Log-aesthetic curves and generalized Archimedean spirals

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

Computer Aided Geometric Design Pub Date : 2025-07-03 DOI:10.1016/j.cagd.2025.102468

Péter Salvi

引用次数: 0

Abstract

We show that the radials of log-aesthetic curves are generalized Archimedean spirals. Examining the logarithmic curvature histogram reveals that these radials have an inherent similarity to the associated log-aesthetic curves, and can also be used as computationally inexpensive approximants. Different kinds of fits are proposed and discussed through examples. A possible generalization of log-aesthetic curves based on generalized Archimedean spirals is also explored.

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对数美曲线与广义阿基米德螺旋

我们证明了对数曲线的径向是广义阿基米德螺旋。检查对数曲率直方图显示，这些径向与相关的对数美学曲线具有固有的相似性，并且也可以用作计算廉价的近似值。提出了不同的拟合形式，并通过实例进行了讨论。本文还探讨了基于广义阿基米德螺旋的对数美学曲线的一种可能的推广。

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.