NUAT T-splines of odd bi-degree and local refinement  

作　　者：DUAN Xiao-juan WANG Guo-zhao 

机构地区：[1]Department of Mathematics, Zhejiang University

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2014年第4期410-421,共12页高校应用数学学报（英文版）（B辑）

基　　金：Supported by the National Natural Science Foundation of China(60933008 and 61272300)

摘　　要：This paper presents a new kind of spline surfaces, named non-uniform algebraic- trigonometric T-spline surfaces （NUAT T-splines for short） of odd hi-degree. The NUAT T- spline surfaces are defined by applying the T-spline framework to the non-uniform algebraic- trigonometric B-spline surfaces （NUAT B-spline surfaces）. Based on the knot insertion algorithm of the NUAT B-splines, a local refinement algorithm for the NUAT T-splines is given. This algorithm guarantees that the resulting control grid is a T-mesh as the original one. Finally, we prove that, for any NUAT T-spline of odd hi-degree, the linear independence of its blending functions can be determined by computing the rank of the NUAT T-spline-to-NUAT B-spline transformation matrix.This paper presents a new kind of spline surfaces, named non-uniform algebraic- trigonometric T-spline surfaces （NUAT T-splines for short） of odd hi-degree. The NUAT T- spline surfaces are defined by applying the T-spline framework to the non-uniform algebraic- trigonometric B-spline surfaces （NUAT B-spline surfaces）. Based on the knot insertion algorithm of the NUAT B-splines, a local refinement algorithm for the NUAT T-splines is given. This algorithm guarantees that the resulting control grid is a T-mesh as the original one. Finally, we prove that, for any NUAT T-spline of odd hi-degree, the linear independence of its blending functions can be determined by computing the rank of the NUAT T-spline-to-NUAT B-spline transformation matrix.

关 键 词：odd bi-degree non-uniform algebraic-trigonometric T-spline local refinement blending function linear independence. 

分 类 号：O186.11[理学—数学]