public void readCache(SimplexCache cache, DistanceProxy proxyA, Transform transformA,
DistanceProxy proxyB, Transform transformB)
{
// Copy data from cache.
m_count = cache.count;
for (int i = 0; i < m_count; ++i)
{
SimplexVertex v = vertices[i];
v.indexA = cache.indexA[i];
v.indexB = cache.indexB[i];
Vec2 wALocal = proxyA.getVertex(v.indexA);
Vec2 wBLocal = proxyB.getVertex(v.indexB);
Transform.mulToOutUnsafe(transformA, wALocal, v.wA);
Transform.mulToOutUnsafe(transformB, wBLocal, v.wB);
v.w.set(v.wB).subLocal(v.wA);
v.a = 0.0d;
}
// Compute the new simplex metric, if it is substantially different than
// old metric then flush the simplex.
if (m_count > 1)
{
double metric1 = cache.metric;
double metric2 = getMetric();
if (metric2 < 0.5d * metric1 || 2.0d * metric1 < metric2 || metric2 < Settings.EPSILON)
{
// Reset the simplex.
m_count = 0;
}
}
// If the cache is empty or invalid ...
if (m_count == 0)
{
SimplexVertex v = vertices[0];
v.indexA = 0;
v.indexB = 0;
Vec2 wALocal = proxyA.getVertex(0);
Vec2 wBLocal = proxyB.getVertex(0);
Transform.mulToOutUnsafe(transformA, wALocal, v.wA);
Transform.mulToOutUnsafe(transformB, wBLocal, v.wB);
v.w.set(v.wB).subLocal(v.wA);
m_count = 1;
}
}
// TODO_ERIN might not need to return the separation
public double initialize(SimplexCache cache, DistanceProxy proxyA, Sweep sweepA,
DistanceProxy proxyB, Sweep sweepB, double t1)
{
m_proxyA = proxyA;
m_proxyB = proxyB;
int count = cache.count;
m_sweepA = sweepA;
m_sweepB = sweepB;
m_sweepA.getTransform(xfa, t1);
m_sweepB.getTransform(xfb, t1);
// log.debug("initializing separation." +
// "cache: "+cache.count+"-"+cache.metric+"-"+cache.indexA+"-"+cache.indexB+""
// "distance: "+proxyA.
if (count == 1)
{
m_type = Type.POINTS;
/*
* Vec2 localPointA = m_proxyA.GetVertex(cache.indexA[0]); Vec2 localPointB =
* m_proxyB.GetVertex(cache.indexB[0]); Vec2 pointA = Mul(transformA, localPointA); Vec2
* pointB = Mul(transformB, localPointB); m_axis = pointB - pointA; m_axis.Normalize();
*/
localPointA.set(m_proxyA.getVertex(cache.indexA[0]));
localPointB.set(m_proxyB.getVertex(cache.indexB[0]));
Transform.mulToOutUnsafe(xfa, localPointA, pointA);
Transform.mulToOutUnsafe(xfb, localPointB, pointB);
m_axis.set(pointB).subLocal(pointA);
double s = m_axis.normalize();
return(s);
}
if (cache.indexA[0] == cache.indexA[1])
{
// Two points on B and one on A.
m_type = Type.FACE_B;
localPointB1.set(m_proxyB.getVertex(cache.indexB[0]));
localPointB2.set(m_proxyB.getVertex(cache.indexB[1]));
temp.set(localPointB2).subLocal(localPointB1);
Vec2.crossToOutUnsafe(temp, 1d, m_axis);
m_axis.normalize();
Rot.mulToOutUnsafe(xfb.q, m_axis, normal);
m_localPoint.set(localPointB1).addLocal(localPointB2).mulLocal(.5d);
Transform.mulToOutUnsafe(xfb, m_localPoint, pointB);
localPointA.set(proxyA.getVertex(cache.indexA[0]));
Transform.mulToOutUnsafe(xfa, localPointA, pointA);
temp.set(pointA).subLocal(pointB);
double s = Vec2.dot(temp, normal);
if (s < 0.0d)
{
m_axis.negateLocal();
s = -s;
}
return(s);
}
else
{
// Two points on A and one or two points on B.
