
                m_impulse *= data.step.dtRatio;
                m_springImpulse *= data.step.dtRatio;
                m_motorImpulse *= data.step.dtRatio;
 
                float axialImpulse = m_springImpulse + m_lowerImpulse - m_upperImpulse;
                b2Vec2 P = m_impulse * m_ay + axialImpulse * m_ax;
                float LA = m_impulse * m_sAy + axialImpulse * m_sAx + m_motorImpulse;
                float LB = m_impulse * m_sBy + axialImpulse * m_sBx + m_motorImpulse;
 
                vA -= m_invMassA * P;
                wA -= m_invIA * LA;
 
                vB += m_invMassB * P;
                wB += m_invIB * LB;
        }
        else
        {
                m_impulse = 0.0f;
                m_springImpulse = 0.0f;
                m_motorImpulse = 0.0f;
                m_lowerImpulse = 0.0f;
                m_upperImpulse = 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 b2WheelJoint::SolveVelocityConstraints(const b2SolverData& data)
{
        float mA = m_invMassA, mB = m_invMassB;
        float iA = m_invIA, iB = m_invIB;
 
        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;
 
        // Solve spring constraint
        {
                float Cdot = b2Dot(m_ax, vB - vA) + m_sBx * wB - m_sAx * wA;
                float impulse = -m_springMass * (Cdot + m_bias + m_gamma * m_springImpulse);
                m_springImpulse += impulse;
 
                b2Vec2 P = impulse * m_ax;
                float LA = impulse * m_sAx;
                float LB = impulse * m_sBx;
 
                vA -= mA * P;
                wA -= iA * LA;
 
                vB += mB * P;
                wB += iB * LB;
        }
 
        // Solve rotational motor constraint
        {
                float Cdot = wB - wA - m_motorSpeed;
                float impulse = -m_motorMass * Cdot;
 
                float oldImpulse = m_motorImpulse;
                float maxImpulse = data.step.dt * m_maxMotorTorque;
                m_motorImpulse = b2Clamp(m_motorImpulse + impulse, -maxImpulse, maxImpulse);
                impulse = m_motorImpulse - oldImpulse;
 
                wA -= iA * impulse;
                wB += iB * impulse;
        }
 
        if (m_enableLimit)
        {
                // Lower limit
                {
                        float C = m_translation - m_lowerTranslation;
                        float Cdot = b2Dot(m_ax, vB - vA) + m_sBx * wB - m_sAx * wA;
                        float impulse = -m_axialMass * (Cdot + b2Max(C, 0.0f) * data.step.inv_dt);
                        float oldImpulse = m_lowerImpulse;
                        m_lowerImpulse = b2Max(m_lowerImpulse + impulse, 0.0f);
                        impulse = m_lowerImpulse - oldImpulse;
 
                        b2Vec2 P = impulse * m_ax;
                        float LA = impulse * m_sAx;
                        float LB = impulse * m_sBx;
 
                        vA -= mA * P;
                        wA -= iA * LA;
                        vB += mB * P;
                        wB += iB * LB;
                }
 
                // Upper limit
                // Note: signs are flipped to keep C positive when the constraint is satisfied.
                // This also keeps the impulse positive when the limit is active.
                {
                        float C = m_upperTranslation - m_translation;
                        float Cdot = b2Dot(m_ax, vA - vB) + m_sAx * wA - m_sBx * wB;
                        float impulse = -m_axialMass * (Cdot + b2Max(C, 0.0f) * data.step.inv_dt);
                        float oldImpulse = m_upperImpulse;
                        m_upperImpulse = b2Max(m_upperImpulse + impulse, 0.0f);
                        impulse = m_upperImpulse - oldImpulse;
 
                        b2Vec2 P = impulse * m_ax;
                        float LA = impulse * m_sAx;
                        float LB = impulse * m_sBx;
 
                        vA += mA * P;
                        wA += iA * LA;
                        vB -= mB * P;
                        wB -= iB * LB;
                }
        }
 
        // Solve point to line constraint
        {
                float Cdot = b2Dot(m_ay, vB - vA) + m_sBy * wB - m_sAy * wA;
                float impulse = -m_mass * Cdot;
                m_impulse += impulse;
 
                b2Vec2 P = impulse * m_ay;
                float LA = impulse * m_sAy;
                float LB = impulse * m_sBy;
 
                vA -= mA * P;
                wA -= iA * LA;
 
                vB += mB * P;
                wB += iB * LB;
        }
 
        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 b2WheelJoint::SolvePositionConstraints(const b2SolverData& data)
{
        b2Vec2 cA = data.positions[m_indexA].c;
        float aA = data.positions[m_indexA].a;
        b2Vec2 cB = data.positions[m_indexB].c;
        float aB = data.positions[m_indexB].a;
 
        float linearError = 0.0f;
 
        if (m_enableLimit)
        {
                b2Rot qA(aA), qB(aB);
 
