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axiosengine/axios/Collision/Collision.cs

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Adding initial files
2012-03-19 23:57:59 +00:00
/*
* 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 System.Runtime.InteropServices;
using FarseerPhysics.Collision.Shapes;
using FarseerPhysics.Common;
using Microsoft.Xna.Framework;
namespace FarseerPhysics.Collision
{
internal enum ContactFeatureType : byte
{
Vertex = 0,
Face = 1,
}
/// <summary>
/// The features that intersect to form the contact point
/// This must be 4 bytes or less.
/// </summary>
public struct ContactFeature
{
/// <summary>
/// Feature index on ShapeA
/// </summary>
public byte IndexA;
/// <summary>
/// Feature index on ShapeB
/// </summary>
public byte IndexB;
/// <summary>
/// The feature type on ShapeA
/// </summary>
public byte TypeA;
/// <summary>
/// The feature type on ShapeB
/// </summary>
public byte TypeB;
}
/// <summary>
/// Contact ids to facilitate warm starting.
/// </summary>
[StructLayout(LayoutKind.Explicit)]
public struct ContactID
{
/// <summary>
/// The features that intersect to form the contact point
/// </summary>
[FieldOffset(0)]
public ContactFeature Features;
/// <summary>
/// Used to quickly compare contact ids.
/// </summary>
[FieldOffset(0)]
public uint Key;
}
/// <summary>
/// A manifold point is a contact point belonging to a contact
/// manifold. It holds details related to the geometry and dynamics
/// of the contact points.
/// The local point usage depends on the manifold type:
/// -ShapeType.Circles: the local center of circleB
/// -SeparationFunction.FaceA: the local center of cirlceB or the clip point of polygonB
/// -SeparationFunction.FaceB: the clip point of polygonA
/// This structure is stored across time steps, so we keep it small.
/// Note: the impulses are used for internal caching and may not
/// provide reliable contact forces, especially for high speed collisions.
/// </summary>
public struct ManifoldPoint
{
/// <summary>
/// Uniquely identifies a contact point between two Shapes
/// </summary>
public ContactID Id;
public Vector2 LocalPoint;
public float NormalImpulse;
public float TangentImpulse;
}
public enum ManifoldType
{
Circles,
FaceA,
FaceB
}
/// <summary>
/// A manifold for two touching convex Shapes.
/// Box2D supports multiple types of contact:
/// - clip point versus plane with radius
/// - point versus point with radius (circles)
/// The local point usage depends on the manifold type:
/// -ShapeType.Circles: the local center of circleA
/// -SeparationFunction.FaceA: the center of faceA
/// -SeparationFunction.FaceB: the center of faceB
/// Similarly the local normal usage:
/// -ShapeType.Circles: not used
/// -SeparationFunction.FaceA: the normal on polygonA
/// -SeparationFunction.FaceB: the normal on polygonB
/// We store contacts in this way so that position correction can
/// account for movement, which is critical for continuous physics.
/// All contact scenarios must be expressed in one of these types.
/// This structure is stored across time steps, so we keep it small.
/// </summary>
public struct Manifold
{
/// <summary>
/// Not use for Type.SeparationFunction.Points
/// </summary>
public Vector2 LocalNormal;
/// <summary>
/// Usage depends on manifold type
/// </summary>
public Vector2 LocalPoint;
/// <summary>
/// The number of manifold points
/// </summary>
public int PointCount;
/// <summary>
/// The points of contact
/// </summary>
public FixedArray2<ManifoldPoint> Points;
public ManifoldType Type;
}
/// <summary>
/// This is used for determining the state of contact points.
/// </summary>
public enum PointState
{
/// <summary>
/// Point does not exist
/// </summary>
Null,
/// <summary>
/// Point was added in the update
/// </summary>
Add,
/// <summary>
/// Point persisted across the update
/// </summary>
Persist,
/// <summary>
/// Point was removed in the update
/// </summary>
Remove,
}
/// <summary>
/// Used for computing contact manifolds.
/// </summary>
public struct ClipVertex
{
public ContactID ID;
public Vector2 V;
}
/// <summary>
/// Ray-cast input data. The ray extends from p1 to p1 + maxFraction * (p2 - p1).
/// </summary>
public struct RayCastInput
{
public float MaxFraction;
public Vector2 Point1, Point2;
}
/// <summary>
/// Ray-cast output data. The ray hits at p1 + fraction * (p2 - p1), where p1 and p2
/// come from RayCastInput.
/// </summary>
public struct RayCastOutput
{
public float Fraction;
public Vector2 Normal;
}
/// <summary>
/// An axis aligned bounding box.
/// </summary>
public struct AABB
{
private static DistanceInput _input = new DistanceInput();
/// <summary>
/// The lower vertex
/// </summary>
public Vector2 LowerBound;
/// <summary>
/// The upper vertex
/// </summary>
public Vector2 UpperBound;
public AABB(Vector2 min, Vector2 max)
: this(ref min, ref max)
{
}
public AABB(ref Vector2 min, ref Vector2 max)
{
LowerBound = min;
UpperBound = max;
}
public AABB(Vector2 center, float width, float height)
{
LowerBound = center - new Vector2(width / 2, height / 2);
UpperBound = center + new Vector2(width / 2, height / 2);
}
/// <summary>
/// Get the center of the AABB.
/// </summary>
/// <value></value>
public Vector2 Center
{
get { return 0.5f * (LowerBound + UpperBound); }
}
/// <summary>
/// Get the extents of the AABB (half-widths).
/// </summary>
/// <value></value>
public Vector2 Extents
{
get { return 0.5f * (UpperBound - LowerBound); }
}
/// <summary>
/// Get the perimeter length
/// </summary>
/// <value></value>
public float Perimeter
{
get
{
float wx = UpperBound.X - LowerBound.X;
float wy = UpperBound.Y - LowerBound.Y;
return 2.0f * (wx + wy);
}
}
/// <summary>
/// Gets the vertices of the AABB.
/// </summary>
/// <value>The corners of the AABB</value>
public Vertices Vertices
{
get
{
Vertices vertices = new Vertices();
vertices.Add(LowerBound);
vertices.Add(new Vector2(LowerBound.X, UpperBound.Y));
vertices.Add(UpperBound);
vertices.Add(new Vector2(UpperBound.X, LowerBound.Y));
return vertices;
}
}
/// <summary>
/// first quadrant
/// </summary>
public AABB Q1
{
get { return new AABB(Center, UpperBound); }
}
public AABB Q2
{
get
{
return new AABB(new Vector2(LowerBound.X, Center.Y), new Vector2(Center.X, UpperBound.Y));
;
}
}
public AABB Q3
{
get { return new AABB(LowerBound, Center); }
}
public AABB Q4
{
get { return new AABB(new Vector2(Center.X, LowerBound.Y), new Vector2(UpperBound.X, Center.Y)); }
}
public Vector2[] GetVertices()
{
Vector2 p1 = UpperBound;
Vector2 p2 = new Vector2(UpperBound.X, LowerBound.Y);
Vector2 p3 = LowerBound;
Vector2 p4 = new Vector2(LowerBound.X, UpperBound.Y);
return new[] { p1, p2, p3, p4 };
}
/// <summary>
/// Verify that the bounds are sorted.
/// </summary>
/// <returns>
/// <c>true</c> if this instance is valid; otherwise, <c>false</c>.
/// </returns>
public bool IsValid()
{
Vector2 d = UpperBound - LowerBound;
bool valid = d.X >= 0.0f && d.Y >= 0.0f;
valid = valid && LowerBound.IsValid() && UpperBound.IsValid();
return valid;
}
/// <summary>
/// Combine an AABB into this one.
