Boundary evaluation of non-convex primitives to produce parametric trimmed surfaces

Abstract

To integrate a CSG-based solid modeler into an existing wireframe/surface modeling system, new boundary evaluation technology has been developed. This scheme uses exact representations for the simple quadric surfaces and both exact and approximate representations of higher-order curved surfaces.It supports parametric primitives (box, wedge, sphere, cylinder, cone, torus), procedural primitives (extrusion, revolution, tube) and a sculptured surface primitive. The output includes curves, parametric trimmed surfaces, and a data structure of adjacency information.An existing boundary evaluator (PADL-2's) has been enhanced to allow a general non-convex faceted primitive with planar and quadric facets. This new hybrid evaluator combines two techniques for curve/primitive classification.PADL-2's existing halfspace-based classification is reserved for the simple convex primitives, and a new ray firing based classification is applied to the non-convex primitives. After evaluation, approximate intersection curves (from intersections involving higher order surfaces) are refined to a specified tolerance by exploiting an exact parametric representation of the surfaces of the primitives. The refined curves and the quadric surface intersection curves are used to create a parametric trimmed surface representation of the solid. This combination of techniques and representations offers advantages in accuracy, robustness and efficiency suitable to a production environment.