some more collision fast paths

src/Collision/NarrowPhase.cs

@@ -13,23 +13,41 @@ namespace MoonWorks.Collision
 
 		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)
+			// If we can use a fast path check, let's do that!
+			if (shapeA is Rectangle rectangleA && shapeB is Rectangle rectangleB && transformA.IsAxisAligned && transformB.IsAxisAligned)
 			{
 				return TestRectangleOverlap(rectangleA, transformA, rectangleB, transformB);
 			}
-			else if (shapeA is Point && shapeB is Rectangle && transformB.Rotation == 0)
+			else if (shapeA is Point && shapeB is Rectangle && transformB.IsAxisAligned)
 			{
 				return TestPointRectangleOverlap((Point) shapeA, transformA, (Rectangle) shapeB, transformB);
 			}
-			else if (shapeA is Rectangle && shapeB is Point && transformA.Rotation == 0)
+			else if (shapeA is Rectangle && shapeB is Point && transformA.IsAxisAligned)
 			{
 				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)
+			else if (shapeA is Rectangle && shapeB is Circle && transformA.IsAxisAligned && transformB.IsUniformScale)
+			{
+				return TestCircleRectangleOverlap((Circle) shapeB, transformB, (Rectangle) shapeA, transformA);
+			}
+			else if (shapeA is Circle && shapeB is Rectangle && transformA.IsUniformScale && transformB.IsAxisAligned)
+			{
+				return TestCircleRectangleOverlap((Circle) shapeA, transformA, (Rectangle) shapeB, transformB);
+			}
+			else if (shapeA is Circle && shapeB is Point && transformA.IsUniformScale)
+			{
+				return TestCirclePointOverlap((Circle) shapeA, transformA, (Point) shapeB, transformB);
+			}
+			else if (shapeA is Point && shapeB is Circle && transformB.IsUniformScale)
+			{
+				return TestCirclePointOverlap((Circle) shapeB, transformB, (Point) shapeA, transformA);
+			}
+			else if (shapeA is Circle circleA && shapeB is Circle circleB && transformA.IsUniformScale && transformB.IsUniformScale)
 			{
 				return TestCircleOverlap(circleA, transformA, circleB, transformB);
 			}
 
+			// Sad, we can't do a fast path optimization. Time for a simplex reduction.
 			return FindCollisionSimplex(shapeA, transformA, shapeB, transformB).Item1;
 		}
 
@@ -49,6 +67,36 @@ namespace MoonWorks.Collision
 			return transformedPoint.X > AABB.Left && transformedPoint.X < AABB.Right && transformedPoint.Y < AABB.Bottom && transformedPoint.Y > AABB.Top;
 		}
 
+		public static bool TestCirclePointOverlap(Circle circle, Transform2D circleTransform, Point point, Transform2D pointTransform)
+		{
+			var circleCenter = circleTransform.Position;
+			var circleRadius = circle.Radius * circleTransform.Scale.X;
+
+			var distanceX = circleCenter.X - pointTransform.Position.X;
+			var distanceY = circleCenter.Y - pointTransform.Position.Y;
+
+			return (distanceX * distanceX) + (distanceY * distanceY) < (circleRadius * circleRadius);
+		}
+
+		/// <summary>
+		/// NOTE: The rectangle must be axis aligned, and the scaling of the circle must be uniform.
+		/// </summary>
+		public static bool TestCircleRectangleOverlap(Circle circle, Transform2D circleTransform, Rectangle rectangle, Transform2D rectangleTransform)
+		{
+			var circleCenter = circleTransform.Position;
+			var circleRadius = circle.Radius * circleTransform.Scale.X;
+			var AABB = rectangle.TransformedAABB(rectangleTransform);
+
+			var closestX = Math.MathHelper.Clamp(circleCenter.X, AABB.Left, AABB.Right);
+			var closestY = Math.MathHelper.Clamp(circleCenter.Y, AABB.Top, AABB.Bottom);
+
+			var distanceX = circleCenter.X - closestX;
+			var distanceY = circleCenter.Y - closestY;
+
+			var distanceSquared = (distanceX * distanceX) + (distanceY * distanceY);
+			return distanceSquared < (circleRadius * circleRadius);
+		}
+
 		public static bool TestCircleOverlap(Circle circleA, Transform2D transformA, Circle circleB, Transform2D transformB)
 		{
 			var radiusA = circleA.Radius * transformA.Scale.X;

src/Math/Transform2D.cs

@@ -8,6 +8,17 @@ namespace MoonWorks.Math
 
 		public Matrix3x2 TransformMatrix { get; }
 
+		public bool IsAxisAligned => Rotation % MathHelper.PiOver2 == 0;
+		public bool IsUniformScale => Scale.X == Scale.Y;
+
+		public Transform2D()
+		{
+			Position = Vector2.Zero;
+			Rotation = 0;
+			Scale = Vector2.One;
+			TransformMatrix = CreateTransformMatrix(Position, Rotation, Scale);
+		}
+
 		public Transform2D(Vector2 position)
 		{
 			Position = position;