b2WheelJoint.cpp

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/*
* Copyright (c) 2006-2007 Erin Catto http://www.box2d.org
*
* This software is provided 'as-is', without any express or implied
* warranty.  In no event will the authors be held liable for any damages
* arising from the use of this software.
* Permission is granted to anyone to use this software for any purpose,
* including commercial applications, and to alter it and redistribute it
* freely, subject to the following restrictions:
* 1. The origin of this software must not be misrepresented; you must not
* claim that you wrote the original software. If you use this software
* in a product, an acknowledgment in the product documentation would be
* appreciated but is not required.
* 2. Altered source versions must be plainly marked as such, and must not be
* misrepresented as being the original software.
* 3. This notice may not be removed or altered from any source distribution.
*/

#include <Box2D/Dynamics/Joints/b2WheelJoint.h>
#include <Box2D/Dynamics/b2Body.h>
#include <Box2D/Dynamics/b2TimeStep.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_maxMotorTorque = def->maxMotorTorque;
        m_motorSpeed = def->motorSpeed;
        m_enableMotor = def->enableMotor;

        m_frequencyHz = def->frequencyHz;
        m_dampingRatio = def->dampingRatio;

        m_bias = 0.0f;
        m_gamma = 0.0f;

        m_ax.SetZero();
        m_ay.SetZero();
}

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;

        float32 mA = m_invMassA, mB = m_invMassB;
        float32 iA = m_invIA, iB = m_invIB;

        b2Vec2 cA = data.positions[m_indexA].c;
        float32 aA = data.positions[m_indexA].a;
        b2Vec2 vA = data.velocities[m_indexA].v;
        float32 wA = data.velocities[m_indexA].w;

        b2Vec2 cB = data.positions[m_indexB].c;
        float32 aB = data.positions[m_indexB].a;
        b2Vec2 vB = data.velocities[m_indexB].v;
        float32 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_springMass = 0.0f;
        m_bias = 0.0f;
        m_gamma = 0.0f;
        if (m_frequencyHz > 0.0f)
        {
                m_ax = b2Mul(qA, m_localXAxisA);
                m_sAx = b2Cross(d + rA, m_ax);
                m_sBx = b2Cross(rB, m_ax);

                float32 invMass = mA + mB + iA * m_sAx * m_sAx + iB * m_sBx * m_sBx;

                if (invMass > 0.0f)
                {
                        m_springMass = 1.0f / invMass;

                        float32 C = b2Dot(d, m_ax);

                        // Frequency
                        float32 omega = 2.0f * b2_pi * m_frequencyHz;

                        // Damping coefficient
                        float32 d = 2.0f * m_springMass * m_dampingRatio * omega;

                        // Spring stiffness
                        float32 k = m_springMass * omega * omega;

                        // magic formulas
                        float32 h = data.step.dt;
                        m_gamma = h * (d + h * k);
                        if (m_gamma > 0.0f)
                        {
                                m_gamma = 1.0f / m_gamma;
                        }

                        m_bias = C * h * k * m_gamma;

                        m_springMass = invMass + m_gamma;
                        if (m_springMass > 0.0f)
                        {
                                m_springMass = 1.0f / m_springMass;
                        }
                }
        }
        else
        {
                m_springImpulse = 0.0f;
        }

        // Rotational motor
        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;

                b2Vec2 P = m_impulse * m_ay + m_springImpulse * m_ax;
                float32 LA = m_impulse * m_sAy + m_springImpulse * m_sAx + m_motorImpulse;
                float32 LB = m_impulse * m_sBy + m_springImpulse * 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;
        }

        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)
{
        float32 mA = m_invMassA, mB = m_invMassB;
        float32 iA = m_invIA, iB = m_invIB;

        b2Vec2 vA = data.velocities[m_indexA].v;
        float32 wA = data.velocities[m_indexA].w;
        b2Vec2 vB = data.velocities[m_indexB].v;
        float32 wB = data.velocities[m_indexB].w;

