A Geometric Approach for Multi-Degree Spline  

作　　者：李新 黄章进 刘昭 

机构地区：[1]School of Mathematical Science,University of Science and Technology of China [2]School of Computer Science,University of Science and Technology of China

出　　处：《Journal of Computer Science & Technology》2012年第4期841-850,共10页计算机科学技术学报（英文版）

基　　金：supported by the National Natural Science Foundation of China under Grant Nos.11031007, 60903148, 60803066;the Chinese Universities Scientific Fund, the Scientific Research Foundation for the Returned Overseas Chinese Scholars of State Education Ministry of China;the Startup Scientific Research Foundation of Chinese Academy of Sciences

摘　　要：Multi-degree spline （MD-spline for short） is a generalization of B-spline which comprises of polynomial segments of various degrees. The present paper provides a new definition for MD-spline curves in a geometric intuitive way based on an efficient and simple evaluation algorithm. MD-spline curves maintain various desirable properties of B-spline curves, such as convex hull, local support and variation diminishing properties. They can also be refined exactly with knot insertion. The continuity between two adjacent segments with different degrees is at least C1 and that between two adjacent segments of same degrees d is C^d-1. Benefited by the exact refinement algorithm, we also provide several operators for MD-spline curves, such as converting each curve segment into Bezier form, an efficient merging algorithm and a new curve subdivision scheme which allows different degrees for each segment.Multi-degree spline （MD-spline for short） is a generalization of B-spline which comprises of polynomial segments of various degrees. The present paper provides a new definition for MD-spline curves in a geometric intuitive way based on an efficient and simple evaluation algorithm. MD-spline curves maintain various desirable properties of B-spline curves, such as convex hull, local support and variation diminishing properties. They can also be refined exactly with knot insertion. The continuity between two adjacent segments with different degrees is at least C1 and that between two adjacent segments of same degrees d is C^d-1. Benefited by the exact refinement algorithm, we also provide several operators for MD-spline curves, such as converting each curve segment into Bezier form, an efficient merging algorithm and a new curve subdivision scheme which allows different degrees for each segment.

关 键 词：SPLINE B-SPLINE multi-degree spline MERGING 

分 类 号：O186.11[理学—数学] TP391.72[理学—基础数学]