Utility functions for working with polygons, lines, and other vector math. More...

Detailed Description

Utility functions for working with polygons, lines, and other vector math.

All functions which accepts Vector3s but work in 2D space uses the XZ space if nothing else is said.

Version: A lot of functions in this class have been moved to the VectorMath class the names have changed slightly and everything now consistently assumes a left handed coordinate system now instead of sometimes using a left handed one and sometimes using a right handed one. This is why the 'Left' methods redirect to methods named 'Right'. The functionality is exactly the same.

Static Public Member Functions
static Vector3	ClosestPointOnTriangle (Vector3[] triangle, Vector3 point)
	Returns the closest point on the triangle.

static Vector2	ClosestPointOnTriangle (Vector2 a, Vector2 b, Vector2 c, Vector2 p)
	Closest point on the triangle abc to the point p.

static Vector3	ClosestPointOnTriangle (Vector3 a, Vector3 b, Vector3 c, Vector3 p)
	Closest point on the triangle abc to the point p.

static Vector3	ClosestPointOnTriangleXZ (Vector3 a, Vector3 b, Vector3 c, Vector3 p)
	Closest point on the triangle abc to the point p when seen from above.

static void	CompressMesh (List< Int3 > vertices, List< int > triangles, out Int3[] outVertices, out int[] outTriangles)
	Compress the mesh by removing duplicate vertices.

static bool	ContainsPoint (Vector3 a, Vector3 b, Vector3 c, Vector3 p)
	Returns if the triangle ABC contains the point p in XZ space.

static bool	ContainsPoint (Int3 a, Int3 b, Int3 c, Int3 p)
	Returns if the triangle ABC contains the point p.

static bool	ContainsPoint (Int2 a, Int2 b, Int2 c, Int2 p)
	Returns if the triangle ABC contains the point p.

static bool	ContainsPoint (Vector3[] polyPoints, Vector3 p)
	Checks if p is inside the polygon (XZ space)

static bool	ContainsPoint (Vector2[] polyPoints, Vector2 p)
	Checks if p is inside the polygon.

static bool	ContainsPointXZ (Vector3 a, Vector3 b, Vector3 c, Vector3 p)
	Returns if the triangle ABC contains the point p in XZ space.

static bool	ContainsPointXZ (Int3 a, Int3 b, Int3 c, Int3 p)
	Returns if the triangle ABC contains the point p.

static bool	ContainsPointXZ (Vector3[] polyPoints, Vector3 p)
	Checks if p is inside the polygon (XZ space).

static Vector3[]	ConvexHull (Vector3[] points)
	Calculates convex hull in XZ space for the points.

static Vector3[]	ConvexHullXZ (Vector3[] points)
	Calculates convex hull in XZ space for the points.

static float	DistanceSegmentSegment3D (Vector3 s1, Vector3 e1, Vector3 s2, Vector3 e2)
	Get the 3D minimum distance between 2 segments Input: two 3D line segments S1 and S2.

static bool	IntersectionFactor (Int3 start1, Int3 end1, Int3 start2, Int3 end2, out float factor1, out float factor2)
	Returns the intersection factors for line 1 and line 2.

static bool	IntersectionFactor (Vector3 start1, Vector3 end1, Vector3 start2, Vector3 end2, out float factor1, out float factor2)
	Returns the intersection factors for line 1 and line 2.

static float	IntersectionFactor (Vector3 start1, Vector3 end1, Vector3 start2, Vector3 end2)
	Returns the intersection factor for line 1 with line 2.

static float	IntersectionFactorRay (Int3 start1, Int3 end1, Int3 start2, Int3 end2)
	Returns the intersection factor for line 1 with ray 2.

static bool	IntersectionFactorRaySegment (Int3 start1, Int3 end1, Int3 start2, Int3 end2)
	Returns if the ray (start1, end1) intersects the segment (start2, end2).

static Vector3	IntersectionPoint (Vector3 start1, Vector3 end1, Vector3 start2, Vector3 end2)
	Returns the intersection point between the two lines.

static Vector3	IntersectionPoint (Vector3 start1, Vector3 end1, Vector3 start2, Vector3 end2, out bool intersects)
	Returns the intersection point between the two lines.

static Vector2	IntersectionPoint (Vector2 start1, Vector2 end1, Vector2 start2, Vector2 end2)
	Returns the intersection point between the two lines.

