content: /*
   * FXGL - JavaFX Game Library. The MIT License (MIT).
   * Copyright (c) AlmasB (almaslvl@gmail.com).
   * See LICENSE for details.
   */
  package com.almasb.fxgl.physics.box2d.dynamics.contacts;
  
  import com.almasb.fxgl.core.math.FXGLMath;
  import com.almasb.fxgl.core.math.Vec2;
  import com.almasb.fxgl.physics.box2d.collision.Manifold;
  import com.almasb.fxgl.physics.box2d.collision.ManifoldPoint;
  import com.almasb.fxgl.physics.box2d.collision.WorldManifold;
  import com.almasb.fxgl.physics.box2d.collision.shapes.Shape;
  import com.almasb.fxgl.physics.box2d.common.JBoxSettings;
  import com.almasb.fxgl.physics.box2d.common.Mat22;
  import com.almasb.fxgl.physics.box2d.common.Rotation;
  import com.almasb.fxgl.physics.box2d.common.Transform;
  import com.almasb.fxgl.physics.box2d.dynamics.Body;
  import com.almasb.fxgl.physics.box2d.dynamics.Fixture;
  import com.almasb.fxgl.physics.box2d.dynamics.TimeStep;
  import com.almasb.fxgl.physics.box2d.dynamics.contacts.ContactVelocityConstraint.VelocityConstraintPoint;
  
  /**
   * @author Daniel
   */
  public final class ContactSolver {
  
      /**
       * For each solver, this is the initial number of constraints in the array, which expands as
       * needed.
       */
      private static final int INITIAL_NUM_CONSTRAINTS = 256;
  
      /**
       * Ensure a reasonable condition number. for the block solver
       */
      private static final float k_maxConditionNumber = 100.0f;
  
      private Position[] m_positions;
      private Velocity[] m_velocities;
      private ContactPositionConstraint[] m_positionConstraints = new ContactPositionConstraint[INITIAL_NUM_CONSTRAINTS];
      private ContactVelocityConstraint[] m_velocityConstraints = new ContactVelocityConstraint[INITIAL_NUM_CONSTRAINTS];
  
      private Contact[] m_contacts;
      private int m_count;
  
      public ContactSolver() {
          for (int i = 0; i < INITIAL_NUM_CONSTRAINTS; i++) {
              m_positionConstraints[i] = new ContactPositionConstraint();
              m_velocityConstraints[i] = new ContactVelocityConstraint();
          }
      }
  
      public ContactVelocityConstraint[] getVelocityConstraints() {
          return m_velocityConstraints;
      }
  
      public void init(ContactSolverDef def) {
          TimeStep step = def.step;
          m_count = def.count;
  
          if (m_positionConstraints.length < m_count) {
              ContactPositionConstraint[] old = m_positionConstraints;
              m_positionConstraints = new ContactPositionConstraint[Math.max(old.length * 2, m_count)];
              System.arraycopy(old, 0, m_positionConstraints, 0, old.length);
              for (int i = old.length; i < m_positionConstraints.length; i++) {
                  m_positionConstraints[i] = new ContactPositionConstraint();
              }
          }
  
          if (m_velocityConstraints.length < m_count) {
              ContactVelocityConstraint[] old = m_velocityConstraints;
              m_velocityConstraints = new ContactVelocityConstraint[Math.max(old.length * 2, m_count)];
              System.arraycopy(old, 0, m_velocityConstraints, 0, old.length);
              for (int i = old.length; i < m_velocityConstraints.length; i++) {
                  m_velocityConstraints[i] = new ContactVelocityConstraint();
              }
          }
  
          m_positions = def.positions;
          m_velocities = def.velocities;
          m_contacts = def.contacts;
  
          for (int i = 0; i < m_count; ++i) {
              final Contact contact = m_contacts[i];
  
              final Fixture fixtureA = contact.m_fixtureA;
              final Fixture fixtureB = contact.m_fixtureB;
              final Shape shapeA = fixtureA.getShape();
              final Shape shapeB = fixtureB.getShape();
              final float radiusA = shapeA.getRadius();
              final float radiusB = shapeB.getRadius();
              final Body bodyA = fixtureA.getBody();
              final Body bodyB = fixtureB.getBody();
              final Manifold manifold = contact.getManifold();
  
              int pointCount = manifold.pointCount;
              assert pointCount > 0;
  
              ContactVelocityConstraint vc = m_velocityConstraints[i];
              vc.friction = contact.getFriction();
              vc.restitution = contact.getRestitution();
              vc.tangentSpeed = contact.getTangentSpeed();
              vc.indexA = bodyA.m_islandIndex;
              vc.indexB = bodyB.m_islandIndex;
              vc.invMassA = bodyA.m_invMass;
              vc.invMassB = bodyB.m_invMass;
              vc.invIA = bodyA.m_invI;
              vc.invIB = bodyB.m_invI;
              vc.contactIndex = i;
              vc.pointCount = pointCount;
              vc.K.setZero();
              vc.normalMass.setZero();
  
