Equivalence Conditions of Two B,zier Curves in the Euclidean Geometry
IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A-SCIENCE, cilt.42, ss.1563-1577, 2018 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 42
- Basım Tarihi: 2018
- Doi Numarası: 10.1007/s40995-016-0129-1
- Dergi Adı: IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A-SCIENCE
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.1563-1577
- Anahtar Kelimeler: Bezier curve, Control invariant, Euclidean geometry, BEZIER CURVES, OBJECT RECOGNITION, INVARIANTS, SURFACES, COINCIDENCE, CURVATURE, PARAMETRIZATIONS, SYSTEMS
- Karadeniz Teknik Üniversitesi Adresli: Evet
Özet
Let G be the group M(n) generated by all orthogonal transformations and translations of the n-dimensional Euclidean space or G be the subgroup of M(n) generated by rotations and translations of . This paper presents the conditions of G-equivalence for two B,zier curves in of degree m, where . Moreover, two minimal complete systems of control G-invariants of a B,zier curve are obtained. The definition of a non-directional B,zier curve is introduced and a complete system of control G-invariants of this curve is obtained. Correlations between elements of the second minimal complete system of control M(n)-invariants are investigated.