Improved Maximum Angle Estimate for Longest-Edge Bisection-Reference-Cited by-同舟云学术

Improved Maximum Angle Estimate for Longest-Edge Bisection

Published:2021-12 Issue:04 Volume:31 Page:183-192
ISSN:0218-1959
Container-title:International Journal of Computational Geometry & Applications
language:en
Short-container-title:Int. J. Comput. Geom. Appl.

Author:

Korotov Sergey¹^ORCID,Fredrik Lund Lars²,Eivind Vatne Jon³

Affiliation:

1. Division of Mathematics and Physics, UKK, Mälardalen University, Box 883, 721 23 Västerås, Sweden

2. Department of Computer Science, Electrical Engineering and Mathematical Sciences, Faculty of Engineering and Science, Western Norway University of Applied Sciences, Postbox 7030, 5020 Bergen, Norway

3. Department of Economics, Norwegian Business School (BI), Kong Christian Frederiks plass 5, 5006 Bergen, Norway

Abstract

In this note we construct an upper estimate on the maximum angles of triangles generated by the longest-edge bisection algorithms applied to a triangle. This upper bound considerably improves upon one inherited from the well-known minimum angle estimation, thus providing tighter two-sided estimation of the angles generated by bisections. This estimate also guarantees the validity of the maximum angle condition, widely used in finite element analysis and computer graphics.

Publisher

World Scientific Pub Co Pte Ltd

Subject

Applied Mathematics,Computational Mathematics,Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218195922500017

Reference13 articles.

1. On global and local mesh refinements by a generalized conforming bisection algorithm

2. Strong regularity of a family of face-to-face partitions generated by the longest-edge bisection algorithm

3. Properties of the longest-edge n-section refinement scheme for triangular meshes

4. Longest-edgen-section algorithms: Properties and open problems

5. A lower bound on the angles of triangles constructed by bisecting the longest side

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