 
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
Ineldgasse 16b/I, A8010 Graz, Austria
auren@igi.tugraz.ac.at
2 Department of Architecture and Architectural Systems, Kyoto University
YoshidaHonmachi, Sakyoku, Kyoto, 6068501 Japan
fnaoki, kojima, ohsakig@archi.kyotou.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 suÆciently large). That is, the produced
triangular mesh is uniform in these respects.
