Finding a Triangular Mesh with a Constant Number of Different Edge Lengths

Shin-ichi TANIGAWA  Naoki KATOH  

Publication
IEICE TRANSACTIONS on Information and Systems   Vol.E89-D   No.8   pp.2364-2371
Publication Date: 2006/08/01
Online ISSN: 1745-1361
DOI: 10.1093/ietisy/e89-d.8.2364
Print ISSN: 0916-8532
Type of Manuscript: INVITED PAPER (Special Section on Invited Papers from New Horizons in Computing)
Category: 
Keyword: 
computational geometry,  Delaunay triangulation,  Voronoi diagram,  

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Summary: 
We consider the problem of triangulating an x-monotone polygon with a small number of different edge lengths using Steiner points. Given a parameter α, where 0<α<1, we shall present an algorithm for finding an almost uniform triangular mesh with 3π/8α2+o(1/α2) different edge lengths such that every edge length is between l and (2+α)l. Experiments demonstrate the effectiveness of this algorithm.