static Vector2	IntersectionPoint (Vector2 start1, Vector2 end1, Vector2 start2, Vector2 end2, out bool intersects)
	Returns the intersection point between the two lines.

static Vector3	IntersectionPointOptimized (Vector3 start1, Vector3 dir1, Vector3 start2, Vector3 dir2)
	Intersection point between two infinite lines.

static Vector3	IntersectionPointOptimized (Vector3 start1, Vector3 dir1, Vector3 start2, Vector3 dir2, out bool intersects)
	Intersection point between two infinite lines.

static bool	Intersects (Int2 start1, Int2 end1, Int2 start2, Int2 end2)
	Returns if the line segment a2 - b2 intersects the line segment a - b.

static bool	Intersects (Int3 start1, Int3 end1, Int3 start2, Int3 end2)
	Returns if the line segment a2 - b2 intersects the line segment a - b.

static bool	Intersects (Vector3 start1, Vector3 end1, Vector3 start2, Vector3 end2)
	Returns if the two line segments intersects.

static bool	IntersectsUnclamped (Vector3 a, Vector3 b, Vector3 a2, Vector3 b2)
	Returns if the line segment a2 - b2 intersects the infinite line a - b.

static bool	IsClockwise (Vector3 a, Vector3 b, Vector3 c)
	Returns if the points a in a clockwise order.

static bool	IsClockwise (Int3 a, Int3 b, Int3 c)
	Returns if the points a in a clockwise order.

static bool	IsClockwiseMargin (Vector3 a, Vector3 b, Vector3 c)
	Returns if the points a in a clockwise order.

static bool	IsClockwiseMargin (Int3 a, Int3 b, Int3 c)
	Returns true if the points a in a clockwise order or if they are colinear.

static bool	IsClockwiseMargin (Int2 a, Int2 b, Int2 c)
	Returns true if the points a in a clockwise order or if they are colinear.

static bool	IsColinear (Int3 a, Int3 b, Int3 c)
	Returns if the points are colinear (lie on a straight line)

static bool	IsColinear (Vector3 a, Vector3 b, Vector3 c)
	Returns if the points are colinear (lie on a straight line)

static bool	IsColinearAlmost (Int3 a, Int3 b, Int3 c)
	Returns if the points are colinear (lie on a straight line)

static bool	Left (Vector3 a, Vector3 b, Vector3 p)
	Returns if p lies on the left side of the line a - b.

static bool	Left (Vector2 a, Vector2 b, Vector2 p)
	Returns if p lies on the left side of the line a - b.

static bool	Left (Int3 a, Int3 b, Int3 p)
	Returns if p lies on the left side of the line a - b.

static bool	Left (Int2 a, Int2 b, Int2 p)
	Returns if p lies on the left side of the line a - b.

static bool	LeftNotColinear (Vector3 a, Vector3 b, Vector3 p)
	Returns if p lies on the left side of the line a - b.

static bool	LeftNotColinear (Int3 a, Int3 b, Int3 p)
	Returns if p lies on the left side of the line a - b.

static bool	LineIntersectsBounds (Bounds bounds, Vector3 a, Vector3 b)
	Does the line segment intersect the bounding box.

static int	SampleYCoordinateInTriangle (Int3 p1, Int3 p2, Int3 p3, Int3 p)
	Sample Y coordinate of the triangle (p1, p2, p3) at the point p in XZ space.

static Vector3	SegmentIntersectionPoint (Vector3 start1, Vector3 end1, Vector3 start2, Vector3 end2, out bool intersects)
	Returns the intersection point between the two line segments in XZ space.

static long	TriangleArea (Int3 a, Int3 b, Int3 c)
	Signed area of a triangle in the XZ plane multiplied by 2.

static float	TriangleArea (Vector3 a, Vector3 b, Vector3 c)
	Signed area of a triangle in the XZ plane multiplied by 2.

static long	TriangleArea2 (Int3 a, Int3 b, Int3 c)
	Signed area of a triangle in the XZ plane multiplied by 2.

static float	TriangleArea2 (Vector3 a, Vector3 b, Vector3 c)
	Signed area of a triangle in the XZ plane multiplied by 2.

Static Private Attributes
static readonly Dictionary < Int3, int >	cached_Int3_int_dict = new Dictionary<Int3, int>()
	Cached dictionary to avoid excessive allocations.