/// </summary>
/// <param name="aabb">The aabb.</param>
public void Combine(ref AABB aabb)
{
LowerBound = Vector2.Min(LowerBound, aabb.LowerBound);
UpperBound = Vector2.Max(UpperBound, aabb.UpperBound);
}
/// <summary>
/// Combine two AABBs into this one.
/// </summary>
/// <param name="aabb1">The aabb1.</param>
/// <param name="aabb2">The aabb2.</param>
public void Combine(ref AABB aabb1, ref AABB aabb2)
{
LowerBound = Vector2.Min(aabb1.LowerBound, aabb2.LowerBound);
UpperBound = Vector2.Max(aabb1.UpperBound, aabb2.UpperBound);
}
/// <summary>
/// Does this aabb contain the provided AABB.
/// </summary>
/// <param name="aabb">The aabb.</param>
/// <returns>
/// <c>true</c> if it contains the specified aabb; otherwise, <c>false</c>.
/// </returns>
public bool Contains(ref AABB aabb)
{
bool result = true;
result = result && LowerBound.X <= aabb.LowerBound.X;
result = result && LowerBound.Y <= aabb.LowerBound.Y;
result = result && aabb.UpperBound.X <= UpperBound.X;
result = result && aabb.UpperBound.Y <= UpperBound.Y;
return result;
}
/// <summary>
/// Determines whether the AAABB contains the specified point.
/// </summary>
/// <param name="point">The point.</param>
/// <returns>
/// <c>true</c> if it contains the specified point; otherwise, <c>false</c>.
/// </returns>
public bool Contains(ref Vector2 point)
{
//using epsilon to try and gaurd against float rounding errors.
if ((point.X > (LowerBound.X + Settings.Epsilon) && point.X < (UpperBound.X - Settings.Epsilon) &&
(point.Y > (LowerBound.Y + Settings.Epsilon) && point.Y < (UpperBound.Y - Settings.Epsilon))))
{
return true;
}
return false;
}
public static bool TestOverlap(AABB a, AABB b)
{
return TestOverlap(ref a, ref b);
}
public static bool TestOverlap(ref AABB a, ref AABB b)
{
Vector2 d1 = b.LowerBound - a.UpperBound;
Vector2 d2 = a.LowerBound - b.UpperBound;
if (d1.X > 0.0f || d1.Y > 0.0f)
return false;
if (d2.X > 0.0f || d2.Y > 0.0f)
return false;
return true;
}
public static bool TestOverlap(Shape shapeA, int indexA,
Shape shapeB, int indexB,
ref Transform xfA, ref Transform xfB)
{
_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;
}
// From Real-time Collision Detection, p179.
public bool RayCast(out RayCastOutput output, ref RayCastInput input)
{
output = new RayCastOutput();
float tmin = -Settings.MaxFloat;
float tmax = Settings.MaxFloat;
Vector2 p = input.Point1;
Vector2 d = input.Point2 - input.Point1;
Vector2 absD = MathUtils.Abs(d);
Vector2 normal = Vector2.Zero;
for (int i = 0; i < 2; ++i)
{
float absD_i = i == 0 ? absD.X : absD.Y;
float lowerBound_i = i == 0 ? LowerBound.X : LowerBound.Y;
float upperBound_i = i == 0 ? UpperBound.X : UpperBound.Y;
float p_i = i == 0 ? p.X : p.Y;
if (absD_i < Settings.Epsilon)
{
// Parallel.
if (p_i < lowerBound_i || upperBound_i < p_i)
{
return false;
}
}
else
{
float d_i = i == 0 ? d.X : d.Y;
float inv_d = 1.0f / d_i;
float t1 = (lowerBound_i - p_i) * inv_d;
float t2 = (upperBound_i - p_i) * inv_d;
// Sign of the normal vector.
float s = -1.0f;
if (t1 > t2)
{
MathUtils.Swap(ref t1, ref t2);
s = 1.0f;
}
// Push the min up
if (t1 > tmin)
{
if (i == 0)
{
normal.X = s;
}
else
{
normal.Y = s;
}
tmin = t1;
}
// Pull the max down
tmax = Math.Min(tmax, t2);
if (tmin > tmax)
{
return false;
}
}
}
// Does the ray start inside the box?
// Does the ray intersect beyond the max fraction?
if (tmin < 0.0f || input.MaxFraction < tmin)
{
return false;
}
// Intersection.
output.Fraction = tmin;
output.Normal = normal;
return true;
}
}
/// <summary>
/// Edge shape plus more stuff.
/// </summary>
public struct FatEdge
{
public bool HasVertex0, HasVertex3;
public Vector2 Normal;
public Vector2 V0, V1, V2, V3;
}
/// <summary>
/// This lets us treate and edge shape and a polygon in the same
/// way in the SAT collider.
/// </summary>
public class EPProxy
{
public Vector2 Centroid;
public int Count;
public Vector2[] Normals = new Vector2[Settings.MaxPolygonVertices];
public Vector2[] Vertices = new Vector2[Settings.MaxPolygonVertices];
}
public struct EPAxis
{
public int Index;
public float Separation;
public EPAxisType Type;
}
public enum EPAxisType
{
Unknown,
EdgeA,
EdgeB,
}
public static class Collision
{
private static FatEdge _edgeA;
private static EPProxy _proxyA = new EPProxy();
private static EPProxy _proxyB = new EPProxy();
private static Transform _xf;
private static Vector2 _limit11, _limit12;
private static Vector2 _limit21, _limit22;
private static float _radius;
private static Vector2[] _tmpNormals = new Vector2[2];
/// <summary>
/// Evaluate the manifold with supplied transforms. This assumes
/// modest motion from the original state. This does not change the
/// point count, impulses, etc. The radii must come from the Shapes
/// that generated the manifold.
