Oswin Aichholzer, Wolfgang Aigner, Franz Aurenhammer, Katerina Čech
Dobiášová, Bert Jüttler, and Günter Rote:
Triangulations with circular arcs

In "Graph Drawing". GD 2011, Proceedings of the 19th International
Symposium on Graph Drawing, Eindhoven, September 2011, Revised Selected Papers.
Editors: Marc van Kreveld and Bettina Speckmann, Lecture Notes in Computer
Science, 7034, SpringerVerlag, 2012, pp. 296–307. doi:10.1007/9783642258787_29

Journal of Graph Algorithms and
Applications 19, no. 1 (2015), 43–65.
doi:10.7155/jgaa.00346
An important objective in the choice of a triangulation of a point set is
that the smallest angle becomes as large as possible. In the straightline
case, it is known that the Delaunay triangulation is optimal in this respect.
We propose and study the concept of a circular arc triangulation, which
offers additional flexibility for enlarging small angles. We show that angle
optimization and related questions lead to a linear programming problem that
can be solved by simple graphtheoretic methods.
Last update: January 27, 2015.