Intersection between shapes

The intersection $S$ between two shapes $A$ and $B$ in $RR^n$ is $S = A nn B$ .

Practice

Pastel implements several algorithms for finding the intersection between a pair of shapes. Describing the possible intersection shape is slower than simply finding out if the shapes overlap. If this is the need, you should use the algorithms for overlap testing instead. The implemented algorithms are listed in the following table.

Shape/Shape	AlignedBox	Box	Sphere	Plane	Segment	Triangle	Line	Ray
AlignedBox	nD
Box	-	-
Sphere	-	-	-
Plane	?	+	nD	+
Segment	+	+	+	-	-
Triangle	?	?	-	?	-	-1D,+2D,3D,-nD
Line	nD	nD	nD	nD	-	2D, 3D, -nD	-
Ray	nD	+	nD	nD	-	+	-	-

where

’-‘ means the algorithm is not sensible or will not be implemented because the intersection shape can’t be described.
’?’ means the algorithm could be useful but probably too rarely.
’+’ means the algorithm would be useful but has not been implemented yet.
‘1D’, ‘2D’, ‘3D’, and ‘nD’ denote dimensions in which the tests operate.

Files

Intersection between a 2-flat and a plane

Intersection between a line and a box

Intersection between a line and a plane

Intersection between a line and a sphere

Intersection between a line and a triangle

Intersection between a line and an aligned box

Intersection between a line and an aligned plane

Intersection between a line segment and a half-space

Intersection between a plane and a sphere

Intersection between a ray and a plane

Intersection between a ray and a sphere

Intersection between a ray and an aligned box

Intersection between a ray and an aligned plane

Intersection between an aligned box and a line segment

Intersection between an aligned box and a plane

Intersection between two aligned boxes

intersect_alignedbox_alignedbox.h

Intersection between two triangles