                b2Vec2 rA = b2Mul(qA, m_localAnchorA - m_localCenterA);
                b2Vec2 rB = b2Mul(qB, m_localAnchorB - m_localCenterB);
                b2Vec2 d = (cB - cA) + rB - rA;
 
                b2Vec2 ax = b2Mul(qA, m_localXAxisA);
                float sAx = b2Cross(d + rA, m_ax);
                float sBx = b2Cross(rB, m_ax);
 
                float C = 0.0f;
                float translation = b2Dot(ax, d);
                if (b2Abs(m_upperTranslation - m_lowerTranslation) < 2.0f * b2_linearSlop)
                {
                        C = translation;
                }
                else if (translation <= m_lowerTranslation)
                {
                        C = b2Min(translation - m_lowerTranslation, 0.0f);
                }
                else if (translation >= m_upperTranslation)
                {
                        C = b2Max(translation - m_upperTranslation, 0.0f);
                }
 
                if (C != 0.0f)
                {
 
                        float invMass = m_invMassA + m_invMassB + m_invIA * sAx * sAx + m_invIB * sBx * sBx;
                        float impulse = 0.0f;
                        if (invMass != 0.0f)
                        {
                                impulse = -C / invMass;
                        }
 
                        b2Vec2 P = impulse * ax;
                        float LA = impulse * sAx;
                        float LB = impulse * sBx;
 
                        cA -= m_invMassA * P;
                        aA -= m_invIA * LA;
                        cB += m_invMassB * P;
                        aB += m_invIB * LB;
 
                        linearError = b2Abs(C);
                }
        }
 
        // Solve perpendicular constraint
        {
                b2Rot qA(aA), qB(aB);
 
                b2Vec2 rA = b2Mul(qA, m_localAnchorA - m_localCenterA);
                b2Vec2 rB = b2Mul(qB, m_localAnchorB - m_localCenterB);
                b2Vec2 d = (cB - cA) + rB - rA;
 
                b2Vec2 ay = b2Mul(qA, m_localYAxisA);
 
                float sAy = b2Cross(d + rA, ay);
                float sBy = b2Cross(rB, ay);
 
                float C = b2Dot(d, ay);
 
                float invMass = m_invMassA + m_invMassB + m_invIA * m_sAy * m_sAy + m_invIB * m_sBy * m_sBy;
 
                float impulse = 0.0f;
                if (invMass != 0.0f)
                {
                        impulse = - C / invMass;
                }
 
                b2Vec2 P = impulse * ay;
                float LA = impulse * sAy;
                float LB = impulse * sBy;
 
                cA -= m_invMassA * P;
                aA -= m_invIA * LA;
                cB += m_invMassB * P;
                aB += m_invIB * LB;
 
                linearError = b2Max(linearError, b2Abs(C));
        }
 
        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;
}
 
b2Vec2 b2WheelJoint::GetAnchorA() const
{
        return m_bodyA->GetWorldPoint(m_localAnchorA);
}
 
b2Vec2 b2WheelJoint::GetAnchorB() const
{
        return m_bodyB->GetWorldPoint(m_localAnchorB);
}
 
b2Vec2 b2WheelJoint::GetReactionForce(float inv_dt) const
{
        return inv_dt * (m_impulse * m_ay + (m_springImpulse + m_lowerImpulse - m_upperImpulse) * m_ax);
}
 
float b2WheelJoint::GetReactionTorque(float inv_dt) const
{
        return inv_dt * m_motorImpulse;
}
 
float b2WheelJoint::GetJointTranslation() const
{
        b2Body* bA = m_bodyA;
        b2Body* bB = m_bodyB;
 
        b2Vec2 pA = bA->GetWorldPoint(m_localAnchorA);
        b2Vec2 pB = bB->GetWorldPoint(m_localAnchorB);
        b2Vec2 d = pB - pA;
        b2Vec2 axis = bA->GetWorldVector(m_localXAxisA);
 
        float translation = b2Dot(d, axis);
        return translation;
}
 
float b2WheelJoint::GetJointLinearSpeed() 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;
        float wA = bA->m_angularVelocity;
        float wB = bB->m_angularVelocity;
 
        float speed = b2Dot(d, b2Cross(wA, axis)) + b2Dot(axis, vB + b2Cross(wB, rB) - vA - b2Cross(wA, rA));
        return speed;
}
 
float b2WheelJoint::GetJointAngle() const
{
        b2Body* bA = m_bodyA;
        b2Body* bB = m_bodyB;
        return bB->m_sweep.a - bA->m_sweep.a;
}
 
float b2WheelJoint::GetJointAngularSpeed() const
{
        float wA = m_bodyA->m_angularVelocity;
        float wB = m_bodyB->m_angularVelocity;
        return wB - wA;
}
 
