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.

Keywords

• Polynomial curve,B\'{e}zier curve,Invariant,Linear similarity group

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