Global balancing of a triangular mesh
New algorithm for Steiner triangular mesh balancing is proposed. The algorithm is based on the least squares method and minimizes the standart deviation of triangulation angles cosines from the optimal value of 0.5. The algorithm has no limitations and therefore can be applied to any triangulations...
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Belarusian State University
2018-05-01
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Series: | Журнал Белорусского государственного университета: Математика, информатика |
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Online Access: | https://journals.bsu.by/index.php/mathematics/article/view/889 |
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doaj-e460d419ac334c97890e84125d1976cc2020-11-25T02:07:42ZbelBelarusian State University Журнал Белорусского государственного университета: Математика, информатика 2520-65082617-39562018-05-0118894889Global balancing of a triangular meshDenis D. Vasilkov0Belarusian State University, Niezaliežnasci Avenue, 4, 220030, Minsk, BelarusNew algorithm for Steiner triangular mesh balancing is proposed. The algorithm is based on the least squares method and minimizes the standart deviation of triangulation angles cosines from the optimal value of 0.5. The algorithm has no limitations and therefore can be applied to any triangulations obtained by triangular mesh refinement algorithms, for example Ruppert or Erten and Üngör algorithms, without increasing the resulting number of points and without breaking the edge connections. Experiments indicate that the proposed algorithm significantly increases the number of angles in range from 50 to 70° and doesnʼt lead to create triangles with significantly smaller minimum angles. The algorithm can be effectively implemented using specialized software packages for quick solving sparse linear systems using the leastsquares method, for example SuiteSparse. Therefore the algorithm is easy to implement.https://journals.bsu.by/index.php/mathematics/article/view/889triangulationmesh generationmesh refinementsteiner pointstriangular mesh topologyleast squares methodinterpolation error |
collection |
DOAJ |
language |
Belarusian |
format |
Article |
sources |
DOAJ |
author |
Denis D. Vasilkov |
spellingShingle |
Denis D. Vasilkov Global balancing of a triangular mesh Журнал Белорусского государственного университета: Математика, информатика triangulation mesh generation mesh refinement steiner points triangular mesh topology least squares method interpolation error |
author_facet |
Denis D. Vasilkov |
author_sort |
Denis D. Vasilkov |
title |
Global balancing of a triangular mesh |
title_short |
Global balancing of a triangular mesh |
title_full |
Global balancing of a triangular mesh |
title_fullStr |
Global balancing of a triangular mesh |
title_full_unstemmed |
Global balancing of a triangular mesh |
title_sort |
global balancing of a triangular mesh |
publisher |
Belarusian State University |
series |
Журнал Белорусского государственного университета: Математика, информатика |
issn |
2520-6508 2617-3956 |
publishDate |
2018-05-01 |
description |
New algorithm for Steiner triangular mesh balancing is proposed. The algorithm is based on the least squares method and minimizes the standart deviation of triangulation angles cosines from the optimal value of 0.5. The algorithm has no limitations and therefore can be applied to any triangulations obtained by triangular mesh refinement algorithms, for example Ruppert or Erten and Üngör algorithms, without increasing the resulting number of points and without breaking the edge connections. Experiments indicate that the proposed algorithm significantly increases the number of angles in range from 50 to 70° and doesnʼt lead to create triangles with significantly smaller minimum angles. The algorithm can be effectively implemented using specialized software packages for quick solving sparse linear systems using the leastsquares method, for example SuiteSparse. Therefore the algorithm is easy to implement. |
topic |
triangulation mesh generation mesh refinement steiner points triangular mesh topology least squares method interpolation error |
url |
https://journals.bsu.by/index.php/mathematics/article/view/889 |
work_keys_str_mv |
AT denisdvasilkov globalbalancingofatriangularmesh |
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1724930231515480064 |