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
相关论文
共 50 条
  • [31] Total torsion of curves in three-dimensional manifolds
    Pansonato, Claudia C.
    Costa, Sueli I. R.
    GEOMETRIAE DEDICATA, 2008, 136 (01) : 111 - 121
  • [32] Foliations by Curves on Three-Dimensional Segre Varieties
    Ballico, Edoardo
    BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 2022, 48 (06) : 3727 - 3742
  • [33] Total torsion of curves in three-dimensional manifolds
    Claudia C. Pansonato
    Sueli I. R. Costa
    Geometriae Dedicata, 2008, 136
  • [34] Fitting plane curves to three-dimensional points
    Antonopoulos, A
    JOURNAL OF SURVEYING ENGINEERING-ASCE, 2004, 130 (02): : 73 - 78
  • [35] Elliptic Curves and Three-Dimensional Flow Patterns
    Brian J. Cantwell
    Nonlinear Dynamics, 2000, 22 : 29 - 38
  • [36] Foliations by Curves on Three-Dimensional Segre Varieties
    Edoardo Ballico
    Bulletin of the Iranian Mathematical Society, 2022, 48 : 3727 - 3742
  • [37] Three-Dimensional Classification of Thoracic Scoliotic Curves
    Sangole, Archana P.
    Aubin, Carl-Eric
    Labelle, Hubert
    Stokes, Ian A. F.
    Lenke, Lawrence G.
    Jackson, Roger
    Newton, Peter
    SPINE, 2009, 34 (01) : 91 - 99
  • [38] Evidence of three-dimensional variability in scoliotic curves
    Carpineta, L
    Labelle, H
    CLINICAL ORTHOPAEDICS AND RELATED RESEARCH, 2003, (412) : 139 - 148
  • [39] Soliton curves in three-dimensional space forms
    Kawakubo, Satoshi
    JOURNAL OF GEOMETRY AND PHYSICS, 2018, 133 : 242 - 259
  • [40] Elliptic curves and three-dimensional flow patterns
    Cantwell, BJ
    NONLINEAR DYNAMICS, 2000, 22 (01) : 29 - 38
12345