Detail publikačního výsledku

DIGITAL JORDAN SURFACES ARISING FROM TETRAHEDRAL TILING

ŠLAPAL, J.

Originální název

DIGITAL JORDAN SURFACES ARISING FROM TETRAHEDRAL TILING

Anglický název

DIGITAL JORDAN SURFACES ARISING FROM TETRAHEDRAL TILING

Druh

Článek WoS

Originální abstrakt

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.

Anglický abstrakt

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.

Klíčová slova

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

Klíčová slova v angličtině

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

Autoři

ŠLAPAL, J.

Rok RIV

2025

Vydáno

17.06.2024

Nakladatel

De Gruyter

Místo

Bratislava

ISSN

1337-2211

Periodikum

Mathematica Slovaca

Svazek

74

Číslo

3

Stát

Slovenská republika

Strany od

723

Strany do

736

Strany počet

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"
}