Member Function Documentation

static Vector3 ClosestPointOnTriangle	(	Vector3[]	triangle,
		Vector3	point
	)

static

Returns the closest point on the triangle.

The triangle array must have a length of at least 3.

See Also: ClosesPointOnTriangle(Vector3,Vector3,Vector3,Vector3);

Deprecated:: Scheduled for removal since it is not used by any part of the A* Pathfinding Project

static Vector2 ClosestPointOnTriangle	(	Vector2	a,
		Vector2	b,
		Vector2	c,
		Vector2	p
	)

static

Closest point on the triangle abc to the point p.

See Also: 'Real Time Collision Detection' by Christer Ericson, chapter 5.1, page 141

static Vector3 ClosestPointOnTriangle	(	Vector3	a,
		Vector3	b,
		Vector3	c,
		Vector3	p
	)

static

Closest point on the triangle abc to the point p.

See Also: 'Real Time Collision Detection' by Christer Ericson, chapter 5.1, page 141

static Vector3 ClosestPointOnTriangleXZ	(	Vector3	a,
		Vector3	b,
		Vector3	c,
		Vector3	p
	)

static

Closest point on the triangle abc to the point p when seen from above.

See Also: 'Real Time Collision Detection' by Christer Ericson, chapter 5.1, page 141

static void CompressMesh	(	List< Int3 >	vertices,
		List< int >	triangles,
		out Int3[]	outVertices,
		out int[]	outTriangles
	)

static

Compress the mesh by removing duplicate vertices.

Parameters

vertices	Vertices of the input mesh
triangles	Triangles of the input mesh
outVertices	Vertices of the output mesh.
outTriangles	Triangles of the output mesh.

Vertices that differ by only 1 along the y coordinate will also be merged together.

Warning: This function is not threadsafe. It uses some cached structures to reduce allocations.

static bool ContainsPoint	(	Vector3	a,
		Vector3	b,
		Vector3	c,
		Vector3	p
	)

static

Returns if the triangle ABC contains the point p in XZ space.

static bool ContainsPoint	(	Int3	a,
		Int3	b,
		Int3	c,
		Int3	p
	)

static

Returns if the triangle ABC contains the point p.

static bool ContainsPoint	(	Int2	a,
		Int2	b,
		Int2	c,
		Int2	p
	)

static

Returns if the triangle ABC contains the point p.

The triangle vertices are assumed to be laid out in clockwise order.

static bool ContainsPoint	(	Vector3[]	polyPoints,
		Vector3	p
	)

static

Checks if p is inside the polygon (XZ space)

Author: http://unifycommunity.com/wiki/index.php?title=PolyContainsPoint (Eric5h5)

static bool ContainsPoint	(	Vector2[]	polyPoints,
		Vector2	p
	)

static

Checks if p is inside the polygon.

Author: http://unifycommunity.com/wiki/index.php?title=PolyContainsPoint (Eric5h5)

static bool ContainsPointXZ	(	Vector3	a,
		Vector3	b,
		Vector3	c,
		Vector3	p
	)

static

Returns if the triangle ABC contains the point p in XZ space.

The triangle vertices are assumed to be laid out in clockwise order.

static bool ContainsPointXZ	(	Int3	a,
		Int3	b,
		Int3	c,
		Int3	p
	)

static

Returns if the triangle ABC contains the point p.

The triangle vertices are assumed to be laid out in clockwise order.

static bool ContainsPointXZ	(	Vector3[]	polyPoints,
		Vector3	p
	)

static

Checks if p is inside the polygon (XZ space).

Author: http://unifycommunity.com/wiki/index.php?title=PolyContainsPoint (Eric5h5)

static Vector3 [] ConvexHull ( Vector3[] points )

static

Calculates convex hull in XZ space for the points.

Implemented using the very simple Gift Wrapping Algorithm which has a complexity of O(nh) where n is the number of points and h is the number of points on the hull, so it is in the worst case quadratic.

Deprecated:: Use ConvexHullXZ instead

static Vector3 [] ConvexHullXZ ( Vector3[] points )

static

Calculates convex hull in XZ space for the points.

Implemented using the very simple Gift Wrapping Algorithm which has a complexity of O(nh) where n is the number of points and h is the number of points on the hull, so it is in the worst case quadratic.

static float DistanceSegmentSegment3D	(	Vector3	s1,
		Vector3	e1,
		Vector3	s2,
		Vector3	e2
	)

static

Get the 3D minimum distance between 2 segments Input: two 3D line segments S1 and S2.

