Publication detail

Approximation of Voronoï cell attributes using parallel solution

MAŠEK, J. VOŘECHOVSKÝ, M.

Original Title

Approximation of Voronoï cell attributes using parallel solution

Type

journal article in Web of Science

Language

English

Original Abstract

This paper concerns an algorithm for fast parallel approximation of selected attributes of hyper-dimensional Voronoï cells in a unit hypercube. The presented algorithm does not require the construction of a corresponding Voronoï diagram (usually by employing the Quick Hull algorithm) which typically is a highly computationally demanding task, especially when performed in higher dimensions. The algorithm is suitable for both the clipped and periodic variants of Voronoï tessellation and provides a significant speedup in a convenient range of practical usage. For the purposes of approximation of selected scalar properties of Voronoï cells, only the distances of points in sample are evaluated using an adequately fine underlying orthogonal mesh. The algorithm estimates e.g. the volumes and centroids of Voronoï cells, radii and coordinates of centers of the corresponding Delaunay hyper-circles. The paper also provides quite accurate explicit error estimators for the extracted attributes due to rasterization and thus the user is given a control over the accuracy by selecting an appropriate discretization density. Among numerous fields in which Voronoï diagrams are being utilized, the authors are concerned with optimization of point samples for the Design of Experiments and also with weighting of integration points in Monte Carlo type integration. In these applications, selected scalar topological descriptors of Voronoï diagrams are being repeatedly computed. As the full Voronoï diagram is not of interest but the resulting cell volumes or shape descriptions have to be repeatedly computed, the presented parallel solution seems highly suitable for these applications.

Keywords

Voronoï diagram; approximation by rasterization; parallel solution; error of hyper-dimensional raster

Authors

MAŠEK, J.; VOŘECHOVSKÝ, M.

Released

5. 4. 2019

Publisher

Elsevier

ISBN

0965-9978

Periodical

ADVANCES IN ENGINEERING SOFTWARE

Year of study

132

Number

132

State

United Kingdom of Great Britain and Northern Ireland

Pages from

7

Pages to

17

Pages count

11

URL

https://www.sciencedirect.com/science/article/pii/S0965997818311578

BibTex

@article{BUT156510,
  author="Jan {Mašek} and Miroslav {Vořechovský}",
  title="Approximation of Voronoï cell attributes using parallel solution",
  journal="ADVANCES IN ENGINEERING SOFTWARE",
  year="2019",
  volume="132",
  number="132",
  pages="7--17",
  doi="10.1016/j.advengsoft.2019.03.012",
  issn="0965-9978",
  url="https://www.sciencedirect.com/science/article/pii/S0965997818311578"
}