Rational Bézier curves with infinitely many integral points

Petroula Dospra

Archivum Mathematicum (2023)

  • Volume: 059, Issue: 4, page 339-349
  • ISSN: 0044-8753

Abstract

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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.

How to cite

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Dospra, Petroula. "Rational Bézier curves with infinitely many integral points." Archivum Mathematicum 059.4 (2023): 339-349. <http://eudml.org/doc/299130>.

@article{Dospra2023,
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.},
author = {Dospra, Petroula},
journal = {Archivum Mathematicum},
keywords = {Bézier curve; rational Bézier curve; curve of genus 0; integral point},
language = {eng},
number = {4},
pages = {339-349},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Rational Bézier curves with infinitely many integral points},
url = {http://eudml.org/doc/299130},
volume = {059},
year = {2023},
}

TY - JOUR
AU - Dospra, Petroula
TI - Rational Bézier curves with infinitely many integral points
JO - Archivum Mathematicum
PY - 2023
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 059
IS - 4
SP - 339
EP - 349
AB - 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.
LA - eng
KW - Bézier curve; rational Bézier curve; curve of genus 0; integral point
UR - http://eudml.org/doc/299130
ER -

References

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  1. Farine, G., Curves and Surfaces for CAGD. A Practical Guide, fifth ed., Academic Press, 2002. (2002) 
  2. Hoschek, J., Lasser, D., Fundamentals of Computer Aided Geometric Design, AK Peters, 1993. (1993) MR1258308
  3. Mortenson, M.E., Geometric Modelling, Industrial Press Inc., 2006. (2006) MR0794672
  4. Poulakis, D., 10.1090/S0002-9939-02-06841-7, Proc. Amer. Math. Soc. 131 (2) (2002), 1357–1359. (2002) MR1949864DOI10.1090/S0002-9939-02-06841-7
  5. Poulakis, D., Voskos, E., 10.1006/jsco.2000.0420, J. Symbolic Comput. 30 (2000), 573–582. (2000) MR1797269DOI10.1006/jsco.2000.0420
  6. Poulakis, D., Voskos, E., 10.1006/jsco.2001.0515, J. Symbolic Comput. 33 (2002), 479–491. (2002) MR1890582DOI10.1006/jsco.2001.0515
  7. Ramanantoanina, A., Hormann, K., 10.1016/j.cagd.2021.102003, Comput. Aided Geom. Design 88 (2021), 11 pp., 102003. (2021) MR4263538DOI10.1016/j.cagd.2021.102003

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