A* Pathfinding Project  4.0.9 The A* Pathfinding Project for Unity 3D
Polygon Class Reference

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 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 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

< 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.

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.

'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.

'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)

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

Checks if p is inside the polygon.

 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).

 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:
 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:
 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:
 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:
 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:
 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:
 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:
 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:
 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:
 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:
 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:
 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:
 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:
 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:
 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:
 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)

IntersectionPoint
Deprecated:
 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:
 static bool IsClockwise ( Int3 a, Int3 b, Int3 c )
static

Returns if the points a in a clockwise order.

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

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

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

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

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

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

Deprecated:
 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

Deprecated:
Use VectorMath.RightOrColinearXZ instead. Note that it now uses a left handed coordinate system (same as Unity)
 static bool Left ( Vector2 a, Vector2 b, Vector2 p )
static

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

Also returns true if the points are colinear

Deprecated:
Use VectorMath.RightOrColinear instead. Note that it now uses a left handed coordinate system (same as Unity)
 static bool Left ( Int3 a, Int3 b, Int3 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

Deprecated:
Use VectorMath.RightOrColinearXZ instead. Note that it now uses a left handed coordinate system (same as Unity)
 static bool Left ( Int2 a, Int2 b, Int2 p )
static

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

Also returns true if the points are colinear

Deprecated:
Use VectorMath.RightOrColinear instead. Note that it now uses a left handed coordinate system (same as Unity)
 static bool LeftNotColinear ( Vector3 a, Vector3 b, Vector3 p )
static

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

Uses XZ space. Does not return true if the points are colinear.

Deprecated:
Use VectorMath.RightXZ instead. Note that it now uses a left handed coordinate system (same as Unity)
 static bool LeftNotColinear ( Int3 a, Int3 b, Int3 p )
static

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

Uses XZ space.

Deprecated:
Use VectorMath.RightXZ instead. Note that it now uses a left handed coordinate system (same as Unity)
 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.

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

Returns the intersection point between the two line segments in XZ space.

Lines are NOT treated as infinite. start1 is returned if the line segments do not intersect The point will be returned along the line [start1, end1] (this matters only for the y coordinate).

Deprecated:
 static long TriangleArea ( Int3 a, Int3 b, Int3 c )
static

Signed area of a triangle in the XZ plane multiplied by 2.

This will be negative for clockwise triangles and positive for counter-clockwise ones. This method can handle larger numbers than TriangleArea2(Int3)

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

Signed area of a triangle in the XZ plane multiplied by 2.

This will be negative for clockwise triangles and positive for counter-clockwise ones. Idential to TriangleArea2(Vector3), kept for compability.

 static long TriangleArea2 ( Int3 a, Int3 b, Int3 c )
static

Signed area of a triangle in the XZ plane multiplied by 2.

This will be negative for clockwise triangles and positive for counter-clockwise ones

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

Signed area of a triangle in the XZ plane multiplied by 2.

This will be negative for clockwise triangles and positive for counter-clockwise ones.

## Member Data Documentation

 readonly Dictionary cached_Int3_int_dict = new Dictionary()
staticprivate

Cached dictionary to avoid excessive allocations.

The documentation for this class was generated from the following file:
• /Users/arong/Unity/a-pathfinding-project/Assets/AstarPathfindingProject/Core/AstarMath.cs