A computation of a crystalline flow starting from non-admissible polygon using expanding selfsimilar solutions

Hidekata Hontani, Mi Ho Giga, Yoshikazu Giga, Koichiro Deguchi

Research output: Chapter in Book/Report/Conference proceedingChapter

3 Citations (Scopus)

Abstract

A numerical method for obtaining a crystalline flow from a given polygon is presented. A crystalline flow is a discrete version of a classical curvature flow. In a crystalline flow, a given polygon evolves, and it remains polygonal through the evolving process. Each facet moves keeping its normal direction, and the normal velocity is determined by the length of the facet. In some cases, a set of new facets sprout out at the very beginning of the evolving process. The facet length is governed by a system of singular ordinary differential equations. The proposed method solves the system of ODEs, and obtain the length of each new facet, systematically. Experimental results show that the method obtains a crystalline flow from a given polygon successfully.

Original languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
EditorsIngela Nystrom, Gabriella Sanniti di Baja, Stina Svensson
PublisherSpringer Verlag
Pages465-474
Number of pages10
ISBN (Electronic)3540204997, 9783540204992
DOIs
Publication statusPublished - 2003

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2886
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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