Hermite subdivision schemes for manifold-valued Hermite data

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

Computer Aided Geometric Design Pub Date : 2024-05-13 DOI:10.1016/j.cagd.2024.102342

Hofit Ben-Zion Vardi, Nira Dyn, Nir Sharon

引用次数: 0

Abstract

This paper introduces a family of subdivision schemes that generate curves over manifolds from manifold-Hermite data. This data consists of points and tangent directions sampled from a curve over a manifold. Using a manifold-Hermite average based on the De Casteljau algorithm as our main building block, we show how to adapt a geometric approach for curve approximation over manifold-Hermite data. The paper presents the various definitions and provides several analysis methods for characterizing properties of both the average and the resulting subdivision schemes based on it. Demonstrative figures accompany the paper's presentation and analysis.

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流形值 Hermite 数据的 Hermite 细分方案

本文介绍了一系列细分方案，这些方案可根据流形-赫米特数据生成流形上的曲线。这些数据包括从流形上的曲线中采样的点和切线方向。我们以基于 De Casteljau 算法的流形-Hermite 平均法为主要构件，展示了如何采用几何方法对流形-Hermite 数据进行曲线逼近。本文介绍了各种定义，并提供了几种分析方法，用于描述平均值和基于平均值的细分方案的特性。本文的介绍和分析还附有演示图。

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.