              ContactPositionConstraint pc = m_positionConstraints[i];
              pc.indexA = bodyA.m_islandIndex;
              pc.indexB = bodyB.m_islandIndex;
              pc.invMassA = bodyA.m_invMass;
              pc.invMassB = bodyB.m_invMass;
              pc.localCenterA.set(bodyA.m_sweep.localCenter);
              pc.localCenterB.set(bodyB.m_sweep.localCenter);
              pc.invIA = bodyA.m_invI;
              pc.invIB = bodyB.m_invI;
              pc.localNormal.set(manifold.localNormal);
              pc.localPoint.set(manifold.localPoint);
              pc.pointCount = pointCount;
              pc.radiusA = radiusA;
              pc.radiusB = radiusB;
              pc.type = manifold.type;
  
              for (int j = 0; j < pointCount; j++) {
                  ManifoldPoint cp = manifold.points[j];
                  VelocityConstraintPoint vcp = vc.points[j];
  
                  if (step.warmStarting) {
                      vcp.normalImpulse = step.dtRatio * cp.normalImpulse;
                      vcp.tangentImpulse = step.dtRatio * cp.tangentImpulse;
                  } else {
                      vcp.normalImpulse = 0;
                      vcp.tangentImpulse = 0;
                  }
  
                  vcp.rA.setZero();
                  vcp.rB.setZero();
                  vcp.normalMass = 0;
                  vcp.tangentMass = 0;
                  vcp.velocityBias = 0;
                  pc.localPoints[j].x = cp.localPoint.x;
                  pc.localPoints[j].y = cp.localPoint.y;
              }
          }
      }
  
      public void warmStart() {
          // Warm start.
          for (int i = 0; i < m_count; ++i) {
              final ContactVelocityConstraint vc = m_velocityConstraints[i];
  
              int indexA = vc.indexA;
              int indexB = vc.indexB;
              float mA = vc.invMassA;
              float iA = vc.invIA;
              float mB = vc.invMassB;
              float iB = vc.invIB;
              int pointCount = vc.pointCount;
  
              Vec2 vA = m_velocities[indexA].v;
              float wA = m_velocities[indexA].w;
              Vec2 vB = m_velocities[indexB].v;
              float wB = m_velocities[indexB].w;
  
              Vec2 normal = vc.normal;
              float tangentx = 1.0f * normal.y;
              float tangenty = -1.0f * normal.x;
  
              for (int j = 0; j < pointCount; ++j) {
                  VelocityConstraintPoint vcp = vc.points[j];
                  float Px = tangentx * vcp.tangentImpulse + normal.x * vcp.normalImpulse;
                  float Py = tangenty * vcp.tangentImpulse + normal.y * vcp.normalImpulse;
  
                  wA -= iA * (vcp.rA.x * Py - vcp.rA.y * Px);
                  vA.x -= Px * mA;
                  vA.y -= Py * mA;
                  wB += iB * (vcp.rB.x * Py - vcp.rB.y * Px);
                  vB.x += Px * mB;
                  vB.y += Py * mB;
              }
              m_velocities[indexA].w = wA;
              m_velocities[indexB].w = wB;
          }
      }
  
      // djm pooling, and from above
      private final Transform xfA = new Transform();
      private final Transform xfB = new Transform();
      private final WorldManifold worldManifold = new WorldManifold();
  
      public void initializeVelocityConstraints() {
  
          // Warm start.
          for (int i = 0; i < m_count; ++i) {
              ContactVelocityConstraint vc = m_velocityConstraints[i];
              ContactPositionConstraint pc = m_positionConstraints[i];
  
              float radiusA = pc.radiusA;
              float radiusB = pc.radiusB;
              Manifold manifold = m_contacts[vc.contactIndex].getManifold();
  
              int indexA = vc.indexA;
              int indexB = vc.indexB;
  
              float mA = vc.invMassA;
              float mB = vc.invMassB;
              float iA = vc.invIA;
              float iB = vc.invIB;
              Vec2 localCenterA = pc.localCenterA;
              Vec2 localCenterB = pc.localCenterB;
  
              Vec2 cA = m_positions[indexA].c;
              float aA = m_positions[indexA].a;
              Vec2 vA = m_velocities[indexA].v;
              float wA = m_velocities[indexA].w;
  
              Vec2 cB = m_positions[indexB].c;
              float aB = m_positions[indexB].a;
              Vec2 vB = m_velocities[indexB].v;
              float wB = m_velocities[indexB].w;
  
              assert manifold.pointCount > 0;
  
              final Rotation xfAq = xfA.q;
              final Rotation xfBq = xfB.q;
              xfAq.set(aA);
              xfBq.set(aB);
              xfA.p.x = cA.x - (xfAq.c * localCenterA.x - xfAq.s * localCenterA.y);
              xfA.p.y = cA.y - (xfAq.s * localCenterA.x + xfAq.c * localCenterA.y);
              xfB.p.x = cB.x - (xfBq.c * localCenterB.x - xfBq.s * localCenterB.y);
              xfB.p.y = cB.y - (xfBq.s * localCenterB.x + xfBq.c * localCenterB.y);
  
              worldManifold.initialize(manifold, xfA, radiusA, xfB, radiusB);
  
              final Vec2 vcnormal = vc.normal;
              vcnormal.set(worldManifold.getNormalX(), worldManifold.getNormalY());
  
              int pointCount = vc.pointCount;
              for (int j = 0; j < pointCount; ++j) {
                  VelocityConstraintPoint vcp = vc.points[j];
                  Vec2 wmPj = worldManifold.getPoint(j);
                  final Vec2 vcprA = vcp.rA;
                  final Vec2 vcprB = vcp.rB;
                  vcprA.x = wmPj.x - cA.x;
                  vcprA.y = wmPj.y - cA.y;
                  vcprB.x = wmPj.x - cB.x;
                  vcprB.y = wmPj.y - cB.y;
  
                  float rnA = vcprA.x * vcnormal.y - vcprA.y * vcnormal.x;
                  float rnB = vcprB.x * vcnormal.y - vcprB.y * vcnormal.x;
  
                  float kNormal = mA + mB + iA * rnA * rnA + iB * rnB * rnB;
  
                  vcp.normalMass = kNormal > 0.0f ? 1.0f / kNormal : 0.0f;
  
                  float tangentx = 1.0f * vcnormal.y;
                  float tangenty = -1.0f * vcnormal.x;
  
                  float rtA = vcprA.x * tangenty - vcprA.y * tangentx;
                  float rtB = vcprB.x * tangenty - vcprB.y * tangentx;
  
                  float kTangent = mA + mB + iA * rtA * rtA + iB * rtB * rtB;
  
                  vcp.tangentMass = kTangent > 0.0f ? 1.0f / kTangent : 0.0f;
  