bool b2WheelJoint::IsLimitEnabled() const
{
        return m_enableLimit;
}
 
void b2WheelJoint::EnableLimit(bool flag)
{
        if (flag != m_enableLimit)
        {
                m_bodyA->SetAwake(true);
                m_bodyB->SetAwake(true);
                m_enableLimit = flag;
                m_lowerImpulse = 0.0f;
                m_upperImpulse = 0.0f;
        }
}
 
float b2WheelJoint::GetLowerLimit() const
{
        return m_lowerTranslation;
}
 
float b2WheelJoint::GetUpperLimit() const
{
        return m_upperTranslation;
}
 
void b2WheelJoint::SetLimits(float lower, float 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_lowerImpulse = 0.0f;
                m_upperImpulse = 0.0f;
        }
}
 
bool b2WheelJoint::IsMotorEnabled() const
{
        return m_enableMotor;
}
 
void b2WheelJoint::EnableMotor(bool flag)
{
        if (flag != m_enableMotor)
        {
                m_bodyA->SetAwake(true);
                m_bodyB->SetAwake(true);
                m_enableMotor = flag;
        }
}
 
void b2WheelJoint::SetMotorSpeed(float speed)
{
        if (speed != m_motorSpeed)
        {
                m_bodyA->SetAwake(true);
                m_bodyB->SetAwake(true);
                m_motorSpeed = speed;
        }
}
 
void b2WheelJoint::SetMaxMotorTorque(float torque)
{
        if (torque != m_maxMotorTorque)
        {
                m_bodyA->SetAwake(true);
                m_bodyB->SetAwake(true);
                m_maxMotorTorque = torque;
        }
}
 
float b2WheelJoint::GetMotorTorque(float inv_dt) const
{
        return inv_dt * m_motorImpulse;
}
 
void b2WheelJoint::SetStiffness(float stiffness)
{
        m_stiffness = stiffness;
}
 
float b2WheelJoint::GetStiffness() const
{
        return m_stiffness;
}
 
void b2WheelJoint::SetDamping(float damping)
{
        m_damping = damping;
}
 
float b2WheelJoint::GetDamping() const
{
        return m_damping;
}
 
void b2WheelJoint::Dump()
{
        // FLT_DECIMAL_DIG == 9
 
        int32 indexA = m_bodyA->m_islandIndex;
        int32 indexB = m_bodyB->m_islandIndex;
 
        b2Dump("  b2WheelJointDef 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.localAnchorA.Set(%.9g, %.9g);\n", m_localAnchorA.x, m_localAnchorA.y);
        b2Dump("  jd.localAnchorB.Set(%.9g, %.9g);\n", m_localAnchorB.x, m_localAnchorB.y);
        b2Dump("  jd.localAxisA.Set(%.9g, %.9g);\n", m_localXAxisA.x, m_localXAxisA.y);
        b2Dump("  jd.enableMotor = bool(%d);\n", m_enableMotor);
        b2Dump("  jd.motorSpeed = %.9g;\n", m_motorSpeed);
        b2Dump("  jd.maxMotorTorque = %.9g;\n", m_maxMotorTorque);
        b2Dump("  jd.stiffness = %.9g;\n", m_stiffness);
        b2Dump("  jd.damping = %.9g;\n", m_damping);
        b2Dump("  joints[%d] = m_world->CreateJoint(&jd);\n", m_index);
}
 
void b2WheelJoint::Draw(b2Draw* draw) const
{
        const b2Transform& xfA = m_bodyA->GetTransform();
        const b2Transform& xfB = m_bodyB->GetTransform();
        b2Vec2 pA = b2Mul(xfA, m_localAnchorA);
        b2Vec2 pB = b2Mul(xfB, m_localAnchorB);
 
        b2Vec2 axis = b2Mul(xfA.q, m_localXAxisA);
 
        b2Color c1(0.7f, 0.7f, 0.7f);
        b2Color c2(0.3f, 0.9f, 0.3f);
        b2Color c3(0.9f, 0.3f, 0.3f);
        b2Color c4(0.3f, 0.3f, 0.9f);
        b2Color c5(0.4f, 0.4f, 0.4f);
 
        draw->DrawSegment(pA, pB, c5);
 
        if (m_enableLimit)
        {
                b2Vec2 lower = pA + m_lowerTranslation * axis;
                b2Vec2 upper = pA + m_upperTranslation * axis;
                b2Vec2 perp = b2Mul(xfA.q, m_localYAxisA);
                draw->DrawSegment(lower, upper, c1);
                draw->DrawSegment(lower - 0.5f * perp, lower + 0.5f * perp, c2);
                draw->DrawSegment(upper - 0.5f * perp, upper + 0.5f * perp, c3);
        }
        else
        {
                draw->DrawSegment(pA - 1.0f * axis, pA + 1.0f * axis, c1);
        }
 
        draw->DrawPoint(pA, 5.0f, c1);
        draw->DrawPoint(pB, 5.0f, c4);
}