public override void Update(GameSettings settings, GameTime gameTime)
{
base.Update(settings, gameTime);
DistanceInput input = new DistanceInput();
input.ProxyA.Set(_polygonA, 0);
input.ProxyB.Set(_polygonB, 0);
input.TransformA = _transformA;
input.TransformB = _transformB;
input.UseRadii = true;
SimplexCache cache;
cache.Count = 0;
DistanceOutput output;
Distance.ComputeDistance(out output, out cache, input);
DebugView.DrawString(50, TextLine, "Distance = {0:n7}", output.Distance);
TextLine += 15;
DebugView.DrawString(50, TextLine, "Iterations = {0:n0}", output.Iterations);
TextLine += 15;
DebugView.BeginCustomDraw();
{
Color color = new Color(0.9f, 0.9f, 0.9f);
CCVector2[] v = new CCVector2[Settings.MaxPolygonVertices];
for (int i = 0; i < _polygonA.Vertices.Count; ++i)
{
v[i] = (CCVector2)MathUtils.Multiply(ref _transformA, _polygonA.Vertices[i]);
}
DebugView.DrawPolygon(v, _polygonA.Vertices.Count, color);
for (int i = 0; i < _polygonB.Vertices.Count; ++i)
{
v[i] = (CCVector2)MathUtils.Multiply(ref _transformB, _polygonB.Vertices[i]);
}
DebugView.DrawPolygon(v, _polygonB.Vertices.Count, color);
}
Vector2 x1 = output.PointA;
Vector2 x2 = output.PointB;
DebugView.DrawPoint(x1, 0.5f, new Color(1.0f, 0.0f, 0.0f));
DebugView.DrawPoint(x2, 0.5f, new Color(1.0f, 0.0f, 0.0f));
DebugView.DrawSegment(x1, x2, new Color(1.0f, 1.0f, 0.0f));
DebugView.EndCustomDraw();
}
public static void ComputeDistance(out DistanceOutput output,
out SimplexCache cache,
DistanceInput input)
{
cache = new SimplexCache();
++GJKCalls;
// Initialize the simplex.
Simplex simplex = new Simplex();
simplex.ReadCache(ref cache, input.ProxyA, ref input.TransformA, input.ProxyB, ref input.TransformB);
// Get simplex vertices as an array.
const int k_maxIters = 20;
// These store the vertices of the last simplex so that we
// can check for duplicates and prevent cycling.
FixedArray3<int> saveA = new FixedArray3<int>();
FixedArray3<int> saveB = new FixedArray3<int>();
Vector2 closestPoint = simplex.GetClosestPoint();
float distanceSqr1 = closestPoint.LengthSquared();
float distanceSqr2 = distanceSqr1;
// Main iteration loop.
int iter = 0;
while (iter < k_maxIters)
{
// Copy simplex so we can identify duplicates.
int saveCount = simplex.Count;
for (int i = 0; i < saveCount; ++i)
{
saveA[i] = simplex.V[i].IndexA;
saveB[i] = simplex.V[i].IndexB;
}
switch (simplex.Count)
{
case 1:
break;
case 2:
simplex.Solve2();
break;
case 3:
simplex.Solve3();
break;
default:
Debug.Assert(false);
break;
}
// If we have 3 points, then the origin is in the corresponding triangle.
if (simplex.Count == 3)
{
break;
}
// Compute closest point.
Vector2 p = simplex.GetClosestPoint();
distanceSqr2 = p.LengthSquared();
// Ensure progress
if (distanceSqr2 >= distanceSqr1)
{
//break;
}
distanceSqr1 = distanceSqr2;
// Get search direction.
Vector2 d = simplex.GetSearchDirection();
// 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;
}
// Compute a tentative new simplex vertex using support points.
