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**Automatic three-dimensional mesh generation by the finite octree technique.**
*(English)*
Zbl 0755.65116

The automatic generation of finite element meshes for general three- dimensional geometries represents a topic of active research. A number of algorithmic approaches have been proposed for performing this task. This paper presents an automatic mesh generator that combines octree decomposition techniques with octant level meshing procedures. The procedure is the result of several years of development of quadtree- and octree-based mesh generation techniques.

The finite octree mesh generator has been designed to meet the needs of fully automatic mesh generation of non-manifold objects of arbitrary geometric complexity. The basic concept of the octree representation consists of placing the object of interest in a parallelepiped, typically a cube, which totally encloses it. This parallelepiped is then subdivided into its eight octants which are then recursively subdivided a number of times based on criteria defined by the application.

The mesh generator is capable of meshing non-manifold models of arbitrary geometric complexity through the explicit tracking and enforcement of geometric compatibility and geometric similarity at each step of the meshing process. The results section demonstrates a linear growth rate with respect to the number of elements. Future researches of the authors to improve the finite octree procedures will include the ability to match to existing meshes and supporting directional refinement.

The finite octree mesh generator has been designed to meet the needs of fully automatic mesh generation of non-manifold objects of arbitrary geometric complexity. The basic concept of the octree representation consists of placing the object of interest in a parallelepiped, typically a cube, which totally encloses it. This parallelepiped is then subdivided into its eight octants which are then recursively subdivided a number of times based on criteria defined by the application.

The mesh generator is capable of meshing non-manifold models of arbitrary geometric complexity through the explicit tracking and enforcement of geometric compatibility and geometric similarity at each step of the meshing process. The results section demonstrates a linear growth rate with respect to the number of elements. Future researches of the authors to improve the finite octree procedures will include the ability to match to existing meshes and supporting directional refinement.

Reviewer: G.Dimitriu (Iaşi)

### MSC:

65N50 | Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs |

65D18 | Numerical aspects of computer graphics, image analysis, and computational geometry |

### Keywords:

automatic three-dimensional mesh generation; Delaunay triangulation; automatic generation of finite element meshes; three-dimensional geometries; octree decomposition techniques; octant level meshing; arbitrary geometric complexity
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\textit{M. S. Shephard} and \textit{M. K. Georges}, Int. J. Numer. Methods Eng. 32, No. 4, 709--749 (1991; Zbl 0755.65116)

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