103 lines
3.5 KiB
C#
103 lines
3.5 KiB
C#
/*
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* Implementation of the Expanding Polytope Algorithm
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* as based on the following blog post:
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* https://blog.hamaluik.ca/posts/building-a-collision-engine-part-2-2d-penetration-vectors/
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*/
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using Microsoft.Xna.Framework;
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using MoonTools.Core.Structs;
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using System;
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using System.Collections.Generic;
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namespace MoonTools.Core.Bonk
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{
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enum PolygonWinding
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{
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Clockwise,
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CounterClockwise
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}
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public static class EPA2D
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{
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// vector returned gives direction from A to B
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public static Vector2 Intersect(IShape2D shapeA, Transform2D Transform2DA, IShape2D shapeB, Transform2D Transform2DB, IEnumerable<Vector2> givenSimplexVertices)
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{
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var simplexVertices = new SimplexVertices(new Vector2?[36]);
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foreach (var vertex in givenSimplexVertices)
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{
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simplexVertices.Add(vertex);
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}
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var e0 = (simplexVertices[1].X - simplexVertices[0].X) * (simplexVertices[1].Y + simplexVertices[0].Y);
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var e1 = (simplexVertices[2].X - simplexVertices[1].X) * (simplexVertices[2].Y + simplexVertices[1].Y);
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var e2 = (simplexVertices[0].X - simplexVertices[2].X) * (simplexVertices[0].Y + simplexVertices[2].Y);
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var winding = e0 + e1 + e2 >= 0 ? PolygonWinding.Clockwise : PolygonWinding.CounterClockwise;
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Vector2 intersection = default;
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for (int i = 0; i < 32; i++)
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{
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var edge = FindClosestEdge(winding, simplexVertices);
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var support = CalculateSupport(shapeA, Transform2DA, shapeB, Transform2DB, edge.normal);
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var distance = Vector2.Dot(support, edge.normal);
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intersection = edge.normal;
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intersection *= distance;
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if (Math.Abs(distance - edge.distance) <= float.Epsilon)
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{
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return intersection;
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}
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else
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{
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simplexVertices.Insert(edge.index, support);
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}
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}
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return intersection;
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}
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private static Edge FindClosestEdge(PolygonWinding winding, SimplexVertices simplexVertices)
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{
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var closestDistance = float.PositiveInfinity;
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var closestNormal = Vector2.Zero;
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var closestIndex = 0;
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for (int i = 0; i < simplexVertices.Count; i++)
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{
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var j = i + 1;
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if (j >= simplexVertices.Count) { j = 0; }
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Vector2 edge = simplexVertices[j] - simplexVertices[i];
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Vector2 norm;
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if (winding == PolygonWinding.Clockwise)
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{
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norm = new Vector2(edge.Y, -edge.X);
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}
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else
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{
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norm = new Vector2(-edge.Y, edge.X);
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}
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norm.Normalize();
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var dist = Vector2.Dot(norm, simplexVertices[i]);
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if (dist < closestDistance)
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{
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closestDistance = dist;
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closestNormal = norm;
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closestIndex = j;
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}
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}
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return new Edge(closestDistance, closestNormal, closestIndex);
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}
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private static Vector2 CalculateSupport(IShape2D shapeA, Transform2D Transform2DA, IShape2D shapeB, Transform2D Transform2DB, Vector2 direction)
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{
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return shapeA.Support(direction, Transform2DA) - shapeB.Support(-direction, Transform2DB);
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}
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}
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}
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