Rational Curves in the Three-dimensional Sphere

被引：4

作者：

Georgiev, Georgi H. ^{[1
]}

机构：

[1] Konstantin Preslavsky Univ Shumen, Fac Math & Informat, Shumen, Bulgaria

来源：

APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS | 2010年 / 1293卷

关键词：

Three-dimensional sphere; Bezier curves; Quaternion algebra;

D O I：

10.1063/1.3515576

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the three-dimensional sphere as a hypersurface embedded in the four-dimensional Euclidean space. The pre-images of polynomial and rational curves in the Euclidean 3-space under stereographic projection form a special class of rational curves on 3-sphere. We investigate these spherical curves in terms of Cartesian coordinates and quaternions.

引用

页码：133 / 140

页数：8

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