SYMBOLIC BLOCK DECOMPOSITION IN HEXAHEDRAL MESH GENERATION

Andrzej Adamek; Barbara Głut

doi:10.7494/csci.2005.7.4.7

Authors

Andrzej Adamek Akademia Górniczo-Hutnicza
Barbara Głut Akademia Górniczo-Hutnicza

DOI:

https://doi.org/10.7494/csci.2005.7.4.7

Keywords:

hexahedral mesh generation, block decomposition, medial axis transform, oriented Voronoi graph, oriented MAT graph

Abstract

Hexahedral mesh generation for three-dimensional solid objects is often done in stages. Usually an object is ﬁrst subdivided into simple-shaped subregions, which then are ﬁlled withhexahedral ﬁnite elements. This article presents an automatic subdividing method of polyhedron with planar faces. The subdivision is based on medial surface, axes and nodes of a solid.The main emphasis is put on creating a topology of subregions. Obtaining such a topologyinvolves deﬁning a graph structure OMG which contains necessary information about medialsurface topology and object topology, followed by simple symbolic processing on it.

Downloads

Download data is not yet available.

Author Biographies

Andrzej Adamek, Akademia Górniczo-Hutnicza

Doktorant, Katedra Informatyki
Barbara Głut, Akademia Górniczo-Hutnicza

Katedra Informatyki

References

Benzley S. E., Perry E., Merkley K., Clark B., Sjaardema G.: A comparision of all hexagonal and all tetrahedral ﬁnite element meshes for elastic and elastic-plastic analysis. Proceedings 4th International Meshing Roundtable, Sandia National Laboratories, Albuquerque, 1995, 179–192

Mitchell S. A.: A characterization of the quadrilateral meshes of a surface which admit a compatible hexahedral mesh of the enclosed volume. Proceedings STACS’96, Grenoble, 1996

Aprice M., Armstrong C. G.: Hexahedral mesh generation by medial surface subdivision: Part I. Solids with convex edges. International Journal for Numerical Methods in Engineering, vol. 38, 1995, 3335–3359

Etzion M., Rappoport A.: Computing Voronoi skeletons of a 3-D polyhedron by space subdivision. Computational Geometry Theory and Application, vol. 21, 2002, 87–120

Blum H.: A transformation for extracting new descriptors of shape. In: W. Wathen-Dun, (ed.), Models for the Perception of Speech and Visual Form. MIT Pres, Cambridge, MA, 1967, 362–380

Stifter S.: The Roider method: a method for static and dynamic collision detection. C. Hoﬀman (ed.) Issues in Robotics and Non-Linear Geometry, JAI Press, 1990

Blum H.: Biological Shape and Visual Science. Journal of Theoretical Biology, vol. 38, 1973, 205–287

Nackman L. R., Pizer S. M.: Three-dimensional shape description using the symmetric axis transform 1:theory. IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-7, 1985

Aurenhammer F.: Voronoi diagrams: a survey of a fundamental geometric data structure. ACM Computing Surveys, 1991, 345–405

Okabe A., Bboots, Sugihara K.: Spatial Tesselations: Concepts and Applications of Voronoi Diagrams. Willey, 1992

Lavender D., Bowyer A., Davenport J., Wallis A., Woodwark J.: Voronoi Diagrams of Set-Theoretic solid Models. IEEE Computer Graphics and Applications, 1992, 69–77

Tam T. K. H., Armstrong C. G.: Finite element mesh control by integer preprograming. International Journal for Numerical Methods in Engineering, vol. 36, 1993, 2581–2605

Blacker T. D., Stephenson M. B.: Paving: A New approach to automated quadrilateral mesh generation. International Journal for Numerical Methods in Engineering, vol. 32, 1991, 811–847

Aprice M., Armstrong C. G.: Hexahedral mesh generation by medial surface subdivision: Part II. Solids with ﬂat and concave edges. International Journal for Numerical Methods in Engineering, vol. 40, 1997, 111–136