        // Solve spring constraint
        {
                float32 Cdot = b2Dot(m_ax, vB - vA) + m_sBx * wB - m_sAx * wA;
                float32 impulse = -m_springMass * (Cdot + m_bias + m_gamma * m_springImpulse);
                m_springImpulse += impulse;

                b2Vec2 P = impulse * m_ax;
                float32 LA = impulse * m_sAx;
                float32 LB = impulse * m_sBx;

                vA -= mA * P;
                wA -= iA * LA;

                vB += mB * P;
                wB += iB * LB;
        }

        // Solve rotational motor constraint
        {
                float32 Cdot = wB - wA - m_motorSpeed;
                float32 impulse = -m_motorMass * Cdot;

                float32 oldImpulse = m_motorImpulse;
                float32 maxImpulse = data.step.dt * m_maxMotorTorque;
                m_motorImpulse = b2Clamp(m_motorImpulse + impulse, -maxImpulse, maxImpulse);
                impulse = m_motorImpulse - oldImpulse;

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

        // Solve point to line constraint
        {
                float32 Cdot = b2Dot(m_ay, vB - vA) + m_sBy * wB - m_sAy * wA;
                float32 impulse = -m_mass * Cdot;
                m_impulse += impulse;

                b2Vec2 P = impulse * m_ay;
                float32 LA = impulse * m_sAy;
                float32 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;
        float32 aA = data.positions[m_indexA].a;
        b2Vec2 cB = data.positions[m_indexB].c;
        float32 aB = data.positions[m_indexB].a;

        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);

        float32 sAy = b2Cross(d + rA, ay);
        float32 sBy = b2Cross(rB, ay);

        float32 C = b2Dot(d, ay);

        float32 k = m_invMassA + m_invMassB + m_invIA * m_sAy * m_sAy + m_invIB * m_sBy * m_sBy;

        float32 impulse;
        if (k != 0.0f)
        {
                impulse = - C / k;
        }
        else
        {
                impulse = 0.0f;
        }

        b2Vec2 P = impulse * ay;
        float32 LA = impulse * sAy;
        float32 LB = impulse * sBy;

        cA -= m_invMassA * P;
        aA -= m_invIA * LA;
        cB += m_invMassB * P;
        aB += m_invIB * 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 b2Abs(C) <= 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(float32 inv_dt) const
{
        return inv_dt * (m_impulse * m_ay + m_springImpulse * m_ax);
}

float32 b2WheelJoint::GetReactionTorque(float32 inv_dt) const
{
        return inv_dt * m_motorImpulse;
}

float32 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);

        float32 translation = b2Dot(d, axis);
        return translation;
}

float32 b2WheelJoint::GetJointSpeed() const
{
        float32 wA = m_bodyA->m_angularVelocity;
        float32 wB = m_bodyB->m_angularVelocity;
        return wB - wA;
}

bool b2WheelJoint::IsMotorEnabled() const
{
        return m_enableMotor;
}

void b2WheelJoint::EnableMotor(bool flag)
{
        m_bodyA->SetAwake(true);
        m_bodyB->SetAwake(true);
        m_enableMotor = flag;
}

void b2WheelJoint::SetMotorSpeed(float32 speed)
{
        m_bodyA->SetAwake(true);
        m_bodyB->SetAwake(true);
        m_motorSpeed = speed;
}

void b2WheelJoint::SetMaxMotorTorque(float32 torque)
{
        m_bodyA->SetAwake(true);
        m_bodyB->SetAwake(true);
        m_maxMotorTorque = torque;
}

float32 b2WheelJoint::GetMotorTorque(float32 inv_dt) const
{
        return inv_dt * m_motorImpulse;
}

void b2WheelJoint::Dump()
{
        int32 indexA = m_bodyA->m_islandIndex;
        int32 indexB = m_bodyB->m_islandIndex;

        b2Log("  b2WheelJointDef 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.enableMotor = bool(%d);\n", m_enableMotor);
        b2Log("  jd.motorSpeed = %.15lef;\n", m_motorSpeed);
        b2Log("  jd.maxMotorTorque = %.15lef;\n", m_maxMotorTorque);
        b2Log("  jd.frequencyHz = %.15lef;\n", m_frequencyHz);
        b2Log("  jd.dampingRatio = %.15lef;\n", m_dampingRatio);
        b2Log("  joints[%d] = m_world->CreateJoint(&jd);\n", m_index);
}