Twelve-parameter symmetric affine 3D coordinate transformation based on dual quaternions
SURVEY REVIEW, cilt.58, sa.409, ss.345-357, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 58 Sayı: 409
- Basım Tarihi: 2026
- Doi Numarası: 10.1080/00396265.2025.2556558
- Dergi Adı: SURVEY REVIEW
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Environment Index, Geobase
- Sayfa Sayıları: ss.345-357
- Anahtar Kelimeler: 12-parameter affine 3D transformation, Computer vision, Dual quaternion, Gimbal lock, Symmetric and asymmetric transformation
- Ondokuz Mayıs Üniversitesi Adresli: Evet
Özet
The aim of a coordinate transformation is to determine the coordinates of a point in a second coordinate system, given their known values in the first system. The subject of coordinate transformations has applications in a wide range of areas. There are different types of coordinate transformation methods: orthogonal, similarity, affine, projective, and polynomial transformations. In this study, we considered a symmetric 12-parameter 3D affine transformation based on the dual quaternion. The performances of different transformation models were compared. We also sought to determine which transformation model to use. A transformation implementation including gimbal lock has been added as an Appendix to clearly demonstrate the advantages of quaternions over Euler angles.