Triangulations with Circular Arcs

Oswin Aichholzer, Wolfgang Aigner, Franz Aurenhammer, Katerina Cech Dobiásová, Bert Jüttler, Günter 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.