# Angles of Arc-Polygons and Lombardi Drawings of Cacti

@inproceedings{Eppstein2021AnglesOA, title={Angles of Arc-Polygons and Lombardi Drawings of Cacti}, author={David Eppstein and Daniel Frishberg and Martha C. Osegueda}, booktitle={CCCG}, year={2021} }

We characterize the triples of interior angles that are possible in non-self-crossing triangles with circular-arc sides, and we prove that a given cyclic sequence of angles can be realized by a non-self-crossing polygon with circular-arc sides whenever all angles are ≤ π. As a consequence of these results, we prove that every cactus has a planar Lombardi drawing (a drawing with edges depicted as circular arcs, meeting at equal angles at each vertex) for its natural embedding in which every… Expand

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