b2_prismatic_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_prismatic_joint.h"
#include "box2d/b2_time_step.h"
 
// Linear constraint (point-to-line)
// d = p2 - p1 = x2 + r2 - x1 - r1
// C = dot(perp, d)
// Cdot = dot(d, cross(w1, perp)) + dot(perp, v2 + cross(w2, r2) - v1 - cross(w1, r1))
//      = -dot(perp, v1) - dot(cross(d + r1, perp), w1) + dot(perp, v2) + dot(cross(r2, perp), v2)
// J = [-perp, -cross(d + r1, perp), perp, cross(r2,perp)]
//
// Angular constraint
// C = a2 - a1 + a_initial
// Cdot = w2 - w1
// J = [0 0 -1 0 0 1]
//
// K = J * invM * JT
//
// J = [-a -s1 a s2]
//     [0  -1  0  1]
// a = perp
// s1 = cross(d + r1, a) = cross(p2 - x1, a)
// s2 = cross(r2, a) = cross(p2 - x2, a)
 
// Motor/Limit linear constraint
// C = dot(ax1, d)
// Cdot = -dot(ax1, v1) - dot(cross(d + r1, ax1), w1) + dot(ax1, v2) + dot(cross(r2, ax1), v2)
// J = [-ax1 -cross(d+r1,ax1) ax1 cross(r2,ax1)]
 
// Predictive limit is applied even when the limit is not active.
// Prevents a constraint speed that can lead to a constraint error in one time step.
// Want C2 = C1 + h * Cdot >= 0
// Or:
// Cdot + C1/h >= 0
// I do not apply a negative constraint error because that is handled in position correction.
// So:
// Cdot + max(C1, 0)/h >= 0
 
// Block Solver
// We develop a block solver that includes the angular and linear constraints. This makes the limit stiffer.
//
// The Jacobian has 2 rows:
// J = [-uT -s1 uT s2] // linear
//     [0   -1   0  1] // angular
//
// u = perp
// s1 = cross(d + r1, u), s2 = cross(r2, u)
// a1 = cross(d + r1, v), a2 = cross(r2, v)
 
void b2PrismaticJointDef::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);
        referenceAngle = bodyB->GetAngle() - bodyA->GetAngle();
}
 
b2PrismaticJoint::b2PrismaticJoint(const b2PrismaticJointDef* def)
: b2Joint(def)
{
        m_localAnchorA = def->localAnchorA;
        m_localAnchorB = def->localAnchorB;
        m_localXAxisA = def->localAxisA;
        m_localXAxisA.Normalize();
        m_localYAxisA = b2Cross(1.0f, m_localXAxisA);
        m_referenceAngle = def->referenceAngle;
 
        m_impulse.SetZero();
        m_axialMass = 0.0f;
        m_motorImpulse = 0.0f;
        m_lowerImpulse = 0.0f;
        m_upperImpulse = 0.0f;
 
        m_lowerTranslation = def->lowerTranslation;
        m_upperTranslation = def->upperTranslation;
 
        b2Assert(m_lowerTranslation <= m_upperTranslation);
 
        m_maxMotorForce = def->maxMotorForce;
        m_motorSpeed = def->motorSpeed;
        m_enableLimit = def->enableLimit;
        m_enableMotor = def->enableMotor;
 
        m_translation = 0.0f;
        m_axis.SetZero();
        m_perp.SetZero();
}
 
void b2PrismaticJoint::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);
 
        // Compute the effective masses.
        b2Vec2 rA = b2Mul(qA, m_localAnchorA - m_localCenterA);
        b2Vec2 rB = b2Mul(qB, m_localAnchorB - m_localCenterB);
        b2Vec2 d = (cB - cA) + rB - rA;
 
        float mA = m_invMassA, mB = m_invMassB;
        float iA = m_invIA, iB = m_invIB;
 
