- Turkish Journal of Mathematics and Computer Science
- Vol: 10 Special Issue
- On the control invariants of planar Bezier curves for the groups M(2) and SM(2)
On the control invariants of planar Bezier curves for the groups M(2) and SM(2)
Authors : Idris Ören
Pages : 74-81
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Publication Date : 2018-12-29
Article Type : Other
Abstract :Let G=M(2) be the group generated by all orthogonal transformations and translations of the 2-dimensional Euclidean space E 2 or G=SM(2) be the subgroup of M(2) generated by rotations and translations of E 2 . In this paper, global G -invariants of plane Bezier curves in E 2 are introduced. Using complex numbers and the global G -invariants of a plane B curves, for given two plane B curves x(t) and y(t) , evident forms of all transformations g\in G , carrying x(t) to y(t) , are obtained. Similar results are given for plane polynomial curves.Keywords : B\'{e}zier curve, Invariant, Euclidean space