Geodesic
Global balancing of a triangular mesh
Journal of the Belarusian State University. Mathematics and Informatics, Tome 1 (2018), pp. 88-94.

Voir la notice de l'article provenant de la source Math-Net.Ru

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 Ungor 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 does not 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.
Keywords: triangulation; mesh generation; mesh refinement; Steiner points; triangular mesh topology; least squares method; interpolation error. 
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D. D. Vasilkov. Global balancing of a triangular mesh. Journal of the Belarusian State University. Mathematics and Informatics, Tome 1 (2018), pp. 88-94. http://geodesic.mathdoc.fr/item/BGUMI_2018_1_a9/

[1] G. Farin, “Curves and surfaces for CAGD”, San Diego: Acad. Press, 1997

[2] J. R. Shewchuk, “What is a good linear finite element”, 11th International Meshing Roundtable, 2002, 115–126, New York: Ithaca

[3] L. Paul-Chew, “Guaranteed-quality mesh generation for curved surfaces”, Proceedings of the Ninth Annual Symposium on Computational Geometry (San Diego), 1993, 274–280, New York: ACM | DOI

[4] J. Ruppert, “A Delaunay refinement algorithm for quality 2-dimensional mesh generation”, J. Algorithms, 18 (1995), 548–585 | DOI | MR | Zbl

[5] H. Erten, A. Ungor, “Triangulations with locally optimal steiner points”, Eurographics Symposium on Geometry Processing (Barcelona), 2007, 1–10 | MR

[6] C. C. Paige, M. A. Saunders, “LSQR: An algorithm for sparse linear equations and sparse least squares”, ACM Trans. Math. Soft, 8 (1982), 43–71 | DOI | MR | Zbl

[7] S. Rennich, D. Stosic, T. A. Davis, “Accelerating sparse cholesky factorization on GPUs”, Architectures and Algorithms: IA3 Seventh Workshop on Irregul. Appl. (Denver), 2014 | MR