Canal Surfaces with Quaternions

被引：32

作者：

Aslan, Selahattin ^{[1
]}

Yayli, Yusuf ^{[1
]}

机构：

[1] Ankara Univ, Dept Math, TR-06100 Ankara, Turkey

来源：

ADVANCES IN APPLIED CLIFFORD ALGEBRAS | 2016年 / 26卷 / 01期

关键词：

Canal surfaces; Tubular surfaces; Generalized tubes; Bishop frame; Darboux frame; Quaternions; Rotation matrices;

D O I：

10.1007/s00006-015-0602-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Quaternions are more usable than three Euler angles in the three dimensional Euclidean space. Thus, many laws in different fields can be given by the quaternions. In this study, we show that canal surfaces and tube surfaces can be obtained by the quaternion product and by the matrix representation. Also, we show that the equation of canal surface given by the different frames of its spine curve can be obtained by the same unit quaternion. In addition, these surfaces are obtained by the homothetic motion. Then, we give some results.

引用

页码：31 / 38

页数：8

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