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Tree-based control space structures for discrete metric sources in 3D meshing

Głut Barbara, Jurczyk Tomasz

Computer Science

2019

Vol. 20 (4)

493--509

This article compares the different variations of the octree and kd-tree structures used to create a control space based on a set of discrete metric point-sources. The control space thus created supervises the generation of the mesh providing efficient access to the required information on the desired shape and size of the mesh elements at each point of the discretized domain. Structures are compared in terms of computational and memory complexity as well as regarding the accuracy of the approximation of the set of discrete metric sources in the created control space structure.

Tree structures for adaptive control space in 3D meshing

Jurczyk T., Głut B.

Computer Science

2016

Vol. 17 (4)

541--560

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.

Preparation of control space for remeshing polygonal surfaces

Jurczyk T., Głut B.

Computer Science

2013

Vol. 14 (4)

547--561

The subject of the article concerns the issues of remeshing, transforming a polygonal mesh into a triangular mesh adapted to its surface. From the initial polygonal mesh, the curvature of surface and boundary is retrieved and used to calculate a metric tensor varying in three-dimensional space. In the proposed approach, the curvature is computed using local approximation of surfaces and curves on the basis of vertices of the polygonal mesh. An essential part of the presented remeshing procedure is a creation of a control space structure based on the retrieved discrete data. The subsequent process of remeshing is then supervised by the contents of this auxiliary structure. The article presents various aspects related to the procedure of initialization, creation, and adjustment of the control space structure.