b2_revolute_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_revolute_joint.h"
#include "box2d/b2_time_step.h"

// Point-to-point constraint
// C = p2 - p1
// 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)

// Motor constraint
// Cdot = w2 - w1
// J = [0 0 -1 0 0 1]
// K = invI1 + invI2

void b2RevoluteJointDef::Initialize(b2Body* bA, b2Body* bB, const b2Vec2& anchor)
{
        bodyA = bA;
        bodyB = bB;
        localAnchorA = bodyA->GetLocalPoint(anchor);
        localAnchorB = bodyB->GetLocalPoint(anchor);
        referenceAngle = bodyB->GetAngle() - bodyA->GetAngle();
}

b2RevoluteJoint::b2RevoluteJoint(const b2RevoluteJointDef* def)
: b2Joint(def)
{
        m_localAnchorA = def->localAnchorA;
        m_localAnchorB = def->localAnchorB;
        m_referenceAngle = def->referenceAngle;

        m_impulse.SetZero();
        m_axialMass = 0.0f;
        m_motorImpulse = 0.0f;
        m_lowerImpulse = 0.0f;
        m_upperImpulse = 0.0f;

        m_lowerAngle = def->lowerAngle;
        m_upperAngle = def->upperAngle;
        m_maxMotorTorque = def->maxMotorTorque;
        m_motorSpeed = def->motorSpeed;
        m_enableLimit = def->enableLimit;
        m_enableMotor = def->enableMotor;

        m_angle = 0.0f;
}

void b2RevoluteJoint::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 aA = data.positions[m_indexA].a;
        b2Vec2 vA = data.velocities[m_indexA].v;
        float wA = data.velocities[m_indexA].w;

        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);

        m_rA = b2Mul(qA, m_localAnchorA - m_localCenterA);
        m_rB = b2Mul(qB, m_localAnchorB - 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*r1x-r2y*iB*r2x, mA+r1x^2*iA+mB+r2x^2*iB]

        float mA = m_invMassA, mB = m_invMassB;
        float iA = m_invIA, iB = m_invIB;

        m_K.ex.x = mA + mB + m_rA.y * m_rA.y * iA + m_rB.y * m_rB.y * iB;
        m_K.ey.x = -m_rA.y * m_rA.x * iA - m_rB.y * m_rB.x * iB;
        m_K.ex.y = m_K.ey.x;
        m_K.ey.y = mA + mB + m_rA.x * m_rA.x * iA + m_rB.x * m_rB.x * iB;

        m_axialMass = iA + iB;
        bool fixedRotation;
        if (m_axialMass > 0.0f)
        {
                m_axialMass = 1.0f / m_axialMass;
                fixedRotation = false;
        }
        else
        {
                fixedRotation = true;
        }

        m_angle = aB - aA - m_referenceAngle;
        if (m_enableLimit == false || fixedRotation)
        {
                m_lowerImpulse = 0.0f;
                m_upperImpulse = 0.0f;
        }

        if (m_enableMotor == false || fixedRotation)
        {
                m_motorImpulse = 0.0f;
        }

        if (data.step.warmStarting)
        {
                // Scale impulses to support a variable time step.
                m_impulse *= data.step.dtRatio;
                m_motorImpulse *= data.step.dtRatio;
                m_lowerImpulse *= data.step.dtRatio;
                m_upperImpulse *= data.step.dtRatio;

                float axialImpulse = m_motorImpulse + m_lowerImpulse - m_upperImpulse;
                b2Vec2 P(m_impulse.x, m_impulse.y);

                vA -= mA * P;
                wA -= iA * (b2Cross(m_rA, P) + axialImpulse);

                vB += mB * P;
                wB += iB * (b2Cross(m_rB, P) + axialImpulse);
        }
        else
        {
                m_impulse.SetZero();
                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 b2RevoluteJoint::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;

        bool fixedRotation = (iA + iB == 0.0f);

        // Solve motor constraint.
        if (m_enableMotor && fixedRotation == false)
        {
                float Cdot = wB - wA - m_motorSpeed;
                float impulse = -m_axialMass * 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 && fixedRotation == false)
        {
                // Lower limit
                {
                        float C = m_angle - m_lowerAngle;
                        float Cdot = wB - 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;

