line test + improving AABB sweep
parent
72573219ed
commit
1916415fb4
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@ -66,6 +66,14 @@ namespace MoonWorks.Collision.Fixed
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);
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}
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// When you don't know which values are smaller!
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public static AABB2D Create(Fix64 x1, Fix64 y1, Fix64 x2, Fix64 y2)
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{
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var min = new Vector2(Fix64.Min(x1, x2), Fix64.Min(y1, y2));
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var max = new Vector2(Fix64.Max(x1, x2), Fix64.Max(y1, y2));
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return new AABB2D(min, max);
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}
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static readonly Fix64 Half = Fix64.FromFraction(1, 2);
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/// <summary>
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@ -112,9 +120,9 @@ namespace MoonWorks.Collision.Fixed
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var extent = aabb.Max - center;
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var newCenter = Vector2.Transform(center, transform.TransformMatrix);
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var newExtent = Vector2.TransformNormal(extent, AbsoluteMatrix(transform.TransformMatrix));
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var newExtent = Vector2.TransformNormal(extent, AbsoluteMatrix(transform.TransformMatrix));
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return new AABB2D(newCenter - newExtent, newCenter + newExtent);
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return new AABB2D(newCenter - newExtent, newCenter + newExtent);
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}
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public AABB2D Compose(AABB2D aabb)
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@ -185,67 +193,25 @@ namespace MoonWorks.Collision.Fixed
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return a.Left < b.Right && a.Right > b.Left && a.Top < b.Bottom && a.Bottom > b.Top;
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}
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// FIXME: this is broken
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public static bool SweepTest(AABB2D a, AABB2D b, Vector2 aMovement, Vector2 bMovement, out Fix64 normalizedTime)
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private static AABB2D RotateAroundOrigin(AABB2D aabb)
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{
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if (TestOverlap(a, b))
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{
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normalizedTime = Fix64.Zero;
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return true;
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}
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return Create(-aabb.Min.X, -aabb.Min.Y, -aabb.Max.X, -aabb.Max.Y);
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}
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normalizedTime = Fix64.One;
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private static AABB2D MinkowskiSum(AABB2D a, AABB2D b)
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{
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return new AABB2D(a.Min.X + b.Min.X, a.Min.Y + b.Min.Y, a.Max.X + b.Max.X, a.Max.Y + b.Max.Y);
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}
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var relativeVelocity = bMovement - aMovement;
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public static bool SweepTest(AABB2D a, AABB2D b, Vector2 aMovement, Vector2 bMovement, out Fix64 entry, out Fix64 exit)
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{
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var rotatedA = RotateAroundOrigin(a);
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var sum = MinkowskiSum(rotatedA, b);
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Vector2 entry = Vector2.Zero;
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if (a.Max.X < b.Min.X && relativeVelocity.X < 0)
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{
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entry.X = (a.Max.X - b.Min.X) / relativeVelocity.X;
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}
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else if (b.Max.X < a.Min.X && relativeVelocity.X > 0)
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{
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entry.X = (a.Min.X - b.Max.X) / relativeVelocity.X;
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}
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var relativeMovement = aMovement - bMovement;
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var line = new Line(Vector2.Zero, relativeMovement);
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if (a.Max.Y < b.Min.Y && relativeVelocity.Y < 0)
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{
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entry.Y = (a.Max.Y - b.Min.Y) / relativeVelocity.Y;
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}
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else if (b.Max.Y > a.Min.Y && relativeVelocity.Y > 0)
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{
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entry.Y = (a.Min.Y - b.Max.Y) / relativeVelocity.Y;
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}
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Vector2 exit = new Vector2(Fix64.MaxValue, Fix64.MaxValue);
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if (b.Max.X > a.Min.X && relativeVelocity.X < 0)
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{
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exit.X = (a.Min.X - b.Max.X) / relativeVelocity.X;
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}
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else if (a.Max.X > b.Min.X && relativeVelocity.X > 0)
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{
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exit.Y = (a.Max.X - b.Min.X) / relativeVelocity.X;
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}
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if (b.Max.Y > a.Min.Y && relativeVelocity.Y < 0)
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{
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exit.Y = (a.Min.Y - b.Max.Y) / relativeVelocity.Y;
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}
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else if (a.Max.Y > b.Min.Y && relativeVelocity.Y > 0)
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{
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exit.Y = (a.Max.Y - b.Min.Y) / relativeVelocity.Y;
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}
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Fix64 firstTime = Fix64.Max(entry.X, entry.Y);
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Fix64 lastTime = Fix64.Min(exit.X, exit.Y);
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if (firstTime <= lastTime && firstTime > 0)
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{
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normalizedTime = firstTime;
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return true;
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}
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return false;
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return NarrowPhase.TestLineAABBOverlap(line, sum, out entry, out exit);
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}
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public override bool Equals(object obj)
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@ -93,6 +93,13 @@ namespace MoonWorks.Collision.Fixed
