# Properties of triangulations obtained by the longest-edge bisection

Open Mathematics (2014)

• Volume: 12, Issue: 12, page 1796-1810
• ISSN: 2391-5455

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## Abstract

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The Longest-Edge (LE) bisection of a triangle is obtained by joining the midpoint of its longest edge with the opposite vertex. Here two properties of the longest-edge bisection scheme for triangles are proved. For any triangle, the number of distinct triangles (up to similarity) generated by longest-edge bisection is finite. In addition, if LE-bisection is iteratively applied to an initial triangle, then minimum angle of the resulting triangles is greater or equal than a half of the minimum angle of the initial angle. The novelty of the proofs is the use of an hyperbolic metric in a shape space for triangles.

## How to cite

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Francisco Perdomo, and Ángel Plaza. "Properties of triangulations obtained by the longest-edge bisection." Open Mathematics 12.12 (2014): 1796-1810. <http://eudml.org/doc/268957>.

@article{FranciscoPerdomo2014,
abstract = {The Longest-Edge (LE) bisection of a triangle is obtained by joining the midpoint of its longest edge with the opposite vertex. Here two properties of the longest-edge bisection scheme for triangles are proved. For any triangle, the number of distinct triangles (up to similarity) generated by longest-edge bisection is finite. In addition, if LE-bisection is iteratively applied to an initial triangle, then minimum angle of the resulting triangles is greater or equal than a half of the minimum angle of the initial angle. The novelty of the proofs is the use of an hyperbolic metric in a shape space for triangles.},
author = {Francisco Perdomo, Ángel Plaza},
journal = {Open Mathematics},
keywords = {Triangulation; Longest-edge bisection; Mesh refinement; Mesh regularity; Finite element method; triangulation; longest-edge bisection; mesh refinement; mesh regularity; finite element method},
language = {eng},
number = {12},
pages = {1796-1810},
title = {Properties of triangulations obtained by the longest-edge bisection},
url = {http://eudml.org/doc/268957},
volume = {12},
year = {2014},
}

TY - JOUR
AU - Francisco Perdomo
AU - Ángel Plaza
TI - Properties of triangulations obtained by the longest-edge bisection
JO - Open Mathematics
PY - 2014
VL - 12
IS - 12
SP - 1796
EP - 1810
AB - The Longest-Edge (LE) bisection of a triangle is obtained by joining the midpoint of its longest edge with the opposite vertex. Here two properties of the longest-edge bisection scheme for triangles are proved. For any triangle, the number of distinct triangles (up to similarity) generated by longest-edge bisection is finite. In addition, if LE-bisection is iteratively applied to an initial triangle, then minimum angle of the resulting triangles is greater or equal than a half of the minimum angle of the initial angle. The novelty of the proofs is the use of an hyperbolic metric in a shape space for triangles.
LA - eng
KW - Triangulation; Longest-edge bisection; Mesh refinement; Mesh regularity; Finite element method; triangulation; longest-edge bisection; mesh refinement; mesh regularity; finite element method
UR - http://eudml.org/doc/268957
ER -

## References

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