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We show that any PSLG has an acute conforming triangulation with an upper angle bound that is strictly less than 90 degrees and that depends only on the minimal angle occurring in the PSLG. In fact, all angles are inside the interval I_0= [theta_0, 90 -\theta_0/2] for some fixed theta_0>0 independent of the PSLG except for triangles T containing a vertex v where the PSLG has an interior angle theta_v < \theta_0; then T is an isosceles triangle with angles in I_v = [theta_v, 90 -\theta_v/2].
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Uniformly Acute Triangulations of Polygons
We show that any polygon P has an acute triangulation where every angle lies in the interval I=[30, 75] (degrees), except for triangles T that contain a vertex v of P where P has an interior angle theta_v < 30; then T is an isosceles triangle with angles \theta_v and 90 -\theta_v/2.
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- Award ID(s):
- 2303987
- PAR ID:
- 10513243
- Publisher / Repository:
- Springer
- Date Published:
- Journal Name:
- Discrete & Computational Geometry
- Volume:
- 70
- Issue:
- 4
- ISSN:
- 0179-5376
- Page Range / eLocation ID:
- 1571 to 1592
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/s00454-023-00525-w
