Geometric information and rational parametrization of nonsingular cubic blending surfaces (Q642753)

Summary: 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 \textit{T. G. Berry} and \textit{R. R. Patterson} in [Comput. Aided Geom. Des. 18, No. 8, 723--738 (2001; Zbl 0983.68221)], 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.