# Arc triangulations

**O. Aichholzer, W. Aigner, F. Aurenhammer, K. Cech
Dobiašova, B. Jüttler, and G. Rote**

### Abstract:

An important objective in the choice of a triangulation of a given point set is
that the smallest angle becomes as large as possible. In the straight line
case, it is known that the Delaunay triangulation is optimal in this respect.
We propose and study the concept of a circular arc triangulation, a simple
and effective alternative that offers flexibility for additionally enlarging
small angles. We show that angle optimization and related questions lead to
linear programming problems that can be formulated as simple graph-theoretic
problems, and we define flipping operations in arc triangles. Moreover,
special classes of arc triangulations are considered, for applications in
finite element methods and graph drawing.

**Reference:** O. Aichholzer, W. Aigner, F. Aurenhammer, K. Cech
Dobiašova, B. Jüttler, and G. Rote.
Arc triangulations.
In *Proc. European Workshop on Computational Geometry EuroCG
'2010*, pages 17-20, Dortmund, Germany, 2010.