/// </summary>
/// <param name="manifold">The manifold.</param>
/// <param name="transformA">The transform for A.</param>
/// <param name="radiusA">The radius for A.</param>
/// <param name="transformB">The transform for B.</param>
/// <param name="radiusB">The radius for B.</param>
/// <param name="normal">World vector pointing from A to B</param>
/// <param name="points">Torld contact point (point of intersection).</param>
public static void GetWorldManifold(ref Manifold manifold,
ref Transform transformA, float radiusA,
ref Transform transformB, float radiusB, out Vector2 normal,
out FixedArray2<Vector2> points)
{
points = new FixedArray2<Vector2>();
normal = Vector2.Zero;
if (manifold.PointCount == 0)
{
normal = Vector2.UnitY;
return;
}
switch (manifold.Type)
{
case ManifoldType.Circles:
{
Vector2 tmp = manifold.Points[0].LocalPoint;
float pointAx = transformA.Position.X + transformA.R.Col1.X * manifold.LocalPoint.X +
transformA.R.Col2.X * manifold.LocalPoint.Y;
float pointAy = transformA.Position.Y + transformA.R.Col1.Y * manifold.LocalPoint.X +
transformA.R.Col2.Y * manifold.LocalPoint.Y;
float pointBx = transformB.Position.X + transformB.R.Col1.X * tmp.X +
transformB.R.Col2.X * tmp.Y;
float pointBy = transformB.Position.Y + transformB.R.Col1.Y * tmp.X +
transformB.R.Col2.Y * tmp.Y;
normal.X = 1;
normal.Y = 0;
float result = (pointAx - pointBx) * (pointAx - pointBx) +
(pointAy - pointBy) * (pointAy - pointBy);
if (result > Settings.Epsilon * Settings.Epsilon)
{
float tmpNormalx = pointBx - pointAx;
float tmpNormaly = pointBy - pointAy;
float factor = 1f / (float)Math.Sqrt(tmpNormalx * tmpNormalx + tmpNormaly * tmpNormaly);
normal.X = tmpNormalx * factor;
normal.Y = tmpNormaly * factor;
}
Vector2 c = Vector2.Zero;
c.X = (pointAx + radiusA * normal.X) + (pointBx - radiusB * normal.X);
c.Y = (pointAy + radiusA * normal.Y) + (pointBy - radiusB * normal.Y);
points[0] = 0.5f * c;
}
break;
case ManifoldType.FaceA:
{
normal.X = transformA.R.Col1.X * manifold.LocalNormal.X +
transformA.R.Col2.X * manifold.LocalNormal.Y;
normal.Y = transformA.R.Col1.Y * manifold.LocalNormal.X +
transformA.R.Col2.Y * manifold.LocalNormal.Y;
float planePointx = transformA.Position.X + transformA.R.Col1.X * manifold.LocalPoint.X +
transformA.R.Col2.X * manifold.LocalPoint.Y;
float planePointy = transformA.Position.Y + transformA.R.Col1.Y * manifold.LocalPoint.X +
transformA.R.Col2.Y * manifold.LocalPoint.Y;
for (int i = 0; i < manifold.PointCount; ++i)
{
Vector2 tmp = manifold.Points[i].LocalPoint;
float clipPointx = transformB.Position.X + transformB.R.Col1.X * tmp.X +
transformB.R.Col2.X * tmp.Y;
float clipPointy = transformB.Position.Y + transformB.R.Col1.Y * tmp.X +
transformB.R.Col2.Y * tmp.Y;
float value = (clipPointx - planePointx) * normal.X + (clipPointy - planePointy) * normal.Y;
Vector2 c = Vector2.Zero;
c.X = (clipPointx + (radiusA - value) * normal.X) + (clipPointx - radiusB * normal.X);
c.Y = (clipPointy + (radiusA - value) * normal.Y) + (clipPointy - radiusB * normal.Y);
points[i] = 0.5f * c;
}
}
break;
case ManifoldType.FaceB:
{
normal.X = transformB.R.Col1.X * manifold.LocalNormal.X +
transformB.R.Col2.X * manifold.LocalNormal.Y;
normal.Y = transformB.R.Col1.Y * manifold.LocalNormal.X +
transformB.R.Col2.Y * manifold.LocalNormal.Y;
float planePointx = transformB.Position.X + transformB.R.Col1.X * manifold.LocalPoint.X +
transformB.R.Col2.X * manifold.LocalPoint.Y;
float planePointy = transformB.Position.Y + transformB.R.Col1.Y * manifold.LocalPoint.X +
transformB.R.Col2.Y * manifold.LocalPoint.Y;
for (int i = 0; i < manifold.PointCount; ++i)
{
Vector2 tmp = manifold.Points[i].LocalPoint;
float clipPointx = transformA.Position.X + transformA.R.Col1.X * tmp.X +
transformA.R.Col2.X * tmp.Y;
float clipPointy = transformA.Position.Y + transformA.R.Col1.Y * tmp.X +
transformA.R.Col2.Y * tmp.Y;
float value = (clipPointx - planePointx) * normal.X + (clipPointy - planePointy) * normal.Y;
Vector2 c = Vector2.Zero;
c.X = (clipPointx - radiusA * normal.X) + (clipPointx + (radiusB - value) * normal.X);
c.Y = (clipPointy - radiusA * normal.Y) + (clipPointy + (radiusB - value) * normal.Y);
points[i] = 0.5f * c;
}
// Ensure normal points from A to B.
normal *= -1;
}
break;
default:
normal = Vector2.UnitY;
break;
}
}
public static void GetPointStates(out FixedArray2<PointState> state1, out FixedArray2<PointState> state2,
ref Manifold manifold1, ref Manifold manifold2)
{
state1 = new FixedArray2<PointState>();
state2 = new FixedArray2<PointState>();
// Detect persists and removes.
for (int i = 0; i < manifold1.PointCount; ++i)
{
ContactID id = manifold1.Points[i].Id;
state1[i] = PointState.Remove;
for (int j = 0; j < manifold2.PointCount; ++j)
{
if (manifold2.Points[j].Id.Key == id.Key)
{
state1[i] = PointState.Persist;
break;
}
}
}
// Detect persists and adds.
for (int i = 0; i < manifold2.PointCount; ++i)
{
ContactID id = manifold2.Points[i].Id;
state2[i] = PointState.Add;
for (int j = 0; j < manifold1.PointCount; ++j)
{
if (manifold1.Points[j].Id.Key == id.Key)
{
state2[i] = PointState.Persist;
break;
}
}
}
}
/// Compute the collision manifold between two circles.
public static void CollideCircles(ref Manifold manifold,
CircleShape circleA, ref Transform xfA,
CircleShape circleB, ref Transform xfB)
{
manifold.PointCount = 0;
float pAx = xfA.Position.X + xfA.R.Col1.X * circleA.Position.X + xfA.R.Col2.X * circleA.Position.Y;
float pAy = xfA.Position.Y + xfA.R.Col1.Y * circleA.Position.X + xfA.R.Col2.Y * circleA.Position.Y;
float pBx = xfB.Position.X + xfB.R.Col1.X * circleB.Position.X + xfB.R.Col2.X * circleB.Position.Y;
float pBy = xfB.Position.Y + xfB.R.Col1.Y * circleB.Position.X + xfB.R.Col2.Y * circleB.Position.Y;
float distSqr = (pBx - pAx) * (pBx - pAx) + (pBy - pAy) * (pBy - pAy);
float radius = circleA.Radius + circleB.Radius;
if (distSqr > radius * radius)
{
return;
}
manifold.Type = ManifoldType.Circles;
manifold.LocalPoint = circleA.Position;
manifold.LocalNormal = Vector2.Zero;
manifold.PointCount = 1;
ManifoldPoint p0 = manifold.Points[0];
p0.LocalPoint = circleB.Position;
p0.Id.Key = 0;
manifold.Points[0] = p0;
}
/// <summary>
/// Compute the collision manifold between a polygon and a circle.
/// </summary>
/// <param name="manifold">The manifold.</param>
/// <param name="polygonA">The polygon A.</param>
/// <param name="transformA">The transform of A.</param>
/// <param name="circleB">The circle B.</param>
/// <param name="transformB">The transform of B.</param>
public static void CollidePolygonAndCircle(ref Manifold manifold,
PolygonShape polygonA, ref Transform transformA,
CircleShape circleB, ref Transform transformB)
{
manifold.PointCount = 0;
// Compute circle position in the frame of the polygon.
