Optimization for Parameters of Generalized Bézier Patch

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 pa-rameters 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.