Creation and boundary evaluation of CSG-models

Abstract

This paper deals with one particular type of solid model representation. Constructive solid geometry (CSG) describes solids in terms of primitive shapes combined by Boolean operators. The goal of this paper is to present an algorithm suitable for the visualization of a given CSG-object for verification purposes. To accomplish this, the CSG representation is to be converted into a polygonal boundary representation (B-Rep), which allows the easy display of the solid's visible edges and surfaces. An algorithm performing this conversion is called a “boundary evaluator.” This paper describes the fundamental concepts leading to this new algorithm and presents some examples. The boundary evaluator described here follows the following steps: (1) A polygonal mesh is created that covers the primitive shapes. (2) Interfering polygons are repertedly subdivided until the resulting mesh contains the intersection curves between the primitives. (3) The location and validity of all polygons must be determined since only valid polygons reflect the solid's final shape. (4) Adjoining coplanar polygons are collected and merged by deleting their common edges. The final result of this procedure is a consistent, nonredundant polygon mesh describing the given solid model. Now the object may be displayed by simple perspective plots, by isometric projections, by hidden line drawings, or through the use of hidden surface removal techniques as color-shaded pictures. The algorithm presented here has been successfully used to create a variety of renderings of various CSG-models. The interpretation, display, and validation of computer-generated CSG models is essential for the successful use of such models in the engineering design process.