A shift-invariant C12-subdivision algorithm which rotates the lattice

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

Computer Aided Geometric Design Pub Date : 2025-03-18 DOI:10.1016/j.cagd.2025.102430

Cédric Gérot , Malcolm A. Sabin

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Abstract

In order to study differential properties of a subdivision surface at a markpoint, it is necessary to parametrise it over a so-called characteristic map defined as the infinite union of

C^{k}

-parametrised rings. Construction of this map is known when a single step of the subdivision scheme does not rotate a regular lattice. Otherwise, two steps are considered as they realign the lattice and its subdivided version. We present a new subdivision scheme which rotates the lattice and nevertheless allows a direct construction of the characteristic map. It is eigenanalysed with techniques introduced in a companion article and proved to define a

C_{1}^{2}

-algorithm around a face-centre. This scheme generalises Loop's scheme, allowing the designer to choose between extraordinary vertices or faces in regard to the shape of the mesh, the location of the extraordinary elements, and the aimed limit shape.

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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.