Investigations of a functional version of a blending surface scheme for regular data interpolation

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.2024.102345

Stephen Mann

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Abstract

This paper describes an implementation and tests of a blending scheme for regularly sampled data interpolation, and in particular studies the order of approximation for the method. This particular implementation is a special case of an earlier scheme by Fang for fitting a parametric surface to interpolate the vertices of a closed polyhedron with n-sided faces, where a surface patch is constructed for each face of the polyhedron, and neighbouring faces can meet with a user specified order of continuity. The specialization described in this paper considers functions of the form $z = f (x, y)$ with the patches meeting with $C^{2}$ continuity. This restriction allows for investigation of order of approximation, and it is shown that the functional version of Fang's scheme has polynomial precision.

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对用于常规数据插值的混合曲面方案功能版本的研究

本文描述了一种用于规则采样数据插值的混合方案的实施和测试，特别研究了该方法的近似阶次。这种特殊的实现方法是方方早先提出的参数曲面拟合方案的一个特例，该方案用于对具有 n 个面的封闭多面体的顶点进行插值，为多面体的每个面构建一个曲面补丁，相邻面可以按照用户指定的连续性顺序相接。本文中描述的特殊化考虑了z=f(x,y)形式的函数，其补丁以 C2 连续性相接。这一限制允许对近似阶数进行研究，并表明方氏方案的函数版本具有多项式精度。

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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.