Canal Surfaces with Quaternions

Aslan S., YAYLI Y.

ADVANCES IN APPLIED CLIFFORD ALGEBRAS, cilt.26, sa.1, ss.31-38, 2016 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 26 Sayı: 1
  • Basım Tarihi: 2016
  • Doi Numarası: 10.1007/s00006-015-0602-5
  • Dergi Adı: ADVANCES IN APPLIED CLIFFORD ALGEBRAS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.31-38
  • Anahtar Kelimeler: Canal surfaces, Tubular surfaces, Generalized tubes, Bishop frame, Darboux frame, Quaternions, Rotation matrices
  • Ankara Üniversitesi Adresli: Evet

Özet

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.