MoonTools.Bonk/Bonk/NarrowPhase/NarrowPhase.cs

306 lines
12 KiB
C#
Raw Normal View History

2020-02-21 02:07:59 +00:00
using MoonTools.Structs;
using System.Numerics;
2020-02-21 02:07:59 +00:00
namespace MoonTools.Bonk
{
public static class NarrowPhase
{
private enum PolygonWinding
{
Clockwise,
CounterClockwise
}
/// <summary>
/// Tests if two shape-transform pairs are overlapping. Automatically detects fast-path optimizations.
/// </summary>
public static bool TestCollision(IShape2D shapeA, Transform2D transformA, IShape2D shapeB, Transform2D transformB)
{
if (shapeA is Rectangle rectangleA && shapeB is Rectangle rectangleB && transformA.Rotation == 0 && transformB.Rotation == 0)
{
return TestRectangleOverlap(rectangleA, transformA, rectangleB, transformB);
}
else if (shapeA is Point && shapeB is Rectangle && transformB.Rotation == 0)
{
return TestPointRectangleOverlap((Point)shapeA, transformA, (Rectangle)shapeB, transformB);
}
else if (shapeA is Rectangle && shapeB is Point && transformA.Rotation == 0)
{
return TestPointRectangleOverlap((Point)shapeB, transformB, (Rectangle)shapeA, transformA);
}
else if (shapeA is Circle circleA && shapeB is Circle circleB && transformA.Scale.X == transformA.Scale.Y && transformB.Scale.X == transformB.Scale.Y)
{
return TestCircleOverlap(circleA, transformA, circleB, transformB);
}
return FindCollisionSimplex(shapeA, transformA, shapeB, transformB).Item1;
}
/// <summary>
/// Fast path for axis-aligned rectangles. If the transforms have non-zero rotation this will be inaccurate.
/// </summary>
/// <param name="rectangleA"></param>
/// <param name="transformA"></param>
/// <param name="rectangleB"></param>
/// <param name="transformB"></param>
/// <returns></returns>
public static bool TestRectangleOverlap(Rectangle rectangleA, Transform2D transformA, Rectangle rectangleB, Transform2D transformB)
{
var firstAABB = rectangleA.TransformedAABB(transformA);
var secondAABB = rectangleB.TransformedAABB(transformB);
return firstAABB.Left <= secondAABB.Right && firstAABB.Right >= secondAABB.Left && firstAABB.Top <= secondAABB.Bottom && firstAABB.Bottom >= secondAABB.Top;
}
/// <summary>
/// Fast path for overlapping point and axis-aligned rectangle. The rectangle transform must have non-zero rotation.
/// </summary>
/// <param name="point"></param>
/// <param name="pointTransform"></param>
/// <param name="rectangle"></param>
/// <param name="rectangleTransform"></param>
/// <returns></returns>
public static bool TestPointRectangleOverlap(Point point, Transform2D pointTransform, Rectangle rectangle, Transform2D rectangleTransform)
{
var transformedPoint = pointTransform.Position;
var AABB = rectangle.TransformedAABB(rectangleTransform);
return transformedPoint.X >= AABB.Left && transformedPoint.X <= AABB.Right && transformedPoint.Y <= AABB.Bottom && transformedPoint.Y >= AABB.Top;
}
/// <summary>
/// Fast path for overlapping circles. The circles must have uniform scaling.
/// </summary>
/// <param name="circleA"></param>
/// <param name="transformA"></param>
/// <param name="circleB"></param>
/// <param name="transformB"></param>
/// <returns></returns>
public static bool TestCircleOverlap(Circle circleA, Transform2D transformA, Circle circleB, Transform2D transformB)
{
var radiusA = circleA.Radius * transformA.Scale.X;
var radiusB = circleB.Radius * transformB.Scale.Y;
var centerA = transformA.Position;
var centerB = transformB.Position;
var distanceSquared = (centerA - centerB).LengthSquared();
var radiusSumSquared = (radiusA + radiusB) * (radiusA + radiusB);
return distanceSquared <= radiusSumSquared;
}
/// <summary>
/// Tests if the two shape-transform pairs are overlapping, and returns a simplex that can be used by the EPA algorithm to determine a miminum separating vector.
/// </summary>
public static (bool, Simplex2D) FindCollisionSimplex(IShape2D shapeA, Transform2D transformA, IShape2D shapeB, Transform2D transformB)
{
var minkowskiDifference = new MinkowskiDifference(shapeA, transformA, shapeB, transformB);
var c = minkowskiDifference.Support(Vector2.UnitX);
var b = minkowskiDifference.Support(-Vector2.UnitX);
return Check(minkowskiDifference, c, b);
}
/// <summary>
/// Returns a minimum separating vector in the direction from A to B.
