b2_distance_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_distance_joint.h"
#include "box2d/b2_time_step.h"

// 1-D constrained system
// m (v2 - v1) = lambda
// v2 + (beta/h) * x1 + gamma * lambda = 0, gamma has units of inverse mass.
// x2 = x1 + h * v2

// 1-D mass-damper-spring system
// m (v2 - v1) + h * d * v2 + h * k * 

// C = norm(p2 - p1) - L
// u = (p2 - p1) / norm(p2 - p1)
// Cdot = dot(u, v2 + cross(w2, r2) - v1 - cross(w1, r1))
// J = [-u -cross(r1, u) u cross(r2, u)]
// K = J * invM * JT
//   = invMass1 + invI1 * cross(r1, u)^2 + invMass2 + invI2 * cross(r2, u)^2


void b2DistanceJointDef::Initialize(b2Body* b1, b2Body* b2,
                                                                        const b2Vec2& anchor1, const b2Vec2& anchor2)
{
        bodyA = b1;
        bodyB = b2;
        localAnchorA = bodyA->GetLocalPoint(anchor1);
        localAnchorB = bodyB->GetLocalPoint(anchor2);
        b2Vec2 d = anchor2 - anchor1;
        length = b2Max(d.Length(), b2_linearSlop);
        minLength = length;
        maxLength = length;
}

b2DistanceJoint::b2DistanceJoint(const b2DistanceJointDef* def)
: b2Joint(def)
{
        m_localAnchorA = def->localAnchorA;
        m_localAnchorB = def->localAnchorB;
        m_length = b2Max(def->length, b2_linearSlop);
        m_minLength = b2Max(def->minLength, b2_linearSlop);
        m_maxLength = b2Max(def->maxLength, m_minLength);
        m_stiffness = def->stiffness;
        m_damping = def->damping;

        m_gamma = 0.0f;
        m_bias = 0.0f;
        m_impulse = 0.0f;
        m_lowerImpulse = 0.0f;
        m_upperImpulse = 0.0f;
        m_currentLength = 0.0f;
}

void b2DistanceJoint::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);

        m_rA = b2Mul(qA, m_localAnchorA - m_localCenterA);
        m_rB = b2Mul(qB, m_localAnchorB - m_localCenterB);
        m_u = cB + m_rB - cA - m_rA;

        // Handle singularity.
        m_currentLength = m_u.Length();
        if (m_currentLength > b2_linearSlop)
        {
                m_u *= 1.0f / m_currentLength;
        }
        else
        {
                m_u.Set(0.0f, 0.0f);
                m_mass = 0.0f;
                m_impulse = 0.0f;
                m_lowerImpulse = 0.0f;
                m_upperImpulse = 0.0f;
        }

        float crAu = b2Cross(m_rA, m_u);
        float crBu = b2Cross(m_rB, m_u);
        float invMass = m_invMassA + m_invIA * crAu * crAu + m_invMassB + m_invIB * crBu * crBu;
        m_mass = invMass != 0.0f ? 1.0f / invMass : 0.0f;

        if (m_stiffness > 0.0f && m_minLength < m_maxLength)
        {
                // soft
                float C = m_currentLength - m_length;

                float d = m_damping;
                float k = m_stiffness;

                // magic formulas
                float h = data.step.dt;

                // gamma = 1 / (h * (d + h * k))
                // the extra factor of h in the denominator is since the lambda is an impulse, not a force
                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;

                invMass += m_gamma;
                m_softMass = invMass != 0.0f ? 1.0f / invMass : 0.0f;
        }
        else
        {
                // rigid
                m_gamma = 0.0f;
                m_bias = 0.0f;
                m_softMass = m_mass;
        }

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

                b2Vec2 P = (m_impulse + m_lowerImpulse - m_upperImpulse) * m_u;
                vA -= m_invMassA * P;
                wA -= m_invIA * b2Cross(m_rA, P);
                vB += m_invMassB * P;
                wB += m_invIB * b2Cross(m_rB, P);
        }
        else
        {
                m_impulse = 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 b2DistanceJoint::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;

        if (m_minLength < m_maxLength)
        {
                if (m_stiffness > 0.0f)
                {
                        // Cdot = dot(u, v + cross(w, r))
                        b2Vec2 vpA = vA + b2Cross(wA, m_rA);
                        b2Vec2 vpB = vB + b2Cross(wB, m_rB);
                        float Cdot = b2Dot(m_u, vpB - vpA);

                        float impulse = -m_softMass * (Cdot + m_bias + m_gamma * m_impulse);
                        m_impulse += impulse;

                        b2Vec2 P = impulse * m_u;
                        vA -= m_invMassA * P;
                        wA -= m_invIA * b2Cross(m_rA, P);
                        vB += m_invMassB * P;
                        wB += m_invIB * b2Cross(m_rB, P);
                }

                // lower
                {
                        float C = m_currentLength - m_minLength;
                        float bias = b2Max(0.0f, C) * data.step.inv_dt;

                        b2Vec2 vpA = vA + b2Cross(wA, m_rA);
                        b2Vec2 vpB = vB + b2Cross(wB, m_rB);
                        float Cdot = b2Dot(m_u, vpB - vpA);

