5×5片双三次Bézier曲面片的一类C^2光滑拼接方案  

A Class of C^2 Smooth Connection Scheme for 5×5 Bicubic Bézier Surface Patches

作　　者：陈炼[1] 汤正诠[1] 贾红丽[1] 

机构地区：[1]上海大学理学院,上海200444

出　　处：《应用数学与计算数学学报》2007年第2期1-9,共9页Communication on Applied Mathematics and Computation

摘　　要：文章提出的5×5片双三次Bézier样条插值曲面的反算算法是受颅骨补缺仿生支架的三维数学建模的激发而产生的.针对于中间有一大片空缺而只有四个边角上可以给出插值条件的需要用很多双三次Bézier曲面片通过拼接来拟合的这样一类曲面,在解决曲面片的反算和连续光滑拼接的四个问题的基础上,本文设计出5×5片双三次Bézier曲面片的一种C^2光滑拼接的方案,并分析了控制顶点解的存在唯一性,还给出了应用实例.最后把方案进行拓展,在理论上设计分析了(5+4n_1)×(5+4n_2)片双三次Bézier曲面片的光滑拼接.The inverse algorithm of 5×5 bicubic Bézier spline interpolation surface is motivated by the three-dimensional mathematics modelling of the bionic scaffold for the skull fills.This paper considers the fitting of a class of surfaces where (1) a large number of bicubic Bézier patches are required in the fitting,(2) the middle of the surface is vacating, (3) only the interpolation data of four corners of the surface patch are known.We design a class of connection scheme of 5×5 bicubic Bézier patches based on the solutions to four problems of inverse calculation and smooth connection of the patches.We also analyze the existence and uniqueness of the control vertices,and give an application example. Finally,we theoretically analyze the smooth connection of (5+4n_1)×(5+4n_2) bicubic Bézier patches.

关 键 词：双三次Bézier曲面片 光滑拼接 控制顶点 

分 类 号：O187[理学—数学]