Returns: the shortest squared distance between S1 and S2

Deprecated:: Use VectorMath.SqrDistanceSegmentSegment instead

static bool IntersectionFactor	(	Int3	start1,
		Int3	end1,
		Int3	start2,
		Int3	end2,
		out float	factor1,
		out float	factor2
	)

static

Returns the intersection factors for line 1 and line 2.

The intersection factors is a distance along the line start - end where the other line intersects it.

intersectionPoint = start1 + factor1 * (end1-start1)

intersectionPoint2 = start2 + factor2 * (end2-start2)

Lines are treated as infinite.
false is returned if the lines are parallel and true if they are not. Only the XZ coordinates are used.

Deprecated:: Use VectorMath.LineIntersectionFactorXZ instead

static bool IntersectionFactor	(	Vector3	start1,
		Vector3	end1,
		Vector3	start2,
		Vector3	end2,
		out float	factor1,
		out float	factor2
	)

static

Returns the intersection factors for line 1 and line 2.

The intersection factors is a distance along the line start - end where the other line intersects it.

intersectionPoint = start1 + factor1 * (end1-start1)

intersectionPoint2 = start2 + factor2 * (end2-start2)

Lines are treated as infinite.
false is returned if the lines are parallel and true if they are not. Only the XZ coordinates are used.

Deprecated:: Use VectorMath.LineIntersectionFactorXZ instead

static float IntersectionFactor	(	Vector3	start1,
		Vector3	end1,
		Vector3	start2,
		Vector3	end2
	)

static

Returns the intersection factor for line 1 with line 2.

The intersection factor is a distance along the line start1 - end1 where the line start2 - end2 intersects it.

intersectionPoint = start1 + intersectionFactor * (end1-start1)

. Lines are treated as infinite.
-1 is returned if the lines are parallel (note that this is a valid return value if they are not parallel too) *

Deprecated:: Use VectorMath.LineIntersectionFactorXZ instead

static float IntersectionFactorRay	(	Int3	start1,
		Int3	end1,
		Int3	start2,
		Int3	end2
	)

static

Returns the intersection factor for line 1 with ray 2.

The intersection factors is a factor distance along the line start - end where the other line intersects it.

intersectionPoint = start1 + factor * (end1-start1)

Lines are treated as infinite.

The second "line" is treated as a ray, meaning only matches on start2 or forwards towards end2 (and beyond) will be returned If the point lies on the wrong side of the ray start, Nan will be returned.

NaN is returned if the lines are parallel. *

Deprecated:: Use VectorMath.LineRayIntersectionFactorXZ instead

static bool IntersectionFactorRaySegment	(	Int3	start1,
		Int3	end1,
		Int3	start2,
		Int3	end2
	)

static

Returns if the ray (start1, end1) intersects the segment (start2, end2).

false is returned if the lines are parallel. Only the XZ coordinates are used.

Todo:: Double check that this actually works

Deprecated:: Use VectorMath.RaySegmentIntersectXZ instead

static Vector3 IntersectionPoint	(	Vector3	start1,
		Vector3	end1,
		Vector3	start2,
		Vector3	end2
	)

static

Returns the intersection point between the two lines.

Lines are treated as infinite. start1 is returned if the lines are parallel

Deprecated:: Use VectorMath.LineIntersectionPointXZ instead

static Vector3 IntersectionPoint	(	Vector3	start1,
		Vector3	end1,
		Vector3	start2,
		Vector3	end2,
		out bool	intersects
	)

static

Returns the intersection point between the two lines.

Lines are treated as infinite. start1 is returned if the lines are parallel

Deprecated:: Use VectorMath.LineIntersectionPointXZ instead

static Vector2 IntersectionPoint	(	Vector2	start1,
		Vector2	end1,
		Vector2	start2,
		Vector2	end2
	)

static

Returns the intersection point between the two lines.

Lines are treated as infinite. start1 is returned if the lines are parallel

Deprecated:: Use VectorMath.LineIntersectionPoint instead

static Vector2 IntersectionPoint	(	Vector2	start1,
		Vector2	end1,
		Vector2	start2,
		Vector2	end2,
		out bool	intersects
	)

static

Returns the intersection point between the two lines.

