The construction of circular surfaces with quaternions


Canakci Z., TUNCER O. O. , GÖK İ., YAYLI Y.

ASIAN-EUROPEAN JOURNAL OF MATHEMATICS, vol.12, no.7, 2019 (Journal Indexed in ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 12 Issue: 7
  • Publication Date: 2019
  • Doi Number: 10.1142/s1793557119500918
  • Title of Journal : ASIAN-EUROPEAN JOURNAL OF MATHEMATICS

Abstract

In this paper, we obtain equations of circular surfaces by using unit quaternions and express these surfaces in terms of homothetic motions. Furthermore, we introduce new roller coaster surfaces constructed by the spherical indicatrices of a spatial curve in Euclidean 3-space. Then, we express parametric equations of roller coaster surfaces by means of unit quaternions and orthogonal matrices corresponding to these quaternions. Moreover, we present some illustrated examples.