                  // Setup a velocity bias for restitution.
                  vcp.velocityBias = 0.0f;
                  float tempx = vB.x + -wB * vcprB.y - vA.x - (-wA * vcprA.y);
                  float tempy = vB.y + wB * vcprB.x - vA.y - (wA * vcprA.x);
                  float vRel = vcnormal.x * tempx + vcnormal.y * tempy;
                  if (vRel < -JBoxSettings.velocityThreshold) {
                      vcp.velocityBias = -vc.restitution * vRel;
                  }
              }
  
              // If we have two points, then prepare the block solver.
              if (vc.pointCount == 2) {
                  VelocityConstraintPoint vcp1 = vc.points[0];
                  VelocityConstraintPoint vcp2 = vc.points[1];
                  float rn1A = vcp1.rA.x * vcnormal.y - vcp1.rA.y * vcnormal.x;
                  float rn1B = vcp1.rB.x * vcnormal.y - vcp1.rB.y * vcnormal.x;
                  float rn2A = vcp2.rA.x * vcnormal.y - vcp2.rA.y * vcnormal.x;
                  float rn2B = vcp2.rB.x * vcnormal.y - vcp2.rB.y * vcnormal.x;
  
                  float k11 = mA + mB + iA * rn1A * rn1A + iB * rn1B * rn1B;
                  float k22 = mA + mB + iA * rn2A * rn2A + iB * rn2B * rn2B;
                  float k12 = mA + mB + iA * rn1A * rn2A + iB * rn1B * rn2B;
                  if (k11 * k11 < k_maxConditionNumber * (k11 * k22 - k12 * k12)) {
                      // K is safe to invert.
                      vc.K.ex.x = k11;
                      vc.K.ex.y = k12;
                      vc.K.ey.x = k12;
                      vc.K.ey.y = k22;
                      vc.K.invertToOut(vc.normalMass);
                  } else {
                      // The constraints are redundant, just use one.
                      // TODO_ERIN use deepest?
                      vc.pointCount = 1;
                  }
              }
          }
      }
  
      @SuppressWarnings("PMD.AvoidBranchingStatementAsLastInLoop")
      public void solveVelocityConstraints() {
          for (int i = 0; i < m_count; ++i) {
              final ContactVelocityConstraint vc = m_velocityConstraints[i];
  
              int indexA = vc.indexA;
              int indexB = vc.indexB;
  
              float mA = vc.invMassA;
              float mB = vc.invMassB;
              float iA = vc.invIA;
              float iB = vc.invIB;
              int pointCount = vc.pointCount;
  
              Vec2 vA = m_velocities[indexA].v;
              float wA = m_velocities[indexA].w;
              Vec2 vB = m_velocities[indexB].v;
              float wB = m_velocities[indexB].w;
  
              Vec2 normal = vc.normal;
              final float normalx = normal.x;
              final float normaly = normal.y;
              float tangentx = 1.0f * vc.normal.y;
              float tangenty = -1.0f * vc.normal.x;
              final float friction = vc.friction;
  
              assert pointCount == 1 || pointCount == 2;
  
              // Solve tangent constraints
              for (int j = 0; j < pointCount; ++j) {
                  final VelocityConstraintPoint vcp = vc.points[j];
                  final Vec2 a = vcp.rA;
                  float dvx = -wB * vcp.rB.y + vB.x - vA.x + wA * a.y;
                  float dvy = wB * vcp.rB.x + vB.y - vA.y - wA * a.x;
  
                  // Compute tangent force
                  final float vt = dvx * tangentx + dvy * tangenty - vc.tangentSpeed;
                  float lambda = vcp.tangentMass * (-vt);
  
                  // Clamp the accumulated force
                  final float maxFriction = friction * vcp.normalImpulse;
                  final float newImpulse = FXGLMath.clamp(vcp.tangentImpulse + lambda, -maxFriction, maxFriction);
                  lambda = newImpulse - vcp.tangentImpulse;
                  vcp.tangentImpulse = newImpulse;
  
                  // Apply contact impulse
                  // Vec2 P = lambda * tangent;
  
                  final float Px = tangentx * lambda;
                  final float Py = tangenty * lambda;
  
                  // vA -= invMassA * P;
                  vA.x -= Px * mA;
                  vA.y -= Py * mA;
                  wA -= iA * (vcp.rA.x * Py - vcp.rA.y * Px);
  
                  // vB += invMassB * P;
                  vB.x += Px * mB;
                  vB.y += Py * mB;
                  wB += iB * (vcp.rB.x * Py - vcp.rB.y * Px);
              }
  
              // Solve normal constraints
              if (vc.pointCount == 1) {
                  final VelocityConstraintPoint vcp = vc.points[0];
  
                  // Relative velocity at contact
                  // Vec2 dv = vB + Cross(wB, vcp.rB) - vA - Cross(wA, vcp.rA);
  
                  float dvx = -wB * vcp.rB.y + vB.x - vA.x + wA * vcp.rA.y;
                  float dvy = wB * vcp.rB.x + vB.y - vA.y - wA * vcp.rA.x;
  