Lines are treated as infinite. start1 is returned if the lines are parallel

Deprecated:: Use VectorMath.LineIntersectionPoint instead

static Vector3 IntersectionPointOptimized	(	Vector3	start1,
		Vector3	dir1,
		Vector3	start2,
		Vector3	dir2
	)

static

Intersection point between two infinite lines.

Lines are treated as infinite. If the lines are parallel 'start1' will be returned. Intersections are calculated on the XZ plane.

Deprecated:: Use VectorMath.LineDirIntersectionPointXZ instead

static Vector3 IntersectionPointOptimized	(	Vector3	start1,
		Vector3	dir1,
		Vector3	start2,
		Vector3	dir2,
		out bool	intersects
	)

static

Intersection point between two infinite lines.

Lines are treated as infinite. If the lines are parallel 'start1' will be returned. Intersections are calculated on the XZ plane.

Deprecated:: Use VectorMath.LineDirIntersectionPointXZ instead

static bool Intersects	(	Int2	start1,
		Int2	end1,
		Int2	start2,
		Int2	end2
	)

static

Returns if the line segment a2 - b2 intersects the line segment a - b.

If only the endpoints coincide, the result is undefined (may be true or false).

Deprecated:: Use VectorMath.SegmentsIntersect instead

static bool Intersects	(	Int3	start1,
		Int3	end1,
		Int3	start2,
		Int3	end2
	)

static

Returns if the line segment a2 - b2 intersects the line segment a - b.

If only the endpoints coincide, the result is undefined (may be true or false).

Note: XZ space

Deprecated:: Use VectorMath.SegmentsIntersectXZ instead

static bool Intersects	(	Vector3	start1,
		Vector3	end1,
		Vector3	start2,
		Vector3	end2
	)

static

Returns if the two line segments intersects.

The lines are NOT treated as infinite (just for clarification)

See Also: IntersectionPoint

Deprecated:: Use VectorMath.SegmentsIntersectXZ instead

static bool IntersectsUnclamped	(	Vector3	a,
		Vector3	b,
		Vector3	a2,
		Vector3	b2
	)

static

Returns if the line segment a2 - b2 intersects the infinite line a - b.

a-b is infinite, a2-b2 is not infinite

static bool IsClockwise	(	Vector3	a,
		Vector3	b,
		Vector3	c
	)

static

Returns if the points a in a clockwise order.

Deprecated:: Use VectorMath.IsClockwiseXZ instead

static bool IsClockwise	(	Int3	a,
		Int3	b,
		Int3	c
	)

static

Returns if the points a in a clockwise order.

Deprecated:: Use VectorMath.IsClockwiseXZ instead

static bool IsClockwiseMargin	(	Vector3	a,
		Vector3	b,
		Vector3	c
	)

static

Returns if the points a in a clockwise order.

Will return true even if the points are colinear or very slightly counter-clockwise (if the signed area of the triangle formed by the points has an area less than or equals to float.Epsilon)

Deprecated:: Use VectorMath.IsClockwiseMarginXZ instead

static bool IsClockwiseMargin	(	Int3	a,
		Int3	b,
		Int3	c
	)

static

Returns true if the points a in a clockwise order or if they are colinear.

Deprecated:: Use VectorMath.IsClockwiseOrColinearXZ instead

static bool IsClockwiseMargin	(	Int2	a,
		Int2	b,
		Int2	c
	)

static

Returns true if the points a in a clockwise order or if they are colinear.

Deprecated:: Use VectorMath.IsClockwiseOrColinear instead

static bool IsColinear	(	Int3	a,
		Int3	b,
		Int3	c
	)

static

Returns if the points are colinear (lie on a straight line)

Deprecated:: Use VectorMath.IsColinearXZ instead

static bool IsColinear	(	Vector3	a,
		Vector3	b,
		Vector3	c
	)

static

Returns if the points are colinear (lie on a straight line)

Deprecated:: Use VectorMath.IsColinearXZ instead

static bool IsColinearAlmost	(	Int3	a,
		Int3	b,
		Int3	c
	)

static

Returns if the points are colinear (lie on a straight line)

Deprecated:: Use VectorMath.IsColinearAlmostXZ instead

static bool Left	(	Vector3	a,
		Vector3	b,
		Vector3	p
	)

static