m_type = Type.FACE_A;
localPointA1.set(m_proxyA.getVertex(cache.indexA[0]));
localPointA2.set(m_proxyA.getVertex(cache.indexA[1]));
temp.set(localPointA2).subLocal(localPointA1);
Vec2.crossToOutUnsafe(temp, 1.0d, m_axis);
m_axis.normalize();
Rot.mulToOutUnsafe(xfa.q, m_axis, normal);
m_localPoint.set(localPointA1).addLocal(localPointA2).mulLocal(.5d);
Transform.mulToOutUnsafe(xfa, m_localPoint, pointA);
localPointB.set(m_proxyB.getVertex(cache.indexB[0]));
Transform.mulToOutUnsafe(xfb, localPointB, pointB);
temp.set(pointB).subLocal(pointA);
double s = Vec2.dot(temp, normal);
if (s < 0.0d)
{
m_axis.negateLocal();
s = -s;
}
return(s);
}
}
/**
* Compute the upper bound on time before two shapes penetrate. Time is represented as a fraction
* between [0,tMax]. This uses a swept separating axis and may miss some intermediate,
* non-tunneling collision. If you change the time interval, you should call this function again.
* Note: use Distance to compute the contact point and normal at the time of impact.
*
* @param output
* @param input
*/
public void timeOfImpact(TOIOutput output, TOIInput input)
{
// CCD via the local separating axis method. This seeks progression
// by computing the largest time at which separation is maintained.
++toiCalls;
output.state = TOIOutputState.UNKNOWN;
output.t = input.tMax;
DistanceProxy proxyA = input.proxyA;
DistanceProxy proxyB = input.proxyB;
sweepA.set(input.sweepA);
sweepB.set(input.sweepB);
// Large rotations can make the root finder fail, so we normalize the
// sweep angles.
sweepA.normalize();
sweepB.normalize();
double tMax = input.tMax;
double totalRadius = proxyA.m_radius + proxyB.m_radius;
// djm: whats with all these constants?
double target = MathUtils.max(Settings.linearSlop, totalRadius - 3.0d * Settings.linearSlop);
double tolerance = 0.25d * Settings.linearSlop;
double t1 = 0d;
int iter = 0;
cache.count = 0;
distanceInput.proxyA = input.proxyA;
distanceInput.proxyB = input.proxyB;
distanceInput.useRadii = false;
// The outer loop progressively attempts to compute new separating axes.
// This loop terminates when an axis is repeated (no progress is made).
for (;;)
{
sweepA.getTransform(xfA, t1);
sweepB.getTransform(xfB, t1);
// System.out.printf("sweepA: %f, %f, sweepB: %f, %f",
// sweepA.c.x, sweepA.c.y, sweepB.c.x, sweepB.c.y);
// Get the distance between shapes. We can also use the results
// to get a separating axis
distanceInput.transformA = xfA;
distanceInput.transformB = xfB;
pool.getDistance().distance(distanceOutput, cache, distanceInput);
// System.out.printf("Dist: %f at points %f, %f and %f, %f. %d iterations",
// distanceOutput.distance, distanceOutput.pointA.x, distanceOutput.pointA.y,
// distanceOutput.pointB.x, distanceOutput.pointB.y,
// distanceOutput.iterations);
// If the shapes are overlapped, we give up on continuous collision.
if (distanceOutput.distance <= 0d)
{
// System.out.println("failure, overlapped");
// Failure!
output.state = TOIOutputState.OVERLAPPED;
output.t = 0d;
break;
}
if (distanceOutput.distance < target + tolerance)
{
// System.out.println("touching, victory");
// Victory!
output.state = TOIOutputState.TOUCHING;
output.t = t1;
break;
}
// Initialize the separating axis.
fcn.initialize(cache, proxyA, sweepA, proxyB, sweepB, t1);
// Compute the TOI on the separating axis. We do this by successively
// resolving the deepest point. This loop is bounded by the number of
// vertices.
bool done = false;
double t2 = tMax;
int pushBackIter = 0;
for (;;)
{
// Find the deepest point at t2. Store the witness point indices.
double s2 = fcn.findMinSeparation(indexes, t2);
// System.out.printf("s2: %f", s2);
// Is the configuration separated?
if (s2 > target + tolerance)
{
// Victory!
