DIGITAL JORDAN SURFACES ARISING FROM TETRAHEDRAL TILING

článek v časopise ve Web of Science, Jimp

en

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.

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.

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

17.06.2024

De Gruyter

Bratislava

1337-2211

74

3

723–736

14