SimplexVertex vertex = simplex.V[simplex.Count];
vertex.IndexA = input.ProxyA.GetSupport(MathUtils.MultiplyT(ref input.TransformA.R, -d));
vertex.WA = MathUtils.Multiply(ref input.TransformA, input.ProxyA.Vertices[vertex.IndexA]);
vertex.IndexB = input.ProxyB.GetSupport(MathUtils.MultiplyT(ref input.TransformB.R, d));
vertex.WB = MathUtils.Multiply(ref input.TransformB, input.ProxyB.Vertices[vertex.IndexB]);
vertex.W = vertex.WB - vertex.WA;
simplex.V[simplex.Count] = vertex;
// Iteration count is equated to the number of support point calls.
++iter;
++GJKIters;
// 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.Count;
}
GJKMaxIters = Math.Max(GJKMaxIters, iter);
// Prepare output.
simplex.GetWitnessPoints(out output.PointA, out output.PointB);
output.Distance = (output.PointA - output.PointB).Length();
output.Iterations = iter;
// Cache the simplex.
simplex.WriteCache(ref cache);
// Apply radii if requested.
if (input.UseRadii)
{
float rA = input.ProxyA.Radius;
float rB = input.ProxyB.Radius;
if (output.Distance > rA + rB && output.Distance > Settings.Epsilon)
{
// Shapes are still no overlapped.
// Move the witness points to the outer surface.
output.Distance -= rA + rB;
Vector2 normal = output.PointB - output.PointA;
normal.Normalize();
output.PointA += rA * normal;
output.PointB -= rB * normal;
}
else
{
// Shapes are overlapped when radii are considered.
// Move the witness points to the middle.
Vector2 p = 0.5f * (output.PointA + output.PointB);
output.PointA = p;
output.PointB = p;
output.Distance = 0.0f;
}
}
}
public static void ComputeDistance(out DistanceOutput output, out SimplexCache cache, DistanceInput input)
{
cache = new SimplexCache();
if (Settings.EnableDiagnostics) //FPE: We only gather diagnostics when enabled
{
++GJKCalls;
}
// Initialize the simplex.
Simplex simplex = new Simplex();
simplex.ReadCache(ref cache, input.ProxyA, ref input.TransformA, input.ProxyB, ref input.TransformB);
// These store the vertices of the last simplex so that we
// can check for duplicates and prevent cycling.
FixedArray3 <int> saveA = new FixedArray3 <int>();
FixedArray3 <int> saveB = new FixedArray3 <int>();
//float distanceSqr1 = Settings.MaxFloat;
// Main iteration loop.
int iter = 0;
while (iter < Settings.MaxGJKIterations)
{
// Copy simplex so we can identify duplicates.
int saveCount = simplex.Count;
for (int i = 0; i < saveCount; ++i)
{
saveA[i] = simplex.V[i].IndexA;
saveB[i] = simplex.V[i].IndexB;
}
switch (simplex.Count)
{
case 1:
break;
case 2:
simplex.Solve2();
break;
case 3:
simplex.Solve3();
break;
default:
Debug.Assert(false);
break;
}
// If we have 3 points, then the origin is in the corresponding triangle.
if (simplex.Count == 3)
{
break;
}
//FPE: This code was not used anyway.
// Compute closest point.
//Vector2 p = simplex.GetClosestPoint();
//float distanceSqr2 = p.LengthSquared();
// Ensure progress
//if (distanceSqr2 >= distanceSqr1)
//{
//break;
//}
//distanceSqr1 = distanceSqr2;
// Get search direction.
Vector2 d = simplex.GetSearchDirection();
// 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;
}
// Compute a tentative new simplex vertex using support points.
SimplexVertex vertex = simplex.V[simplex.Count];
vertex.IndexA = input.ProxyA.GetSupport(MathUtils.MulT(input.TransformA.q, -d));
vertex.WA = MathUtils.Mul(ref input.TransformA, input.ProxyA.Vertices[vertex.IndexA]);
vertex.IndexB = input.ProxyB.GetSupport(MathUtils.MulT(input.TransformB.q, d));
vertex.WB = MathUtils.Mul(ref input.TransformB, input.ProxyB.Vertices[vertex.IndexB]);
vertex.W = vertex.WB - vertex.WA;
simplex.V[simplex.Count] = vertex;
// Iteration count is equated to the number of support point calls.
