球面插值PH曲线  

Hermitian Interpolation with Spherical Pythagorean-Hodograph Curves

作　　者：马元魁[1] 张天平[2] 康宝生[3] 

机构地区：[1]西北工业大学现代设计与集成制造技术教育部重点实验室,西安710072 [2]陕西师范大学数学与信息科学学院,西安710062 [3]西北大学信息科学与技术学院,西安710069

出　　处：《工程数学学报》2008年第3期442-448,共7页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金项目(60372072,60573177).

摘　　要：本文讨论球面上PH曲线的C1Hermite插值问题。基于球极投影保持PH性质这一特性,通过球极投影把球面数据投影到平面上,构造一条平面PH曲线。然后,逆投影回球面得到一条球面有理插值PH曲线。球面PH曲线对球面数据达到C1插值,拓宽了PH曲线在机器人路径的设计、数控加工的计算等方面的应用范围。The C^1 Hermitian interpolation with spherical Pythagorean-Hodograph（PH） curve is discussed. Under the stereographic projection, the initial data on the sphere are projected to a plane. A planar PH curve is then constructed. Thirdly, by projecting the curve to the sphere, a spherical rational PH curve is generated. During the above process, the stereographic projection preserving PH is utilized and the spherical C^1 PH curve is constructed, which can be nsed in the design for the locus of robots and CNC （Computerized Numerical Control） interpolating, etc.

关 键 词：HERMITE插值 PH曲线 球极投影 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]