B-spline curve approximation with transformer neural networks

Abstract

Approximating a curve with a B-spline is a well-known problem with many challenges. Computing parametric values and knot vector that leads to the best approximation of a point sequence is an open problem. Existing methods are usually based on heuristics, genetic algorithms, or meta-heuristics. Nowadays, Deep Neural Networks have demonstrated their usefulness as shown in the use of a Multi-Layer Perceptron in the existing literature. Since its inception, the Transformer architecture has achieved state-of-the-art in multiple domains, like Natural Language Processing and Computer Vision. In this paper, we propose a method for knot placement that focuses on using a Transformer neural network architecture for B-spline approximation. We present and compare the results of our ongoing experimentations with Transformers for B-spline curve approximation. We conclude with possible improvements and modifications to our method for future experiments.