A generalization of surface family with common line of curvature

作者：Li, Cai-Yun; Wang, Ren-Hong; Zhu, Chun-Gang^*

来源：Applied Mathematics and Computation, 2013, 219(17): 9500-9507.

DOI：10.1016/j.amc.2013.03.077

• Line of curvature
• Frenet frame
• Marching-scale functions

We can represent the surface with a linear combination of the components of Frenet-Serret frame. Based on this representation, in the work of Li et al. [C.-Y. Li, R.-H. Wang, C.-G. Zhu, Parametric representation of a surface pencil with a common line of curvature, Comput. Aided Des. 43 (9) (2011) 1110-1117], we derive the necessary and sufficient condition on the marching-scale functions for which the given curve is a line of curvature of the resulting surface. For convenience, we assumed the marching-scale functions can be decomposed into two factors. In this paper, we derive the sufficient condition for the given curve as a line of curvature of the surface when the marching-scale functions are in more general expressions. Finally, we give some representative examples to illustrate the convenience and efficiency of this method.

• 出版日期2013-5-1
• 单位大连理工大学