Topology guaranteed and error controlled curve tracing for parametric surface-surface intersection

IF 1.3 4区计算机科学 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Computer Aided Geometric Design Pub Date : 2025-04-11 DOI:10.1016/j.cagd.2025.102432

Bingwei Zhang , Jin-San Cheng , Yu-Shen Liu , Zhaoqi Zhang

引用次数: 0

Abstract

We present a novel and efficient curve tracing method of the intersection of two parametric surfaces with error bound controlled and correct topology. Our method decomposes the 4D intersection curve in the parameter space into strongly monotonic curve segments such that their corresponding 3D curve segments in the model space are also strongly monotonic. This decomposition strategy can prevent straying or looping and maintain the 3D topology between the curve segments. Furthermore, by controlling the density of decomposition in the model space, our method can easily control the error bound of the numerical approximation of the curve segments. As a result, our method is very efficient compared to previous related work. Our experiments support our claims.

查看原文本刊更多论文

参数曲面相交的拓扑保证和误差控制曲线跟踪

提出了一种误差界可控且拓扑正确的两参数曲面交点曲线跟踪方法。我们的方法将参数空间中的四维相交曲线分解为强单调曲线段，使其在模型空间中对应的三维曲线段也是强单调的。这种分解策略可以防止曲线段之间的偏离或循环，保持曲线段之间的三维拓扑结构。此外，通过控制模型空间中的分解密度，我们的方法可以很容易地控制曲线段数值逼近的误差界。因此，与以往的相关工作相比，我们的方法是非常高效的。我们的实验支持我们的主张。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

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.