                        wA -= iA * impulse;
                        wB += iB * impulse;
                }

                // 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_upperAngle - m_angle;
                        float Cdot = wA - 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;

                        wA += iA * impulse;
                        wB -= iB * impulse;
                }
        }

        // Solve point-to-point constraint
        {
                b2Vec2 Cdot = vB + b2Cross(wB, m_rB) - vA - b2Cross(wA, m_rA);
                b2Vec2 impulse = m_K.Solve(-Cdot);

                m_impulse.x += impulse.x;
                m_impulse.y += impulse.y;

                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 b2RevoluteJoint::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;

        b2Rot qA(aA), qB(aB);

        float angularError = 0.0f;
        float positionError = 0.0f;

        bool fixedRotation = (m_invIA + m_invIB == 0.0f);

        // Solve angular limit constraint
        if (m_enableLimit && fixedRotation == false)
        {
                float angle = aB - aA - m_referenceAngle;
                float C = 0.0f;

                if (b2Abs(m_upperAngle - m_lowerAngle) < 2.0f * b2_angularSlop)
                {
                        // Prevent large angular corrections
                        C = b2Clamp(angle - m_lowerAngle, -b2_maxAngularCorrection, b2_maxAngularCorrection);
                }
                else if (angle <= m_lowerAngle)
                {
                        // Prevent large angular corrections and allow some slop.
                        C = b2Clamp(angle - m_lowerAngle + b2_angularSlop, -b2_maxAngularCorrection, 0.0f);
                }
                else if (angle >= m_upperAngle)
                {
                        // Prevent large angular corrections and allow some slop.
                        C = b2Clamp(angle - m_upperAngle - b2_angularSlop, 0.0f, b2_maxAngularCorrection);
                }

                float limitImpulse = -m_axialMass * C;
                aA -= m_invIA * limitImpulse;
                aB += m_invIB * limitImpulse;
                angularError = b2Abs(C);
        }

        // Solve point-to-point constraint.
        {
                qA.Set(aA);
                qB.Set(aB);
                b2Vec2 rA = b2Mul(qA, m_localAnchorA - m_localCenterA);
                b2Vec2 rB = b2Mul(qB, m_localAnchorB - m_localCenterB);

                b2Vec2 C = cB + rB - cA - rA;
                positionError = C.Length();

                float mA = m_invMassA, mB = m_invMassB;
                float iA = m_invIA, iB = m_invIB;

                b2Mat22 K;
                K.ex.x = mA + mB + iA * rA.y * rA.y + iB * rB.y * rB.y;
                K.ex.y = -iA * rA.x * rA.y - iB * rB.x * rB.y;
                K.ey.x = K.ex.y;
                K.ey.y = mA + mB + iA * rA.x * rA.x + iB * rB.x * rB.x;

                b2Vec2 impulse = -K.Solve(C);

                cA -= mA * impulse;
                aA -= iA * b2Cross(rA, impulse);

                cB += mB * impulse;
                aB += iB * b2Cross(rB, impulse);
        }

        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 positionError <= b2_linearSlop && angularError <= b2_angularSlop;
}

b2Vec2 b2RevoluteJoint::GetAnchorA() const
{
        return m_bodyA->GetWorldPoint(m_localAnchorA);
}

b2Vec2 b2RevoluteJoint::GetAnchorB() const
{
        return m_bodyB->GetWorldPoint(m_localAnchorB);
}

b2Vec2 b2RevoluteJoint::GetReactionForce(float inv_dt) const
{
        b2Vec2 P(m_impulse.x, m_impulse.y);
        return inv_dt * P;
}

float b2RevoluteJoint::GetReactionTorque(float inv_dt) const
{
        return inv_dt * (m_motorImpulse + m_lowerImpulse - m_upperImpulse);
}

float b2RevoluteJoint::GetJointAngle() const
{
        b2Body* bA = m_bodyA;
        b2Body* bB = m_bodyB;
        return bB->m_sweep.a - bA->m_sweep.a - m_referenceAngle;
}

