Discrete mathematics and Mathematical cybernetics

Global balancing of a triangular mesh

D. D. Vasilkov

Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

Abstract: 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.

UDC: 004.925.83

Received: 07.06.2017