content: /*
   * FXGL - JavaFX Game Library. The MIT License (MIT).
   * Copyright (c) AlmasB (almaslvl@gmail.com).
   * See LICENSE for details.
   */
  /**
   * Created at 3:38:38 AM Jan 15, 2011
   */
  package com.almasb.fxgl.physics.box2d.dynamics.joints;
  
  import com.almasb.fxgl.core.math.FXGLMath;
  import com.almasb.fxgl.core.math.Vec2;
  import com.almasb.fxgl.core.math.Vec3;
  import com.almasb.fxgl.physics.box2d.common.JBoxSettings;
  import com.almasb.fxgl.physics.box2d.common.Mat33;
  import com.almasb.fxgl.physics.box2d.common.Rotation;
  import com.almasb.fxgl.physics.box2d.dynamics.SolverData;
  import com.almasb.fxgl.physics.box2d.pooling.IWorldPool;
  
  //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
  
  /**
   * A weld joint essentially glues two bodies together. A weld joint may distort somewhat because the
   * island constraint solver is approximate.
   *
   * @author Daniel Murphy
   */
  public class WeldJoint extends Joint {
  
      private float m_frequencyHz;
      private float m_dampingRatio;
      private float m_bias;
  
      // Solver shared
      private final Vec2 m_localAnchorA;
      private final Vec2 m_localAnchorB;
      private float m_referenceAngle;
      private float m_gamma;
      private final Vec3 m_impulse;
  
  
      // Solver temp
      private int m_indexA;
      private int m_indexB;
      private final Vec2 m_rA = new Vec2();
      private final Vec2 m_rB = new Vec2();
      private final Vec2 m_localCenterA = new Vec2();
      private final Vec2 m_localCenterB = new Vec2();
      private float m_invMassA;
      private float m_invMassB;
      private float m_invIA;
      private float m_invIB;
      private final Mat33 m_mass = new Mat33();
  
      protected WeldJoint(IWorldPool argWorld, WeldJointDef def) {
          super(argWorld, def);
          m_localAnchorA = new Vec2(def.localAnchorA);
          m_localAnchorB = new Vec2(def.localAnchorB);
          m_referenceAngle = def.referenceAngle;
          m_frequencyHz = def.frequencyHz;
          m_dampingRatio = def.dampingRatio;
  
          m_impulse = new Vec3();
          m_impulse.setZero();
      }
  
      public float getReferenceAngle() {
          return m_referenceAngle;
      }
  
      public Vec2 getLocalAnchorA() {
          return m_localAnchorA;
      }
  
      public Vec2 getLocalAnchorB() {
          return m_localAnchorB;
      }
  
      public float getFrequency() {
          return m_frequencyHz;
      }
  
      public void setFrequency(float frequencyHz) {
          this.m_frequencyHz = frequencyHz;
      }
  
      public float getDampingRatio() {
          return m_dampingRatio;
      }
  
      public void setDampingRatio(float dampingRatio) {
          this.m_dampingRatio = dampingRatio;
      }
  
      @Override
      public void getAnchorA(Vec2 argOut) {
          m_bodyA.getWorldPointToOut(m_localAnchorA, argOut);
      }
  
      @Override
      public void getAnchorB(Vec2 argOut) {
          m_bodyB.getWorldPointToOut(m_localAnchorB, argOut);
      }
  
      @Override
      public void getReactionForce(float inv_dt, Vec2 argOut) {
          argOut.set(m_impulse.x, m_impulse.y);
          argOut.mulLocal(inv_dt);
      }
  
      @Override
      public float getReactionTorque(float inv_dt) {
          return inv_dt * m_impulse.z;
      }
  
      @Override
      public void initVelocityConstraints(final SolverData data) {
          m_indexA = m_bodyA.m_islandIndex;
          m_indexB = m_bodyB.m_islandIndex;
          m_localCenterA.set(m_bodyA.m_sweep.localCenter);
          m_localCenterB.set(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;
  
