Test for intersection between box and tetrahedron

Abstract

A procedure for determining whether a box intersects a tetrahedron is developed. The procedure uses interval arithmetic tools and barycentric coordinates, and it gives a guaranteed answer (modulo rounding errors). The basic geometric idea uses the separating plane approach. The procedure is robust and easy to implement. Numerical examples are given for each of the possible results (i.e., inclusion, overlap and exclusion).

Keywords:

• Tetrahedron
• box
• geometric intersection
• barycentric coordinates
• range computations
• interval analysis

AMS Classifications:

• 65G10
• 51-04
• 68A10

C. R. Categories:

• G 2.2