Use of Free-Form Low-Degree Algebraic Surfaces in Solid     Modeling
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{'SignBlockName': 'Bruce Kramer', 'PO_EMAI': 'bkramer@nsf.gov', 'PO_PHON': '7032925348'}
The fields of surface modeling and solid modeling, which are               likely to form the basis for future computer-aided design (CAD)                 systems, have been developing independently.  Today users of systems            based on one or the other technique find they require the                       functionality of both types of                                                  systems simultaneously.  The goal of this research is to provide a              technique for modeling free-form surfaces in a manner which                     facilitates their incorporation in solid modeling systems.                           The surfaces used in this technique will be described by                   algebraic functions defined within a parallelepiped.  By using                  control points contained in the parallelepiped, the algebraic                   function can be expressed with B-splines, automatically allowing for            continuity throughout the surface.                                                   These algebraic surfaces can be implemented easily in solid                modelers since the implicit surface equation defines specific half-             spaces.  A useful free-form primitive will be obtained by clipping              them against the parallelepiped and then rendering as solids.  Ray              tracing methods will be efficiently applied to these surfaces, since            the ray intersection equation is a univariate polynomial whose                  degree is the degree of the surface.
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