超限插值曲面造型的连分式方法与光滑拼接研究

项目名称： 超限插值曲面造型的连分式方法与光滑拼接研究

项目编号： No.61272024

项目类型： 面上项目

立项/批准年度： 2013

项目学科： 自动化技术、计算机技术

项目作者： 赵欢喜

作者单位： 中南大学

项目金额： 61万元

中文摘要： 本项目讨论向量函数广义逆及其偏广义逆，提出有理超限插值曲面造型的连分式插值算法，这将丰富连分式插值理论，且把传统的多项式Gordon 超限插值曲面造型推广到有理情形，并讨论基于融合的超限插值曲面片的光滑拼接方法。具体地说，研究向量函数广义逆及其偏广义逆的定义，以及基于此定义下的连分式定义、连分式计算的递推公式；研究单方向一元连分式构造超限插值曲面片以及切触超限插值曲面片的方法；研究单方向超限插值曲面片基于融合的光滑拼接；研究矩形网格与三角网格下有理超限插值曲面片的二元连分式造型算法及其基于融合的光滑拼接；然后研究当轮廓曲线或网格曲线为B-样条曲线时，所构造的有理超限插值曲面片的NURBS表示；最后探讨连分式超限插值造型方法的一些应用如管道曲面、医学三维可视化造型等。本课题研究成果将推广Coons,Gordon等提出的超限插值曲面造型技术，并对曲面造型具有重要的科学意义和工程应用。

中文关键词： 有理曲面；有理插值样条曲面；连分式；有理超限插值曲面；函数广义逆

英文摘要： Based on the generalised inverse and partial generalised inverse of vector-valued function, the rational transfinite interpolation surface mondeling is presented via continued fractions interpolation approach. This will enrich the continued fraction interpolation theory, and traditional polynomial transfinite interpolation surface modeling is extended to the rational case. In this project, smooth joining of the transfinite interpolation surface patch is also discussed via blending approach. For more details, first，the definitions of the generalized inverse and partial generalised inverse are discussed , and by means of the above definitions, the vector-valued functionn continued fraction is defined, recursive formula of the continued fraction calculation are also disscussed; transfinite interpolation surface patch and osculatory transfinite interpolation surface patch in one-direction is discussed via continued fractions interpolation algorithm;The smooth joining of the transfinition interpolation surface patch in one-direction is discussed; The rational transfinite interpolation surface patch on rectangular grid and triangur grid is constructed via bivariate continued fraction and its smooth connection; Then, when profile curve and mesh curve is the B-spline one,how the constructed rational transfinite inte

英文关键词： rational surface；rational interpolation spline surface；continued fractions；rational transfinite interpolation surface；function generalised inverse