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Conversion between triangular and rectangular Bézier patches

✍ Scribed by Shi-Min Hu

Book ID
104304886
Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
99 KB
Volume
18
Category
Article
ISSN
0167-8396

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✦ Synopsis

This paper presents an explicit formula that converts a triangular Bézier patch of degree n to a degenerate rectangular Bézier patch of degree n × n by reparametrization. Based on this formula, we develop a method for approximating a degenerate rectangular Bézier patch by three nondegenerate Bézier patches; more patches can be introduced by subdivision to meet a user-specified error tolerance.

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Necessary and sufficient conditions for geometric C 7 continuity (GC 7) that cover all the four combinations between rectangular and triangular B6zier surface patches are presented. Further, some more practical sufficient conditions are developed. The GC ~ conditions in several special cases might b