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Uniformly Acute Triangulations of PSLGs

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Abstract

We show that any PSLG \(\Gamma \) has an acute conforming triangulation \(\mathcal T\) with an upper angle bound that is strictly less than \(90^\circ \) and that depends only on the minimal angle occurring in \(\Gamma \). In fact, all angles are inside \([\theta _0,90^\circ -\theta _0/2]\) for some fixed \(\theta _0>0\) independent of \(\Gamma \), except for triangles T containing a vertex v of \(\Gamma \) where \(\Gamma \) has an interior angle \(\theta _v<\theta _0\); then T is an isosceles triangle with angles in the sharpest possible interval \([\theta _v,90^\circ -\theta _v/2]\).

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  1. Mathematics Department, Stony Brook University, Stony Brook, NY, 11794-3651, USA

    Christopher J. Bishop

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  1. Christopher J. Bishop
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Correspondence to Christopher J. Bishop.

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Data sharing not applicable to this article as no datasets were generated or analyzed during the current study. The author is partially supported by NSF Grant DMS 1906259.

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Bishop, C.J. Uniformly Acute Triangulations of PSLGs. Discrete Comput Geom 70, 1090–1120 (2023). https://doi.org/10.1007/s00454-023-00524-x

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