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Approximating Uniform Triangular Meshes in Polygons Franz Aurenhammer 1 , Naoki Katoh 2 , Hiromichi Kojima 2
 

Summary: Approximating Uniform Triangular Meshes in Polygons
Franz Aurenhammer 1 , Naoki Katoh 2 , Hiromichi Kojima 2
Makoto Ohsaki 2 , and Yinfeng Xu 3
1 Institute for Theoretical Computer Science, Graz University of Technology
In eldgasse 16b/I, A-8010 Graz, Austria
auren@igi.tu-graz.ac.at
2 Department of Architecture and Architectural Systems, Kyoto University
Yoshida-Honmachi, Sakyo-ku, Kyoto, 606-8501 Japan
fnaoki, kojima, ohsakig@archi.kyoto-u.ac.jp
3 School of Management, Xi'an Jiaotong University
Xi'an, 710049 P.R.China
yfxu@xjtu.edu.cn
Abstract
We consider the problem of triangulating a convex polygon using n Steiner points under
the following optimality criteria: (1) minimizing the overall edge length ratio, (2) mini-
mizing the maximum edge length, and (3) minimizing the maximum triangle perimeter.
We establish a relation of these problems to a certain extreme packing problem. Based
on this relationship, we develop a heuristic producing constant approximations for all the
optimality criteria above (provided n is chosen su∆ciently large). That is, the produced
triangular mesh is uniform in these respects.

  

Source: Aurenhammer, Franz - Institute for Theoretical Computer Science, Technische Universitšt Graz

 

Collections: Computer Technologies and Information Sciences