The Definition and Ray-Tracing of B-Spline Objects in a Combinatorial Solid Geometric Modeling System

Report No. ARL-RP-428
Authors: Paul R. Stay
Date/Pages: April 2013; 10 pages
Abstract: Traditionally there has been a distinction between Combinatorial Solid Geometry (CSG) modeling systems and Sculptured Surface Design modeling systems. CSG modeling systems largely model parts which are unsculptured and consist of combinations of common shapes like spheres, prisms, ellipsoids, and the like. These shapes are represented as planar half spaces, and algebraic quadratic surfaces. The boolean combination of these surfaces is usually performed by ray-tracing. Sculptured Surface Design concerns itself with modeling the surface of an object, i.e., the boundaries of an object like an aircraft, a ship, or an automobile. The boundaries are represented by using parametric tensor-product surfaces consisting of Bezier curves and Nonuniform Rational B-spline Surfaces (NURBS). There are many times however, when both modeling approaches are needed. In particular it is often desirable to introduce free-form surfaces into the CSG system. Recent advances in ray-tracing free-form surfaces have allowed the integration of free-form objects in CSG systems. This presentation will discuss the development and integration of NURBS into the Ballistics Research Laboratory CSG modeling system.
Distribution: Approved for public release
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Last Update / Reviewed: April 1, 2013