An algorithm for discrete booleans with applications to finite element modeling of complex systems

Abstract

In this paper we describe a robust algorithm for three-dimensional boolean operations between boundary representation objects whose geometry is given by discrete (faceted) data. The algorithm presents a new approach for computing the intersection graph which is critical for robustness. It uses elementary computational-geometry operations such as, facet–segment intersection, point containment in simplices and edge recovery in a plane, to produce high-level boolean operations including union, intersection, difference as well as the imprint of the boundary of one object onto another. We also demonstrate the extension and application of the algorithm to mesh-based volumes. We show the robustness and efficacy of our algorithm by employing it to model complex three-dimensional finite element mesh models such as a complete ship where some of the model components are defined in a CAD-based system while others come from legacy mesh-based facetized representations. Use of our algorithm has enabled automation of modeling of very complex configurations reducing the turnaround time for analyses-ready numerical representations from several months to hours or less.