Vector2 c =
new Vector2(
transformB.Position.X + transformB.R.Col1.X * circleB.Position.X +
transformB.R.Col2.X * circleB.Position.Y,
transformB.Position.Y + transformB.R.Col1.Y * circleB.Position.X +
transformB.R.Col2.Y * circleB.Position.Y);
Vector2 cLocal =
new Vector2(
(c.X - transformA.Position.X) * transformA.R.Col1.X +
(c.Y - transformA.Position.Y) * transformA.R.Col1.Y,
(c.X - transformA.Position.X) * transformA.R.Col2.X +
(c.Y - transformA.Position.Y) * transformA.R.Col2.Y);
// Find the min separating edge.
int normalIndex = 0;
float separation = -Settings.MaxFloat;
float radius = polygonA.Radius + circleB.Radius;
int vertexCount = polygonA.Vertices.Count;
for (int i = 0; i < vertexCount; ++i)
{
Vector2 value1 = polygonA.Normals[i];
Vector2 value2 = cLocal - polygonA.Vertices[i];
float s = value1.X * value2.X + value1.Y * value2.Y;
if (s > radius)
{
// Early out.
return;
}
if (s > separation)
{
separation = s;
normalIndex = i;
}
}
// Vertices that subtend the incident face.
int vertIndex1 = normalIndex;
int vertIndex2 = vertIndex1 + 1 < vertexCount ? vertIndex1 + 1 : 0;
Vector2 v1 = polygonA.Vertices[vertIndex1];
Vector2 v2 = polygonA.Vertices[vertIndex2];
// If the center is inside the polygon ...
if (separation < Settings.Epsilon)
{
manifold.PointCount = 1;
manifold.Type = ManifoldType.FaceA;
manifold.LocalNormal = polygonA.Normals[normalIndex];
manifold.LocalPoint = 0.5f * (v1 + v2);
ManifoldPoint p0 = manifold.Points[0];
p0.LocalPoint = circleB.Position;
p0.Id.Key = 0;
manifold.Points[0] = p0;
return;
}
// Compute barycentric coordinates
float u1 = (cLocal.X - v1.X) * (v2.X - v1.X) + (cLocal.Y - v1.Y) * (v2.Y - v1.Y);
float u2 = (cLocal.X - v2.X) * (v1.X - v2.X) + (cLocal.Y - v2.Y) * (v1.Y - v2.Y);
if (u1 <= 0.0f)
{
float r = (cLocal.X - v1.X) * (cLocal.X - v1.X) + (cLocal.Y - v1.Y) * (cLocal.Y - v1.Y);
if (r > radius * radius)
{
return;
}
manifold.PointCount = 1;
manifold.Type = ManifoldType.FaceA;
manifold.LocalNormal = cLocal - v1;
float factor = 1f /
(float)
Math.Sqrt(manifold.LocalNormal.X * manifold.LocalNormal.X +
manifold.LocalNormal.Y * manifold.LocalNormal.Y);
manifold.LocalNormal.X = manifold.LocalNormal.X * factor;
manifold.LocalNormal.Y = manifold.LocalNormal.Y * factor;
manifold.LocalPoint = v1;
ManifoldPoint p0b = manifold.Points[0];
p0b.LocalPoint = circleB.Position;
p0b.Id.Key = 0;
manifold.Points[0] = p0b;
}
else if (u2 <= 0.0f)
{
float r = (cLocal.X - v2.X) * (cLocal.X - v2.X) + (cLocal.Y - v2.Y) * (cLocal.Y - v2.Y);
if (r > radius * radius)
{
return;
}
manifold.PointCount = 1;
manifold.Type = ManifoldType.FaceA;
manifold.LocalNormal = cLocal - v2;
float factor = 1f /
(float)
Math.Sqrt(manifold.LocalNormal.X * manifold.LocalNormal.X +
manifold.LocalNormal.Y * manifold.LocalNormal.Y);
manifold.LocalNormal.X = manifold.LocalNormal.X * factor;
manifold.LocalNormal.Y = manifold.LocalNormal.Y * factor;
manifold.LocalPoint = v2;
ManifoldPoint p0c = manifold.Points[0];
p0c.LocalPoint = circleB.Position;
p0c.Id.Key = 0;
manifold.Points[0] = p0c;
}
else
{
Vector2 faceCenter = 0.5f * (v1 + v2);
Vector2 value1 = cLocal - faceCenter;
Vector2 value2 = polygonA.Normals[vertIndex1];
float separation2 = value1.X * value2.X + value1.Y * value2.Y;
if (separation2 > radius)
{
return;
}
manifold.PointCount = 1;
manifold.Type = ManifoldType.FaceA;
manifold.LocalNormal = polygonA.Normals[vertIndex1];
manifold.LocalPoint = faceCenter;
ManifoldPoint p0d = manifold.Points[0];
p0d.LocalPoint = circleB.Position;
p0d.Id.Key = 0;
manifold.Points[0] = p0d;
}
}
/// <summary>
/// Compute the collision manifold between two polygons.
/// </summary>
/// <param name="manifold">The manifold.</param>
/// <param name="polyA">The poly A.</param>
/// <param name="transformA">The transform A.</param>
/// <param name="polyB">The poly B.</param>
/// <param name="transformB">The transform B.</param>
public static void CollidePolygons(ref Manifold manifold,
PolygonShape polyA, ref Transform transformA,
PolygonShape polyB, ref Transform transformB)
{
manifold.PointCount = 0;
float totalRadius = polyA.Radius + polyB.Radius;
int edgeA = 0;
float separationA = FindMaxSeparation(out edgeA, polyA, ref transformA, polyB, ref transformB);
if (separationA > totalRadius)
return;
int edgeB = 0;
float separationB = FindMaxSeparation(out edgeB, polyB, ref transformB, polyA, ref transformA);
if (separationB > totalRadius)
return;
PolygonShape poly1; // reference polygon
PolygonShape poly2; // incident polygon
Transform xf1, xf2;
int edge1; // reference edge
bool flip;
const float k_relativeTol = 0.98f;
const float k_absoluteTol = 0.001f;
if (separationB > k_relativeTol * separationA + k_absoluteTol)
{
poly1 = polyB;
poly2 = polyA;
xf1 = transformB;
xf2 = transformA;
edge1 = edgeB;
manifold.Type = ManifoldType.FaceB;
flip = true;
}
else
{
poly1 = polyA;
poly2 = polyB;
xf1 = transformA;
xf2 = transformB;
edge1 = edgeA;
manifold.Type = ManifoldType.FaceA;
flip = false;
}
FixedArray2<ClipVertex> incidentEdge;
FindIncidentEdge(out incidentEdge, poly1, ref xf1, edge1, poly2, ref xf2);
int count1 = poly1.Vertices.Count;
int iv1 = edge1;
int iv2 = edge1 + 1 < count1 ? edge1 + 1 : 0;
Vector2 v11 = poly1.Vertices[iv1];
Vector2 v12 = poly1.Vertices[iv2];
float localTangentX = v12.X - v11.X;
float localTangentY = v12.Y - v11.Y;
float factor = 1f / (float)Math.Sqrt(localTangentX * localTangentX + localTangentY * localTangentY);
localTangentX = localTangentX * factor;
localTangentY = localTangentY * factor;
Vector2 localNormal = new Vector2(localTangentY, -localTangentX);
Vector2 planePoint = 0.5f * (v11 + v12);
Vector2 tangent = new Vector2(xf1.R.Col1.X * localTangentX + xf1.R.Col2.X * localTangentY,
xf1.R.Col1.Y * localTangentX + xf1.R.Col2.Y * localTangentY);
float normalx = tangent.Y;
float normaly = -tangent.X;
v11 = new Vector2(xf1.Position.X + xf1.R.Col1.X * v11.X + xf1.R.Col2.X * v11.Y,
xf1.Position.Y + xf1.R.Col1.Y * v11.X + xf1.R.Col2.Y * v11.Y);
v12 = new Vector2(xf1.Position.X + xf1.R.Col1.X * v12.X + xf1.R.Col2.X * v12.Y,
xf1.Position.Y + xf1.R.Col1.Y * v12.X + xf1.R.Col2.Y * v12.Y);
// Face offset.
float frontOffset = normalx * v11.X + normaly * v11.Y;
// Side offsets, extended by polytope skin thickness.
float sideOffset1 = -(tangent.X * v11.X + tangent.Y * v11.Y) + totalRadius;
float sideOffset2 = tangent.X * v12.X + tangent.Y * v12.Y + totalRadius;
// Clip incident edge against extruded edge1 side edges.