                        float impulse = -m_mass * (Cdot + bias);
                        float oldImpulse = m_lowerImpulse;
                        m_lowerImpulse = b2Max(0.0f, m_lowerImpulse + impulse);
                        impulse = m_lowerImpulse - oldImpulse;
                        b2Vec2 P = impulse * m_u;

                        vA -= m_invMassA * P;
                        wA -= m_invIA * b2Cross(m_rA, P);
                        vB += m_invMassB * P;
                        wB += m_invIB * b2Cross(m_rB, P);
                }

                // upper
                {
                        float C = m_maxLength - m_currentLength;
                        float bias = b2Max(0.0f, C) * data.step.inv_dt;

                        b2Vec2 vpA = vA + b2Cross(wA, m_rA);
                        b2Vec2 vpB = vB + b2Cross(wB, m_rB);
                        float Cdot = b2Dot(m_u, vpA - vpB);

                        float impulse = -m_mass * (Cdot + bias);
                        float oldImpulse = m_upperImpulse;
                        m_upperImpulse = b2Max(0.0f, m_upperImpulse + impulse);
                        impulse = m_upperImpulse - oldImpulse;
                        b2Vec2 P = -impulse * m_u;

                        vA -= m_invMassA * P;
                        wA -= m_invIA * b2Cross(m_rA, P);
                        vB += m_invMassB * P;
                        wB += m_invIB * b2Cross(m_rB, P);
                }
        }
        else
        {
                // Equal limits

                // Cdot = dot(u, v + cross(w, r))
                b2Vec2 vpA = vA + b2Cross(wA, m_rA);
                b2Vec2 vpB = vB + b2Cross(wB, m_rB);
                float Cdot = b2Dot(m_u, vpB - vpA);

                float impulse = -m_mass * Cdot;
                m_impulse += impulse;

                b2Vec2 P = impulse * m_u;
                vA -= m_invMassA * P;
                wA -= m_invIA * b2Cross(m_rA, P);
                vB += m_invMassB * P;
                wB += m_invIB * b2Cross(m_rB, P);
        }

        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 b2DistanceJoint::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);

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

        float length = u.Normalize();
        float C;
        if (m_minLength == m_maxLength)
        {
                C = length - m_minLength;
        }
        else if (length < m_minLength)
        {
                C = length - m_minLength;
        }
        else if (m_maxLength < length)
        {
                C = length - m_maxLength;
        }
        else
        {
                return true;
        }

        float impulse = -m_mass * C;
        b2Vec2 P = impulse * u;

        cA -= m_invMassA * P;
        aA -= m_invIA * b2Cross(rA, P);
        cB += m_invMassB * P;
        aB += m_invIB * b2Cross(rB, P);

        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 b2DistanceJoint::GetAnchorA() const
{
        return m_bodyA->GetWorldPoint(m_localAnchorA);
}

b2Vec2 b2DistanceJoint::GetAnchorB() const
{
        return m_bodyB->GetWorldPoint(m_localAnchorB);
}

b2Vec2 b2DistanceJoint::GetReactionForce(float inv_dt) const
{
        b2Vec2 F = inv_dt * (m_impulse + m_lowerImpulse - m_upperImpulse) * m_u;
        return F;
}

float b2DistanceJoint::GetReactionTorque(float inv_dt) const
{
        B2_NOT_USED(inv_dt);
        return 0.0f;
}

float b2DistanceJoint::SetLength(float length)
{
        m_impulse = 0.0f;
        m_length = b2Max(b2_linearSlop, length);
        return m_length;
}

float b2DistanceJoint::SetMinLength(float minLength)
{
        m_lowerImpulse = 0.0f;
        m_minLength = b2Clamp(minLength, b2_linearSlop, m_maxLength);
        return m_minLength;
}

float b2DistanceJoint::SetMaxLength(float maxLength)
{
        m_upperImpulse = 0.0f;
        m_maxLength = b2Max(maxLength, m_minLength);
        return m_maxLength;
}

float b2DistanceJoint::GetCurrentLength() const
{
        b2Vec2 pA = m_bodyA->GetWorldPoint(m_localAnchorA);
        b2Vec2 pB = m_bodyB->GetWorldPoint(m_localAnchorB);
        b2Vec2 d = pB - pA;
        float length = d.Length();
        return length;
}

void b2DistanceJoint::Dump()
{
        int32 indexA = m_bodyA->m_islandIndex;
        int32 indexB = m_bodyB->m_islandIndex;

        b2Dump("  b2DistanceJointDef 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.length = %.9g;\n", m_length);
        b2Dump("  jd.minLength = %.9g;\n", m_minLength);
        b2Dump("  jd.maxLength = %.9g;\n", m_maxLength);
        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 b2DistanceJoint::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 = pB - pA;
        float length = axis.Normalize();

        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(0.4f, 0.4f, 0.4f);

        draw->DrawSegment(pA, pB, c4);
        
        b2Vec2 pRest = pA + m_length * axis;
        draw->DrawPoint(pRest, 8.0f, c1);

        if (m_minLength != m_maxLength)
        {
                if (m_minLength > b2_linearSlop)
                {
                        b2Vec2 pMin = pA + m_minLength * axis;
                        draw->DrawPoint(pMin, 4.0f, c2);
                }

                if (m_maxLength < FLT_MAX)
                {
                        b2Vec2 pMax = pA + m_maxLength * axis;
                        draw->DrawPoint(pMax, 4.0f, c3);
                }
        }
}