Boolean operations in solid modeling: Boundary evaluation and merging algorithms

Abstract

Solid modeling plays a key role in electromechanical CAD/CAM, three-dimensional computer graphics, computer vision, robotics, and other disciplines and activities that deal with spatial phenomena. Almost all contemporary solid modeling systems support Boolean operations akin to set intersection, union, and difference on solids. Boundary representations (face/edge/vertex structures) for solids defined through Boolean operations are generated in these modelers by using so-called boundary evaluation and boundary merging procedures. These are the most complex and delicate software modules in a solid modeler. This paper describes boundary evaluation algorithms used by the PADL solid modeling systems developed at the University of Rochester, and discusses other known approaches in terms of concepts that emerged from the PADL work, notably set membership classification and neighborhood manipulation.