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 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 12 Issue: 7
  • Publication Date: 2019
  • Doi Number: 10.1142/s1793557119500918
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, zbMATH
  • Keywords: Circular surface, roller coaster surface, alternative moving frame, quaternions, homothetic motions, SPLIT QUATERNIONS, CANAL SURFACES, ROTATIONS
  • Hacettepe University Affiliated: Yes


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.