b2WeldJoint.cpp

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/*
* Copyright (c) 2006-2011 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/b2WeldJoint.h>
#include <Box2D/Dynamics/b2Body.h>
#include <Box2D/Dynamics/b2TimeStep.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)

// Angle constraint
// C = angle2 - angle1 - referenceAngle
// Cdot = w2 - w1
// J = [0 0 -1 0 0 1]
// K = invI1 + invI2

void b2WeldJointDef::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();
}

b2WeldJoint::b2WeldJoint(const b2WeldJointDef* def)
: b2Joint(def)
{
        m_localAnchorA = def->localAnchorA;
        m_localAnchorB = def->localAnchorB;
        m_referenceAngle = def->referenceAngle;
        m_frequencyHz = def->frequencyHz;
        m_dampingRatio = def->dampingRatio;

        m_impulse.SetZero();
}

void b2WeldJoint::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 aA = data.positions[m_indexA].a;
        b2Vec2 vA = data.velocities[m_indexA].v;
        float32 wA = data.velocities[m_indexA].w;

        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);

        m_rA = b2Mul(qA, m_localAnchorA - m_localCenterA);
        m_rB = b2Mul(qB, m_localAnchorB - m_localCenterB);

        // J = [-I -r1_skew I r2_skew]
        //     [ 0       -1 0       1]
        // 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]

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

        b2Mat33 K;
        K.ex.x = mA + mB + m_rA.y * m_rA.y * iA + m_rB.y * m_rB.y * iB;
        K.ey.x = -m_rA.y * m_rA.x * iA - m_rB.y * m_rB.x * iB;
        K.ez.x = -m_rA.y * iA - m_rB.y * iB;
        K.ex.y = K.ey.x;
        K.ey.y = mA + mB + m_rA.x * m_rA.x * iA + m_rB.x * m_rB.x * iB;
        K.ez.y = m_rA.x * iA + m_rB.x * iB;
        K.ex.z = K.ez.x;
        K.ey.z = K.ez.y;
        K.ez.z = iA + iB;

        if (m_frequencyHz > 0.0f)
        {
                K.GetInverse22(&m_mass);

                float32 invM = iA + iB;
                float32 m = invM > 0.0f ? 1.0f / invM : 0.0f;

                float32 C = aB - aA - m_referenceAngle;

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

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

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

                // magic formulas
                float32 h = data.step.dt;
                m_gamma = h * (d + h * k);
                m_gamma = m_gamma != 0.0f ? 1.0f / m_gamma : 0.0f;
                m_bias = C * h * k * m_gamma;

                invM += m_gamma;
                m_mass.ez.z = invM != 0.0f ? 1.0f / invM : 0.0f;
        }
        else if (K.ez.z == 0.0f)
        {
                K.GetInverse22(&m_mass);
                m_gamma = 0.0f;
                m_bias = 0.0f;
        }
        else
        {
                K.GetSymInverse33(&m_mass);
                m_gamma = 0.0f;
                m_bias = 0.0f;
        }

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

                b2Vec2 P(m_impulse.x, m_impulse.y);

                vA -= mA * P;
                wA -= iA * (b2Cross(m_rA, P) + m_impulse.z);

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

        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 b2WeldJoint::SolveVelocityConstraints(const b2SolverData& data)
{
        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;

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

        if (m_frequencyHz > 0.0f)
        {
                float32 Cdot2 = wB - wA;

                float32 impulse2 = -m_mass.ez.z * (Cdot2 + m_bias + m_gamma * m_impulse.z);
                m_impulse.z += impulse2;

                wA -= iA * impulse2;
                wB += iB * impulse2;

                b2Vec2 Cdot1 = vB + b2Cross(wB, m_rB) - vA - b2Cross(wA, m_rA);

                b2Vec2 impulse1 = -b2Mul22(m_mass, Cdot1);
                m_impulse.x += impulse1.x;
                m_impulse.y += impulse1.y;

                b2Vec2 P = impulse1;