// System.out.println("separated");
output.state = TOIOutputState.SEPARATED;
output.t = tMax;
done = true;
break;
}
// Has the separation reached tolerance?
if (s2 > target - tolerance)
{
// System.out.println("advancing");
// Advance the sweeps
t1 = t2;
break;
}
// Compute the initial separation of the witness points.
double s1 = fcn.evaluate(indexes[0], indexes[1], t1);
// Check for initial overlap. This might happen if the root finder
// runs out of iterations.
// System.out.printf("s1: %f, target: %f, tolerance: %f", s1, target,
// tolerance);
if (s1 < target - tolerance)
{
// System.out.println("failed?");
output.state = TOIOutputState.FAILED;
output.t = t1;
done = true;
break;
}
// Check for touching
if (s1 <= target + tolerance)
{
// System.out.println("touching?");
// Victory! t1 should hold the TOI (could be 0.0).
output.state = TOIOutputState.TOUCHING;
output.t = t1;
done = true;
break;
}
// Compute 1D root of: f(x) - target = 0
int rootIterCount = 0;
double a1 = t1, a2 = t2;
for (;;)
{
// Use a mix of the secant rule and bisection.
double t;
if ((rootIterCount & 1) == 1)
{
// Secant rule to improve convergence.
t = a1 + (target - s1) * (a2 - a1) / (s2 - s1);
}
else
{
// Bisection to guarantee progress.
t = 0.5d * (a1 + a2);
}
double s = fcn.evaluate(indexes[0], indexes[1], t);
if (MathUtils.abs(s - target) < tolerance)
{
// t2 holds a tentative value for t1
t2 = t;
break;
}
// Ensure we continue to bracket the root.
if (s > target)
{
a1 = t;
s1 = s;
}
else
{
a2 = t;
s2 = s;
}
++rootIterCount;
++toiRootIters;
// djm: whats with this? put in settings?
if (rootIterCount == 50)
{
break;
}
}
toiMaxRootIters = MathUtils.max(toiMaxRootIters, rootIterCount);
++pushBackIter;
if (pushBackIter == Settings.maxPolygonVertices)
{
break;
}
}
++iter;
++toiIters;
if (done)
{
// System.out.println("done");
break;
}
if (iter == MAX_ITERATIONS)
{
// System.out.println("failed, root finder stuck");
// Root finder got stuck. Semi-victory.
output.state = TOIOutputState.FAILED;
output.t = t1;
break;
}
}
// System.out.printf("sweeps: %f, %f, %f; %f, %f, %f", input.s)
toiMaxIters = MathUtils.max(toiMaxIters, iter);
}
/**
* Compute the closest points between two shapes. Supports any combination of: CircleShape and
* PolygonShape. The simplex cache is input/output. On the first call set SimplexCache.count to
* zero.
*
* @param output
* @param cache
* @param input
*/
public void distance(DistanceOutput output, SimplexCache cache,
DistanceInput input)
{
GJK_CALLS++;
DistanceProxy proxyA = input.proxyA;
DistanceProxy proxyB = input.proxyB;
Transform transformA = input.transformA;
Transform transformB = input.transformB;
// Initialize the simplex.
simplex.readCache(cache, proxyA, transformA, proxyB, transformB);
// Get simplex vertices as an array.
SimplexVertex[] vertices = simplex.vertices;
// These store the vertices of the last simplex so that we
// can check for duplicates and prevent cycling.
