/*
* Farseer Physics Engine based on Box2D.XNA port:
* Copyright (c) 2010 Ian Qvist
*
* Box2D.XNA port of Box2D:
* Copyright (c) 2009 Brandon Furtwangler, Nathan Furtwangler
*
* Original source Box2D:
* Copyright (c) 2006-2009 Erin Catto http://www.gphysics.com
*
* This software is provided 'as-is', without any express or implied
* warranty. In no event will the authors be held liable for any damages
* arising from the use of this software.
* Permission is granted to anyone to use this software for any purpose,
* including commercial applications, and to alter it and redistribute it
* freely, subject to the following restrictions:
* 1. The origin of this software must not be misrepresented; you must not
* claim that you wrote the original software. If you use this software
* in a product, an acknowledgment in the product documentation would be
* appreciated but is not required.
* 2. Altered source versions must be plainly marked as such, and must not be
* misrepresented as being the original software.
* 3. This notice may not be removed or altered from any source distribution.
*/
using System;
using System.Diagnostics;
using FarseerPhysics.Common;
using Microsoft.Xna.Framework;
namespace FarseerPhysics.Collision
{
/// <summary>
/// Input parameters for CalculateTimeOfImpact
/// </summary>
public class TOIInput
{
public DistanceProxy ProxyA = new DistanceProxy();
public DistanceProxy ProxyB = new DistanceProxy();
public Sweep SweepA;
public Sweep SweepB;
public float TMax; // defines sweep interval [0, tMax]
}
public enum TOIOutputState
{
Unknown,
Failed,
Overlapped,
Touching,
Seperated,
}
public struct TOIOutput
{
public TOIOutputState State;
public float T;
}
public enum SeparationFunctionType
{
Points,
FaceA,
FaceB
}
public static class SeparationFunction
{
private static Vector2 _axis;
private static Vector2 _localPoint;
private static DistanceProxy _proxyA = new DistanceProxy();
private static DistanceProxy _proxyB = new DistanceProxy();
private static Sweep _sweepA, _sweepB;
private static SeparationFunctionType _type;
public static void Set(ref SimplexCache cache,
DistanceProxy proxyA, ref Sweep sweepA,
DistanceProxy proxyB, ref Sweep sweepB,
float t1)
{
_localPoint = Vector2.Zero;
_proxyA = proxyA;
_proxyB = proxyB;
int count = cache.Count;
Debug.Assert(0 < count && count < 3);
_sweepA = sweepA;
_sweepB = sweepB;
Transform xfA, xfB;
_sweepA.GetTransform(out xfA, t1);
_sweepB.GetTransform(out xfB, t1);
if (count == 1)
{
_type = SeparationFunctionType.Points;
Vector2 localPointA = _proxyA.Vertices[cache.IndexA[0]];
Vector2 localPointB = _proxyB.Vertices[cache.IndexB[0]];
Vector2 pointA = MathUtils.Multiply(ref xfA, localPointA);
Vector2 pointB = MathUtils.Multiply(ref xfB, localPointB);
_axis = pointB - pointA;
_axis.Normalize();
return;
}
else if (cache.IndexA[0] == cache.IndexA[1])
{
// Two points on B and one on A.
_type = SeparationFunctionType.FaceB;
Vector2 localPointB1 = proxyB.Vertices[cache.IndexB[0]];
Vector2 localPointB2 = proxyB.Vertices[cache.IndexB[1]];
Vector2 a = localPointB2 - localPointB1;
_axis = new Vector2(a.Y, -a.X);
_axis.Normalize();
Vector2 normal = MathUtils.Multiply(ref xfB.R, _axis);
_localPoint = 0.5f * (localPointB1 + localPointB2);
Vector2 pointB = MathUtils.Multiply(ref xfB, _localPoint);
Vector2 localPointA = proxyA.Vertices[cache.IndexA[0]];
Vector2 pointA = MathUtils.Multiply(ref xfA, localPointA);
float s = Vector2.Dot(pointA - pointB, normal);
if (s < 0.0f)
{
_axis = -_axis;
s = -s;
}
return;
}
else
{
// Two points on A and one or two points on B.
