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| A new algorithm for designing developable Bézier surfaces |
| ZHANG Xing-wang, WANG Guo-jin |
| Institute of Computer Images and Graphics, Zhejiang University, Hangzhou 310027, China; State Key Laboratory of CAD & CG, Zhejiang University, Hangzhou 310027, China |
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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.
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Received: 20 March 2006
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