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return TestCollision(rectangle, transformA, rectangleB, transformB);
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}
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}
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else if (shapeA is Line line)
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{
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if (shapeB is Line lineB)
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{
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return TestCollision(line, transformA, lineB, transformB);
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}
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}
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return FindCollisionSimplex(shapeA, transformA, shapeB, transformB).Item1;
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}
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@ -172,6 +179,11 @@ namespace MoonWorks.Collision.Fixed
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}
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}
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public static bool TestCollision(in Line lineA, in Transform2D transformA, in Line lineB, in Transform2D transformB)
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{
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return TestLineOverlap(lineA, transformA, lineB, transformB);
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static bool TestRectangleOverlap(in Rectangle rectangleA, in Transform2D transformA, in Rectangle rectangleB, in Transform2D transformB)
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{
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@ -237,6 +249,92 @@ namespace MoonWorks.Collision.Fixed
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return distanceSquared < radiusSumSquared;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static bool TestLineOverlap(in Line lineA, in Transform2D transformA, in Line lineB, in Transform2D transformB)
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{
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var b = lineA.End - lineA.Start;
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var d = lineB.End - lineB.Start;
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var bDotDPerp = b.X * d.Y - b.Y * d.X;
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if (bDotDPerp == Fix64.Zero)
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{
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return false;
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}
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var c = lineB.Start - lineA.Start;
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var t = (c.X * d.Y - c.Y * d.X) / bDotDPerp;
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if (t < 0 || t > 1)
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{
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return false;
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}
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var u = (c.X * b.Y - c.Y * b.X) / bDotDPerp;
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if (u < 0 || u > 1)
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{
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return false;
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}
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return true;
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}
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public static bool TestLineOverlap(in Line lineA, in Transform2D transformA, in Line lineB, in Transform2D transformB, out Vector2 intersection)
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{
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intersection = Vector2.Zero;
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var b = lineA.End - lineA.Start;
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var d = lineB.End - lineB.Start;
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var bDotDPerp = b.X * d.Y - b.Y * d.X;
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if (bDotDPerp == Fix64.Zero)
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{
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return false;
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}
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var c = lineB.Start - lineA.Start;
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var t = (c.X * d.Y - c.Y * d.X) / bDotDPerp;
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if (t < 0 || t > 1)
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{
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return false;
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}
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var u = (c.X * b.Y - c.Y * b.X) / bDotDPerp;
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if (u < 0 || u > 1)
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{
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return false;
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}
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intersection = lineA.Start + t * b;
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return true;
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}
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public static bool TestLineAABBOverlap(in Line line, in AABB2D aabb, out Fix64 entry, out Fix64 exit)
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{
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entry = Fix64.MinValue;
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exit = Fix64.MaxValue;
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var lineDirection = line.End - line.Start;
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if (lineDirection.X != Fix64.Zero)
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{
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var tx1 = (aabb.Min.X - line.Start.X) / lineDirection.X;
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var tx2 = (aabb.Max.X - line.Start.X) / lineDirection.X;
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entry = Fix64.Max(entry, Fix64.Min(tx1, tx2));
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exit = Fix64.Min(exit, Fix64.Max(tx1, tx2));
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}
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if (lineDirection.Y != Fix64.Zero)
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{
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var ty1 = (aabb.Min.Y - line.Start.Y) / lineDirection.Y;
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var ty2 = (aabb.Max.Y - line.Start.Y) / lineDirection.Y;
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entry = Fix64.Max(entry, Fix64.Min(ty1, ty2));
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exit = Fix64.Min(exit, Fix64.Max(ty1, ty2));
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}
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return exit >= entry;
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}
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public static bool TestPointOverlap(in Point pointA, in Transform2D transformA, in Point pointB, in Transform2D transformB)
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{
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return transformA.Position == transformB.Position;
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@ -250,47 +348,47 @@ namespace MoonWorks.Collision.Fixed
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return Check(minkowskiDifference, c, b);
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}
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public unsafe static Vector2 Intersect(IShape2D shapeA, Transform2D Transform2DA, IShape2D shapeB, Transform2D Transform2DB, Simplex2D simplex)
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{
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if (shapeA == null) { throw new System.ArgumentNullException(nameof(shapeA)); }
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if (shapeB == null) { throw new System.ArgumentNullException(nameof(shapeB)); }
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if (!simplex.TwoSimplex) { throw new System.ArgumentException("Simplex must be a 2-Simplex.", nameof(simplex)); }
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public unsafe static Vector2 Intersect(IShape2D shapeA, Transform2D Transform2DA, IShape2D shapeB, Transform2D Transform2DB, Simplex2D simplex)
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{
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if (shapeA == null) { throw new System.ArgumentNullException(nameof(shapeA)); }
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if (shapeB == null) { throw new System.ArgumentNullException(nameof(shapeB)); }
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if (!simplex.TwoSimplex) { throw new System.ArgumentException("Simplex must be a 2-Simplex.", nameof(simplex)); }
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var epsilon = Fix64.FromFraction(1, 10000);
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var a = simplex.A;
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var b = simplex.B.Value;
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var c = simplex.C.Value;
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var b = simplex.B.Value;
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var c = simplex.C.Value;
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Vector2 intersection = default;
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Vector2 intersection = default;
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for (var i = 0; i < 32; i++)
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{
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var edge = FindClosestEdge(simplex);
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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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for (var i = 0; i < 32; i++)
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{
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var edge = FindClosestEdge(simplex);
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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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intersection = edge.Normal;
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intersection *= distance;
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if (Fix64.Abs(distance - edge.Distance) <= 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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if (Fix64.Abs(distance - edge.Distance) <= 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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simplex.Insert(support, edge.Index);
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}
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}
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}
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}
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return intersection; // close enough
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}
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return intersection; // close enough
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}
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private static unsafe Edge FindClosestEdge(Simplex2D simplex)
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{
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private static unsafe Edge FindClosestEdge(Simplex2D simplex)
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{
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var closestDistance = Fix64.MaxValue;
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var closestNormal = Vector2.Zero;
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var closestIndex = 0;
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var closestNormal = Vector2.Zero;
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var closestIndex = 0;
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for (var i = 0; i < 4; i += 1)
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{
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@ -315,136 +413,136 @@ namespace MoonWorks.Collision.Fixed
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}
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}
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return new Edge
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return new Edge
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{
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Distance = closestDistance,
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Normal = closestNormal,
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Index = closestIndex
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};
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}
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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private static Vector2 CalculateSupport<T, U>(T shapeA, Transform2D Transform2DA, U shapeB, Transform2D Transform2DB, Vector2 direction) where T : IShape2D where U : IShape2D
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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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return shapeA.Support(direction, Transform2DA) - shapeB.Support(-direction, Transform2DB);
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}
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private static (bool, Simplex2D) Check<T, U>(MinkowskiDifference<T, U> minkowskiDifference, Vector2 c, Vector2 b) where T : IShape2D where U : IShape2D
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{
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var cb = c - b;
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var c0 = -c;
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var d = Direction(cb, c0);
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return DoSimplex(minkowskiDifference, new Simplex2D(b, c), d);
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}
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{
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var cb = c - b;
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var c0 = -c;
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var d = Direction(cb, c0);
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return DoSimplex(minkowskiDifference, new Simplex2D(b, c), d);
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}
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private static (bool, Simplex2D) DoSimplex<T, U>(MinkowskiDifference<T, U> minkowskiDifference, Simplex2D simplex, Vector2 direction) where T : IShape2D where U : IShape2D
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{
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var a = minkowskiDifference.Support(direction);
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var notPastOrigin = Vector2.Dot(a, direction) < Fix64.Zero;
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var (intersects, newSimplex, newDirection) = EnclosesOrigin(a, simplex);
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private static (bool, Simplex2D) DoSimplex<T, U>(MinkowskiDifference<T, U> minkowskiDifference, Simplex2D simplex, Vector2 direction) where T : IShape2D where U : IShape2D
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{
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var a = minkowskiDifference.Support(direction);
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var notPastOrigin = Vector2.Dot(a, direction) < Fix64.Zero;
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var (intersects, newSimplex, newDirection) = EnclosesOrigin(a, simplex);
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if (notPastOrigin)
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{
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return (false, default(Simplex2D));
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}
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else if (intersects)
