| Computer & Information Science |
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| Computation of lower derivatives of rational triangular Bézier surfaces and their bounds estimation |
| ZHANG Lei, WANG Guo-jin |
| Department of Mathematics, Zhejiang University, Hangzhou 310027, China; State Key Laboratory of CAD & CG, Zhejiang University, Hangzhou 310027, China |
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Abstract By introducing the homogenous coordinates, degree elevation formulas and combinatorial identities, also by using multiplication of Bernstein polynomials and identity transformation on equations, this paper presents some explicit formulas of the first and second derivatives of rational triangular Bézier surface with respect to each variable (including the mixed derivative) and derives some estimations of bound both on the direction and magnitude of the corresponding derivatives. All the results above have value not only in surface theory but also in practice.
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Received: 12 September 2004
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