arXiv Open Access 2021

Angles of Arc-Polygons and Lombardi Drawings of Cacti

David Eppstein Daniel Frishberg Martha C. Osegueda

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Abstrak

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 at most pi. 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 cycle of the cactus is a face of the drawing. However, there exist planar embeddings of cacti that do not have planar Lombardi drawings.

Topik & Kata Kunci

cs.CG

Penulis (3)

David Eppstein

Daniel Frishberg

Martha C. Osegueda

Format Sitasi

APA MLA BibTeX

Eppstein, D., Frishberg, D., Osegueda, M.C. (2021). Angles of Arc-Polygons and Lombardi Drawings of Cacti. https://arxiv.org/abs/2107.03615

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Informasi Jurnal

Tahun Terbit: 2021
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