A Computation of a Crystalline Flow Starting from Non-admissible Polygon Using Expanding Selfsimilar Solutions

  • Hidekata Hontani
  • Mi-Ho Giga
  • Yoshikazu Giga
  • Koichiro Deguchi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2886)


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.


Convex Polygon Initial Contour Outward Unit Normal Vector Polygonal Curve Adjacent Facet 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Hidekata Hontani
    • 1
  • Mi-Ho Giga
    • 2
  • Yoshikazu Giga
    • 2
  • Koichiro Deguchi
    • 3
  1. 1.Department of InformaticsYamagata UniversityYamagataJapan
  2. 2.Department of MathematicsHokkaido UniversityHokkaidoJapan
  3. 3.Department of System Information ScienceTohoku UniversityMiyagiJapan

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