R&D result detail

Original Title

DIGITAL JORDAN SURFACES ARISING FROM TETRAHEDRAL TILING

English Title

DIGITAL JORDAN SURFACES ARISING FROM TETRAHEDRAL TILING

Type

WoS Article

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.

English 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.

Key words in English

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

Authors

ŠLAPAL, J.

RIV year

2025

Released

17.06.2024

Publisher

De Gruyter

Location

Bratislava

ISBN

1337-2211

Periodical

Mathematica Slovaca

Volume

74

Number

3

State

Slovak Republic

Pages from

723

Pages to

736

Pages count

14

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="0139-9918",
  url="https://www.degruyter.com/document/doi/10.1515/ms-2024-0055/html"
}