GC1 continuity conditions between adjacent rectangular and triangular Bézier surface patches
✍ Scribed by D. Liu; J. Hoschek
- Publisher
- Elsevier Science
- Year
- 1989
- Tongue
- English
- Weight
- 422 KB
- Volume
- 21
- Category
- Article
- ISSN
- 0010-4485
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✦ Synopsis
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 be useful for CAD surface modelling. computer-aided design, rectangular and triangular B6zier surface patches, GC 7 continuity conditions, geometric continuity.
Rectangular and triangular Bezier surface methods together form one of the main techniques for surface modelling in CAGD. In CAD/CAM applications the continuity between adjacent B&zier patches is an important and complicated problem, especially in situations where there are many patches.
GC 1 (or VC ~, V 1, G ~) continuity conditions for rectangular and triangular B~zier patches have been researched by several authors, such as Bezier 1, Faux and Pratt 2, Veron et al. ~, Farin 4, Boehm et al. 5 and Piper 6, but only within the limits of some sufficient conditions. Of these papers, Farin's results have a straightforward geometric interpretation and are most effective. Later, Liu 7 discussed geometric smoothness conditions between rectangular B~zier patches.
In this paper the GC ~ necessary and sufficient conditions which cover all four combinations of rectangular and triangular B~zier patches are obtained. Some more practical sufficient conditions are also obtained. The GC ~ conditions in several special cases might be used in CAD for surface modelling.