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IBM Journal of Research and Development  
Volume 31, Number 3, Page 314 (1987)
Computer-aided Design
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Trimmed-surface algorithms for the evaluation and interrogation of solid boundary representations

by R. T. Farouki
Although trimmed surfaces play a fundamental role in the derivation and processing of solid boundary representations, they have received little attention to date. We propose a trimmed-surface formulation appropriate to the Boolean combination of primitives bounded by a family of elementary surface patches (e.g., planes, quadrics, ruled surfaces, surfaces of revolution) with dual parametric rational polynomial and implicit algebraic equations. Partial intersections between pairs of primitive surface patches are formulated precisely as algebraic curves in the parameter space of each patch. These curves are dissected into monotonic branches by the identification of a characteristic point set. The consolidation of all partial intersections yields a system of piecewise-algebraic loops which define a trimming boundary enclosing a parametric domain for the trimmed patch. With few exceptions, the trimmed-surface formulation is based on precisely defined mathematical procedures, in order to achieve maximum robustness. Some basic interrogation algorithms for solids bounded by trimmed-surface elements are also presented, including procedures for ray-tracing, point/solid classification, sectioning, and computation of surface area, volume, center of gravity, moments of inertia, and other mass properties.
Related Subjects: Algorithms; Computer-aided design; Graphics; Mathematics (applied); Solid modeling