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{
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return (true, new Simplex2D(simplex.A, simplex.B.Value, a));
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}
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else
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{
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return DoSimplex(minkowskiDifference, newSimplex, newDirection);
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}
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}
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if (notPastOrigin)
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{
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return (false, default(Simplex2D));
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}
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else if (intersects)
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{
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return (true, new Simplex2D(simplex.A, simplex.B.Value, a));
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}
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else
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{
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return DoSimplex(minkowskiDifference, newSimplex, newDirection);
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}
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}
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private static (bool, Simplex2D, Vector2) EnclosesOrigin(Vector2 a, Simplex2D simplex)
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{
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if (simplex.ZeroSimplex)
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{
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return HandleZeroSimplex(a, simplex.A);
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}
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else if (simplex.OneSimplex)
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{
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return HandleOneSimplex(a, simplex.A, simplex.B.Value);
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}
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else
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{
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return (false, simplex, Vector2.Zero);
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}
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}
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private static (bool, Simplex2D, Vector2) EnclosesOrigin(Vector2 a, Simplex2D simplex)
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{
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if (simplex.ZeroSimplex)
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{
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return HandleZeroSimplex(a, simplex.A);
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}
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else if (simplex.OneSimplex)
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{
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return HandleOneSimplex(a, simplex.A, simplex.B.Value);
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}
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else
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{
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return (false, simplex, Vector2.Zero);
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}
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}
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private static (bool, Simplex2D, Vector2) HandleZeroSimplex(Vector2 a, Vector2 b)
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{
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var ab = b - a;
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var a0 = -a;
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var (newSimplex, newDirection) = SameDirection(ab, a0) ? (new Simplex2D(a, b), Perpendicular(ab, a0)) : (new Simplex2D(a), a0);
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return (false, newSimplex, newDirection);
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}
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private static (bool, Simplex2D, Vector2) HandleZeroSimplex(Vector2 a, Vector2 b)
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{
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var ab = b - a;
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var a0 = -a;
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var (newSimplex, newDirection) = SameDirection(ab, a0) ? (new Simplex2D(a, b), Perpendicular(ab, a0)) : (new Simplex2D(a), a0);
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return (false, newSimplex, newDirection);
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}
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private static (bool, Simplex2D, Vector2) HandleOneSimplex(Vector2 a, Vector2 b, Vector2 c)
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{
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var a0 = -a;
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var ab = b - a;
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var ac = c - a;
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var abp = Perpendicular(ab, -ac);
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var acp = Perpendicular(ac, -ab);
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private static (bool, Simplex2D, Vector2) HandleOneSimplex(Vector2 a, Vector2 b, Vector2 c)
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{
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var a0 = -a;
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var ab = b - a;
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var ac = c - a;
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var abp = Perpendicular(ab, -ac);
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var acp = Perpendicular(ac, -ab);
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if (SameDirection(abp, a0))
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{
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if (SameDirection(ab, a0))
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{
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return (false, new Simplex2D(a, b), abp);
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}
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else
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{
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return (false, new Simplex2D(a), a0);
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}
|
||||
}
|
||||
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);
|
||||
}
|
||||
}
|
||||
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, Fix64.Zero);
|
||||
var B = new Vector3(b.X, b.Y, Fix64.Zero);
|
||||
var C = new Vector3(c.X, c.Y, Fix64.Zero);
|
||||
private static Vector2 TripleProduct(Vector2 a, Vector2 b, Vector2 c)
|
||||
{
|
||||
var A = new Vector3(a.X, a.Y, Fix64.Zero);
|
||||
var B = new Vector3(b.X, b.Y, Fix64.Zero);
|
||||
var C = new Vector3(c.X, c.Y, Fix64.Zero);
|
||||
|
||||
var first = Vector3.Cross(A, B);
|
||||
var second = Vector3.Cross(first, C);
|
||||
var first = Vector3.Cross(A, B);
|
||||
var second = Vector3.Cross(first, C);
|
||||
|
||||
return new Vector2(second.X, second.Y);
|
||||
}
|
||||
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 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;
|
||||
}
|
||||
|
||||
[MethodImpl(MethodImplOptions.AggressiveInlining)]
|
||||
private static bool SameDirection(Vector2 a, Vector2 b)
|
||||
{
|
||||
return Vector2.Dot(a, b) > Fix64.Zero;
|
||||
}
|
||||
{
|
||||
return Vector2.Dot(a, b) > Fix64.Zero;
|
||||
}
|
||||
|
||||
private static Vector2 Perpendicular(Vector2 a, Vector2 b)
|
||||
{
|
||||
return TripleProduct(a, b, a);
|
||||
}
|
||||
private static Vector2 Perpendicular(Vector2 a, Vector2 b)
|
||||
{
|
||||
return TripleProduct(a, b, a);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
|
|
|||
Loading…
Reference in New Issue