                  // Compute normal impulse
                  final float vn = dvx * normalx + dvy * normaly;
                  float lambda = -vcp.normalMass * (vn - vcp.velocityBias);
  
                  // Clamp the accumulated impulse
                  float a = vcp.normalImpulse + lambda;
                  final float newImpulse = a > 0.0f ? a : 0.0f;
                  lambda = newImpulse - vcp.normalImpulse;
                  vcp.normalImpulse = newImpulse;
  
                  // Apply contact impulse
                  float Px = normalx * lambda;
                  float Py = normaly * lambda;
  
                  // vA -= invMassA * P;
                  vA.x -= Px * mA;
                  vA.y -= Py * mA;
                  wA -= iA * (vcp.rA.x * Py - vcp.rA.y * Px);
  
                  // vB += invMassB * P;
                  vB.x += Px * mB;
                  vB.y += Py * mB;
                  wB += iB * (vcp.rB.x * Py - vcp.rB.y * Px);
              } else {
                  // Block solver developed in collaboration with Dirk Gregorius (back in 01/07 on Box2D_Lite).
                  // Build the mini LCP for this contact patch
                  //
                  // vn = A * x + b, vn >= 0, , vn >= 0, x >= 0 and vn_i * x_i = 0 with i = 1..2
                  //
                  // A = J * W * JT and J = ( -n, -r1 x n, n, r2 x n )
                  // b = vn_0 - velocityBias
                  //
                  // The system is solved using the "Total enumeration method" (s. Murty). The complementary
                  // constraint vn_i * x_i
                  // implies that we must have in any solution either vn_i = 0 or x_i = 0. So for the 2D
                  // contact problem the cases
                  // vn1 = 0 and vn2 = 0, x1 = 0 and x2 = 0, x1 = 0 and vn2 = 0, x2 = 0 and vn1 = 0 need to be
                  // tested. The first valid
                  // solution that satisfies the problem is chosen.
                  //
                  // In order to account of the accumulated impulse 'a' (because of the iterative nature of
                  // the solver which only requires
                  // that the accumulated impulse is clamped and not the incremental impulse) we change the
                  // impulse variable (x_i).
                  //
                  // Substitute:
                  //
                  // x = a + d
                  //
                  // a := old total impulse
                  // x := new total impulse
                  // d := incremental impulse
                  //
                  // For the current iteration we extend the formula for the incremental impulse
                  // to compute the new total impulse:
                  //
                  // vn = A * d + b
                  // = A * (x - a) + b
                  // = A * x + b - A * a
                  // = A * x + b'
                  // b' = b - A * a;
  
                  final VelocityConstraintPoint cp1 = vc.points[0];
                  final VelocityConstraintPoint cp2 = vc.points[1];
                  final Vec2 cp1rA = cp1.rA;
                  final Vec2 cp1rB = cp1.rB;
                  final Vec2 cp2rA = cp2.rA;
                  final Vec2 cp2rB = cp2.rB;
                  float ax = cp1.normalImpulse;
                  float ay = cp2.normalImpulse;
  
                  assert ax >= 0.0f && ay >= 0.0f;
                  // Relative velocity at contact
                  // Vec2 dv1 = vB + Cross(wB, cp1.rB) - vA - Cross(wA, cp1.rA);
                  float dv1x = -wB * cp1rB.y + vB.x - vA.x + wA * cp1rA.y;
                  float dv1y = wB * cp1rB.x + vB.y - vA.y - wA * cp1rA.x;
  
                  // Vec2 dv2 = vB + Cross(wB, cp2.rB) - vA - Cross(wA, cp2.rA);
                  float dv2x = -wB * cp2rB.y + vB.x - vA.x + wA * cp2rA.y;
                  float dv2y = wB * cp2rB.x + vB.y - vA.y - wA * cp2rA.x;
  
                  // Compute normal velocity
                  float vn1 = dv1x * normalx + dv1y * normaly;
                  float vn2 = dv2x * normalx + dv2y * normaly;
  
                  float bx = vn1 - cp1.velocityBias;
                  float by = vn2 - cp2.velocityBias;
  
                  // Compute b'
                  Mat22 R = vc.K;
                  bx -= R.ex.x * ax + R.ey.x * ay;
                  by -= R.ex.y * ax + R.ey.y * ay;
  
                  // final float k_errorTol = 1e-3f;
                  // B2_NOT_USED(k_errorTol);
                  for (; ; ) {
                      //
                      // Case 1: vn = 0
                      //
                      // 0 = A * x' + b'
                      //
                      // Solve for x':
                      //
                      // x' = - inv(A) * b'
                      //
                      // Vec2 x = - Mul(c.normalMass, b);
                      Mat22 R1 = vc.normalMass;
                      float xx = R1.ex.x * bx + R1.ey.x * by;
                      float xy = R1.ex.y * bx + R1.ey.y * by;
                      xx *= -1;
                      xy *= -1;
  
                      if (xx >= 0.0f && xy >= 0.0f) {
                          // Get the incremental impulse
                          // Vec2 d = x - a;
                          float dx = xx - ax;
                          float dy = xy - ay;
  
                          // Apply incremental impulse
                          // Vec2 P1 = d.x * normal;
                          // Vec2 P2 = d.y * normal;
                          float P1x = dx * normalx;
                          float P1y = dx * normaly;
                          float P2x = dy * normalx;
                          float P2y = dy * normaly;
  
              /*
               * vA -= invMassA * (P1 + P2); wA -= invIA * (Cross(cp1.rA, P1) + Cross(cp2.rA, P2));
               * 
               * vB += invMassB * (P1 + P2); wB += invIB * (Cross(cp1.rB, P1) + Cross(cp2.rB, P2));
               */
  
