RECOGNITION OF COMPLEX POLYNOMIAL BÉZIER CURVES UNDER SIMILARITY TRANSFORMATIONS

Abstract

In this paper, similarity groups in the complex plane s, polyno- mial curves and complex Bézier curves in s are introduced. Global similarity invariants of polynomial curves and complex Bézier curves in s are given in terms of complex functions. The problem of similarity of two polynomial curves in s are solved. Moreover, in case two polynomial curve (complex Bézier curve) are similar for the similarity group, a general form of all similarity transfor- mations, carrying one curve into the other curve, are obtained.