/*******************************************************************************
* Copyright (c) 2013, Daniel Murphy
* All rights reserved.
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* are permitted provided that the following conditions are met:
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package org.jbox2d.dynamics.contacts;
import org.jbox2d.collision.Manifold;
import org.jbox2d.collision.ManifoldPoint;
import org.jbox2d.collision.WorldManifold;
import org.jbox2d.collision.shapes.Shape;
import org.jbox2d.common.Mat22;
import org.jbox2d.common.MathUtils;
import org.jbox2d.common.Rot;
import org.jbox2d.common.Settings;
import org.jbox2d.common.Transform;
import org.jbox2d.common.Vec2;
import org.jbox2d.dynamics.Body;
import org.jbox2d.dynamics.Fixture;
import org.jbox2d.dynamics.TimeStep;
import org.jbox2d.dynamics.contacts.ContactVelocityConstraint.VelocityConstraintPoint;
/**
* @author Daniel
*/
public class ContactSolver {
public static final boolean DEBUG_SOLVER = false;
public static final float k_errorTol = 1e-3f;
/**
* For each solver, this is the initial number of constraints in the array, which expands as
* needed.
*/
public static final int INITIAL_NUM_CONSTRAINTS = 256;
/**
* Ensure a reasonable condition number. for the block solver
*/
public static final float k_maxConditionNumber = 100.0f;
public TimeStep m_step;
public Position[] m_positions;
public Velocity[] m_velocities;
public ContactPositionConstraint[] m_positionConstraints;
public ContactVelocityConstraint[] m_velocityConstraints;
public Contact[] m_contacts;
public int m_count;
public ContactSolver() {
m_positionConstraints = new ContactPositionConstraint[INITIAL_NUM_CONSTRAINTS];
m_velocityConstraints = new ContactVelocityConstraint[INITIAL_NUM_CONSTRAINTS];
for (int i = 0; i < INITIAL_NUM_CONSTRAINTS; i++) {
m_positionConstraints[i] = new ContactPositionConstraint();
m_velocityConstraints[i] = new ContactVelocityConstraint();
}
}
public final void init(ContactSolverDef def) {
// System.out.println("Initializing contact solver");
m_step = def.step;
m_count = def.count;
if (m_positionConstraints.length < m_count) {
ContactPositionConstraint[] old = m_positionConstraints;
m_positionConstraints = new ContactPositionConstraint[MathUtils.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[MathUtils.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) {
// System.out.println("contacts: " + m_count);
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.m_radius;
final float radiusB = shapeB.m_radius;
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.m_friction;
vc.restitution = contact.m_restitution;
vc.tangentSpeed = contact.m_tangentSpeed;
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;
// System.out.println("contact point count: " + pointCount);
for (int j = 0; j < pointCount; j++) {
ManifoldPoint cp = manifold.points[j];
VelocityConstraintPoint vcp = vc.points[j];
if (m_step.warmStarting) {
// assert(cp.normalImpulse == 0);
// System.out.println("contact normal impulse: " + cp.normalImpulse);
vcp.normalImpulse = m_step.dtRatio * cp.normalImpulse;
vcp.tangentImpulse = m_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 final 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 Rot xfAq = xfA.q;
final Rot 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.x = worldManifold.normal.x;
vcnormal.y = worldManifold.normal.y;
int pointCount = vc.pointCount;
for (int j = 0; j < pointCount; ++j) {
VelocityConstraintPoint vcp = vc.points[j];
Vec2 wmPj = worldManifold.points[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 < -Settings.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;
}
}
}
}
public final 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 =
MathUtils.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;
/*
* #if B2_DEBUG_SOLVER == 1 // Postconditions dv1 = vB + Cross(wB, cp1.rB) - vA -
* Cross(wA, cp1.rA); dv2 = vB + Cross(wB, cp2.rB) - vA - Cross(wA, cp2.rA);
*
