Curves in Zn

Authors:
Grit Thürmer
Affiliations:
-
Venue:
DGCI '02 Proceedings of the 10th International Conference on Discrete Geometry for Computer Imagery
Year:
2002

Citing 8
Cited 0

Digital topology: a comparison of the graph-based and topological approaches

Topology and category theory in computer science
Graphs generalizing closed curves with linear construction of the Hamiltonian cycle: parametrization of discretized curves

Theoretical Computer Science
Rapid previewing via volume-based solid modeling

SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
Fundamentals of surface voxelization

Graphical Models and Image Processing
A definition of surfaces of Z3 . A new 3D discrete Jordan theorem

Theoretical Computer Science
Connectivity in Digital Pictures

Journal of the ACM (JACM)
Arcs and Curves in Digital Pictures

Journal of the ACM (JACM)
Volume-Sampled 3D Modeling

IEEE Computer Graphics and Applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

A new definition of closed curves in n-dimensional discrete space is proposed. This definition can be viewed as a generalization of closed quasi curves and is intended to overcome the limitations of known definitions for practical purposes. Following the proposed definition, a set of points forms a closed curve in discrete space if the set admits a parameterization, i.e. there exists a Hamiltonian cycle in the set. Adjacencies that do not indicate the parameterization are allowed only between points that are "close to each other" along the parameterization. Additionally, it is proven that discrete curves satisfying the new definition in two-dimensional discrete space have the Jordan property.