Uniformly Acute Triangulations of Polygons

Christopher J. Bishop

doi:10.1007/s00454-023-00525-w

Uniformly Acute Triangulations of Polygons

Christopher J. Bishop

Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

We show that any polygon Γ has an acute triangulation T where every angle lies in the interval [30 ^∘, 75 ^∘] , except for triangles that contain a vertex v of Γ where Γ has an interior angle θ_v< 30 ^∘ ; such triangles are isosceles with angles θ_v , and 90 ^∘- θ_v/ 2 .

Original language	English
Pages (from-to)	1571-1592
Number of pages	22
Journal	Discrete and Computational Geometry
Volume	70
Issue number	4
DOIs	https://doi.org/10.1007/s00454-023-00525-w
State	Published - Dec 2023

Keywords

Acute triangulation
Conformal maps
Optimal meshing
Schwarz–Christoffel formula
Steiner points

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10.1007/s00454-023-00525-w

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title = "Uniformly Acute Triangulations of Polygons",

abstract = "We show that any polygon Γ has an acute triangulation T where every angle lies in the interval [30 ∘, 75 ∘] , except for triangles that contain a vertex v of Γ where Γ has an interior angle θv< 30 ∘ ; such triangles are isosceles with angles θv , and 90 ∘- θv/ 2 .",

keywords = "Acute triangulation, Conformal maps, Optimal meshing, Schwarz{\textendash}Christoffel formula, Steiner points",

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note = "Publisher Copyright: {\textcopyright} 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.",

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AU - Bishop, Christopher J.

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N2 - We show that any polygon Γ has an acute triangulation T where every angle lies in the interval [30 ∘, 75 ∘] , except for triangles that contain a vertex v of Γ where Γ has an interior angle θv< 30 ∘ ; such triangles are isosceles with angles θv , and 90 ∘- θv/ 2 .

AB - We show that any polygon Γ has an acute triangulation T where every angle lies in the interval [30 ∘, 75 ∘] , except for triangles that contain a vertex v of Γ where Γ has an interior angle θv< 30 ∘ ; such triangles are isosceles with angles θv , and 90 ∘- θv/ 2 .

KW - Acute triangulation

KW - Conformal maps

KW - Optimal meshing

KW - Schwarz–Christoffel formula

KW - Steiner points

UR - https://www.scopus.com/pages/publications/85164124420

U2 - 10.1007/s00454-023-00525-w

DO - 10.1007/s00454-023-00525-w

M3 - Article

AN - SCOPUS:85164124420

SN - 0179-5376

VL - 70

SP - 1571

EP - 1592

JO - Discrete and Computational Geometry

JF - Discrete and Computational Geometry

IS - 4

ER -

Uniformly Acute Triangulations of Polygons

Abstract

Keywords

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