FixedArray2<ClipVertex> clipPoints1;
FixedArray2<ClipVertex> clipPoints2;
// Clip to box side 1
int np = ClipSegmentToLine(out clipPoints1, ref incidentEdge, -tangent, sideOffset1, iv1);
if (np < 2)
return;
// Clip to negative box side 1
np = ClipSegmentToLine(out clipPoints2, ref clipPoints1, tangent, sideOffset2, iv2);
if (np < 2)
{
return;
}
// Now clipPoints2 contains the clipped points.
manifold.LocalNormal = localNormal;
manifold.LocalPoint = planePoint;
int pointCount = 0;
for (int i = 0; i < Settings.MaxManifoldPoints; ++i)
{
Vector2 value = clipPoints2[i].V;
float separation = normalx * value.X + normaly * value.Y - frontOffset;
if (separation <= totalRadius)
{
ManifoldPoint cp = manifold.Points[pointCount];
Vector2 tmp = clipPoints2[i].V;
float tmp1X = tmp.X - xf2.Position.X;
float tmp1Y = tmp.Y - xf2.Position.Y;
cp.LocalPoint.X = tmp1X * xf2.R.Col1.X + tmp1Y * xf2.R.Col1.Y;
cp.LocalPoint.Y = tmp1X * xf2.R.Col2.X + tmp1Y * xf2.R.Col2.Y;
cp.Id = clipPoints2[i].ID;
if (flip)
{
// Swap features
ContactFeature cf = cp.Id.Features;
cp.Id.Features.IndexA = cf.IndexB;
cp.Id.Features.IndexB = cf.IndexA;
cp.Id.Features.TypeA = cf.TypeB;
cp.Id.Features.TypeB = cf.TypeA;
}
manifold.Points[pointCount] = cp;
++pointCount;
}
}
manifold.PointCount = pointCount;
}
/// <summary>
/// Compute contact points for edge versus circle.
/// This accounts for edge connectivity.
/// </summary>
/// <param name="manifold">The manifold.</param>
/// <param name="edgeA">The edge A.</param>
/// <param name="transformA">The transform A.</param>
/// <param name="circleB">The circle B.</param>
/// <param name="transformB">The transform B.</param>
public static void CollideEdgeAndCircle(ref Manifold manifold,
EdgeShape edgeA, ref Transform transformA,
CircleShape circleB, ref Transform transformB)
{
manifold.PointCount = 0;
// Compute circle in frame of edge
Vector2 Q = MathUtils.MultiplyT(ref transformA, MathUtils.Multiply(ref transformB, ref circleB._position));
Vector2 A = edgeA.Vertex1, B = edgeA.Vertex2;
Vector2 e = B - A;
// Barycentric coordinates
float u = Vector2.Dot(e, B - Q);
float v = Vector2.Dot(e, Q - A);
float radius = edgeA.Radius + circleB.Radius;
ContactFeature cf;
cf.IndexB = 0;
cf.TypeB = (byte)ContactFeatureType.Vertex;
Vector2 P, d;
// Region A
if (v <= 0.0f)
{
P = A;
d = Q - P;
float dd;
Vector2.Dot(ref d, ref d, out dd);
if (dd > radius * radius)
{
return;
}
// Is there an edge connected to A?
if (edgeA.HasVertex0)
{
Vector2 A1 = edgeA.Vertex0;
Vector2 B1 = A;
Vector2 e1 = B1 - A1;
float u1 = Vector2.Dot(e1, B1 - Q);
// Is the circle in Region AB of the previous edge?
if (u1 > 0.0f)
{
return;
}
}
cf.IndexA = 0;
cf.TypeA = (byte)ContactFeatureType.Vertex;
manifold.PointCount = 1;
manifold.Type = ManifoldType.Circles;
manifold.LocalNormal = Vector2.Zero;
manifold.LocalPoint = P;
ManifoldPoint mp = new ManifoldPoint();
mp.Id.Key = 0;
mp.Id.Features = cf;
mp.LocalPoint = circleB.Position;
manifold.Points[0] = mp;
return;
}
// Region B
if (u <= 0.0f)
{
P = B;
d = Q - P;
float dd;
Vector2.Dot(ref d, ref d, out dd);
if (dd > radius * radius)
{
return;
}
// Is there an edge connected to B?
if (edgeA.HasVertex3)
{
Vector2 B2 = edgeA.Vertex3;
Vector2 A2 = B;
Vector2 e2 = B2 - A2;
float v2 = Vector2.Dot(e2, Q - A2);
// Is the circle in Region AB of the next edge?
if (v2 > 0.0f)
{
return;
}
}
cf.IndexA = 1;
cf.TypeA = (byte)ContactFeatureType.Vertex;
manifold.PointCount = 1;
manifold.Type = ManifoldType.Circles;
manifold.LocalNormal = Vector2.Zero;
manifold.LocalPoint = P;
ManifoldPoint mp = new ManifoldPoint();
mp.Id.Key = 0;
mp.Id.Features = cf;
mp.LocalPoint = circleB.Position;
manifold.Points[0] = mp;
return;
}
// Region AB
float den;
Vector2.Dot(ref e, ref e, out den);
Debug.Assert(den > 0.0f);
P = (1.0f / den) * (u * A + v * B);
d = Q - P;
float dd2;
Vector2.Dot(ref d, ref d, out dd2);
if (dd2 > radius * radius)
{
return;
}
Vector2 n = new Vector2(-e.Y, e.X);
if (Vector2.Dot(n, Q - A) < 0.0f)
{
n = new Vector2(-n.X, -n.Y);
}
n.Normalize();
cf.IndexA = 0;
cf.TypeA = (byte)ContactFeatureType.Face;
manifold.PointCount = 1;
manifold.Type = ManifoldType.FaceA;
manifold.LocalNormal = n;
manifold.LocalPoint = A;
ManifoldPoint mp2 = new ManifoldPoint();
mp2.Id.Key = 0;
mp2.Id.Features = cf;
mp2.LocalPoint = circleB.Position;
manifold.Points[0] = mp2;
}
/// <summary>
/// Collides and edge and a polygon, taking into account edge adjacency.
/// </summary>
/// <param name="manifold">The manifold.</param>
/// <param name="edgeA">The edge A.</param>
/// <param name="xfA">The xf A.</param>
/// <param name="polygonB">The polygon B.</param>
/// <param name="xfB">The xf B.</param>
public static void CollideEdgeAndPolygon(ref Manifold manifold,
EdgeShape edgeA, ref Transform xfA,
PolygonShape polygonB, ref Transform xfB)
{
MathUtils.MultiplyT(ref xfA, ref xfB, out _xf);
// Edge geometry
_edgeA.V0 = edgeA.Vertex0;
_edgeA.V1 = edgeA.Vertex1;
_edgeA.V2 = edgeA.Vertex2;
_edgeA.V3 = edgeA.Vertex3;
Vector2 e = _edgeA.V2 - _edgeA.V1;
// Normal points outwards in CCW order.
