Rational C1 cubic Powell–Sabin B-splines with application to representation of ruled surfaces

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics Pub Date : 2024-09-26 DOI:10.1016/j.cam.2024.116292

Jan Grošelj, Ada Šadl Praprotnik

引用次数: 0

Abstract

This paper defines rational

C^{1}

cubic Powell–Sabin splines and analyses their basic properties. A rational B-spline basis is established and an algorithm for determining the corresponding control points and weights by using the blossoming operator is presented. The capability of the introduced splines to represent rational cubic triangular Bézier patches and quadratic NURPS is discussed and explicit conversion formulas are provided. Moreover, the application of the rational

C^{1}

cubic Powell–Sabin splines to representation of ruled surfaces is studied, showing that the cubic splines can give smoother parametrizations than the NURPS.

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有理 C1 立方 Powell-Sabin B 样条曲线在规则曲面表示中的应用

本文定义了有理 C1 立方 Powell-Sabin 样条曲线并分析了其基本特性。本文建立了有理 B 样条曲线的基础，并提出了一种利用绽放算子确定相应控制点和权重的算法。讨论了引入的样条曲线表示有理立方三角贝塞尔斑块和二次 NURPS 的能力，并提供了明确的转换公式。此外，还研究了有理 C1 立方 Powell-Sabin 样条曲线在规则曲面表示中的应用，结果表明立方样条曲线能给出比 NURPS 更平滑的参数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Computational and Applied Mathematics 数学-应用数学

CiteScore

5.40

自引率

4.20%

发文量

437

审稿时长

3.0 months

期刊介绍： The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest. The audience consists of: applied mathematicians, numerical analysts, computational scientists and engineers.