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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);
+}