_edgeA.Normal = new Vector2(e.Y, -e.X);
_edgeA.Normal.Normalize();
_edgeA.HasVertex0 = edgeA.HasVertex0;
_edgeA.HasVertex3 = edgeA.HasVertex3;
// Proxy for edge
_proxyA.Vertices[0] = _edgeA.V1;
_proxyA.Vertices[1] = _edgeA.V2;
_proxyA.Normals[0] = _edgeA.Normal;
_proxyA.Normals[1] = -_edgeA.Normal;
_proxyA.Centroid = 0.5f * (_edgeA.V1 + _edgeA.V2);
_proxyA.Count = 2;
// Proxy for polygon
_proxyB.Count = polygonB.Vertices.Count;
_proxyB.Centroid = MathUtils.Multiply(ref _xf, ref polygonB.MassData.Centroid);
for (int i = 0; i < polygonB.Vertices.Count; ++i)
{
_proxyB.Vertices[i] = MathUtils.Multiply(ref _xf, polygonB.Vertices[i]);
_proxyB.Normals[i] = MathUtils.Multiply(ref _xf.R, polygonB.Normals[i]);
}
_radius = 2.0f * Settings.PolygonRadius;
_limit11 = Vector2.Zero;
_limit12 = Vector2.Zero;
_limit21 = Vector2.Zero;
_limit22 = Vector2.Zero;
//Collide(ref manifold); inline start
manifold.PointCount = 0;
//ComputeAdjacency(); inline start
Vector2 v0 = _edgeA.V0;
Vector2 v1 = _edgeA.V1;
Vector2 v2 = _edgeA.V2;
Vector2 v3 = _edgeA.V3;
// Determine allowable the normal regions based on adjacency.
// Note: it may be possible that no normal is admissable.
Vector2 centerB = _proxyB.Centroid;
if (_edgeA.HasVertex0)
{
Vector2 e0 = v1 - v0;
Vector2 e1 = v2 - v1;
Vector2 n0 = new Vector2(e0.Y, -e0.X);
Vector2 n1 = new Vector2(e1.Y, -e1.X);
n0.Normalize();
n1.Normalize();
bool convex = MathUtils.Cross(n0, n1) >= 0.0f;
bool front0 = Vector2.Dot(n0, centerB - v0) >= 0.0f;
bool front1 = Vector2.Dot(n1, centerB - v1) >= 0.0f;
if (convex)
{
if (front0 || front1)
{
_limit11 = n1;
_limit12 = n0;
}
else
{
_limit11 = -n1;
_limit12 = -n0;
}
}
else
{
if (front0 && front1)
{
_limit11 = n0;
_limit12 = n1;
}
else
{
_limit11 = -n0;
_limit12 = -n1;
}
}
}
else
{
_limit11 = Vector2.Zero;
_limit12 = Vector2.Zero;
}
if (_edgeA.HasVertex3)
{
Vector2 e1 = v2 - v1;
Vector2 e2 = v3 - v2;
Vector2 n1 = new Vector2(e1.Y, -e1.X);
Vector2 n2 = new Vector2(e2.Y, -e2.X);
n1.Normalize();
n2.Normalize();
bool convex = MathUtils.Cross(n1, n2) >= 0.0f;
bool front1 = Vector2.Dot(n1, centerB - v1) >= 0.0f;
bool front2 = Vector2.Dot(n2, centerB - v2) >= 0.0f;
if (convex)
{
if (front1 || front2)
{
_limit21 = n2;
_limit22 = n1;
}
else
{
_limit21 = -n2;
_limit22 = -n1;
}
}
else
{
if (front1 && front2)
{
_limit21 = n1;
_limit22 = n2;
}
else
{
_limit21 = -n1;
_limit22 = -n2;
}
}
}
else
{
_limit21 = Vector2.Zero;
_limit22 = Vector2.Zero;
}
//ComputeAdjacency(); inline end
//EPAxis edgeAxis = ComputeEdgeSeparation(); inline start
EPAxis edgeAxis = ComputeEdgeSeparation();
// If no valid normal can be found than this edge should not collide.
// This can happen on the middle edge of a 3-edge zig-zag chain.
if (edgeAxis.Type == EPAxisType.Unknown)
{
return;
}
if (edgeAxis.Separation > _radius)
{
return;
}
EPAxis polygonAxis = ComputePolygonSeparation();
if (polygonAxis.Type != EPAxisType.Unknown && polygonAxis.Separation > _radius)
{
return;
}
// Use hysteresis for jitter reduction.
const float k_relativeTol = 0.98f;
const float k_absoluteTol = 0.001f;
EPAxis primaryAxis;
if (polygonAxis.Type == EPAxisType.Unknown)
{
primaryAxis = edgeAxis;
}
else if (polygonAxis.Separation > k_relativeTol * edgeAxis.Separation + k_absoluteTol)
{
primaryAxis = polygonAxis;
}
else
{
primaryAxis = edgeAxis;
}
EPProxy proxy1;
EPProxy proxy2;
FixedArray2<ClipVertex> incidentEdge = new FixedArray2<ClipVertex>();
if (primaryAxis.Type == EPAxisType.EdgeA)
{
proxy1 = _proxyA;
proxy2 = _proxyB;
manifold.Type = ManifoldType.FaceA;
}
else
{
proxy1 = _proxyB;
proxy2 = _proxyA;
manifold.Type = ManifoldType.FaceB;
}
int edge1 = primaryAxis.Index;
FindIncidentEdge(ref incidentEdge, proxy1, primaryAxis.Index, proxy2);
int count1 = proxy1.Count;
int iv1 = edge1;
int iv2 = edge1 + 1 < count1 ? edge1 + 1 : 0;
Vector2 v11 = proxy1.Vertices[iv1];
Vector2 v12 = proxy1.Vertices[iv2];
Vector2 tangent = v12 - v11;
tangent.Normalize();
Vector2 normal = MathUtils.Cross(tangent, 1.0f);
Vector2 planePoint = 0.5f * (v11 + v12);
// Face offset.
float frontOffset = Vector2.Dot(normal, v11);
// Side offsets, extended by polytope skin thickness.
float sideOffset1 = -Vector2.Dot(tangent, v11) + _radius;
float sideOffset2 = Vector2.Dot(tangent, v12) + _radius;
// Clip incident edge against extruded edge1 side edges.
FixedArray2<ClipVertex> clipPoints1;
FixedArray2<ClipVertex> clipPoints2;
int np;
// Clip to box side 1
np = ClipSegmentToLine(out clipPoints1, ref incidentEdge, -tangent, sideOffset1, iv1);
if (np < Settings.MaxManifoldPoints)
{
return;
}
// Clip to negative box side 1
np = ClipSegmentToLine(out clipPoints2, ref clipPoints1, tangent, sideOffset2, iv2);
if (np < Settings.MaxManifoldPoints)
{
return;
}
// Now clipPoints2 contains the clipped points.