        // Compute motor Jacobian and effective mass.
        {
                m_axis = b2Mul(qA, m_localXAxisA);
                m_a1 = b2Cross(d + rA, m_axis);
                m_a2 = b2Cross(rB, m_axis);
 
                m_axialMass = mA + mB + iA * m_a1 * m_a1 + iB * m_a2 * m_a2;
                if (m_axialMass > 0.0f)
                {
                        m_axialMass = 1.0f / m_axialMass;
                }
        }
 
        // Prismatic constraint.
        {
                m_perp = b2Mul(qA, m_localYAxisA);
 
                m_s1 = b2Cross(d + rA, m_perp);
                m_s2 = b2Cross(rB, m_perp);
 
                float k11 = mA + mB + iA * m_s1 * m_s1 + iB * m_s2 * m_s2;
                float k12 = iA * m_s1 + iB * m_s2;
                float k22 = iA + iB;
                if (k22 == 0.0f)
                {
                        // For bodies with fixed rotation.
                        k22 = 1.0f;
                }
 
                m_K.ex.Set(k11, k12);
                m_K.ey.Set(k12, k22);
        }
 
        if (m_enableLimit)
        {
                m_translation = b2Dot(m_axis, d);
        }
        else
        {
                m_lowerImpulse = 0.0f;
                m_upperImpulse = 0.0f;
        }
 
        if (m_enableMotor == false)
        {
                m_motorImpulse = 0.0f;
        }
 
        if (data.step.warmStarting)
        {
                // Account for 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_perp + axialImpulse * m_axis;
                float LA = m_impulse.x * m_s1 + m_impulse.y + axialImpulse * m_a1;
                float LB = m_impulse.x * m_s2 + m_impulse.y + axialImpulse * m_a2;
 
                vA -= mA * P;
                wA -= iA * LA;
 
                vB += mB * P;
                wB += iB * LB;
        }
        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 b2PrismaticJoint::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;
 
        // Solve linear motor constraint
        if (m_enableMotor)
        {
                float Cdot = b2Dot(m_axis, vB - vA) + m_a2 * wB - m_a1 * wA;
                float impulse = m_axialMass * (m_motorSpeed - Cdot);
                float oldImpulse = m_motorImpulse;
                float maxImpulse = data.step.dt * m_maxMotorForce;
                m_motorImpulse = b2Clamp(m_motorImpulse + impulse, -maxImpulse, maxImpulse);
                impulse = m_motorImpulse - oldImpulse;
 
                b2Vec2 P = impulse * m_axis;
                float LA = impulse * m_a1;
                float LB = impulse * m_a2;
 
                vA -= mA * P;
                wA -= iA * LA;
                vB += mB * P;
                wB += iB * LB;
        }
 
        if (m_enableLimit)
        {
                // Lower limit
                {
                        float C = m_translation - m_lowerTranslation;
                        float Cdot = b2Dot(m_axis, vB - vA) + m_a2 * wB - m_a1 * 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_axis;
                        float LA = impulse * m_a1;
                        float LB = impulse * m_a2;
 
                        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_axis, vA - vB) + m_a1 * wA - m_a2 * 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_axis;
                        float LA = impulse * m_a1;
                        float LB = impulse * m_a2;
 
                        vA += mA * P;
                        wA += iA * LA;
                        vB -= mB * P;
                        wB -= iB * LB;
                }
        }
 
        // Solve the prismatic constraint in block form.
        {
                b2Vec2 Cdot;
                Cdot.x = b2Dot(m_perp, vB - vA) + m_s2 * wB - m_s1 * wA;
                Cdot.y = wB - wA;
 
                b2Vec2 df = m_K.Solve(-Cdot);
                m_impulse += df;
 
                b2Vec2 P = df.x * m_perp;
                float LA = df.x * m_s1 + df.y;
                float LB = df.x * m_s2 + df.y;
 
