Abstract. This paper presents a technique of incorporating anisotropic metric into the Delaunay triangulation algorithm for unstructured mesh generation on 3D parametric surfaces. Both empty circumcircle and inner angles criteria of Delaunay retriangulation can be successfully used with the developed method of coordinate transformation with little adjustments. We investigate the efficiency of mesh generation process for different criteria and the quality of obtained meshes.

The article presents a comparison of several octree-and kd-tree-based structures used for the construction of control space in the process of anisotropic mesh generation and adaptation. The adaptive control space utilized by the authors supervises the construction of meshes by providing the required metric information regarding the desired shape and size of elements of the mesh at each point of the modeled domain. Comparative tests of these auxiliary structures were carried out based on different versions of the tree structures with respect to computational and memory complexity as well as the quality of the generated mesh. Analysis of the results shows that kd-trees (not present in the meshing literature in this role) offer good performance and may become a reasonable alternative to octree structures.

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Abstract. The subject of this article concerns some aspects of the generation of 3D surface meshes, widely used in many scientific applications. This work contains a description of data structure used in the developed mesh generator and issues related to the management of this structure. The proper organization of this structure coupled with the appropriately selected algorithms, allow to achieve the satisfactory efficiency of the mesh generation process.