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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_pulley_joint.h"
+#include "box2d/b2_time_step.h"
+
+// Pulley:
+// length1 = norm(p1 - s1)
+// length2 = norm(p2 - s2)
+// C0 = (length1 + ratio * length2)_initial
+// C = C0 - (length1 + ratio * length2)
+// u1 = (p1 - s1) / norm(p1 - s1)
+// u2 = (p2 - s2) / norm(p2 - s2)
+// Cdot = -dot(u1, v1 + cross(w1, r1)) - ratio * dot(u2, v2 + cross(w2, r2))
+// J = -[u1 cross(r1, u1) ratio * u2 ratio * cross(r2, u2)]
+// K = J * invM * JT
+// = invMass1 + invI1 * cross(r1, u1)^2 + ratio^2 * (invMass2 + invI2 * cross(r2, u2)^2)
+
+void b2PulleyJointDef::Initialize(b2Body* bA, b2Body* bB,
+ const b2Vec2& groundA, const b2Vec2& groundB,
+ const b2Vec2& anchorA, const b2Vec2& anchorB,
+ float r)
+{
+ bodyA = bA;
+ bodyB = bB;
+ groundAnchorA = groundA;
+ groundAnchorB = groundB;
+ localAnchorA = bodyA->GetLocalPoint(anchorA);
+ localAnchorB = bodyB->GetLocalPoint(anchorB);
+ b2Vec2 dA = anchorA - groundA;
+ lengthA = dA.Length();
+ b2Vec2 dB = anchorB - groundB;
+ lengthB = dB.Length();
+ ratio = r;
+ b2Assert(ratio > b2_epsilon);
+}
+
+b2PulleyJoint::b2PulleyJoint(const b2PulleyJointDef* def)
+: b2Joint(def)
+{
+ m_groundAnchorA = def->groundAnchorA;
+ m_groundAnchorB = def->groundAnchorB;
+ m_localAnchorA = def->localAnchorA;
+ m_localAnchorB = def->localAnchorB;
+
+ m_lengthA = def->lengthA;
+ m_lengthB = def->lengthB;
+
+ b2Assert(def->ratio != 0.0f);
+ m_ratio = def->ratio;
+
+ m_constant = def->lengthA + m_ratio * def->lengthB;
+
+ m_impulse = 0.0f;
+}
+
+void b2PulleyJoint::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);
+
+ // Get the pulley axes.
+ m_uA = cA + m_rA - m_groundAnchorA;
+ m_uB = cB + m_rB - m_groundAnchorB;
+
+ float lengthA = m_uA.Length();
+ float lengthB = m_uB.Length();
+
+ if (lengthA > 10.0f * b2_linearSlop)
+ {
+ m_uA *= 1.0f / lengthA;
+ }
+ else
+ {
+ m_uA.SetZero();
+ }
+
+ if (lengthB > 10.0f * b2_linearSlop)
+ {
+ m_uB *= 1.0f / lengthB;
+ }
+ else
+ {
+ m_uB.SetZero();
+ }
+
+ // Compute effective mass.
+ float ruA = b2Cross(m_rA, m_uA);
+ float ruB = b2Cross(m_rB, m_uB);
+
+ float mA = m_invMassA + m_invIA * ruA * ruA;
+ float mB = m_invMassB + m_invIB * ruB * ruB;
+
+ m_mass = mA + m_ratio * m_ratio * mB;
+
+ if (m_mass > 0.0f)
+ {
+ m_mass = 1.0f / m_mass;
+ }
+
+ if (data.step.warmStarting)
+ {
+ // Scale impulses to support variable time steps.
+ m_impulse *= data.step.dtRatio;
+
+ // Warm starting.
+ b2Vec2 PA = -(m_impulse) * m_uA;
+ b2Vec2 PB = (-m_ratio * m_impulse) * m_uB;
+
+ vA += m_invMassA * PA;
+ wA += m_invIA * b2Cross(m_rA, PA);
+ vB += m_invMassB * PB;
+ wB += m_invIB * b2Cross(m_rB, PB);
+ }
+ 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 b2PulleyJoint::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;
+
+ b2Vec2 vpA = vA + b2Cross(wA, m_rA);
+ b2Vec2 vpB = vB + b2Cross(wB, m_rB);
+
+ float Cdot = -b2Dot(m_uA, vpA) - m_ratio * b2Dot(m_uB, vpB);
+ float impulse = -m_mass * Cdot;
+ m_impulse += impulse;
+
+ b2Vec2 PA = -impulse * m_uA;
+ b2Vec2 PB = -m_ratio * impulse * m_uB;
+ vA += m_invMassA * PA;
+ wA += m_invIA * b2Cross(m_rA, PA);
+ vB += m_invMassB * PB;
+ wB += m_invIB * b2Cross(m_rB, PB);
+
+ 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 b2PulleyJoint::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);
+
+ // Get the pulley axes.
