Newton Geometric Iterative Method for B-Spline Curve and Surface Approximation

• Published in: Computer aided design Vol. 172; p. 103716
• Main Authors: Song, Qiuyang, Bo, Pengbo
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.07.2024
• Subjects: Curve and surface approximation; Geometric iterative approximation; Geometric modeling; Geometric optimization; Progressive and iterative approximation; Geometric iterative approximation; Geometric optimization; Geometric modeling; Progressive and iterative approximation; Curve and surface approximation
• ISSN: 0010-4485; 1879-2685
• DOI: 10.1016/j.cad.2024.103716

We introduce a progressive and iterative method for B-spline curve and surface approximation, incorporating parameter correction based on the Newton iterative method. While parameter corrections have been used in existing Geometric Approximation (GA) methods to enhance approximation quality, they suffer from low computational efficiency. Our approach unifies control point updates and parameter corrections in a progressive and iterative procedure, employing a one-step strategy for parameter correction. We provide a theoretical proof of convergence for the algorithm, demonstrating its superior computational efficiency compared to current GA methods. Furthermore, the provided convergence proof offers a methodology for proving the convergence of existing GA methods with location parameter correction. •We propose a GA method that unifies control point update and parameter correction (PC).•We provide proof of the convergence of the proposed algorithm.•Our proof inspires the convergence proof of traditional GA methods with PC.•We provide experiments comparing our method to existing GA methods.