Tree structures for adaptive control space in 3D meshing

The article presents a comparison of several octree- and kd-tree-based struc- tures 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 struc- tures 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.