+ b2Vec2 uA = cA + rA - m_groundAnchorA;
+ b2Vec2 uB = cB + rB - m_groundAnchorB;
+
+ float lengthA = uA.Length();
+ float lengthB = uB.Length();
+
+ if (lengthA > 10.0f * b2_linearSlop)
+ {
+ uA *= 1.0f / lengthA;
+ }
+ else
+ {
+ uA.SetZero();
+ }
+
+ if (lengthB > 10.0f * b2_linearSlop)
+ {
+ uB *= 1.0f / lengthB;
+ }
+ else
+ {
+ uB.SetZero();
+ }
+
+ // Compute effective mass.
+ float ruA = b2Cross(rA, uA);
+ float ruB = b2Cross(rB, uB);
+
+ float mA = m_invMassA + m_invIA * ruA * ruA;
+ float mB = m_invMassB + m_invIB * ruB * ruB;
+
+ float mass = mA + m_ratio * m_ratio * mB;
+
+ if (mass > 0.0f)
+ {
+ mass = 1.0f / mass;
+ }
+
+ float C = m_constant - lengthA - m_ratio * lengthB;
+ float linearError = b2Abs(C);
+
+ float impulse = -mass * C;
+
+ b2Vec2 PA = -impulse * uA;
+ b2Vec2 PB = -m_ratio * impulse * uB;
+
+ cA += m_invMassA * PA;
+ aA += m_invIA * b2Cross(rA, PA);
+ cB += m_invMassB * PB;
+ aB += m_invIB * b2Cross(rB, PB);
+
+ 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;
+}
+
+b2Vec2 b2PulleyJoint::GetAnchorA() const
+{
+ return m_bodyA->GetWorldPoint(m_localAnchorA);
+}
+
+b2Vec2 b2PulleyJoint::GetAnchorB() const
+{
+ return m_bodyB->GetWorldPoint(m_localAnchorB);
+}
+
+b2Vec2 b2PulleyJoint::GetReactionForce(float inv_dt) const
+{
+ b2Vec2 P = m_impulse * m_uB;
+ return inv_dt * P;
+}
+
+float b2PulleyJoint::GetReactionTorque(float inv_dt) const
+{
+ B2_NOT_USED(inv_dt);
+ return 0.0f;
+}
+
+b2Vec2 b2PulleyJoint::GetGroundAnchorA() const
+{
+ return m_groundAnchorA;
+}
+
+b2Vec2 b2PulleyJoint::GetGroundAnchorB() const
+{
+ return m_groundAnchorB;
+}
+
+float b2PulleyJoint::GetLengthA() const
+{
+ return m_lengthA;
+}
+
+float b2PulleyJoint::GetLengthB() const
+{
+ return m_lengthB;
+}
+
+float b2PulleyJoint::GetRatio() const
+{
+ return m_ratio;
+}
+
+float b2PulleyJoint::GetCurrentLengthA() const
+{
+ b2Vec2 p = m_bodyA->GetWorldPoint(m_localAnchorA);
+ b2Vec2 s = m_groundAnchorA;
+ b2Vec2 d = p - s;
+ return d.Length();
+}
+
+float b2PulleyJoint::GetCurrentLengthB() const
+{
+ b2Vec2 p = m_bodyB->GetWorldPoint(m_localAnchorB);
+ b2Vec2 s = m_groundAnchorB;
+ b2Vec2 d = p - s;
+ return d.Length();
+}
+
+void b2PulleyJoint::Dump()
+{
+ int32 indexA = m_bodyA->m_islandIndex;
+ int32 indexB = m_bodyB->m_islandIndex;
+
+ b2Dump(" b2PulleyJointDef 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.groundAnchorA.Set(%.9g, %.9g);\n", m_groundAnchorA.x, m_groundAnchorA.y);
+ b2Dump(" jd.groundAnchorB.Set(%.9g, %.9g);\n", m_groundAnchorB.x, m_groundAnchorB.y);
+ 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.lengthA = %.9g;\n", m_lengthA);
+ b2Dump(" jd.lengthB = %.9g;\n", m_lengthB);
+ b2Dump(" jd.ratio = %.9g;\n", m_ratio);
+ b2Dump(" joints[%d] = m_world->CreateJoint(&jd);\n", m_index);
+}
+
+void b2PulleyJoint::ShiftOrigin(const b2Vec2& newOrigin)
+{
+ m_groundAnchorA -= newOrigin;
+ m_groundAnchorB -= newOrigin;
+}