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.

Invisibility coherence is a new technique developed to decrease the time necessary to render shaded images by existing scan-line hidden surface algorithms. Invisibility coherence is a technique for removing portions of a scene that are not likely to be visible. If a large portion of the scene is invisible, as is often the case in three-dimensional computer graphics, the processing time eliminated may be substantial. Invisibility coherence takes advantage of the observation that a minimal amount of processing needs to be done on objects (polygons, patches, or surfaces) that will be hidden by other objects closer to the viewer. This fact can be used to increase the efficiency of current scan-line algorithms, including both polygon-based and parametrically curved surface-based algorithms.