          // Vec2 cA = data.positions[m_indexA].c;
          float aA = data.positions[m_indexA].a;
          Vec2 vA = data.velocities[m_indexA].v;
          float wA = data.velocities[m_indexA].w;
  
          // Vec2 cB = data.positions[m_indexB].c;
          float aB = data.positions[m_indexB].a;
          Vec2 vB = data.velocities[m_indexB].v;
          float wB = data.velocities[m_indexB].w;
  
          final Rotation qA = pool.popRot();
          final Rotation qB = pool.popRot();
          final Vec2 temp = pool.popVec2();
  
          qA.set(aA);
          qB.set(aB);
  
          // Compute the effective masses.
          Rotation.mulToOutUnsafe(qA, temp.set(m_localAnchorA).subLocal(m_localCenterA), m_rA);
          Rotation.mulToOutUnsafe(qB, temp.set(m_localAnchorB).subLocal(m_localCenterB), m_rB);
  
          // 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]
  
          float mA = m_invMassA, mB = m_invMassB;
          float iA = m_invIA, iB = m_invIB;
  
          final Mat33 K = pool.popMat33();
  
          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);
  
              float invM = iA + iB;
              float m = invM > 0.0f ? 1.0f / invM : 0.0f;
  
              float C = aB - aA - m_referenceAngle;
  
              // Frequency
              float omega = 2.0f * (float) FXGLMath.PI * m_frequencyHz;
  
              // Damping coefficient
              float d = 2.0f * m * m_dampingRatio * omega;
  
              // Spring stiffness
              float k = m * omega * omega;
  
              // magic formulas
              float 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 {
              K.getSymInverse33(m_mass);
              m_gamma = 0.0f;
              m_bias = 0.0f;
          }
  
          if (data.step.warmStarting) {
              final Vec2 P = pool.popVec2();
              // Scale impulses to support a variable time step.
              m_impulse.mulLocal(data.step.dtRatio);
  
              P.set(m_impulse.x, m_impulse.y);
  
              vA.x -= mA * P.x;
              vA.y -= mA * P.y;
              wA -= iA * (Vec2.cross(m_rA, P) + m_impulse.z);
  
              vB.x += mB * P.x;
              vB.y += mB * P.y;
              wB += iB * (Vec2.cross(m_rB, P) + m_impulse.z);
              pool.pushVec2(1);
          } else {
              m_impulse.setZero();
          }
  
          data.velocities[m_indexA].w = wA;
          data.velocities[m_indexB].w = wB;
  
          pool.pushVec2(1);
          pool.pushRot(2);
          pool.pushMat33(1);
      }
  
      @Override
      public void solveVelocityConstraints(final SolverData data) {
          Vec2 vA = data.velocities[m_indexA].v;
          float wA = data.velocities[m_indexA].w;
          Vec2 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;
  
          final Vec2 Cdot1 = pool.popVec2();
          final Vec2 P = pool.popVec2();
          final Vec2 temp = pool.popVec2();
          if (m_frequencyHz > 0.0f) {
              float Cdot2 = wB - wA;
  
              float impulse2 = -m_mass.ez.z * (Cdot2 + m_bias + m_gamma * m_impulse.z);
              m_impulse.z += impulse2;
  
              wA -= iA * impulse2;
              wB += iB * impulse2;
  
              Vec2.crossToOutUnsafe(wB, m_rB, Cdot1);
              Vec2.crossToOutUnsafe(wA, m_rA, temp);
              Cdot1.addLocal(vB).subLocal(vA).subLocal(temp);
  
              final Vec2 impulse1 = P;
              Mat33.mul22ToOutUnsafe(m_mass, Cdot1, impulse1);
              impulse1.negateLocal();
  
              m_impulse.x += impulse1.x;
              m_impulse.y += impulse1.y;
  
              vA.x -= mA * P.x;
              vA.y -= mA * P.y;
              wA -= iA * Vec2.cross(m_rA, P);
  