_type = SeparationFunctionType.FaceA;
Vector2 localPointA1 = _proxyA.Vertices[cache.IndexA[0]];
Vector2 localPointA2 = _proxyA.Vertices[cache.IndexA[1]];
Vector2 a = localPointA2 - localPointA1;
_axis = new Vector2(a.Y, -a.X);
_axis.Normalize();
Vector2 normal = MathUtils.Multiply(ref xfA.R, _axis);
_localPoint = 0.5f * (localPointA1 + localPointA2);
Vector2 pointA = MathUtils.Multiply(ref xfA, _localPoint);
Vector2 localPointB = _proxyB.Vertices[cache.IndexB[0]];
Vector2 pointB = MathUtils.Multiply(ref xfB, localPointB);
float s = Vector2.Dot(pointB - pointA, normal);
if (s < 0.0f)
{
_axis = -_axis;
s = -s;
}
return;
}
}
public static float FindMinSeparation(out int indexA, out int indexB, float t)
{
Transform xfA, xfB;
_sweepA.GetTransform(out xfA, t);
_sweepB.GetTransform(out xfB, t);
switch (_type)
{
case SeparationFunctionType.Points:
{
Vector2 axisA = MathUtils.MultiplyT(ref xfA.R, _axis);
Vector2 axisB = MathUtils.MultiplyT(ref xfB.R, -_axis);
indexA = _proxyA.GetSupport(axisA);
indexB = _proxyB.GetSupport(axisB);
Vector2 localPointA = _proxyA.Vertices[indexA];
Vector2 localPointB = _proxyB.Vertices[indexB];
Vector2 pointA = MathUtils.Multiply(ref xfA, localPointA);
Vector2 pointB = MathUtils.Multiply(ref xfB, localPointB);
float separation = Vector2.Dot(pointB - pointA, _axis);
return separation;
}
case SeparationFunctionType.FaceA:
{
Vector2 normal = MathUtils.Multiply(ref xfA.R, _axis);
Vector2 pointA = MathUtils.Multiply(ref xfA, _localPoint);
Vector2 axisB = MathUtils.MultiplyT(ref xfB.R, -normal);
indexA = -1;
indexB = _proxyB.GetSupport(axisB);
Vector2 localPointB = _proxyB.Vertices[indexB];
Vector2 pointB = MathUtils.Multiply(ref xfB, localPointB);
float separation = Vector2.Dot(pointB - pointA, normal);
return separation;
}
case SeparationFunctionType.FaceB:
{
Vector2 normal = MathUtils.Multiply(ref xfB.R, _axis);
Vector2 pointB = MathUtils.Multiply(ref xfB, _localPoint);
Vector2 axisA = MathUtils.MultiplyT(ref xfA.R, -normal);
indexB = -1;
indexA = _proxyA.GetSupport(axisA);
Vector2 localPointA = _proxyA.Vertices[indexA];
Vector2 pointA = MathUtils.Multiply(ref xfA, localPointA);
float separation = Vector2.Dot(pointA - pointB, normal);
return separation;
}
default:
Debug.Assert(false);
indexA = -1;
indexB = -1;
return 0.0f;
}
}
public static float Evaluate(int indexA, int indexB, float t)
{
Transform xfA, xfB;
_sweepA.GetTransform(out xfA, t);
_sweepB.GetTransform(out xfB, t);
switch (_type)
{
case SeparationFunctionType.Points:
{
Vector2 axisA = MathUtils.MultiplyT(ref xfA.R, _axis);
Vector2 axisB = MathUtils.MultiplyT(ref xfB.R, -_axis);
Vector2 localPointA = _proxyA.Vertices[indexA];
Vector2 localPointB = _proxyB.Vertices[indexB];
Vector2 pointA = MathUtils.Multiply(ref xfA, localPointA);
Vector2 pointB = MathUtils.Multiply(ref xfB, localPointB);
float separation = Vector2.Dot(pointB - pointA, _axis);
return separation;
}
case SeparationFunctionType.FaceA:
{
Vector2 normal = MathUtils.Multiply(ref xfA.R, _axis);
Vector2 pointA = MathUtils.Multiply(ref xfA, _localPoint);
Vector2 axisB = MathUtils.MultiplyT(ref xfB.R, -normal);
Vector2 localPointB = _proxyB.Vertices[indexB];
Vector2 pointB = MathUtils.Multiply(ref xfB, localPointB);
float separation = Vector2.Dot(pointB - pointA, normal);
return separation;
}
case SeparationFunctionType.FaceB:
{
Vector2 normal = MathUtils.Multiply(ref xfB.R, _axis);
Vector2 pointB = MathUtils.Multiply(ref xfB, _localPoint);
Vector2 axisA = MathUtils.MultiplyT(ref xfA.R, -normal);
Vector2 localPointA = _proxyA.Vertices[indexA];
Vector2 pointA = MathUtils.Multiply(ref xfA, localPointA);
float separation = Vector2.Dot(pointA - pointB, normal);
return separation;
}
default:
Debug.Assert(false);
return 0.0f;
}
}
}
public static class TimeOfImpact
{
// CCD via the local separating axis method. This seeks progression
// by computing the largest time at which separation is maintained.
public static int TOICalls, TOIIters, TOIMaxIters;
public static int TOIRootIters, TOIMaxRootIters;
private static DistanceInput _distanceInput = new DistanceInput();
/// <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)
{
++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.
SimplexCache cache;
_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;
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);
}
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;
}
++rootIterCount;
++TOIRootIters;
if (rootIterCount == 50)
{
break;
}
}
TOIMaxRootIters = Math.Max(TOIMaxRootIters, rootIterCount);
++pushBackIter;
if (pushBackIter == Settings.MaxPolygonVertices)
{
break;
}
}
++iter;
++TOIIters;
if (done)
{
break;
}
if (iter == k_maxIterations)
{
// Root finder got stuck. Semi-victory.
output.State = TOIOutputState.Failed;
output.T = t1;
break;
}
}
TOIMaxIters = Math.Max(TOIMaxIters, iter);
}
}
}
Submit an article or tip