Detecting Similarities of Bezier Curves for the Groups $LSim(E_{2}), LSim^{+}( E_{2})$

Abstract

In this paper, for linear similarity groups, global invariants of plane Bezier curves ( plane polynomial curves) in $E_{2}$ are introduced. Using complex numbers and the global $G$-invariants of a plane Bezier curve( a plane polynomial curve), for given two plane Bezier curves (plane polynomial curves) $x(t)$ and $y(t)$, evident forms of all transformations $g\in G$, carrying $x(t)$ to $y(t)$, are obtained.