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球面上的几何连续插值
引用本文:罗钟铉,王倩.球面上的几何连续插值[J].数学研究及应用,2012,32(4):379-391.
作者姓名:罗钟铉  王倩
作者单位:大连理工大学数学科学学院, 辽宁 大连 116024; 大连理工大学软件学院, 辽宁 大连 116600;大连理工大学数学科学学院, 辽宁 大连 116024
基金项目:国家自然科学基金 (Grant Nos.61033012; 10801023; 10911140268).
摘    要:In this paper, a new method for geometrically continuous interpolation in spheres is proposed. The method is entirely based on the spherical B′ezier curves defined by the generalized de Casteljau algorithm. Firstly we compute the tangent directions and curvature vectors at the endpoints of a spherical B′ezier curve. Then, based on the above results, we design a piecewise spherical B′ezier curve with G 1 and G 2 continuity. In order to get the optimal piecewise curve according to two different criteria, we also give a constructive method to determine the shape parameters of the curve. According to the method, any given spherical points can be directly interpolated in the sphere. Experimental results also demonstrate that the method performs well both in uniform speed and magnitude of covariant acceleration.

关 键 词:interpolation  sphere  geometric  continuity  B′ezier.
收稿时间:4/9/2011 12:00:00 AM
修稿时间:2011/10/31 0:00:00

Geometrically Continuous Interpolation in Spheres
Zhongxuan LUO and Qian WANG.Geometrically Continuous Interpolation in Spheres[J].Journal of Mathematical Research with Applications,2012,32(4):379-391.
Authors:Zhongxuan LUO and Qian WANG
Institution:School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China; School of Software, Dalian University of Technology, Liaoning 116620, P. R. China;School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China;
Abstract:In this paper, a new method for geometrically continuous interpolation in spheres is proposed. The method is entirely based on the spherical B\'ezier curves defined by the generalized de Casteljau algorithm. Firstly we compute the tangent directions and curvature vectors at the endpoints of a spherical B\'ezier curve. Then, based on the above results, we design a piecewise spherical B\'ezier curve with $G^1$ and $G^2$ continuity. In order to get the optimal piecewise curve according to two different criteria, we also give a constructive method to determine the shape parameters of the curve. According to the method, any given spherical points can be directly interpolated in the sphere. Experimental results also demonstrate that the method performs well both in uniform speed and magnitude of covariant acceleration.
Keywords:interpolation  sphere  geometric continuity  B\'ezier  
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