* // Compute normal velocity vn1 = Dot(dv1, normal); vn2 = Dot(dv2, normal);
*
* assert(Abs(vn1 - cp1.velocityBias) < k_errorTol); assert(Abs(vn2 - cp2.velocityBias)
* < k_errorTol); #endif
*/
if (DEBUG_SOLVER) {
// Postconditions
Vec2 dv1 = vB.add(Vec2.cross(wB, cp1rB).subLocal(vA).subLocal(Vec2.cross(wA, cp1rA)));
Vec2 dv2 = vB.add(Vec2.cross(wB, cp2rB).subLocal(vA).subLocal(Vec2.cross(wA, cp2rA)));
// Compute normal velocity
vn1 = Vec2.dot(dv1, normal);
vn2 = Vec2.dot(dv2, normal);
assert (MathUtils.abs(vn1 - cp1.velocityBias) < k_errorTol);
assert (MathUtils.abs(vn2 - cp2.velocityBias) < k_errorTol);
}
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;
/*
* #if B2_DEBUG_SOLVER == 1 // Postconditions dv1 = vB + Cross(wB, cp1.rB) - vA -
* Cross(wA, cp1.rA);
*
* // Compute normal velocity vn1 = Dot(dv1, normal);
*
* assert(Abs(vn1 - cp1.velocityBias) < k_errorTol); #endif
*/
if (DEBUG_SOLVER) {
// Postconditions
Vec2 dv1 = vB.add(Vec2.cross(wB, cp1rB).subLocal(vA).subLocal(Vec2.cross(wA, cp1rA)));
// Compute normal velocity
vn1 = Vec2.dot(dv1, normal);
assert (MathUtils.abs(vn1 - cp1.velocityBias) < k_errorTol);
}
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;
/*
* #if B2_DEBUG_SOLVER == 1 // Postconditions dv2 = vB + Cross(wB, cp2.rB) - vA -
* Cross(wA, cp2.rA);
*
* // Compute normal velocity vn2 = Dot(dv2, normal);
*
* assert(Abs(vn2 - cp2.velocityBias) < k_errorTol); #endif
*/
if (DEBUG_SOLVER) {
// Postconditions
Vec2 dv2 = vB.add(Vec2.cross(wB, cp2rB).subLocal(vA).subLocal(Vec2.cross(wA, cp2rA)));
// Compute normal velocity
vn2 = Vec2.dot(dv2, normal);
assert (MathUtils.abs(vn2 - cp2.velocityBias) < k_errorTol);
}
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 final 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;
Vec2 localCenterA = pc.localCenterA;
final float localCenterAx = localCenterA.x;
final float localCenterAy = localCenterA.y;
float mB = pc.invMassB;
float iB = pc.invIB;
Vec2 localCenterB = pc.localCenterB;
final float localCenterBx = localCenterB.x;
final float localCenterBy = 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 Rot xfAq = xfA.q;
final Rot 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);
final Vec2 normal = psm.normal;
final Vec2 point = psm.point;
final 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 = MathUtils.min(minSeparation, separation);
// Prevent large corrections and allow slop.
final float C =
MathUtils.clamp(Settings.baumgarte * (separation + Settings.linearSlop),
-Settings.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].c.set(cA);
m_positions[indexA].a = aA;
// m_positions[indexB].c.set(cB);
m_positions[indexB].a = aB;
}
// We can't expect minSpeparation >= -linearSlop because we don't
// push the separation above -linearSlop.
return minSeparation >= -3.0f * Settings.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 Rot xfAq = xfA.q;
final Rot 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 = MathUtils.min(minSeparation, separation);
// Prevent large corrections and allow slop.
float C =
MathUtils.clamp(Settings.toiBaugarte * (separation + Settings.linearSlop),
-Settings.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].c.set(cA);
m_positions[indexA].a = aA;
// m_positions[indexB].c.set(cB);
m_positions[indexB].a = aB;
}
// We can't expect minSpeparation >= -_linearSlop because we don't
// push the separation above -_linearSlop.
return minSeparation >= -1.5f * Settings.linearSlop;
}
public static class ContactSolverDef {
public TimeStep step;
public Contact[] contacts;
public int count;
public Position[] positions;
public Velocity[] velocities;
}
}
class PositionSolverManifold {
public final Vec2 normal = new Vec2();
public final Vec2 point = new Vec2();
public float separation;
public void initialize(ContactPositionConstraint pc, Transform xfA, Transform xfB, int index) {
assert (pc.pointCount > 0);
final Rot xfAq = xfA.q;
final Rot 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.normalize();
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;
}
}
}