|
Journal of Zhejiang University SCIENCE A
ISSN 1673-565X(Print), 1862-1775(Online), Monthly
2006 Vol.7 No.12 P.2050-2056
A new algorithm for designing developable Bézier surfaces
Abstract: A new algorithm is presented that generates developable Bézier surfaces through a Bézier curve called a directrix. The algorithm is based on differential geometry theory on necessary and sufficient conditions for a surface which is developable, and on degree evaluation formula for parameter curves and linear independence for Bernstein basis. No nonlinear characteristic equations have to be solved. Moreover the vertex for a cone and the edge of regression for a tangent surface can be obtained easily. Aumann’s algorithm for developable surfaces is a special case of this paper.
Key words: Bézier surfaces, Developable surfaces, Bernstein basis, Linear independence, Characteristic equations
References:
Open peer comments: Debate/Discuss/Question/Opinion
<1>
DOI:
10.1631/jzus.2006.A2050
CLC number:
TP391.72
Download Full Text:
Downloaded:
2776
Clicked:
5269
Cited:
0
On-line Access:
Received:
2006-03-20
Revision Accepted:
2006-05-23
Crosschecked: