Recognition of complex polynomial Bezier curves under similarity transformations

Abstract

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

The new characterization of ruled surfaces corresponding dual Bézier curves

“…Numerous studies have been conducted on Bézier curves and surfaces, for example, Farin, 14 Farouki, 15 Hoschek, 16 Tiller and Hanson, 17 Potmann 18 Gray, 19 Chen et al, 20 Pottmann and Paukowitsch, 21 Krasauskas, 22 Reyes, 23 Mainar et al, 24 Jüttler and Wagner, 25 Q.J. Ge and Sirchia, 26 Mavroidis and Roth, 27 and Cholewa et al 28 Some other works 29–49 are given recently.…”