广义带多参Bézier-like曲面及其拼接条件

Generalized Bézier-like surfaces with multiple shape parameters and its continuity conditions

基于一组带形状参数的Bernstein-like基函数,提出一种带多形状参数的高次广义Bézier-like曲面,该曲面既继承了高次Bézier曲面的许多性质,又具有十分灵活的形状可调性,特别是以高次Bézier曲面为其特殊情形;详细分析了Bézier-like曲面的基本性质,讨论了该曲面形状参数的几何意义和一些特殊曲面的构造;为解决工程复杂曲面难以用单一曲面构造的问题,进一步研究了广义Bézier-like曲面的拼接技术,推导了相邻两片广义Bézier-like曲面间G1光滑拼接的几何条件,给出了拼接的具体步骤与实例,并分析了形状参数对拼接后曲面形状的影响规律。数值实例表明,所提方法不仅简单有效、易实现,而且形状方便可调,对CAD/CAM系统中复杂曲面的设计是一种有力的补充。

Based on a class of generalized Bernstein-like basis functions,ageneralized 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.