// (pooled above)
int saveCount = 0;
simplex.getClosestPoint(closestPoint);
double distanceSqr1 = closestPoint.lengthSquared();
double distanceSqr2 = distanceSqr1;
// Main iteration loop
int iter = 0;
while (iter < GJK_MAX_ITERS)
{
// Copy simplex so we can identify duplicates.
saveCount = simplex.m_count;
for (int i = 0; i < saveCount; i++)
{
saveA[i] = vertices[i].indexA;
saveB[i] = vertices[i].indexB;
}
switch (simplex.m_count)
{
case 1:
break;
case 2:
simplex.solve2();
break;
case 3:
simplex.solve3();
break;
}
// If we have 3 points, then the origin is in the corresponding triangle.
if (simplex.m_count == 3)
{
break;
}
// Compute closest point.
simplex.getClosestPoint(closestPoint);
distanceSqr2 = closestPoint.lengthSquared();
// ensure progress
if (distanceSqr2 >= distanceSqr1)
{
// break;
}
distanceSqr1 = distanceSqr2;
// get search direction;
simplex.getSearchDirection(d);
// Ensure the search direction is numerically fit.
if (d.lengthSquared() < Settings.EPSILON * Settings.EPSILON)
{
// The origin is probably contained by a line segment
// or triangle. Thus the shapes are overlapped.
// We can't return zero here even though there may be overlap.
// In case the simplex is a point, segment, or triangle it is difficult
// to determine if the origin is contained in the CSO or very close to it.
break;
}
/*
* SimplexVertex* vertex = vertices + simplex.m_count; vertex.indexA =
* proxyA.GetSupport(MulT(transformA.R, -d)); vertex.wA = Mul(transformA,
* proxyA.GetVertex(vertex.indexA)); Vec2 wBLocal; vertex.indexB =
* proxyB.GetSupport(MulT(transformB.R, d)); vertex.wB = Mul(transformB,
* proxyB.GetVertex(vertex.indexB)); vertex.w = vertex.wB - vertex.wA;
*/
// Compute a tentative new simplex vertex using support points.
SimplexVertex vertex = vertices[simplex.m_count];
Rot.mulTransUnsafe(transformA.q, d.negateLocal(), temp);
vertex.indexA = proxyA.getSupport(temp);
Transform.mulToOutUnsafe(transformA, proxyA.getVertex(vertex.indexA), vertex.wA);
// Vec2 wBLocal;
Rot.mulTransUnsafe(transformB.q, d.negateLocal(), temp);
vertex.indexB = proxyB.getSupport(temp);
Transform.mulToOutUnsafe(transformB, proxyB.getVertex(vertex.indexB), vertex.wB);
vertex.w.set(vertex.wB).subLocal(vertex.wA);
// Iteration count is equated to the number of support point calls.
++iter;
++GJK_ITERS;
// Check for duplicate support points. This is the main termination criteria.
bool duplicate = false;
for (int i = 0; i < saveCount; ++i)
{
if (vertex.indexA == saveA[i] && vertex.indexB == saveB[i])
{
duplicate = true;
break;
}
}
// If we found a duplicate support point we must exit to avoid cycling.
if (duplicate)
{
break;
}
// New vertex is ok and needed.
++simplex.m_count;
}
GJK_MAX_ITERS = MathUtils.max(GJK_MAX_ITERS, iter);
// Prepare output.
simplex.getWitnessPoints(output.pointA, output.pointB);
output.distance = MathUtils.distance(output.pointA, output.pointB);
output.iterations = iter;
// Cache the simplex.
simplex.writeCache(cache);
// Apply radii if requested.
if (input.useRadii)
{
double rA = proxyA.m_radius;
double rB = proxyB.m_radius;
if (output.distance > rA + rB && output.distance > Settings.EPSILON)
{
// Shapes are still no overlapped.
// Move the witness points to the out_er surface.
output.distance -= rA + rB;
normal.set(output.pointB).subLocal(output.pointA);
normal.normalize();
temp.set(normal).mulLocal(rA);
output.pointA.addLocal(temp);
temp.set(normal).mulLocal(rB);
output.pointB.subLocal(temp);
}
else
{
// Shapes are overlapped when radii are considered.
// Move the witness points to the middle.
// Vec2 p = 0.5d * (output.pointA + output.pointB);
output.pointA.addLocal(output.pointB).mulLocal(.5d);
output.pointB.set(output.pointA);
output.distance = 0.0d;
}
}
}