Class Polygon

Vector3 ClosestPointOnTriangle (

Vector3	a
Vector3	b
Vector3	c
Vector3	p

)

Closest point on the triangle abc to the point p.

Vector2 ClosestPointOnTriangle (

Vector2	a
Vector2	b
Vector2	c
Vector2	p

)

Closest point on the triangle abc to the point p.

Vector3 ClosestPointOnTriangleXZ (

Vector3	a
Vector3	b
Vector3	c
Vector3	p

)

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

void CompressMesh (

List<Int3>	vertices	Vertices of the input mesh
List<int>	triangles	Triangles of the input mesh
outInt3[]	outVertices	Vertices of the output mesh.
out int []	outTriangles	Triangles of the output mesh.

)

Compress the mesh by removing duplicate vertices.

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

bool ContainsPoint (

Vector2 []	polyPoints
Vector2	p

)

Checks if p is inside the polygon.

bool ContainsPoint (

Vector3 []	polyPoints
Vector3	p

)

Checks if p is inside the polygon (XZ space)

bool ContainsPoint (

Int2	a
Int2	b
Int2	c
Int2	p

)

Returns if the triangle ABC contains the point p.

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

bool ContainsPoint (

Int3	a
Int3	b
Int3	c
Int3	p

)

Returns if the triangle ABC contains the point p.

bool ContainsPoint (

Vector3	a
Vector3	b
Vector3	c
Vector3	p

)

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

bool ContainsPointXZ (

Vector3 []	polyPoints
Vector3	p

)

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

bool ContainsPointXZ (

Int3	a
Int3	b
Int3	c
Int3	p

)

Returns if the triangle ABC contains the point p.

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

bool ContainsPointXZ (

Vector3	a
Vector3	b
Vector3	c
Vector3	p

)

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

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

Vector3 [] ConvexHullXZ (

Vector3 []

points

)

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.

bool IntersectsUnclamped (

Vector3	a
Vector3	b
Vector3	a2
Vector3	b2

)

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

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

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.

The y coordinate of p is ignored.

void Subdivide (

List<Vector3>	points
List<Vector3>	result
int	subSegments

)

Divides each segment in the list into subSegments segments and fills the result list with the new points.

void TraceContours (

Dictionary<int, int>	outline	outline[a] = b if there is an edge from a to b.
HashSet<int>	hasInEdge	hasInEdge should contain b if outline[a] = b for any key a.
System.Action<List<int >, bool>	results	Will be called once for each contour with the contour as a parameter as well as a boolean indicating if the contour is a cycle or a chain (see image).

)

Given a set of edges between vertices, follows those edges and returns them as chains and cycles.

long TriangleArea (

Int3	a
Int3	b
Int3	c

)

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)

float TriangleArea (

Vector3	a
Vector3	b
Vector3	c

)

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.

float TriangleArea2 (

Vector3	a
Vector3	b
Vector3	c

)

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.

long TriangleArea2 (

Int3	a
Int3	b
Int3	c

)

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

Dictionary<Int3, int> cached_Int3_int_dict = new Dictionary<Int3, int>()

Cached dictionary to avoid excessive allocations.

Vector3 ClosestPointOnTriangle (

Vector3 []	triangle
Vector3	point

)

Returns the closest point on the triangle.

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

Vector3 [] ConvexHull (

Vector3 []

points

)

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.

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.

float IntersectionFactor (

Vector3	start1
Vector3	end1
Vector3	start2
Vector3	end2

)

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) *

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.

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.

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.

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.

float IntersectionFactorRay (

Int3	start1
Int3	end1
Int3	start2
Int3	end2

)

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. *

bool IntersectionFactorRaySegment (

Int3	start1
Int3	end1
Int3	start2
Int3	end2

)

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.

Vector2 IntersectionPoint (

Vector2	start1
Vector2	end1
Vector2	start2
Vector2	end2

)

Returns the intersection point between the two lines.

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

Vector3 IntersectionPoint (

Vector3	start1
Vector3	end1
Vector3	start2
Vector3	end2

)

Returns the intersection point between the two lines.

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

Vector2 IntersectionPoint (

Vector2	start1
Vector2	end1
Vector2	start2
Vector2	end2
out bool	intersects

)

Returns the intersection point between the two lines.

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

Vector3 IntersectionPoint (

Vector3	start1
Vector3	end1
Vector3	start2
Vector3	end2
out bool	intersects

)

Returns the intersection point between the two lines.

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

Vector3 IntersectionPointOptimized (

Vector3	start1
Vector3	dir1
Vector3	start2
Vector3	dir2

)

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.

Vector3 IntersectionPointOptimized (

Vector3	start1
Vector3	dir1
Vector3	start2
Vector3	dir2
out bool	intersects

)

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.

bool Intersects (

Int3	start1
Int3	end1
Int3	start2
Int3	end2

)

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).

bool Intersects (

Vector3	start1
Vector3	end1
Vector3	start2
Vector3	end2

)

Returns if the two line segments intersects.

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

bool Intersects (

Int2	start1
Int2	end1
Int2	start2
Int2	end2

)

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).

bool IsClockwise (

Int3	a
Int3	b
Int3	c

)

Returns if the points a in a clockwise order.

bool IsClockwise (

Vector3	a
Vector3	b
Vector3	c

)

Returns if the points a in a clockwise order.

bool IsClockwiseMargin (

Int2	a
Int2	b
Int2	c

)

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

bool IsClockwiseMargin (

Vector3	a
Vector3	b
Vector3	c

)

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)

bool IsClockwiseMargin (

Int3	a
Int3	b
Int3	c

)

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

bool IsColinear (

Vector3	a
Vector3	b
Vector3	c

)

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

bool IsColinear (

Int3	a
Int3	b
Int3	c

)

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

bool IsColinearAlmost (

Int3	a
Int3	b
Int3	c

)

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

bool Left (

Int2	a
Int2	b
Int2	p

)

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

Also returns true if the points are colinear

bool Left (

Int3	a
Int3	b
Int3	p

)

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

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

bool Left (

Vector3	a
Vector3	b
Vector3	p

)

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

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

bool Left (

Vector2	a
Vector2	b
Vector2	p

)

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

Also returns true if the points are colinear

bool LeftNotColinear (

Vector3	a
Vector3	b
Vector3	p

)

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.

bool LeftNotColinear (

Int3	a
Int3	b
Int3	p

)

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

Uses XZ space.

bool LineIntersectsBounds (

Bounds	bounds
Vector3	a
Vector3	b

)

Does the line segment intersect the bounding box.

The line is NOT treated as infinite.

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.

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).