++iter;
if (Settings.EnableDiagnostics) //FPE: We only gather diagnostics when enabled
{
++GJKIters;
}
// 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.Count;
}
if (Settings.EnableDiagnostics) //FPE: We only gather diagnostics when enabled
{
GJKMaxIters = Math.Max(GJKMaxIters, iter);
}
// Prepare output.
simplex.GetWitnessPoints(out output.PointA, out output.PointB);
output.Distance = (output.PointA - output.PointB).Length();
output.Iterations = iter;
// Cache the simplex.
simplex.WriteCache(ref cache);
// Apply radii if requested.
if (input.UseRadii)
{
float rA = input.ProxyA.Radius;
float rB = input.ProxyB.Radius;
if (output.Distance > rA + rB && output.Distance > Settings.Epsilon)
{
// Shapes are still no overlapped.
// Move the witness points to the outer surface.
output.Distance -= rA + rB;
Vector2 normal = output.PointB - output.PointA;
normal.Normalize();
output.PointA += rA * normal;
output.PointB -= rB * normal;
}
else
{
// Shapes are overlapped when radii are considered.
// Move the witness points to the middle.
Vector2 p = 0.5f * (output.PointA + output.PointB);
output.PointA = p;
output.PointB = p;
output.Distance = 0.0f;
}
}
}
/// <summary>
/// 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.
/// </summary>
/// <param name="output">The output.</param>
/// <param name="input">The input.</param>
public static void CalculateTimeOfImpact(out TOIOutput output, ref TOIInput input)
{
if (Settings.EnableDiagnostics) //FPE: We only gather diagnostics when enabled
{
++TOICalls;
}
output = new TOIOutput();
output.State = TOIOutputState.Unknown;
output.T = input.TMax;
Sweep sweepA = input.SweepA;
Sweep sweepB = input.SweepB;
// Large rotations can make the root finder fail, so we normalize the
// sweep angles.
sweepA.Normalize();
sweepB.Normalize();
float tMax = input.TMax;
float totalRadius = input.ProxyA.Radius + input.ProxyB.Radius;
float target = Math.Max(Settings.LinearSlop, totalRadius - 3.0f * Settings.LinearSlop);
const float tolerance = 0.25f * Settings.LinearSlop;
Debug.Assert(target > tolerance);
float t1 = 0.0f;
const int k_maxIterations = 20;
int iter = 0;
// Prepare input for distance query.
DistanceInput distanceInput = new DistanceInput();
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 (; ;)
{
Transform xfA, xfB;
sweepA.GetTransform(out xfA, t1);
sweepB.GetTransform(out xfB, t1);
// Get the distance between shapes. We can also use the results
// to get a separating axis.
distanceInput.TransformA = xfA;
distanceInput.TransformB = xfB;
DistanceOutput distanceOutput;
SimplexCache cache;
Distance.ComputeDistance(out distanceOutput, out cache, distanceInput);
// If the shapes are overlapped, we give up on continuous collision.
if (distanceOutput.Distance <= 0.0f)
{
// Failure!
output.State = TOIOutputState.Overlapped;
output.T = 0.0f;
break;
}
if (distanceOutput.Distance < target + tolerance)
{
// Victory!
output.State = TOIOutputState.Touching;
output.T = t1;
break;
}
SeparationFunction.Set(ref cache, ref input.ProxyA, ref sweepA, ref input.ProxyB, ref 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;
float t2 = tMax;
int pushBackIter = 0;
for (; ;)
{
// Find the deepest point at t2. Store the witness point indices.