                          vA.x -= mA * (P1x + P2x);
                          vA.y -= mA * (P1y + P2y);
                          vB.x += mB * (P1x + P2x);
                          vB.y += mB * (P1y + P2y);
  
                          wA -= iA * (cp1rA.x * P1y - cp1rA.y * P1x + (cp2rA.x * P2y - cp2rA.y * P2x));
                          wB += iB * (cp1rB.x * P1y - cp1rB.y * P1x + (cp2rB.x * P2y - cp2rB.y * P2x));
  
                          // Accumulate
                          cp1.normalImpulse = xx;
                          cp2.normalImpulse = xy;
  
                          break;
                      }
  
                      //
                      // Case 2: vn1 = 0 and x2 = 0
                      //
                      // 0 = a11 * x1' + a12 * 0 + b1'
                      // vn2 = a21 * x1' + a22 * 0 + '
                      //
                      xx = -cp1.normalMass * bx;
                      xy = 0.0f;
                      vn1 = 0.0f;
                      vn2 = vc.K.ex.y * xx + by;
  
                      if (xx >= 0.0f && vn2 >= 0.0f) {
                          // Get the incremental impulse
                          float dx = xx - ax;
                          float dy = xy - ay;
  
                          // Apply incremental impulse
                          // Vec2 P1 = d.x * normal;
                          // Vec2 P2 = d.y * normal;
                          float P1x = normalx * dx;
                          float P1y = normaly * dx;
                          float P2x = normalx * dy;
                          float P2y = normaly * dy;
  
              /*
               * Vec2 P1 = d.x * normal; Vec2 P2 = d.y * normal; vA -= invMassA * (P1 + P2); wA -=
               * invIA * (Cross(cp1.rA, P1) + Cross(cp2.rA, P2));
               * 
               * vB += invMassB * (P1 + P2); wB += invIB * (Cross(cp1.rB, P1) + Cross(cp2.rB, P2));
               */
  
                          vA.x -= mA * (P1x + P2x);
                          vA.y -= mA * (P1y + P2y);
                          vB.x += mB * (P1x + P2x);
                          vB.y += mB * (P1y + P2y);
  
                          wA -= iA * (cp1rA.x * P1y - cp1rA.y * P1x + (cp2rA.x * P2y - cp2rA.y * P2x));
                          wB += iB * (cp1rB.x * P1y - cp1rB.y * P1x + (cp2rB.x * P2y - cp2rB.y * P2x));
  
                          // Accumulate
                          cp1.normalImpulse = xx;
                          cp2.normalImpulse = xy;
  
                          break;
                      }
  
                      //
                      // Case 3: wB = 0 and x1 = 0
                      //
                      // vn1 = a11 * 0 + a12 * x2' + b1'
                      // 0 = a21 * 0 + a22 * x2' + '
                      //
                      xx = 0.0f;
                      xy = -cp2.normalMass * by;
                      vn1 = vc.K.ey.x * xy + bx;
                      vn2 = 0.0f;
  
                      if (xy >= 0.0f && vn1 >= 0.0f) {
                          // Resubstitute for the incremental impulse
                          float dx = xx - ax;
                          float dy = xy - ay;
  
                          // Apply incremental impulse
              /*
               * Vec2 P1 = d.x * normal; Vec2 P2 = d.y * normal; vA -= invMassA * (P1 + P2); wA -=
               * invIA * (Cross(cp1.rA, P1) + Cross(cp2.rA, P2));
               * 
               * vB += invMassB * (P1 + P2); wB += invIB * (Cross(cp1.rB, P1) + Cross(cp2.rB, P2));
               */
  
                          float P1x = normalx * dx;
                          float P1y = normaly * dx;
                          float P2x = normalx * dy;
                          float P2y = normaly * dy;
  
                          vA.x -= mA * (P1x + P2x);
                          vA.y -= mA * (P1y + P2y);
                          vB.x += mB * (P1x + P2x);
                          vB.y += mB * (P1y + P2y);
  
                          wA -= iA * (cp1rA.x * P1y - cp1rA.y * P1x + (cp2rA.x * P2y - cp2rA.y * P2x));
                          wB += iB * (cp1rB.x * P1y - cp1rB.y * P1x + (cp2rB.x * P2y - cp2rB.y * P2x));
  
                          // Accumulate
                          cp1.normalImpulse = xx;
                          cp2.normalImpulse = xy;
  
                          break;
                      }
  
                      //
                      // Case 4: x1 = 0 and x2 = 0
                      //
                      // vn1 = b1
                      // vn2 = ;
                      xx = 0.0f;
                      xy = 0.0f;
                      vn1 = bx;
                      vn2 = by;
  
                      if (vn1 >= 0.0f && vn2 >= 0.0f) {
                          // Resubstitute for the incremental impulse
                          float dx = xx - ax;
                          float dy = xy - ay;
  
                          // Apply incremental impulse
              /*
               * Vec2 P1 = d.x * normal; Vec2 P2 = d.y * normal; vA -= invMassA * (P1 + P2); wA -=
               * invIA * (Cross(cp1.rA, P1) + Cross(cp2.rA, P2));
               * 
               * vB += invMassB * (P1 + P2); wB += invIB * (Cross(cp1.rB, P1) + Cross(cp2.rB, P2));
               */
  
                          float P1x = normalx * dx;
                          float P1y = normaly * dx;
                          float P2x = normalx * dy;
                          float P2y = normaly * dy;
  
                          vA.x -= mA * (P1x + P2x);
                          vA.y -= mA * (P1y + P2y);
                          vB.x += mB * (P1x + P2x);
                          vB.y += mB * (P1y + P2y);
  
