Publication detail

DIGITAL JORDAN SURFACES ARISING FROM TETRAHEDRAL TILING

ŠLAPAL, J.

Original Title

Type

journal article in Web of Science

Language

English

Original Abstract

We employ closure operators associated with n-ary relations, n > 1 an integer, to provide the digital space Z^3 with connectedness structures. We show that each of the six inscribed tetrahedra obtained by canonical tessellation of a digital cube in Z^3 with edges consisting of 2n - 1 points is connected. This result is used to prove that certain bounding surfaces of the polyhedra in Z^3 that may be face-to-face tiled with such tetrahedra are digital Jordan surfaces (i.e., separate Z^3 into exactly two connected components). An advantage of these Jordan surfaces over those with respect to the Khalimsky topology is that they may possess acute dihedral angles pi/4 while, in the case of the Khalimsky topology, the dihedral angles may never be less than pi/2.

Keywords

n-ary relation, closure operator, canonical tetrahedral tessellation of a cube, 3D face to face tiling, digital Jordan surface.

Authors

ŠLAPAL, J.

Released

17. 6. 2024

Publisher

De Gruyter

Location

Bratislava

ISBN

1337-2211

Periodical

Mathematica Slovaca

Year of study

Number

State

Slovak Republic

Pages from

723

Pages to

736

Pages count

URL

https://www.degruyter.com/document/doi/10.1515/ms-2024-0055/html

BibTex

@article{BUT189058,
  author="Josef {Šlapal}",
  title="DIGITAL JORDAN SURFACES ARISING FROM TETRAHEDRAL TILING",
  journal="Mathematica Slovaca",
  year="2024",
  volume="74",
  number="3",
  pages="723--736",
  doi="10.1515/ms-2024-0055",
  issn="1337-2211",
  url="https://www.degruyter.com/document/doi/10.1515/ms-2024-0055/html"
}