Equivalence Conditions of Two B,zier Curves in the Euclidean Geometry

ÖREN İ.

IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A-SCIENCE, cilt.42, ss.1563-1577, 2018 (SCI-Expanded) identifier identifier

  • 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.