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

                vB += mB * P;
                wB += iB * b2Cross(m_rB, P);
        }
        else
        {
                b2Vec2 Cdot1 = vB + b2Cross(wB, m_rB) - vA - b2Cross(wA, m_rA);
                float32 Cdot2 = wB - wA;
                b2Vec3 Cdot(Cdot1.x, Cdot1.y, Cdot2);

                b2Vec3 impulse = -b2Mul(m_mass, Cdot);
                m_impulse += impulse;

                b2Vec2 P(impulse.x, impulse.y);

                vA -= mA * P;
                wA -= iA * (b2Cross(m_rA, P) + impulse.z);

                vB += mB * P;
                wB += iB * (b2Cross(m_rB, P) + impulse.z);
        }

        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 b2WeldJoint::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);

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

        b2Vec2 rA = b2Mul(qA, m_localAnchorA - m_localCenterA);
        b2Vec2 rB = b2Mul(qB, m_localAnchorB - m_localCenterB);

        float32 positionError, angularError;

        b2Mat33 K;
        K.ex.x = mA + mB + rA.y * rA.y * iA + rB.y * rB.y * iB;
        K.ey.x = -rA.y * rA.x * iA - rB.y * rB.x * iB;
        K.ez.x = -rA.y * iA - rB.y * iB;
        K.ex.y = K.ey.x;
        K.ey.y = mA + mB + rA.x * rA.x * iA + rB.x * rB.x * iB;
        K.ez.y = rA.x * iA + rB.x * iB;
        K.ex.z = K.ez.x;
        K.ey.z = K.ez.y;
        K.ez.z = iA + iB;

        if (m_frequencyHz > 0.0f)
        {
                b2Vec2 C1 =  cB + rB - cA - rA;

                positionError = C1.Length();
                angularError = 0.0f;

                b2Vec2 P = -K.Solve22(C1);

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

                cB += mB * P;
                aB += iB * b2Cross(rB, P);
        }
        else
        {
                b2Vec2 C1 =  cB + rB - cA - rA;
                float32 C2 = aB - aA - m_referenceAngle;

                positionError = C1.Length();
                angularError = b2Abs(C2);

                b2Vec3 C(C1.x, C1.y, C2);
        
                b2Vec3 impulse;
                if (K.ez.z > 0.0f)
                {
                        impulse = -K.Solve33(C);
                }
                else
                {
                        b2Vec2 impulse2 = -K.Solve22(C1);
                        impulse.Set(impulse2.x, impulse2.y, 0.0f);
                }

                b2Vec2 P(impulse.x, impulse.y);

                cA -= mA * P;
                aA -= iA * (b2Cross(rA, P) + impulse.z);

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

        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 b2WeldJoint::GetAnchorA() const
{
        return m_bodyA->GetWorldPoint(m_localAnchorA);
}

b2Vec2 b2WeldJoint::GetAnchorB() const
{
        return m_bodyB->GetWorldPoint(m_localAnchorB);
}

b2Vec2 b2WeldJoint::GetReactionForce(float32 inv_dt) const
{
        b2Vec2 P(m_impulse.x, m_impulse.y);
        return inv_dt * P;
}

float32 b2WeldJoint::GetReactionTorque(float32 inv_dt) const
{
        return inv_dt * m_impulse.z;
}

void b2WeldJoint::Dump()
{
        int32 indexA = m_bodyA->m_islandIndex;
        int32 indexB = m_bodyB->m_islandIndex;

        b2Log("  b2WeldJointDef 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.referenceAngle = %.15lef;\n", m_referenceAngle);
        b2Log("  jd.frequencyHz = %.15lef;\n", m_frequencyHz);
        b2Log("  jd.dampingRatio = %.15lef;\n", m_dampingRatio);
        b2Log("  joints[%d] = m_world->CreateJoint(&jd);\n", m_index);
}