              vB.x += mB * P.x;
              vB.y += mB * P.y;
              wB += iB * Vec2.cross(m_rB, P);
          } else {
              Vec2.crossToOutUnsafe(wA, m_rA, temp);
              Vec2.crossToOutUnsafe(wB, m_rB, Cdot1);
              Cdot1.addLocal(vB).subLocal(vA).subLocal(temp);
              float Cdot2 = wB - wA;
  
              final Vec3 Cdot = pool.popVec3();
              Cdot.set(Cdot1.x, Cdot1.y, Cdot2);
  
              final Vec3 impulse = pool.popVec3();
              Mat33.mulToOutUnsafe(m_mass, Cdot, impulse);
              impulse.negateLocal();
              m_impulse.addLocal(impulse);
  
              P.set(impulse.x, impulse.y);
  
              vA.x -= mA * P.x;
              vA.y -= mA * P.y;
              wA -= iA * (Vec2.cross(m_rA, P) + impulse.z);
  
              vB.x += mB * P.x;
              vB.y += mB * P.y;
              wB += iB * (Vec2.cross(m_rB, P) + impulse.z);
  
              pool.pushVec3(2);
          }
  
          data.velocities[m_indexA].w = wA;
          data.velocities[m_indexB].w = wB;
  
          pool.pushVec2(3);
      }
  
      @Override
      public boolean solvePositionConstraints(final SolverData data) {
          Vec2 cA = data.positions[m_indexA].c;
          float aA = data.positions[m_indexA].a;
          Vec2 cB = data.positions[m_indexB].c;
          float aB = data.positions[m_indexB].a;
          final Rotation qA = pool.popRot();
          final Rotation qB = pool.popRot();
          final Vec2 temp = pool.popVec2();
          final Vec2 rA = pool.popVec2();
          final Vec2 rB = pool.popVec2();
  
          qA.set(aA);
          qB.set(aB);
  
          float mA = m_invMassA, mB = m_invMassB;
          float iA = m_invIA, iB = m_invIB;
  
          Rotation.mulToOutUnsafe(qA, temp.set(m_localAnchorA).subLocal(m_localCenterA), rA);
          Rotation.mulToOutUnsafe(qB, temp.set(m_localAnchorB).subLocal(m_localCenterB), rB);
          float positionError, angularError;
  
          final Mat33 K = pool.popMat33();
          final Vec2 C1 = pool.popVec2();
          final Vec2 P = pool.popVec2();
  
          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) {
              C1.set(cB).addLocal(rB).subLocal(cA).subLocal(rA);
  
              positionError = C1.length();
              angularError = 0.0f;
  
              K.solve22ToOut(C1, P);
              P.negateLocal();
  
              cA.x -= mA * P.x;
              cA.y -= mA * P.y;
              aA -= iA * Vec2.cross(rA, P);
  
              cB.x += mB * P.x;
              cB.y += mB * P.y;
              aB += iB * Vec2.cross(rB, P);
          } else {
              C1.set(cB).addLocal(rB).subLocal(cA).subLocal(rA);
              float C2 = aB - aA - m_referenceAngle;
  
              positionError = C1.length();
              angularError = FXGLMath.abs(C2);
  
              final Vec3 C = pool.popVec3();
              final Vec3 impulse = pool.popVec3();
              C.set(C1.x, C1.y, C2);
  
              K.solve33ToOut(C, impulse);
              impulse.negateLocal();
              P.set(impulse.x, impulse.y);
  
              cA.x -= mA * P.x;
              cA.y -= mA * P.y;
              aA -= iA * (Vec2.cross(rA, P) + impulse.z);
  
              cB.x += mB * P.x;
              cB.y += mB * P.y;
              aB += iB * (Vec2.cross(rB, P) + impulse.z);
              pool.pushVec3(2);
          }
  
          data.positions[m_indexA].a = aA;
          data.positions[m_indexB].a = aB;
  
          pool.pushVec2(5);
          pool.pushRot(2);
          pool.pushMat33(1);
  
          return positionError <= JBoxSettings.linearSlop && angularError <= JBoxSettings.angularSlop;
      }
  }
  