                          wA -= iA * (cp1rA.x * P1y - cp1rA.y * P1x + (cp2rA.x * P2y - cp2rA.y * P2x));
                          wB += iB * (cp1rB.x * P1y - cp1rB.y * P1x + (cp2rB.x * P2y - cp2rB.y * P2x));
  
                          // Accumulate
                          cp1.normalImpulse = xx;
                          cp2.normalImpulse = xy;
  
                          break;
                      }
  
                      // No solution, give up. This is hit sometimes, but it doesn't seem to matter.
                      break;
                  }
              }
  
              // m_velocities[indexA].v.set(vA);
              m_velocities[indexA].w = wA;
              // m_velocities[indexB].v.set(vB);
              m_velocities[indexB].w = wB;
          }
      }
  
      public void storeImpulses() {
          for (int i = 0; i < m_count; i++) {
              final ContactVelocityConstraint vc = m_velocityConstraints[i];
              final Manifold manifold = m_contacts[vc.contactIndex].getManifold();
  
              for (int j = 0; j < vc.pointCount; j++) {
                  manifold.points[j].normalImpulse = vc.points[j].normalImpulse;
                  manifold.points[j].tangentImpulse = vc.points[j].tangentImpulse;
              }
          }
      }
  
    /*
     * #if 0 // Sequential solver. bool ContactSolver::SolvePositionConstraints(float baumgarte) {
     * float minSeparation = 0.0f;
     * 
     * for (int i = 0; i < m_constraintCount; ++i) { ContactConstraint* c = m_constraints + i; Body*
     * bodyA = c.bodyA; Body* bodyB = c.bodyB; float invMassA = bodyA.m_mass * bodyA.m_invMass; float
     * invIA = bodyA.m_mass * bodyA.m_invI; float invMassB = bodyB.m_mass * bodyB.m_invMass; float
     * invIB = bodyB.m_mass * bodyB.m_invI;
     * 
     * Vec2 normal = c.normal;
     * 
     * // Solve normal constraints for (int j = 0; j < c.pointCount; ++j) { ContactConstraintPoint*
     * ccp = c.points + j;
     * 
     * Vec2 r1 = Mul(bodyA.GetXForm().R, ccp.localAnchorA - bodyA.GetLocalCenter()); Vec2 r2 =
     * Mul(bodyB.GetXForm().R, ccp.localAnchorB - bodyB.GetLocalCenter());
     * 
     * Vec2 p1 = bodyA.m_sweep.c + r1; Vec2 p2 = bodyB.m_sweep.c + r2; Vec2 dp = p2 - p1;
     * 
     * // Approximate the current separation. float separation = Dot(dp, normal) + ccp.separation;
     * 
     * // Track max constraint error. minSeparation = Min(minSeparation, separation);
     * 
     * // Prevent large corrections and allow slop. float C = Clamp(baumgarte * (separation +
     * _linearSlop), -_maxLinearCorrection, 0.0f);
     * 
     * // Compute normal impulse float impulse = -ccp.equalizedMass * C;
     * 
     * Vec2 P = impulse * normal;
     * 
     * bodyA.m_sweep.c -= invMassA * P; bodyA.m_sweep.a -= invIA * Cross(r1, P);
     * bodyA.SynchronizeTransform();
     * 
     * bodyB.m_sweep.c += invMassB * P; bodyB.m_sweep.a += invIB * Cross(r2, P);
     * bodyB.SynchronizeTransform(); } }
     * 
     * // We can't expect minSpeparation >= -_linearSlop because we don't // push the separation above
     * -_linearSlop. return minSeparation >= -1.5f * _linearSlop; }
     */
  
      private final PositionSolverManifold psolver = new PositionSolverManifold();
  
      /**
       * Sequential solver.
       */
      public boolean solvePositionConstraints() {
          float minSeparation = 0.0f;
  
          for (int i = 0; i < m_count; ++i) {
              ContactPositionConstraint pc = m_positionConstraints[i];
  
              int indexA = pc.indexA;
              int indexB = pc.indexB;
  
              float mA = pc.invMassA;
              float iA = pc.invIA;
              final float localCenterAx = pc.localCenterA.x;
              final float localCenterAy = pc.localCenterA.y;
  
              float mB = pc.invMassB;
              float iB = pc.invIB;
              final float localCenterBx = pc.localCenterB.x;
              final float localCenterBy = pc.localCenterB.y;
  
              int pointCount = pc.pointCount;
  
              Vec2 cA = m_positions[indexA].c;
              float aA = m_positions[indexA].a;
  
              Vec2 cB = m_positions[indexB].c;
              float aB = m_positions[indexB].a;
  
              // Solve normal constraints
              for (int j = 0; j < pointCount; ++j) {
                  final Rotation xfAq = xfA.q;
                  final Rotation xfBq = xfB.q;
                  xfAq.set(aA);
                  xfBq.set(aB);
                  xfA.p.x = cA.x - xfAq.c * localCenterAx + xfAq.s * localCenterAy;
                  xfA.p.y = cA.y - xfAq.s * localCenterAx - xfAq.c * localCenterAy;
                  xfB.p.x = cB.x - xfBq.c * localCenterBx + xfBq.s * localCenterBy;
                  xfB.p.y = cB.y - xfBq.s * localCenterBx - xfBq.c * localCenterBy;
  
                  psolver.initialize(pc, xfA, xfB, j);
                  final Vec2 normal = psolver.normal;
                  final Vec2 point = psolver.point;
                  final float separation = psolver.separation;
  
                  float rAx = point.x - cA.x;
                  float rAy = point.y - cA.y;
                  float rBx = point.x - cB.x;
                  float rBy = point.y - cB.y;
  