                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;
}
 
// A velocity based solver computes reaction forces(impulses) using the velocity constraint solver.Under this context,
// the position solver is not there to resolve forces.It is only there to cope with integration error.
//
// Therefore, the pseudo impulses in the position solver do not have any physical meaning.Thus it is okay if they suck.
//
// We could take the active state from the velocity solver.However, the joint might push past the limit when the velocity
// solver indicates the limit is inactive.
bool b2PrismaticJoint::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 mA = m_invMassA, mB = m_invMassB;
        float iA = m_invIA, iB = m_invIB;
 
        // Compute fresh Jacobians
        b2Vec2 rA = b2Mul(qA, m_localAnchorA - m_localCenterA);
        b2Vec2 rB = b2Mul(qB, m_localAnchorB - m_localCenterB);
        b2Vec2 d = cB + rB - cA - rA;
 
        b2Vec2 axis = b2Mul(qA, m_localXAxisA);
        float a1 = b2Cross(d + rA, axis);
        float a2 = b2Cross(rB, axis);
        b2Vec2 perp = b2Mul(qA, m_localYAxisA);
 
        float s1 = b2Cross(d + rA, perp);
        float s2 = b2Cross(rB, perp);
 
        b2Vec3 impulse;
        b2Vec2 C1;
        C1.x = b2Dot(perp, d);
        C1.y = aB - aA - m_referenceAngle;
 
        float linearError = b2Abs(C1.x);
        float angularError = b2Abs(C1.y);
 
        bool active = false;
        float C2 = 0.0f;
        if (m_enableLimit)
        {
                float translation = b2Dot(axis, d);
                if (b2Abs(m_upperTranslation - m_lowerTranslation) < 2.0f * b2_linearSlop)
                {
                        C2 = translation;
                        linearError = b2Max(linearError, b2Abs(translation));
                        active = true;
                }
                else if (translation <= m_lowerTranslation)
                {
                        C2 = b2Min(translation - m_lowerTranslation, 0.0f);
                        linearError = b2Max(linearError, m_lowerTranslation - translation);
                        active = true;
                }
                else if (translation >= m_upperTranslation)
                {
                        C2 = b2Max(translation - m_upperTranslation, 0.0f);
                        linearError = b2Max(linearError, translation - m_upperTranslation);
                        active = true;
                }
        }
 
        if (active)
        {
                float k11 = mA + mB + iA * s1 * s1 + iB * s2 * s2;
                float k12 = iA * s1 + iB * s2;
                float k13 = iA * s1 * a1 + iB * s2 * a2;
                float k22 = iA + iB;
                if (k22 == 0.0f)
                {
                        // For fixed rotation
                        k22 = 1.0f;
                }
                float k23 = iA * a1 + iB * a2;
                float k33 = mA + mB + iA * a1 * a1 + iB * a2 * a2;
 
                b2Mat33 K;
                K.ex.Set(k11, k12, k13);
                K.ey.Set(k12, k22, k23);
                K.ez.Set(k13, k23, k33);
 
                b2Vec3 C;
                C.x = C1.x;
                C.y = C1.y;
                C.z = C2;
 
                impulse = K.Solve33(-C);
        }
        else
        {
                float k11 = mA + mB + iA * s1 * s1 + iB * s2 * s2;
                float k12 = iA * s1 + iB * s2;
                float k22 = iA + iB;
                if (k22 == 0.0f)
                {
                        k22 = 1.0f;
                }
 
                b2Mat22 K;
                K.ex.Set(k11, k12);
                K.ey.Set(k12, k22);
 
                b2Vec2 impulse1 = K.Solve(-C1);
                impulse.x = impulse1.x;
                impulse.y = impulse1.y;
                impulse.z = 0.0f;
        }
 
        b2Vec2 P = impulse.x * perp + impulse.z * axis;
        float LA = impulse.x * s1 + impulse.y + impulse.z * a1;
        float LB = impulse.x * s2 + impulse.y + impulse.z * a2;
 
