A shift-invariant C 1 2 -subdivision algorithm which rotates the lattice

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...

Full description

Saved in:
Bibliographic Details
Published inComputer aided geometric design Vol. 118; p. 102430
Main Authors Gérot, Cédric, Sabin, Malcolm A.
Format Journal Article
LanguageEnglish
Published Elsevier 01.05.2025
Subjects
Computational Geometry
Computer Science
Graphics
Differential analysis
Subdivision
Extraordinary face
Characteristic map
Online AccessGet full text
ISSN0167-8396
DOI10.1016/j.cagd.2025.102430

Cover

More Information
Summary: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.
ISSN:0167-8396
DOI:10.1016/j.cagd.2025.102430