Optimization for Parameters of Generalized Bézier Patch

Abstract

: In 2016, Várady, et al. introduced the generalized Bézier patch (GB-patch) using generalized barycentric coordinates and bivariate Bernstein functions. GB-patch has a simple control structure and wonderful geometric properties, but the parameters of Bernstein basis functions are rational polynomial of generalized barycentric coordinates. The linear form of generalized barycentric coordinates is used as parameters of the GB-patch. So, it is convenient to analyze the geometric properties of the patch. Furthermore, it is proved that the new GB-patch has the same blending condition as the original GB-patch between the shared boundary of adjacent patches. Next, the time complexity of the new GB-patch is compared to original GB-patch, which shows that the calculating time is reduced. Finally, several geometric examples are pre-sented to show that the geometric characteristics of the patch are almost the same as those of the original ones.