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Point relative knot matrix for B-spline curve approximation with transformer neural networks

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  • Saillot, Mathis
  • Michel, Dominique
  • Zidna, Ahmed

Abstract

Data-fitting using free-knot B-spline curves comes with many challenges. Obtaining the best approximation by finding the best set of parameters and knots is an open problem known since several decades. Over the years, many different methods have been introduced in the literature. Recent works have introduced new methods using Deep Neural Networks. Notably, the Transformer Neural Network architecture has been successfully applied to the knot placement problem. In this paper, we propose a new matrix representation of knot vectors, that can be used as an output of a Deep Neural Network for curve approximation. We present and compare the results of our method against existing methods. We conclude with possible improvements and modifications to our method for future experiments.

Suggested Citation

  • Saillot, Mathis & Michel, Dominique & Zidna, Ahmed, 2026. "Point relative knot matrix for B-spline curve approximation with transformer neural networks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 249(C), pages 1057-1075.
    • Handle: RePEc:eee:matcom:v:249:y:2026:i:c:p:1057-1075
    DOI: 10.1016/j.matcom.2026.06.016
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