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.

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

static Vector3	ClosestPointOnTriangle (Vector3 tr0, Vector3 tr1, Vector3 tr2, Vector3 point)
	Returns the closest point on the triangle.

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

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

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

static bool	ContainsPoint (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 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 a, Int2 b, Int2 a2, Int2 b2)
	Returns if the line segment a2 - b2 intersects the line segment a - b.

static bool	Intersects (Int3 a, Int3 b, Int3 a2, Int3 b2)
	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 c)
	Returns if p lies on the left side of the line a - b.

static bool	Left (Int2 a, Int2 b, Int2 c)
	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 c)
	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 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 Vector3[]	Subdivide (Vector3[] path, int subdivisions)
	Subdivides path and returns the new array with interpolated values.

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 Public Attributes
static List< Vector3 >	hullCache = new List<Vector3>()

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);

static Vector3 ClosestPointOnTriangle	(	Vector3	tr0,
		Vector3	tr1,
		Vector3	tr2,
		Vector3	point
	)

static

Returns the closest point on the triangle.

Author: Got code from the internet, changed a bit to work with the Unity API

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	(	Int2	a,
		Int2	b,
		Int2	c,
		Int2	p
	)

static

Returns if the triangle ABC contains the point p.

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

static

Returns if the triangle ABC contains the point p.

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 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 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.

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

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.

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.

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)

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.

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

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

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

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

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

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.

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.

static bool Intersects	(	Int2	a,
		Int2	b,
		Int2	a2,
		Int2	b2
	)

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).

static bool Intersects	(	Int3	a,
		Int3	b,
		Int3	a2,
		Int3	b2
	)

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

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

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.

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

static

Returns if the points a in a clockwise order.

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)

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.

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.

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

static

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

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

static

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

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

static

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

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

static