Exploration of Empty Space among Spherical Obstacles via Additively Weighted Voronoi Diagram

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F16%3A43928981" target="_blank" >RIV/49777513:23520/16:43928981 - isvavai.cz</a>

Result on the web

<a href="http://dx.doi.org/10.1111/cgf.12980" target="_blank" >http://dx.doi.org/10.1111/cgf.12980</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1111/cgf.12980" target="_blank" >10.1111/cgf.12980</a>

Result language

angličtina

Original language name

Exploration of Empty Space among Spherical Obstacles via Additively Weighted Voronoi Diagram

Original language description

Properties of granular materials or molecular structures are often studied on a simple geometric model - a set of 3D balls. If the balls simultaneously change in size by a constant speed, topological properties of the empty space outside all these balls may also change. Capturing the changes and their subsequent classification may reveal useful information about the model. This has already been solved for balls of the same size, but only an approximate solution has been reported for balls of different sizes. These solutions work on simplicial complexes derived from the dual structure of the ordinary Voronoi diagram of ball centers and use the mathematical concept of simplicial homology groups. If the balls have different radii, it is more appropriate to use the additively weighted Voronoi diagram (also known as the Apollonius diagram) instead of the ordinary diagram, but the dual structure is no longer a simplicial complex, so the previous approaches cannot be used directly. In this paper, a method is proposed to overcome this problem. The method works with Voronoi edges and vertices instead of the dual structure. Additional bridge edges are introduced to overcome disconnected cases. The output is a tree graph of events where cavities are created or merged during a simulated shrinking of the balls. This graph is then reorganized and filtered according to some criteria to get a more concise information about the development of the empty space in the model

Czech name

—

Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

IN - Informatics

OECD FORD branch

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Project

<a href="/en/project/LO1506" target="_blank" >LO1506: Sustainability support of the centre NTIS - New Technologies for the Information Society</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2016

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

COMPUTER GRAPHICS FORUM

ISSN

1467-8659

e-ISSN

—

Volume of the periodical

35

Issue of the periodical within the volume

5

Country of publishing house

GB - UNITED KINGDOM

Number of pages

10

Pages from-to

249-258

UT code for WoS article

000383444500024

EID of the result in the Scopus database

2-s2.0-84982144055