if (primaryAxis.Type == EPAxisType.EdgeA)
{
manifold.LocalNormal = normal;
manifold.LocalPoint = planePoint;
}
else
{
manifold.LocalNormal = MathUtils.MultiplyT(ref _xf.R, ref normal);
manifold.LocalPoint = MathUtils.MultiplyT(ref _xf, ref planePoint);
}
int pointCount = 0;
for (int i1 = 0; i1 < Settings.MaxManifoldPoints; ++i1)
{
float separation = Vector2.Dot(normal, clipPoints2[i1].V) - frontOffset;
if (separation <= _radius)
{
ManifoldPoint cp = manifold.Points[pointCount];
if (primaryAxis.Type == EPAxisType.EdgeA)
{
cp.LocalPoint = MathUtils.MultiplyT(ref _xf, clipPoints2[i1].V);
cp.Id = clipPoints2[i1].ID;
}
else
{
cp.LocalPoint = clipPoints2[i1].V;
cp.Id.Features.TypeA = clipPoints2[i1].ID.Features.TypeB;
cp.Id.Features.TypeB = clipPoints2[i1].ID.Features.TypeA;
cp.Id.Features.IndexA = clipPoints2[i1].ID.Features.IndexB;
cp.Id.Features.IndexB = clipPoints2[i1].ID.Features.IndexA;
}
manifold.Points[pointCount] = cp;
++pointCount;
}
}
manifold.PointCount = pointCount;
//Collide(ref manifold); inline end
}
private static EPAxis ComputeEdgeSeparation()
{
// EdgeA separation
EPAxis bestAxis;
bestAxis.Type = EPAxisType.Unknown;
bestAxis.Index = -1;
bestAxis.Separation = -Settings.MaxFloat;
_tmpNormals[0] = _edgeA.Normal;
_tmpNormals[1] = -_edgeA.Normal;
for (int i = 0; i < 2; ++i)
{
Vector2 n = _tmpNormals[i];
// Adjacency
bool valid1 = MathUtils.Cross(n, _limit11) >= -Settings.AngularSlop &&
MathUtils.Cross(_limit12, n) >= -Settings.AngularSlop;
bool valid2 = MathUtils.Cross(n, _limit21) >= -Settings.AngularSlop &&
MathUtils.Cross(_limit22, n) >= -Settings.AngularSlop;
if (valid1 == false || valid2 == false)
{
continue;
}
EPAxis axis;
axis.Type = EPAxisType.EdgeA;
axis.Index = i;
axis.Separation = Settings.MaxFloat;
for (int j = 0; j < _proxyB.Count; ++j)
{
float s = Vector2.Dot(n, _proxyB.Vertices[j] - _edgeA.V1);
if (s < axis.Separation)
{
axis.Separation = s;
}
}
if (axis.Separation > _radius)
{
return axis;
}
if (axis.Separation > bestAxis.Separation)
{
bestAxis = axis;
}
}
return bestAxis;
}
private static EPAxis ComputePolygonSeparation()
{
EPAxis axis;
axis.Type = EPAxisType.Unknown;
axis.Index = -1;
axis.Separation = -Settings.MaxFloat;
for (int i = 0; i < _proxyB.Count; ++i)
{
Vector2 n = -_proxyB.Normals[i];
// Adjacency
bool valid1 = MathUtils.Cross(n, _limit11) >= -Settings.AngularSlop &&
MathUtils.Cross(_limit12, n) >= -Settings.AngularSlop;
bool valid2 = MathUtils.Cross(n, _limit21) >= -Settings.AngularSlop &&
MathUtils.Cross(_limit22, n) >= -Settings.AngularSlop;
if (valid1 == false && valid2 == false)
{
continue;
}
float s1 = Vector2.Dot(n, _proxyB.Vertices[i] - _edgeA.V1);
float s2 = Vector2.Dot(n, _proxyB.Vertices[i] - _edgeA.V2);
float s = Math.Min(s1, s2);
if (s > _radius)
{
axis.Type = EPAxisType.EdgeB;
axis.Index = i;
axis.Separation = s;
}
if (s > axis.Separation)
{
axis.Type = EPAxisType.EdgeB;
axis.Index = i;
axis.Separation = s;
}
}
return axis;
}
private static void FindIncidentEdge(ref FixedArray2<ClipVertex> c, EPProxy proxy1, int edge1, EPProxy proxy2)
{
int count2 = proxy2.Count;
Debug.Assert(0 <= edge1 && edge1 < proxy1.Count);
// Get the normal of the reference edge in proxy2's frame.
Vector2 normal1 = proxy1.Normals[edge1];
// Find the incident edge on proxy2.
int index = 0;
float minDot = float.MaxValue;
for (int i = 0; i < count2; ++i)
{
float dot = Vector2.Dot(normal1, proxy2.Normals[i]);
if (dot < minDot)
{
minDot = dot;
index = i;
}
}
// Build the clip vertices for the incident edge.
int i1 = index;
int i2 = i1 + 1 < count2 ? i1 + 1 : 0;
ClipVertex cTemp = new ClipVertex();
cTemp.V = proxy2.Vertices[i1];
cTemp.ID.Features.IndexA = (byte)edge1;
cTemp.ID.Features.IndexB = (byte)i1;
cTemp.ID.Features.TypeA = (byte)ContactFeatureType.Face;
cTemp.ID.Features.TypeB = (byte)ContactFeatureType.Vertex;
c[0] = cTemp;
cTemp.V = proxy2.Vertices[i2];
cTemp.ID.Features.IndexA = (byte)edge1;
cTemp.ID.Features.IndexB = (byte)i2;
cTemp.ID.Features.TypeA = (byte)ContactFeatureType.Face;
cTemp.ID.Features.TypeB = (byte)ContactFeatureType.Vertex;
c[1] = cTemp;
}
/// <summary>
/// Clipping for contact manifolds.
/// </summary>
/// <param name="vOut">The v out.</param>
/// <param name="vIn">The v in.</param>
/// <param name="normal">The normal.</param>
/// <param name="offset">The offset.</param>
/// <param name="vertexIndexA">The vertex index A.</param>
/// <returns></returns>
private static int ClipSegmentToLine(out FixedArray2<ClipVertex> vOut, ref FixedArray2<ClipVertex> vIn,
Vector2 normal, float offset, int vertexIndexA)
{
vOut = new FixedArray2<ClipVertex>();
ClipVertex v0 = vIn[0];
ClipVertex v1 = vIn[1];
// Start with no output points
int numOut = 0;
// Calculate the distance of end points to the line
float distance0 = normal.X * v0.V.X + normal.Y * v0.V.Y - offset;
float distance1 = normal.X * v1.V.X + normal.Y * v1.V.Y - offset;
// If the points are behind the plane
if (distance0 <= 0.0f) vOut[numOut++] = v0;
if (distance1 <= 0.0f) vOut[numOut++] = v1;
// If the points are on different sides of the plane
if (distance0 * distance1 < 0.0f)
{
// Find intersection point of edge and plane
float interp = distance0 / (distance0 - distance1);
ClipVertex cv = vOut[numOut];
cv.V.X = v0.V.X + interp * (v1.V.X - v0.V.X);
cv.V.Y = v0.V.Y + interp * (v1.V.Y - v0.V.Y);
// VertexA is hitting edgeB.
cv.ID.Features.IndexA = (byte)vertexIndexA;
cv.ID.Features.IndexB = v0.ID.Features.IndexB;
cv.ID.Features.TypeA = (byte)ContactFeatureType.Vertex;
cv.ID.Features.TypeB = (byte)ContactFeatureType.Face;
vOut[numOut] = cv;
++numOut;
}
return numOut;
}
/// <summary>
/// Find the separation between poly1 and poly2 for a give edge normal on poly1.
/// </summary>
/// <param name="poly1">The poly1.</param>
/// <param name="xf1">The XF1.</param>
/// <param name="edge1">The edge1.</param>
/// <param name="poly2">The poly2.</param>
/// <param name="xf2">The XF2.</param>
/// <returns></returns>
private static float EdgeSeparation(PolygonShape poly1, ref Transform xf1, int edge1,
PolygonShape poly2, ref Transform xf2)
{
int count2 = poly2.Vertices.Count;
Debug.Assert(0 <= edge1 && edge1 < poly1.Vertices.Count);
// Convert normal from poly1's frame into poly2's frame.
