Rational Bézier curves with infinitely many integral points

Petroula Dospra

Address: Department of Chemical Engineering, University of West Macedonia, Kila, 501 50, Kozani, Greece

E-mail:

Abstract: In this paper we consider rational Bézier curves with control points having rational coordinates and rational weights, and we give necessary and sufficient conditions for such a curve to have infinitely many points with integer coefficients. Furthermore, we give algorithms for the construction of these curves and the computation of theirs points with integer coefficients.

AMSclassification: primary 65D17; secondary 14Q05, 14H25, 14H45, 14H50.

Keywords: Bézier curve, rational Bézier curve, curve of genus 0, integral point.

DOI: 10.5817/AM2023-4-339