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arXiv · 1707.00219

Angle-monotone Paths in Non-obtuse Triangulations

Anna Lubiw·Joseph O'Rourke
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Abstract

We reprove a result of Dehkordi, Frati, and Gudmundsson: every two vertices in a non-obtuse triangulation of a point set are connected by an angle-monotone path--an xy-monotone path in an appropriately rotated coordinate system. We show that this result cannot be extended to angle-monotone spanning trees, but can be extended to boundary-rooted spanning forests. The latter leads to a conjectural edge-unfolding of sufficiently shallow polyhedral convex caps.

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Anna Lubiw, Joseph O'Rourke. 2017-07-01. Angle-monotone Paths in Non-obtuse Triangulations. https://arxiv.org/abs/1707.00219

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