Classification of Toric Surface Patches

Triangular Bézier patch and tensor-product Bézier patch are widely used in Computer Aided Design (CAD). Toric surface patch is a multi-sided generalization of Bézier patch. In this paper, we study the classification of toric surface patches with the theory of equivalent polygons from Combinatorics, and get different types of toric surface patches. Moreover, an recursive algorithm is proposed to get the lists of arbitrary toric surface patches. Furthermore, several geometrical models are given to present shape possibilities of toric surface patches in Computer Aided Geometric Design (CAGD).