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
收藏
页码：133 / 140
页数：8
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