Infinity branches and asymptotic analysis of algebraic space curves: New techniques and applications

IF 1.3 4区计算机科学 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING Computer Aided Geometric Design Pub Date : 2025-03-01 DOI:10.1016/j.cagd.2025.102422

Sonia Pérez-Díaz , Li-Yong Shen , Xin-Yu Wang , R. Magdalena-Benedicto

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引用次数: 0

Abstract

Let

C

represent an irreducible algebraic space curve defined by the real polynomials

f_{i} (x_{1}, x_{2}, x_{3})

for

i = 1, 2

. It is a recognized fact that a birational relationship invariably exists between the points on

C

and those on an associated irreducible plane curve, denoted as

C^{p}

. In this work, we leverage this established relationship to delineate the asymptotic behavior of

C

by examining the asymptotes of

C_{p}

. Building on this foundation, we introduce a novel and practical algorithm designed to efficiently compute the asymptotes of

C

, given that the asymptotes of

C_{p}

have been ascertained.

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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.