Journal of Applied Mathematics
Volume 2011 (2011), Article ID 349315, 16 pages
Research Article

Geometric Information and Rational Parametrization of Nonsingular Cubic Blending Surfaces

Key Laboratory of Symbolic Computation and Knowledge Engineering (Ministry of Education), School of Mathematics, Jilin University, Changchun 130012, China

Received 21 March 2011; Accepted 7 June 2011

Academic Editor: Ke Chen

Copyright © 2011 Minghao Guo et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The techniques for parametrizing nonsingular cubic surfaces have shown to be of great interest in recent years. This paper is devoted to the rational parametrization of nonsingular cubic blending surfaces. We claim that these nonsingular cubic blending surfaces can be parametrized using the symbolic computation due to their excellent geometric properties. Especially for the specific forms of these surfaces, we conclude that they must be 𝐹 3 , 𝐹 4 , or 𝐹 5 surfaces, and a criterion is given for deciding their surface types. Besides, using the algorithm proposed by Berry and Patterson in 2001, we obtain the uniform rational parametric representation of these specific forms. It should be emphasized that our results in this paper are invariant under any nonsingular real projective transform. Two explicit examples are presented at the end of this paper.