Algorithm for generating a conformal quasi-hierarchical triangular mesh that weakly \(\delta\)-approximates given polygonal lines. (Russian, English) Zbl 1199.65061
Zh. Vychisl. Mat. Mat. Fiz. 49, No. 5, 874-878 (2009); translation in Comput. Math., Math. Phys. 49, No. 5, 842-845 (2009).
Summary: An algorithm is proposed for generating a conformal quasi-hierarchical triangular mesh that approximates a set of given polygonal lines to accuracy \(\delta\). The solvability of the problem is guaranteed by the possibility of shifting the polygonal lines within their \(\delta\)-neighborhood. The resulting mesh consists of a small number of triangles and admits a multigrid implementation. An estimate is given for the growing number of mesh triangles with decreasing \(\delta\) (of order \(\log_2^2\delta^{-1})\). The algorithm is applied to a particular set of polygonal lines.
MSC:
| 65D18 | Numerical aspects of computer graphics, image analysis, and computational geometry |
| 65N50 | Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs |
| 65N55 | Multigrid methods; domain decomposition for boundary value problems involving PDEs |