        cA -= mA * P;
        aA -= iA * LA;
        cB += mB * P;
        aB += iB * 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 linearError <= b2_linearSlop && angularError <= b2_angularSlop;
}
 
b2Vec2 b2PrismaticJoint::GetAnchorA() const
{
        return m_bodyA->GetWorldPoint(m_localAnchorA);
}
 
b2Vec2 b2PrismaticJoint::GetAnchorB() const
{
        return m_bodyB->GetWorldPoint(m_localAnchorB);
}
 
b2Vec2 b2PrismaticJoint::GetReactionForce(float inv_dt) const
{
        return inv_dt * (m_impulse.x * m_perp + (m_motorImpulse + m_lowerImpulse - m_upperImpulse) * m_axis);
}
 
float b2PrismaticJoint::GetReactionTorque(float inv_dt) const
{
        return inv_dt * m_impulse.y;
}
 
float b2PrismaticJoint::GetJointTranslation() const
{
        b2Vec2 pA = m_bodyA->GetWorldPoint(m_localAnchorA);
        b2Vec2 pB = m_bodyB->GetWorldPoint(m_localAnchorB);
        b2Vec2 d = pB - pA;
        b2Vec2 axis = m_bodyA->GetWorldVector(m_localXAxisA);
 
        float translation = b2Dot(d, axis);
        return translation;
}
 
float b2PrismaticJoint::GetJointSpeed() 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;
}
 
bool b2PrismaticJoint::IsLimitEnabled() const
{
        return m_enableLimit;
}
 
void b2PrismaticJoint::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 b2PrismaticJoint::GetLowerLimit() const
{
        return m_lowerTranslation;
}
 
float b2PrismaticJoint::GetUpperLimit() const
{
        return m_upperTranslation;
}
 
void b2PrismaticJoint::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 b2PrismaticJoint::IsMotorEnabled() const
{
        return m_enableMotor;
}
 
void b2PrismaticJoint::EnableMotor(bool flag)
{
        if (flag != m_enableMotor)
        {
                m_bodyA->SetAwake(true);
                m_bodyB->SetAwake(true);
                m_enableMotor = flag;
        }
}
 
void b2PrismaticJoint::SetMotorSpeed(float speed)
{
        if (speed != m_motorSpeed)
        {
                m_bodyA->SetAwake(true);
                m_bodyB->SetAwake(true);
                m_motorSpeed = speed;
        }
}
 
void b2PrismaticJoint::SetMaxMotorForce(float force)
{
        if (force != m_maxMotorForce)
        {
                m_bodyA->SetAwake(true);
                m_bodyB->SetAwake(true);
                m_maxMotorForce = force;
        }
}
 
float b2PrismaticJoint::GetMotorForce(float inv_dt) const
{
        return inv_dt * m_motorImpulse;
}
 
void b2PrismaticJoint::Dump()
{
        // FLT_DECIMAL_DIG == 9
 
        int32 indexA = m_bodyA->m_islandIndex;
        int32 indexB = m_bodyB->m_islandIndex;
 
        b2Dump("  b2PrismaticJointDef 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.referenceAngle = %.9g;\n", m_referenceAngle);
        b2Dump("  jd.enableLimit = bool(%d);\n", m_enableLimit);
        b2Dump("  jd.lowerTranslation = %.9g;\n", m_lowerTranslation);
        b2Dump("  jd.upperTranslation = %.9g;\n", m_upperTranslation);
        b2Dump("  jd.enableMotor = bool(%d);\n", m_enableMotor);
        b2Dump("  jd.motorSpeed = %.9g;\n", m_motorSpeed);
        b2Dump("  jd.maxMotorForce = %.9g;\n", m_maxMotorForce);
        b2Dump("  joints[%d] = m_world->CreateJoint(&jd);\n", m_index);
}
 
void b2PrismaticJoint::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);
}