2024/06/14 by Qiang Zou, Zou, Qiang, Lizhen Zhu +1
Engineering · #Advanced Numerical Analysis Techniques #Computational Engineering #Computational Geometry (cs.CG) #FOS: Computer and information sciences #Finance #and Science (cs.CE)
paper · pdf · doi:10.48550/arxiv.2406.09692
openalex publication_date 2024/06/14 · openalex created_date 2024/06/18 · openalex updated_date 2026/07/28
This paper presents a learning-based method to solve the traditional parameterization and knot placement problems in B-spline approximation. Different from conventional heuristic methods or recent AI-based methods, the proposed method does not assume ordered or fixed-size data points as input. There is also no need for manually setting the number of knots. It casts the parameterization and knot placement problems as a sequence-to-sequence translation problem, a generative process automatically determining the number of knots, their placement, parameter values, and their ordering. Once trained, SplineGen demonstrates a notable improvement over existing methods, with a one to two orders of magnitude increase in approximation accuracy on test data.