int indexA, indexB;
float s2 = SeparationFunction.FindMinSeparation(out indexA, out indexB, t2);
// Is the final configuration separated?
if (s2 > target + tolerance)
{
// Victory!
output.State = TOIOutputState.Seperated;
output.T = tMax;
done = true;
break;
}
// Has the separation reached tolerance?
if (s2 > target - tolerance)
{
// Advance the sweeps
t1 = t2;
break;
}
// Compute the initial separation of the witness points.
float s1 = SeparationFunction.Evaluate(indexA, indexB, t1);
// Check for initial overlap. This might happen if the root finder
// runs out of iterations.
if (s1 < target - tolerance)
{
output.State = TOIOutputState.Failed;
output.T = t1;
done = true;
break;
}
// Check for touching
if (s1 <= target + tolerance)
{
// 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;
float a1 = t1, a2 = t2;
for (; ;)
{
// Use a mix of the secant rule and bisection.
float t;
if ((rootIterCount & 1) != 0)
{
// Secant rule to improve convergence.
t = a1 + (target - s1) * (a2 - a1) / (s2 - s1);
}
else
{
// Bisection to guarantee progress.
t = 0.5f * (a1 + a2);
}
++rootIterCount;
if (Settings.EnableDiagnostics) //FPE: We only gather diagnostics when enabled
{
++TOIRootIters;
}
float s = SeparationFunction.Evaluate(indexA, indexB, t);
if (Math.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;
}
if (rootIterCount == 50)
{
break;
}
}
if (Settings.EnableDiagnostics) //FPE: We only gather diagnostics when enabled
{
TOIMaxRootIters = Math.Max(TOIMaxRootIters, rootIterCount);
}
++pushBackIter;
if (pushBackIter == Settings.MaxPolygonVertices)
{
break;
}
}
++iter;
if (Settings.EnableDiagnostics) //FPE: We only gather diagnostics when enabled
{
++TOIIters;
}
if (done)
{
break;
}
if (iter == k_maxIterations)
{
// Root finder got stuck. Semi-victory.
output.State = TOIOutputState.Failed;
output.T = t1;
break;
}
}
if (Settings.EnableDiagnostics) //FPE: We only gather diagnostics when enabled
{
TOIMaxIters = Math.Max(TOIMaxIters, iter);
}
}
/// <summary>
/// Test overlap between the two shapes.
/// </summary>
/// <param name="shapeA">The first shape.</param>
/// <param name="indexA">The index for the first shape.</param>
/// <param name="shapeB">The second shape.</param>
/// <param name="indexB">The index for the second shape.</param>
/// <param name="xfA">The transform for the first shape.</param>
/// <param name="xfB">The transform for the seconds shape.</param>
/// <returns></returns>
public static bool TestOverlap(Shape shapeA, int indexA, Shape shapeB, int indexB, ref Transform xfA, ref Transform xfB)
{
_input = _input ?? new DistanceInput();
_input.ProxyA.Set(shapeA, indexA);
_input.ProxyB.Set(shapeB, indexB);
_input.TransformA = xfA;
_input.TransformB = xfB;
_input.UseRadii = true;
SimplexCache cache;
DistanceOutput output;
Distance.ComputeDistance(out output, out cache, _input);
return output.Distance < 10.0f * Settings.Epsilon;
}
/// <summary>
/// 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.
/// </summary>
/// <param name="output">The output.</param>
/// <param name="input">The input.</param>
public static void CalculateTimeOfImpact(out TOIOutput output, TOIInput input)
{
if (Settings.EnableDiagnostics) //FPE: We only gather diagnostics when enabled
++TOICalls;
output = new TOIOutput();
output.State = TOIOutputState.Unknown;
output.T = input.TMax;
Sweep sweepA = input.SweepA;
Sweep sweepB = input.SweepB;
// Large rotations can make the root finder fail, so we normalize the
// sweep angles.
sweepA.Normalize();
sweepB.Normalize();
float tMax = input.TMax;
float totalRadius = input.ProxyA.Radius + input.ProxyB.Radius;
float target = Math.Max(Settings.LinearSlop, totalRadius - 3.0f * Settings.LinearSlop);
const float tolerance = 0.25f * Settings.LinearSlop;
Debug.Assert(target > tolerance);
float t1 = 0.0f;
const int k_maxIterations = 20;
int iter = 0;
// Prepare input for distance query.
