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

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 (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	Dot (Vector3 lhs, Vector3 rhs)
	Dot product of two vectors.

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 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 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 (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	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	Left (Vector3 a, Vector3 b, Vector3 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	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.

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)

static float	TriangleArea (Vector3 a, Vector3 b, Vector3 c)

static long	TriangleArea2 (Int3 a, Int3 b, Int3 c)
	Area of a triangle This will be negative for clockwise triangles and positive for counter-clockwise ones.

static float	TriangleArea2 (Vector3 a, Vector3 b, Vector3 c)

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

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.

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);

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

static

Returns the closest point on the triangle.

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

Todo:: Uses Dot product to get the sqrMagnitude of a vector, should change to sqrMagnitude for readability and possibly for speed (unlikely though)

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.

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static float Dot	(	Vector3	lhs,
		Vector3	rhs
	)

static

Dot product of two vectors.

Todo:: Why is this function defined here?

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

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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 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 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	(	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

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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)

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

static

Returns if p lies on the left side of the line a - b.

Uses XZ space. Also returns true if the points are colinear

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

static

Returns if p lies on the left side of the line a - b.

Uses XZ space. Also returns true if the points are colinear

static bool LineIntersectsBounds	(	Bounds	bounds,
		Vector3	a,
		Vector3	b
	)

static

Does the line segment intersect the bounding box.

The line is NOT treated as infinite.

Author: Slightly modified code from http://www.3dkingdoms.com/weekly/weekly.php?a=21

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

static

Returns the intersection point between the two line segments.

Lines are NOT treated as infinite. start1 is returned if the line segments do not intersect

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static Vector3 [] Subdivide	(	Vector3[]	path,
		int	subdivisions
	)

static

Subdivides path and returns the new array with interpolated values.

The returned array is path subdivided subdivisions times, the resulting points are interpolated using Mathf.SmoothStep.
If subdivisions is less or equal to 0 (zero), the original array will be returned

The documentation for this class was generated from the following file:

/Users/aron/Unity/AstarPathfindingGIT/Assets/AstarPathfindingProject/Core/AstarMath.cs

Static Public Member Functions

Static Public Attributes

Detailed Description

Member Function Documentation