Technical Report CIS9621

Title: Filleting and Rounding using Trimmed Tensor Product Surfaces
Authors: Gershon Elber and Elaine Cohen
Abstract: The tensor product Bezier and NURBs surface representation is frequently exploited in computer aided geometric design. Yet, this representation is inherently rectangular, a topology that does not easily enable the skinning, filleting and rounding of triangular regions or domains with arbitrary n-sided boundaries. Modern solid modeling systems support tensor product Bezier and NURBs surfaces with the additional ability to represent the trimmed form of these surfaces. This paper explores and presents an approach that allows one to construct regular, nondegenerate positional or tangent plane continuous triangular or n-sided patches, each one as a trimmed tensor product surface. The proposed method is demonstrated on rounding of triangular corners using positional and tangent plane continuity conditions as well as an example of a C^0 hexagonal filleting patch.
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