# Triangulations with circular arcs

**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. When triangulation
edges are straight line segments, it is known that the Delaunay triangulation
is the optimal solution. 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.
Triangulations with circular arcs.
*Journal of Graph Algorithms and Applications*, 19:43-65, 2015.