关键词: 拟伯恩斯坦基函数, 拟Bé, zier曲面, 形状参数, 几何连续

Abstract: Based on a class of generalized Bernstein-like basis functions,a generalized Bézier-like surfaces of order m×n with multiple shape parameters was constructed,which not only inherited the outstanding properties of Bézier Surface of order m×n,but also had good performance on adjusting their shapes by changing multiple shape control parameters.Meanwhile,many properties of generalized Bézier-like surfaces were investigated,such as boundary,degeneracy,symmetry,convex hull,unique presentation,geometrical invariability,affine invariability,interpolation at the corners and tangent plane at the endpoints.To tackle the problem that the engineering complex surfaces could not be constructed by using a single surface,the conditions of G1 continuity between two adjacent generalized Bézier-like surfaces were proposed.In addition,some applications in generalized Bézier-like surfaces design were discussed.The modeling examples showed that the proposed method was effective and easy to implement,which greatly enhances the ability to constructing complex surface by using generalized Bézier-like surfaces.

Key words: Bernstein-like basis functions, Bézier-like surfaces, shape parameter, continuity conditions