float b2RevoluteJoint::GetJointSpeed() const
{
        b2Body* bA = m_bodyA;
        b2Body* bB = m_bodyB;
        return bB->m_angularVelocity - bA->m_angularVelocity;
}

bool b2RevoluteJoint::IsMotorEnabled() const
{
        return m_enableMotor;
}

void b2RevoluteJoint::EnableMotor(bool flag)
{
        if (flag != m_enableMotor)
        {
                m_bodyA->SetAwake(true);
                m_bodyB->SetAwake(true);
                m_enableMotor = flag;
        }
}

float b2RevoluteJoint::GetMotorTorque(float inv_dt) const
{
        return inv_dt * m_motorImpulse;
}

void b2RevoluteJoint::SetMotorSpeed(float speed)
{
        if (speed != m_motorSpeed)
        {
                m_bodyA->SetAwake(true);
                m_bodyB->SetAwake(true);
                m_motorSpeed = speed;
        }
}

void b2RevoluteJoint::SetMaxMotorTorque(float torque)
{
        if (torque != m_maxMotorTorque)
        {
                m_bodyA->SetAwake(true);
                m_bodyB->SetAwake(true);
                m_maxMotorTorque = torque;
        }
}

bool b2RevoluteJoint::IsLimitEnabled() const
{
        return m_enableLimit;
}

void b2RevoluteJoint::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 b2RevoluteJoint::GetLowerLimit() const
{
        return m_lowerAngle;
}

float b2RevoluteJoint::GetUpperLimit() const
{
        return m_upperAngle;
}

void b2RevoluteJoint::SetLimits(float lower, float upper)
{
        b2Assert(lower <= upper);
        
        if (lower != m_lowerAngle || upper != m_upperAngle)
        {
                m_bodyA->SetAwake(true);
                m_bodyB->SetAwake(true);
                m_lowerImpulse = 0.0f;
                m_upperImpulse = 0.0f;
                m_lowerAngle = lower;
                m_upperAngle = upper;
        }
}

void b2RevoluteJoint::Dump()
{
        int32 indexA = m_bodyA->m_islandIndex;
        int32 indexB = m_bodyB->m_islandIndex;

        b2Dump("  b2RevoluteJointDef 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.referenceAngle = %.9g;\n", m_referenceAngle);
        b2Dump("  jd.enableLimit = bool(%d);\n", m_enableLimit);
        b2Dump("  jd.lowerAngle = %.9g;\n", m_lowerAngle);
        b2Dump("  jd.upperAngle = %.9g;\n", m_upperAngle);
        b2Dump("  jd.enableMotor = bool(%d);\n", m_enableMotor);
        b2Dump("  jd.motorSpeed = %.9g;\n", m_motorSpeed);
        b2Dump("  jd.maxMotorTorque = %.9g;\n", m_maxMotorTorque);
        b2Dump("  joints[%d] = m_world->CreateJoint(&jd);\n", m_index);
}

void b2RevoluteJoint::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);

        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->DrawPoint(pA, 5.0f, c4);
        draw->DrawPoint(pB, 5.0f, c5);

        float aA = m_bodyA->GetAngle();
        float aB = m_bodyB->GetAngle();
        float angle = aB - aA - m_referenceAngle;

        const float L = 0.5f;

        b2Vec2 r = L * b2Vec2(cosf(angle), sinf(angle));
        draw->DrawSegment(pB, pB + r, c1);
        draw->DrawCircle(pB, L, c1);

        if (m_enableLimit)
        {
                b2Vec2 rlo = L * b2Vec2(cosf(m_lowerAngle), sinf(m_lowerAngle));
                b2Vec2 rhi = L * b2Vec2(cosf(m_upperAngle), sinf(m_upperAngle));

                draw->DrawSegment(pB, pB + rlo, c2);
                draw->DrawSegment(pB, pB + rhi, c3);
        }

        b2Color color(0.5f, 0.8f, 0.8f);
        draw->DrawSegment(xfA.p, pA, color);
        draw->DrawSegment(pA, pB, color);
        draw->DrawSegment(xfB.p, pB, color);
}