Reflections on the implementation of Boolean Operations with Polyhedral Solids

Proceedings of the TMCE 2006, April 18-22, 2006, Ljubljana, Slovenia
Herbert J. Koelman, SARC, Bussum / The Netherlands (2006)

ABSTRACT

A practical CAD application may significantly benefit from the facility to perform Boolean operations with the modelled objects. Fortunately, the literature provides a plurality of discussions and methods for such operations with polyhedral solids and sculptured solids, while also attention is paid to the possible pitfalls of numerical incompatibilities. So the implementation of a Boolean facility seems to be a matter of implementation rather than a matter of research. However, in the real world, situations may occur for which the published methods offer no solution. To some extent this can be related to numerical issues, but partly it is fundamental, especially with solids that do not really intersect, but only touch each other. This paper identifies and illustrates these problems, and formulates suggestions for modifications to the solution strategies. Furthermore, solutions for the numerical incompatibilities are proposed, and application examples are presented. Finally, it is concluded that our proposed methods provide no fundamental solution, they are practical workarounds instead.