/// </summary>
/// <param name="simplex">A simplex returned by the GJK algorithm.</param>
public unsafe static Vector2 Intersect(IShape2D shapeA, Transform2D Transform2DA, IShape2D shapeB, Transform2D Transform2DB, Simplex2D simplex)
{
if (shapeA == null) { throw new System.ArgumentNullException(nameof(shapeA)); }
if (shapeB == null) { throw new System.ArgumentNullException(nameof(shapeB)); }
if (!simplex.TwoSimplex) { throw new System.ArgumentException("Simplex must be a 2-Simplex.", nameof(simplex)); }
var a = simplex.A;
var b = simplex.B.Value;
var c = simplex.C.Value;
var e0 = (b.X - a.X) * (b.Y + a.Y);
var e1 = (c.X - b.X) * (c.Y + b.Y);
var e2 = (a.X - c.X) * (a.Y + c.Y);
var winding = e0 + e1 + e2 >= 0 ? PolygonWinding.Clockwise : PolygonWinding.CounterClockwise;
var simplexVertices = new SimplexVertexBuffer(simplex.Vertices);
Vector2 intersection = default;
for (var i = 0; i < 32; i++)
{
var edge = FindClosestEdge(winding, simplexVertices);
var support = CalculateSupport(shapeA, Transform2DA, shapeB, Transform2DB, edge.normal);
var distance = Vector2.Dot(support, edge.normal);
intersection = edge.normal;
intersection *= distance;
if (System.Math.Abs(distance - edge.distance) <= float.Epsilon)
{
return intersection;
}
else
{
simplexVertices.Insert(edge.index, support);
}
}
return intersection;
}
private static Edge FindClosestEdge(PolygonWinding winding, SimplexVertexBuffer simplexVertices)
{
var closestDistance = float.PositiveInfinity;
var closestNormal = Vector2.Zero;
var closestIndex = 0;
for (var i = 0; i < simplexVertices.Length; i++)
{
var j = i + 1;
if (j >= simplexVertices.Length) { j = 0; }
var edge = simplexVertices[j] - simplexVertices[i];
Vector2 norm;
if (winding == PolygonWinding.Clockwise)
{
norm = Vector2.Normalize(new Vector2(edge.Y, -edge.X));
}
else
{
norm = Vector2.Normalize(new Vector2(-edge.Y, edge.X));
}
var dist = Vector2.Dot(norm, simplexVertices[i]);
if (dist < closestDistance)
{
closestDistance = dist;
closestNormal = norm;
closestIndex = j;
}
}
return new Edge(closestDistance, closestNormal, closestIndex);
}
private static Vector2 CalculateSupport(IShape2D shapeA, Transform2D Transform2DA, IShape2D shapeB, Transform2D Transform2DB, Vector2 direction)
{
return shapeA.Support(direction, Transform2DA) - shapeB.Support(-direction, Transform2DB);
}
private static (bool, Simplex2D) Check(MinkowskiDifference minkowskiDifference, Vector2 c, Vector2 b)
{
var cb = c - b;
var c0 = -c;
var d = Direction(cb, c0);
return DoSimplex(minkowskiDifference, new Simplex2D(b, c), d);
}
private static (bool, Simplex2D) DoSimplex(MinkowskiDifference minkowskiDifference, Simplex2D simplex, Vector2 direction)
{
var a = minkowskiDifference.Support(direction);
var notPastOrigin = Vector2.Dot(a, direction) < 0;
var (intersects, newSimplex, newDirection) = EnclosesOrigin(a, simplex);
if (notPastOrigin)
{
return (false, default(Simplex2D));
}
else if (intersects)
{
return (true, new Simplex2D(simplex.A, simplex.B.Value, a));
}
else
{
return DoSimplex(minkowskiDifference, newSimplex, newDirection);
}
}
private static (bool, Simplex2D, Vector2) EnclosesOrigin(Vector2 a, Simplex2D simplex)
{
if (simplex.ZeroSimplex)
{
return HandleZeroSimplex(a, simplex.A);
}
else if (simplex.OneSimplex)
{
return HandleOneSimplex(a, simplex.A, simplex.B.Value);
}
else
{
return (false, simplex, Vector2.Zero);
}
}
private static (bool, Simplex2D, Vector2) HandleZeroSimplex(Vector2 a, Vector2 b)
{
var ab = b - a;
var a0 = -a;
var (newSimplex, newDirection) = SameDirection(ab, a0) ? (new Simplex2D(a, b), Perpendicular(ab, a0)) : (new Simplex2D(a), a0);
return (false, newSimplex, newDirection);
}
private static (bool, Simplex2D, Vector2) HandleOneSimplex(Vector2 a, Vector2 b, Vector2 c)
{
var a0 = -a;
var ab = b - a;
var ac = c - a;
var abp = Perpendicular(ab, -ac);
var acp = Perpendicular(ac, -ab);
if (SameDirection(abp, a0))
{
if (SameDirection(ab, a0))
{
return (false, new Simplex2D(a, b), abp);
}
else
{
return (false, new Simplex2D(a), a0);
}
}
else if (SameDirection(acp, a0))
{
if (SameDirection(ac, a0))
{
return (false, new Simplex2D(a, c), acp);
}
else
{
return (false, new Simplex2D(a), a0);
}
}
else
{
return (true, new Simplex2D(b, c), a0);
}
}
private static Vector2 TripleProduct(Vector2 a, Vector2 b, Vector2 c)
{
var A = new Vector3(a.X, a.Y, 0);
var B = new Vector3(b.X, b.Y, 0);
var C = new Vector3(c.X, c.Y, 0);
var first = Vector3.Cross(A, B);
var second = Vector3.Cross(first, C);
return new Vector2(second.X, second.Y);
}
private static Vector2 Direction(Vector2 a, Vector2 b)
{
var d = TripleProduct(a, b, a);
var collinear = d == Vector2.Zero;
return collinear ? new Vector2(a.Y, -a.X) : d;
}
private static bool SameDirection(Vector2 a, Vector2 b)
{
return Vector2.Dot(a, b) > 0;
}
private static Vector2 Perpendicular(Vector2 a, Vector2 b)
{
return TripleProduct(a, b, a);
}
}
}