Tree Structures for Adaptive Control Space in 3d Meshing

Abstract

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.

Tree-based Control Space Structures for Discrete Metric Sources in 3D Meshing

“…As in [16], it has been shown that kd-trees are useful for constructing control space structures. This time, the focus was on the introduction of discrete metric sources into these structures.…”

“…The auxiliary structures dedicated to this purpose may have the form of a Cartesian mesh (either homogeneous [21] or adapted [3]), background mesh [7,19,20,23], or quadtree/octree [18,22,23]. Recently, the application of a kd-tree was also proposed by the authors of [16]. Each of these structures has its advantages and disadvantages.…”

“…The methods used to create and adapt the octree control space are described in greater detail in [10,13,15]. In [16], a kd-tree-based control space structure was proposed and compared with octree. Tests were based on the adaptation of a control space structure to continuous metric sources.…”