Geodesic
Triangulations with Circular Arcs
Journal of Graph Algorithms and Applications, Tome 19 (2015) no. 1, pp. 43-65.

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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.
DOI : 10.7155/jgaa.00346
Keywords: triangulation, circular arcs, graph drawing, finite elements 
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     author = {Oswin Aichholzer and Wolfgang Aigner and Franz Aurenhammer and Kate\v{r}ina \v{C}ech Dobi\'a\v{s}ov\'a and Bert J\"uttler and G\"unter Rote},
     title = {Triangulations with {Circular} {Arcs}},
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Oswin Aichholzer; Wolfgang Aigner; Franz Aurenhammer; Kateřina Čech Dobiášová; Bert Jüttler; Günter Rote. Triangulations with Circular Arcs. Journal of Graph Algorithms and Applications, Tome 19 (2015) no. 1, pp. 43-65. doi : 10.7155/jgaa.00346. http://geodesic.mathdoc.fr/articles/10.7155/jgaa.00346/

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