                  // Track max constraint error.
                  minSeparation = Math.min(minSeparation, separation);
  
                  // Prevent large corrections and allow slop.
                  final float C =
                          FXGLMath.clamp(JBoxSettings.baumgarte * (separation + JBoxSettings.linearSlop),
                                  -JBoxSettings.maxLinearCorrection, 0.0f);
  
                  // Compute the effective mass.
                  final float rnA = rAx * normal.y - rAy * normal.x;
                  final float rnB = rBx * normal.y - rBy * normal.x;
                  final float K = mA + mB + iA * rnA * rnA + iB * rnB * rnB;
  
                  // Compute normal impulse
                  final float impulse = K > 0.0f ? -C / K : 0.0f;
  
                  float Px = normal.x * impulse;
                  float Py = normal.y * impulse;
  
                  cA.x -= Px * mA;
                  cA.y -= Py * mA;
                  aA -= iA * (rAx * Py - rAy * Px);
  
                  cB.x += Px * mB;
                  cB.y += Py * mB;
                  aB += iB * (rBx * Py - rBy * Px);
              }
  
              m_positions[indexA].a = aA;
              m_positions[indexB].a = aB;
          }
  
          // We can't expect minSpeparation >= -linearSlop because we don't
          // push the separation above -linearSlop.
          return minSeparation >= -3.0f * JBoxSettings.linearSlop;
      }
  
      // Sequential position solver for position constraints.
      public boolean solveTOIPositionConstraints(int toiIndexA, int toiIndexB) {
          float minSeparation = 0.0f;
  
          for (int i = 0; i < m_count; ++i) {
              ContactPositionConstraint pc = m_positionConstraints[i];
  
              int indexA = pc.indexA;
              int indexB = pc.indexB;
              Vec2 localCenterA = pc.localCenterA;
              Vec2 localCenterB = pc.localCenterB;
              final float localCenterAx = localCenterA.x;
              final float localCenterAy = localCenterA.y;
              final float localCenterBx = localCenterB.x;
              final float localCenterBy = localCenterB.y;
              int pointCount = pc.pointCount;
  
              float mA = 0.0f;
              float iA = 0.0f;
              if (indexA == toiIndexA || indexA == toiIndexB) {
                  mA = pc.invMassA;
                  iA = pc.invIA;
              }
  
              float mB = 0f;
              float iB = 0f;
              if (indexB == toiIndexA || indexB == toiIndexB) {
                  mB = pc.invMassB;
                  iB = pc.invIB;
              }
  
              Vec2 cA = m_positions[indexA].c;
              float aA = m_positions[indexA].a;
  
              Vec2 cB = m_positions[indexB].c;
              float aB = m_positions[indexB].a;
  
              // Solve normal constraints
              for (int j = 0; j < pointCount; ++j) {
                  final Rotation xfAq = xfA.q;
                  final Rotation xfBq = xfB.q;
                  xfAq.set(aA);
                  xfBq.set(aB);
                  xfA.p.x = cA.x - xfAq.c * localCenterAx + xfAq.s * localCenterAy;
                  xfA.p.y = cA.y - xfAq.s * localCenterAx - xfAq.c * localCenterAy;
                  xfB.p.x = cB.x - xfBq.c * localCenterBx + xfBq.s * localCenterBy;
                  xfB.p.y = cB.y - xfBq.s * localCenterBx - xfBq.c * localCenterBy;
  
                  final PositionSolverManifold psm = psolver;
                  psm.initialize(pc, xfA, xfB, j);
                  Vec2 normal = psm.normal;
  
                  Vec2 point = psm.point;
                  float separation = psm.separation;
  
                  float rAx = point.x - cA.x;
                  float rAy = point.y - cA.y;
                  float rBx = point.x - cB.x;
                  float rBy = point.y - cB.y;
  
                  // Track max constraint error.
                  minSeparation = Math.min(minSeparation, separation);
  
                  // Prevent large corrections and allow slop.
                  float C =
                          FXGLMath.clamp(JBoxSettings.toiBaugarte * (separation + JBoxSettings.linearSlop),
                                  -JBoxSettings.maxLinearCorrection, 0.0f);
  
                  // Compute the effective mass.
                  float rnA = rAx * normal.y - rAy * normal.x;
                  float rnB = rBx * normal.y - rBy * normal.x;
                  float K = mA + mB + iA * rnA * rnA + iB * rnB * rnB;
  
                  // Compute normal impulse
                  float impulse = K > 0.0f ? -C / K : 0.0f;
  
                  float Px = normal.x * impulse;
                  float Py = normal.y * impulse;
  
                  cA.x -= Px * mA;
                  cA.y -= Py * mA;
                  aA -= iA * (rAx * Py - rAy * Px);
  
                  cB.x += Px * mB;
                  cB.y += Py * mB;
                  aB += iB * (rBx * Py - rBy * Px);
              }
  
              m_positions[indexA].a = aA;
              m_positions[indexB].a = aB;
          }
  
          // We can't expect minSpeparation >= -_linearSlop because we don't
          // push the separation above -_linearSlop.
          return minSeparation >= -1.5f * JBoxSettings.linearSlop;
      }
  
      public static class ContactSolverDef {
          public TimeStep step;
          public Contact[] contacts;
          public int count;
          public Position[] positions;
          public Velocity[] velocities;
      }
  
      private static class PositionSolverManifold {
  
          final Vec2 normal = new Vec2();
          final Vec2 point = new Vec2();
          float separation;
  
