On the Control Invariants of Planar Bezier Curves for the Groups ´ M(2) and S M(2)

Özet

Let G = M(2) be the group generated by all orthogonal transformations and translations of the 2-dimensional Euclidean space E2 or G = S M(2) be the subgroup of M(2) generated by rotations and translations ofE2. In this paper, global G-invariants of plane Bezier curves in ´ E2 are introduced. Using complex numbers and theglobal G-invariants of a plane Bezier curves, for given two plane B ´ ezier curves ´ x(t) and y(t), evident forms of alltransformations g ∈ G, carrying x(t) to y(t), are obtained. Similar results are given for plane polynomial curves.