Direct Generation of Contour Files from Constructive Solid Geometry Representations

Geometry processing for layer-based Solid Freeform Fabrication consists of at least two steps: slicing the geometry to obtain the part contours for each layer, and scan-converting the layers for laser scanning (or other device-dependent in-layer processing). This paper discusses the generation of contour files directly from Constructive Solid Geometry (CSG) representations for the Selective Laser Sintering process. Previous work at The University of Texas focused on slicing CSG representations composed of quadric primitives. This paper extends previous work at UT to include the torus, a fourth degree surface, as one of the CSG primitives. Slicing a torus results in a fourth degree equation in two variables, which represents a curve in two-dimensional real space. For. some special cases, this fourth degree equation may be sub-divided into two second degree equations. For the cases where the fourth degree equation cannot be sub-divided, a method is presented to approximate the fourth degree curve with second degree curve segments.