          @SuppressWarnings("PMD.UselessParentheses")
          public void initialize(ContactPositionConstraint pc, Transform xfA, Transform xfB, int index) {
              assert pc.pointCount > 0;
  
              final Rotation xfAq = xfA.q;
              final Rotation xfBq = xfB.q;
              final Vec2 pcLocalPointsI = pc.localPoints[index];
              switch (pc.type) {
                  case CIRCLES: {
                      // Transform.mulToOutUnsafe(xfA, pc.localPoint, pointA);
                      // Transform.mulToOutUnsafe(xfB, pc.localPoints[0], pointB);
                      // normal.set(pointB).subLocal(pointA);
                      // normal.normalize();
                      //
                      // point.set(pointA).addLocal(pointB).mulLocal(.5f);
                      // temp.set(pointB).subLocal(pointA);
                      // separation = Vec2.dot(temp, normal) - pc.radiusA - pc.radiusB;
                      final Vec2 plocalPoint = pc.localPoint;
                      final Vec2 pLocalPoints0 = pc.localPoints[0];
                      final float pointAx = (xfAq.c * plocalPoint.x - xfAq.s * plocalPoint.y) + xfA.p.x;
                      final float pointAy = (xfAq.s * plocalPoint.x + xfAq.c * plocalPoint.y) + xfA.p.y;
                      final float pointBx = (xfBq.c * pLocalPoints0.x - xfBq.s * pLocalPoints0.y) + xfB.p.x;
                      final float pointBy = (xfBq.s * pLocalPoints0.x + xfBq.c * pLocalPoints0.y) + xfB.p.y;
                      normal.x = pointBx - pointAx;
                      normal.y = pointBy - pointAy;
                      normal.getLengthAndNormalize();
  
                      point.x = (pointAx + pointBx) * .5f;
                      point.y = (pointAy + pointBy) * .5f;
                      final float tempx = pointBx - pointAx;
                      final float tempy = pointBy - pointAy;
                      separation = tempx * normal.x + tempy * normal.y - pc.radiusA - pc.radiusB;
                      break;
                  }
  
                  case FACE_A: {
                      // Rot.mulToOutUnsafe(xfAq, pc.localNormal, normal);
                      // Transform.mulToOutUnsafe(xfA, pc.localPoint, planePoint);
                      //
                      // Transform.mulToOutUnsafe(xfB, pc.localPoints[index], clipPoint);
                      // temp.set(clipPoint).subLocal(planePoint);
                      // separation = Vec2.dot(temp, normal) - pc.radiusA - pc.radiusB;
                      // point.set(clipPoint);
                      final Vec2 pcLocalNormal = pc.localNormal;
                      final Vec2 pcLocalPoint = pc.localPoint;
                      normal.x = xfAq.c * pcLocalNormal.x - xfAq.s * pcLocalNormal.y;
                      normal.y = xfAq.s * pcLocalNormal.x + xfAq.c * pcLocalNormal.y;
                      final float planePointx = (xfAq.c * pcLocalPoint.x - xfAq.s * pcLocalPoint.y) + xfA.p.x;
                      final float planePointy = (xfAq.s * pcLocalPoint.x + xfAq.c * pcLocalPoint.y) + xfA.p.y;
  
                      final float clipPointx = (xfBq.c * pcLocalPointsI.x - xfBq.s * pcLocalPointsI.y) + xfB.p.x;
                      final float clipPointy = (xfBq.s * pcLocalPointsI.x + xfBq.c * pcLocalPointsI.y) + xfB.p.y;
                      final float tempx = clipPointx - planePointx;
                      final float tempy = clipPointy - planePointy;
                      separation = tempx * normal.x + tempy * normal.y - pc.radiusA - pc.radiusB;
                      point.x = clipPointx;
                      point.y = clipPointy;
                      break;
                  }
  
                  case FACE_B: {
                      // Rot.mulToOutUnsafe(xfBq, pc.localNormal, normal);
                      // Transform.mulToOutUnsafe(xfB, pc.localPoint, planePoint);
                      //
                      // Transform.mulToOutUnsafe(xfA, pcLocalPointsI, clipPoint);
                      // temp.set(clipPoint).subLocal(planePoint);
                      // separation = Vec2.dot(temp, normal) - pc.radiusA - pc.radiusB;
                      // point.set(clipPoint);
                      //
                      // // Ensure normal points from A to B
                      // normal.negateLocal();
                      final Vec2 pcLocalNormal = pc.localNormal;
                      final Vec2 pcLocalPoint = pc.localPoint;
                      normal.x = xfBq.c * pcLocalNormal.x - xfBq.s * pcLocalNormal.y;
                      normal.y = xfBq.s * pcLocalNormal.x + xfBq.c * pcLocalNormal.y;
                      final float planePointx = (xfBq.c * pcLocalPoint.x - xfBq.s * pcLocalPoint.y) + xfB.p.x;
                      final float planePointy = (xfBq.s * pcLocalPoint.x + xfBq.c * pcLocalPoint.y) + xfB.p.y;
  
                      final float clipPointx = (xfAq.c * pcLocalPointsI.x - xfAq.s * pcLocalPointsI.y) + xfA.p.x;
                      final float clipPointy = (xfAq.s * pcLocalPointsI.x + xfAq.c * pcLocalPointsI.y) + xfA.p.y;
                      final float tempx = clipPointx - planePointx;
                      final float tempy = clipPointy - planePointy;
                      separation = tempx * normal.x + tempy * normal.y - pc.radiusA - pc.radiusB;
                      point.x = clipPointx;
                      point.y = clipPointy;
                      normal.x *= -1;
                      normal.y *= -1;
                  }
                  break;
              }
          }
      }
  }