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

ÖREN İ.

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

  • Publication Type: Article / Article
  • Volume: 42
  • Publication Date: 2018
  • Doi Number: 10.1007/s40995-016-0129-1
  • Journal Name: IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A-SCIENCE
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1563-1577
  • Keywords: Bezier curve, Control invariant, Euclidean geometry, BEZIER CURVES, OBJECT RECOGNITION, INVARIANTS, SURFACES, COINCIDENCE, CURVATURE, PARAMETRIZATIONS, SYSTEMS
  • Karadeniz Technical University Affiliated: Yes

Abstract

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.