Vector2 p1n = poly1.Normals[edge1];
float normalWorldx = xf1.R.Col1.X * p1n.X + xf1.R.Col2.X * p1n.Y;
float normalWorldy = xf1.R.Col1.Y * p1n.X + xf1.R.Col2.Y * p1n.Y;
Vector2 normal = new Vector2(normalWorldx * xf2.R.Col1.X + normalWorldy * xf2.R.Col1.Y,
normalWorldx * xf2.R.Col2.X + normalWorldy * xf2.R.Col2.Y);
// Find support vertex on poly2 for -normal.
int index = 0;
float minDot = Settings.MaxFloat;
for (int i = 0; i < count2; ++i)
{
float dot = Vector2.Dot(poly2.Vertices[i], normal);
if (dot < minDot)
{
minDot = dot;
index = i;
}
}
Vector2 p1ve = poly1.Vertices[edge1];
Vector2 p2vi = poly2.Vertices[index];
return ((xf2.Position.X + xf2.R.Col1.X * p2vi.X + xf2.R.Col2.X * p2vi.Y) -
(xf1.Position.X + xf1.R.Col1.X * p1ve.X + xf1.R.Col2.X * p1ve.Y)) * normalWorldx +
((xf2.Position.Y + xf2.R.Col1.Y * p2vi.X + xf2.R.Col2.Y * p2vi.Y) -
(xf1.Position.Y + xf1.R.Col1.Y * p1ve.X + xf1.R.Col2.Y * p1ve.Y)) * normalWorldy;
}
/// <summary>
/// Find the max separation between poly1 and poly2 using edge normals from poly1.
/// </summary>
/// <param name="edgeIndex">Index of the edge.</param>
/// <param name="poly1">The poly1.</param>
/// <param name="xf1">The XF1.</param>
/// <param name="poly2">The poly2.</param>
/// <param name="xf2">The XF2.</param>
/// <returns></returns>
private static float FindMaxSeparation(out int edgeIndex,
PolygonShape poly1, ref Transform xf1,
PolygonShape poly2, ref Transform xf2)
{
int count1 = poly1.Vertices.Count;
// Vector pointing from the centroid of poly1 to the centroid of poly2.
float dx = (xf2.Position.X + xf2.R.Col1.X * poly2.MassData.Centroid.X +
xf2.R.Col2.X * poly2.MassData.Centroid.Y) -
(xf1.Position.X + xf1.R.Col1.X * poly1.MassData.Centroid.X +
xf1.R.Col2.X * poly1.MassData.Centroid.Y);
float dy = (xf2.Position.Y + xf2.R.Col1.Y * poly2.MassData.Centroid.X +
xf2.R.Col2.Y * poly2.MassData.Centroid.Y) -
(xf1.Position.Y + xf1.R.Col1.Y * poly1.MassData.Centroid.X +
xf1.R.Col2.Y * poly1.MassData.Centroid.Y);
Vector2 dLocal1 = new Vector2(dx * xf1.R.Col1.X + dy * xf1.R.Col1.Y, dx * xf1.R.Col2.X + dy * xf1.R.Col2.Y);
// Find edge normal on poly1 that has the largest projection onto d.
int edge = 0;
float maxDot = -Settings.MaxFloat;
for (int i = 0; i < count1; ++i)
{
float dot = Vector2.Dot(poly1.Normals[i], dLocal1);
if (dot > maxDot)
{
maxDot = dot;
edge = i;
}
}
// Get the separation for the edge normal.
float s = EdgeSeparation(poly1, ref xf1, edge, poly2, ref xf2);
// Check the separation for the previous edge normal.
int prevEdge = edge - 1 >= 0 ? edge - 1 : count1 - 1;
float sPrev = EdgeSeparation(poly1, ref xf1, prevEdge, poly2, ref xf2);
// Check the separation for the next edge normal.
int nextEdge = edge + 1 < count1 ? edge + 1 : 0;
float sNext = EdgeSeparation(poly1, ref xf1, nextEdge, poly2, ref xf2);
// Find the best edge and the search direction.
int bestEdge;
float bestSeparation;
int increment;
if (sPrev > s && sPrev > sNext)
{
increment = -1;
bestEdge = prevEdge;
bestSeparation = sPrev;
}
else if (sNext > s)
{
increment = 1;
bestEdge = nextEdge;
bestSeparation = sNext;
}
else
{
edgeIndex = edge;
return s;
}
// Perform a local search for the best edge normal.
for (; ; )
{
if (increment == -1)
edge = bestEdge - 1 >= 0 ? bestEdge - 1 : count1 - 1;
else
edge = bestEdge + 1 < count1 ? bestEdge + 1 : 0;
s = EdgeSeparation(poly1, ref xf1, edge, poly2, ref xf2);
if (s > bestSeparation)
{
bestEdge = edge;
bestSeparation = s;
}
else
{
break;
}
}
edgeIndex = bestEdge;
return bestSeparation;
}
private static void FindIncidentEdge(out FixedArray2<ClipVertex> c,
PolygonShape poly1, ref Transform xf1, int edge1,
PolygonShape poly2, ref Transform xf2)
{
c = new FixedArray2<ClipVertex>();
int count2 = poly2.Vertices.Count;
Debug.Assert(0 <= edge1 && edge1 < poly1.Vertices.Count);
// Get the normal of the reference edge in poly2's frame.
Vector2 v = poly1.Normals[edge1];
float tmpx = xf1.R.Col1.X * v.X + xf1.R.Col2.X * v.Y;
float tmpy = xf1.R.Col1.Y * v.X + xf1.R.Col2.Y * v.Y;
Vector2 normal1 = new Vector2(tmpx * xf2.R.Col1.X + tmpy * xf2.R.Col1.Y,
tmpx * xf2.R.Col2.X + tmpy * xf2.R.Col2.Y);
// Find the incident edge on poly2.
int index = 0;
float minDot = Settings.MaxFloat;
for (int i = 0; i < count2; ++i)
{
float dot = Vector2.Dot(normal1, poly2.Normals[i]);
if (dot < minDot)
{
minDot = dot;
index = i;
}
}
// Build the clip vertices for the incident edge.
int i1 = index;
int i2 = i1 + 1 < count2 ? i1 + 1 : 0;
ClipVertex cv0 = c[0];
Vector2 v1 = poly2.Vertices[i1];
cv0.V.X = xf2.Position.X + xf2.R.Col1.X * v1.X + xf2.R.Col2.X * v1.Y;
cv0.V.Y = xf2.Position.Y + xf2.R.Col1.Y * v1.X + xf2.R.Col2.Y * v1.Y;
cv0.ID.Features.IndexA = (byte)edge1;
cv0.ID.Features.IndexB = (byte)i1;
cv0.ID.Features.TypeA = (byte)ContactFeatureType.Face;
cv0.ID.Features.TypeB = (byte)ContactFeatureType.Vertex;
c[0] = cv0;
ClipVertex cv1 = c[1];
Vector2 v2 = poly2.Vertices[i2];
cv1.V.X = xf2.Position.X + xf2.R.Col1.X * v2.X + xf2.R.Col2.X * v2.Y;
cv1.V.Y = xf2.Position.Y + xf2.R.Col1.Y * v2.X + xf2.R.Col2.Y * v2.Y;
cv1.ID.Features.IndexA = (byte)edge1;
cv1.ID.Features.IndexB = (byte)i2;
cv1.ID.Features.TypeA = (byte)ContactFeatureType.Face;
cv1.ID.Features.TypeB = (byte)ContactFeatureType.Vertex;
c[1] = cv1;
}
}
}
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