Surface subdivision schemes generated by refinable bivariate spline function vectors
✍ Scribed by Charles K. Chui; Qingtang Jiang
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 409 KB
- Volume
- 15
- Category
- Article
- ISSN
- 1063-5203
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✦ Synopsis
The objective of this paper is to introduce a direct approach for generating local averaging rules for both the √ 3 and 1-to-4 vector subdivision schemes for computer-aided design of smooth surfaces. Our innovation is to directly construct refinable bivariate spline function vectors with minimum supports and highest approximation orders on the six-directional mesh, and to compute their refinement masks which give rise to the matrix-valued coefficient stencils for the surface subdivision schemes. Both the C 1 -quadratic and C 2 -cubic spaces are studied in some detail. In particular, we show that our C 2 -cubic refinement mask for the 1-to-4 subdivision can be slightly modified to yield an adaptive version of Loop's surface subdivision scheme.