# Hexahedral Mesh Generation Using The Embedded Voronoi Graph

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### Feature Based VolumeDecomposition for Automatic Hexahedral

Instead of using the medial surface directly, Sheffer et al. (1998) propose the Embedded Voronoi Graph to guide decomposition. The Embedded Voronoi Graph is an approximation of the Voronoi diagram and the medial surface of bodies. It contains the fill symbolic information of the Voronoi diagram and the medial surface.

### cerca - imr.sandia.gov

such a limitation, the full power of mesh optimization can-not be unlocked [5]. The advent of tools such as paving [6], plastering [7], whisker weaving [8], medial axis and sur-face [9], embedded Voronoi graph [10] or grid-based meth-ods [11 14] for unstructured quadrilateral and hexahedral mesh generation brought the need for a new crop of

### Feature based hex meshing methodology: feature recognition

tion of mesh generation can immediately speed the product design cycle with faster design veriﬁcation. Using hexahe-dral meshes for analysis is preferable to tetrahedral mesh in some applications [1]. Many researchers have been investi-gating algorithms to automate the hexahedral meshing procedure to get all-hexahedral elements models [2].

### Journal of Computational Design and Engineering

embedded Voronoi graph to decompose simple shapes into sweep-able sub-domains. Their approach prevents sharp angles at the boundaries, and uses sweeping algorithm to generate good quality meshes. However, it only works for simple shapes, and sometimes over decomposes the volume. White, Mingwu, Benzley, and

### Table of Contents - Part II - GBV

Multiresolution Remeshing Using Weighted Centroidal Voronoi Diagram Chao-Hung Lin, Chung-Ren Yan, Ji-Hsen Hsu, Tong- Yee Lee 295 Metrie 3D Surface Mesh Generation Using Delaunay Criteria Tornasz Jurezyk, Barbara Glut 302 A Multiresolution Model for Non-photorealistic Rcndering of Trees Celso Campos. Ricardo QUITOS, Joaquin Huerta, Emilio Camahort,

### Hexahedral Mesh Generation using the Embedded Voronoi Graph

Hexahedral Mesh Generation using the Embedded Voronoi Graph Alla Sheffer, Michal Etzion, Ari Rappoport, Michel Bercovier Institute of Computer Science, The Hebrew University, Jerusalem 91904, Israel.

### TopMaker: A Technique for Automatic Multi-Block Topology

presented a subdivision process using the embedded Voronoi graph, which is closely related to the medial axis. Only very simple configurations are shown in Sheffer et al. and the lack of symmetry is somewhat disconcerting. The TopMaker technique focuses on the medial edges. For each medial edge, blocks are added to the topology based on the

### CUBECOVER Parameterization of 3D Volumes

algorithm [TBM95] starts with a quadrilateral mesh on the boundary and extends it to the inner volume. Another ap-proach [SERB98] decomposes the volume into small vol-umetric patches using the embedded Voronoi graph of the object and then remesh the patches into hexahedra. Mean value coordinates are used for 2D surface param-eterization.

### Hexahedral Mesh Generation using the Embedded Voronoi Graph

Hexahedral Mesh Generation using the Embedded Voronoi Graph 249 initial mesh contains 72 elements. Secondly, the algorithm used for computing the medial axis [19] is difﬁcult to implement and not provenly correct. Thirdly, for degenerate vertices and edges, the sug-gested use of midpoint subdivision is likely to lead to poorly shaped elements.

### ggnt 33 ~c? co~~ - UNT Digital Library

Embedded Voronoi Graph to guide decomposition. Chiba et al. [24] introduce an automatic hexahedral mesh generation method based on the shape-recognition and boundary-fit algorithms. Bib-Yaw Shih and Hiroshi Saktnai presatt a mesh generation tool via swept volume decomposition [25]. The algorithms above have their

### Hexahedral Mesh Generation using the Embedded Voronoi Graph

Hexahedral Mesh Generation using the Embedded Voronoi Graph Alla Sheffer, Michal Etzion, Ari Rappoport, Michel Bercovier Institute of Computer Science, The Hebrew University, Jerusalem91904, Israel.

### CUBECOVER Parameterizationof 3D Volumes

umetric patches using the embedded Voronoi graph of the object and then remesh the patches into hexahedra. [LL10] presents an energy minimzation algorithm for hex dominant meshing from Voronoi cells. Mean value coordinates are used for 2D surface param-eterization. These coordinates are extended for star-shaped polyhedral volumes in [FKR05].

### VOLUME DECOMPOSITION AND FEATURE RECOGNITION FOR HEXAHEDRAL

Embedded Voronoi Graph to guide decomposition. Chiba et al. [24] introduce an automatic hexahedral mesh generation method based on the shape-recognition and boundary-fit algorithms. Bih-Yaw Shih and Hiroshi Sakurai present a mesh generation tool via swept volume decomposition [25]. The algorithms above have their

### Hexahedral Meshing of Non-Linear Volumes Using Voronoi Faces

This work extends an algorithm presented in our recent paper [1] for automatic hexahedral meshing, based on the embedded Voronoi graph (EVG). The embedded Voronoi graph contains the full symbolic information of the Voronoi diagram and the medial axis of the object, and a geometric approximation to the real geometry. The