_distanceInput = _distanceInput ?? new DistanceInput();
_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 (; ; )
{
Transform xfA, xfB;
sweepA.GetTransform(out xfA, t1);
sweepB.GetTransform(out xfB, t1);
// Get the distance between shapes. We can also use the results
// to get a separating axis.
_distanceInput.TransformA = xfA;
_distanceInput.TransformB = xfB;
DistanceOutput distanceOutput;
SimplexCache cache;
Distance.ComputeDistance(out distanceOutput, out cache, _distanceInput);
// If the shapes are overlapped, we give up on continuous collision.
if (distanceOutput.Distance <= 0.0f)
{
// Failure!
output.State = TOIOutputState.Overlapped;
output.T = 0.0f;
break;
}
if (distanceOutput.Distance < target + tolerance)
{
// Victory!
output.State = TOIOutputState.Touching;
output.T = t1;
break;
}
SeparationFunction.Set(ref cache, input.ProxyA, ref sweepA, input.ProxyB, ref 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;
float t2 = tMax;
int pushBackIter = 0;
for (; ; )
{
// Find the deepest point at t2. Store the witness point indices.
int indexA, indexB;
float s2 = SeparationFunction.FindMinSeparation(out indexA, out indexB, t2);
// Is the final configuration separated?
if (s2 > target + tolerance)
{
// Victory!
output.State = TOIOutputState.Seperated;
output.T = tMax;
done = true;
break;
}
// Has the separation reached tolerance?
if (s2 > target - tolerance)
{
// Advance the sweeps
t1 = t2;
break;
}
// Compute the initial separation of the witness points.
float s1 = SeparationFunction.Evaluate(indexA, indexB, t1);
// Check for initial overlap. This might happen if the root finder
// runs out of iterations.
if (s1 < target - tolerance)
{
output.State = TOIOutputState.Failed;
output.T = t1;
done = true;
break;
}
// Check for touching
if (s1 <= target + tolerance)
{
// 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;
float a1 = t1, a2 = t2;
for (; ; )
{
// Use a mix of the secant rule and bisection.
float t;
if ((rootIterCount & 1) != 0)
{
// Secant rule to improve convergence.
t = a1 + (target - s1) * (a2 - a1) / (s2 - s1);
}
else
{
// Bisection to guarantee progress.
t = 0.5f * (a1 + a2);
}
++rootIterCount;
if (Settings.EnableDiagnostics) //FPE: We only gather diagnostics when enabled
++TOIRootIters;
float s = SeparationFunction.Evaluate(indexA, indexB, t);
if (Math.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;
}
if (rootIterCount == 50)
{
break;
}
}
if (Settings.EnableDiagnostics) //FPE: We only gather diagnostics when enabled
TOIMaxRootIters = Math.Max(TOIMaxRootIters, rootIterCount);
++pushBackIter;
if (pushBackIter == Settings.MaxPolygonVertices)
{
break;
}
}
++iter;
if (Settings.EnableDiagnostics) //FPE: We only gather diagnostics when enabled
++TOIIters;
if (done)
{
break;
}
if (iter == k_maxIterations)
{
// Root finder got stuck. Semi-victory.
output.State = TOIOutputState.Failed;
output.T = t1;
break;
}
}
if (Settings.EnableDiagnostics) //FPE: We only gather diagnostics when enabled
TOIMaxIters = Math.Max(TOIMaxIters, iter);
}