Background Information and Techniques - Computer Animation: Algorithms and Techniques - page 427

and these min/max values define the bounding slab. See Figure B.20 for a two-dimensional diagram
illustrating the idea. Multiple slabs can be used to form an arbitrarily tight bounding volume of the
convex hull of the polyhedron. A point is inside this bounding volume if the result of the dot product
of it and the normal vector is between the corresponding min/max values for each slab (see Figure B.21
for a two-dimensional example).

p ¼ x; y; z ð Þ vertex

N ¼ a; b; c ð Þ normal (B.32)

PgN ¼ d computing the planar equation constant

d max

d min

Family of planes

Normal vector

FIGURE B.20
Computing a boundary slab for a polyhedron.

A

A

B

B

C

C

Inside of all slabs

Three bounding slabs: A , B , C

Outside of slab B

FIGURE B.21
Multiple bounding slabs.