On a nonlinear version of Lane-Riesenfeld's subdivision schemes converging to piecewise smooth functions preserving high regularity

IF 1.7 4区计算机科学 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Computer Aided Geometric Design Pub Date : 2025-09-16 DOI:10.1016/j.cagd.2025.102485

Sergio Amat , Sonia Busquier , David Levin , Juan Ruiz , Dionisio F. Yáñez

引用次数: 0

Abstract

Lane-Riesenfeld's subdivision schemes provide a versatile tool for generating smooth and detailed curves and surfaces, making them valuable assets in computer graphics and geometric modeling. These schemes offer flexibility in controlling the regularity of the limit function by adjusting some parameters. In this paper, we propose a nonlinear modification of these algorithms for piecewise smooth functions. The new algorithm converges to piecewise smooth limit functions maintaining the high regularity of Lane-Riesenfeld's subdivision schemes in smooth zones. The practical results presented show a very good numerical behavior of the proposed algorithms.

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Lane-Riesenfeld细分格式收敛于保持高正则性的分段光滑函数的一个非线性版本

Lane-Riesenfeld的细分方案为生成光滑和详细的曲线和表面提供了一个通用的工具，使它们成为计算机图形学和几何建模的宝贵资产。这些方案通过调整一些参数来灵活地控制极限函数的正则性。在本文中，我们提出了这些算法的非线性修正，用于分段光滑函数。该算法收敛于分段光滑极限函数，保持了Lane-Riesenfeld细分格式在光滑区域内的高度正则性。实际计算结果表明，所提算法具有良好的数值性能。

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

Computer Aided Geometric Design 工程技术-计算机：软件工程

CiteScore

3.50

自引率

13.30%

发文量

审稿时长

60 days

期刊介绍： The journal Computer Aided Geometric Design is for researchers, scholars, and software developers dealing with mathematical and computational methods for the description of geometric objects as they arise in areas ranging from CAD/CAM to robotics and scientific visualization. The journal publishes original research papers, survey papers and with quick editorial decisions short communications of at most 3 pages. The primary objects of interest are curves, surfaces, and volumes such as splines (NURBS), meshes, subdivision surfaces as well as algorithms to generate, analyze, and manipulate them. This journal will report on new developments in CAGD and its applications, including but not restricted to the following: -Mathematical and Geometric Foundations- Curve, Surface, and Volume generation- CAGD applications in Numerical Analysis, Computational Geometry, Computer Graphics, or Computer Vision- Industrial, medical, and scientific applications. The aim is to collect and disseminate information on computer aided design in one journal. To provide the user community with methods and algorithms for representing curves and surfaces. To illustrate computer aided geometric design by means of interesting applications. To combine curve and surface methods with computer graphics. To explain scientific phenomena by means of computer graphics. To concentrate on the interaction between theory and application. To expose unsolved problems of the practice. To develop new methods in computer aided geometry.