**W. Aigner, F. Aurenhammer, and B. Jüttler**

We define the *triangulation axis* of a simple polygon as an
anisotropic medial axis of whose `unit disks' are line segments or
triangles. The underlying triangulation that specifies the anisotropy can be
varied, to adapt the axis so as to reflect predominant geometrical and
topological features of . Triangulation axes are piecewise linear
skeletons, and typically have much fewer edges and branchings than the
Euclidean medial axis or the straight skeleton of (between and
edges, compared to ). Still, they retain important properties,
as for example the reconstructability of from its skeleton. Triangulation
axes can be easily computed from their defining triangulations in
time. We investigate the effect of using several optimal triangulations
for . In particular, careful edge flipping in the constrained Delaunay
triangulation leads, in overall time, to an axis competitive to
high quality axes requiring time for optimization via dynamic
programming.