On the control invariants of planar Bezier curves for the groups M(2) and SM(2)

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Turkish Journal of Mathematics and Computer Science
Volume: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 : İdris Ören

Pages : 74-81

View : 51 | Download : 8

Publication Date : 2018-12-29

Article Type : Conference Paper

Abstract :Let G=Minsert ignore into journalissuearticles values(2); be the group generated by all orthogonal transformations and translations of the 2-dimensional Euclidean space E 2 or G=SMinsert ignore into journalissuearticles values(2); be the subgroup of Minsert ignore into journalissuearticles values(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 xinsert ignore into journalissuearticles values(t); and yinsert ignore into journalissuearticles values(t); , evident forms of all transformations g\in G , carrying xinsert ignore into journalissuearticles values(t); to yinsert ignore into journalissuearticles values(t); , are obtained. Similar results are given for plane polynomial curves.
Keywords : B` e zier curve, Invariant, Euclidean space

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