Geodesic
Rational Bézier curves with infinitely many integral points
Archivum mathematicum, Tome 59 (2023) no. 4, pp. 339-349

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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.
DOI : 10.5817/AM2023-4-339
Classification : 14H25, 14H45, 14H50, 14Q05, 65D17
Keywords: Bézier curve; rational Bézier curve; curve of genus 0; integral point 
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     title = {Rational {B\'ezier} curves with infinitely many integral points},
     journal = {Archivum mathematicum},
     pages = {339--349},
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     zbl = {07790551},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.5817/AM2023-4-339/}
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Dospra, Petroula. Rational Bézier curves with infinitely many integral points. Archivum mathematicum, Tome 59 (2023) no. 4, pp. 339-349. doi: 10.5817/AM2023-4-339

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