Summary
This paper presents a generic approach to generation of surface and volume unstructured meshes for complex free-form objects, obtained by laser scanning. A four-stage automated procedure is proposed for discrete data sets: surface mesh extraction from Delaunay tetrahedrization of scanned points, surface mesh simplification, definition of triangular interpolating subdivision faces, Delaunay volumetric meshing of obtained geometry. The mesh simplification approach is based on the medial Hausdorff distance envelope between scanned and simplified geometric surface meshes. The simplified mesh is directly used as an unstructured control mesh for subdivision surface representation that precisely captures arbitrary shapes of faces, composing the boundary of scanned objects. CAD model in Boundary Representation retains sharp and smooth features of the geometry for further meshing. Volumetric meshes with the MezGen code are used in the combined Finite-Discrete element methods for simulation of complex phenomena within the integrated Virtual Geoscience Workbench environment (VGW).
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Zienkiewicz O, Taylor R (2000) The finite element method, Volume 1. Butterworth-Heinemann, Oxford
A. Munjiza (2004) The combined discrete finite element method. Wiley, Chichester
Latham J-P, Munjiza A (2004) The modeling of particle systems with real shapes. Phil Trans Royal Soc London 362:1953–1972
Bajaj C, Bernardini F, Xu G (1996) Reconstructing surfaces and functions on surfaces from unorganized three-dimensional data. Algorithmica 19:362–379
Karbacher S, Laboureux X, Schon N, Hausler G (2001) Processing range data for reverse engineering and virtual reality. In: Proceedings of the Third International Conference on 3-D Digital Imaging and Modeling (3DIM’01). Quebec City, Canada, 270–280
Boissonnat J-D, Cazals F (2002) Smooth surface reconstruction via natural neighbour interpolation of distance functions. Comp Geo 22:185–203
Frey P (2004) Generation and adaptation of computational surface meshes from discrete anatomical data. Int J Numer Meth Engng 60:1049–1074
Xue D, Demkowicz L, Bajaj C (2004) Reconstruction of G1 surfaces with biquartic patches for HP Fe Simulations. In: Proceedings of the 13th International Meshing Roundtable, Williamsburg
Mezentsev A, Woehler T (1999) Methods and algorithms of automated CAD repair for incremental surface meshing. In: Proceeding of the 8th International Meshing Roundtable, South Lake Tahoe
Owen S, White D (2003) Mesh-based geometry. Int J Numer Meth Engng 58:375–395
Lang P, Bourouchaki H (2003) Interpolating and meshing 3D surface grids, Int J Numer Meth Engng 58:209–225
Cebral J, Lohner R (1999) From medical images to CFD meshes. In: Proceeding of the 8th International Meshing Roundtable, South Lake Tahoe
Lorensen W, Cline H (1987) Marching Cubes: a high resolution 3D surface reconstruction algorithm. Comp Graph 21(4):163–169
Kolluri R, Shewchuk J, O’Brien J (2004) Spectral surface reconstruction from noisy point clouds. In: Eurographics Symposium on Geometry Processing
Hoppe H, DeRose T, Duchamp T, McDonald J, Stuetzle W (1992) Surface reconstruction from unorganized points. Comp Graph 26(2):71–78
Beall M, Walsh J, Shepard M (2003) Accessing CAD geometry for mesh generation. In: Proceeding of the 12th International Meshing Roundtable
Zorin D, Schroder P, Sweldens W (1996) Interpolating subdivision with arbitrary topology. In: Proceedings of Computer Graphic, ACM SIGGRAPH’96, 189–192
Rypl D, Bittnar Z (2000) Discretization of 3D surfaces reconstructed by interpolating subdivision. In: Proceeding of the 7th International Conference on Numerical Grid Generation in Computational Field Simulations, Whistler
Lee C (2003) Automatic metric 3D surface mesh generation using subdivision surface geometrical model. Part 1: Construction of underlying geometrical model. Int J Numer Meth Engng 56:1593–1614
Lee C (2003) Automatic metric 3D surface mesh generation using subdivision surface geometrical model. Part 2: Mesh generation algorithm and examples. Int J Numer Meth Engng 56:1615–1646
Dyn N, Levin D, Gregory J (1990) A butterfly subdivision scheme for surface interpolation with tension control. In: Proceedings of Computer Graphic, ACM SIGGRAPH’90, 160–169
Loop C (1987) Smooth subdivision surface, based on triangles. MA Thesis, University of Utah, Utah
Chetverikov D, Stepanov D (2002) Robust Euclidian alignment of 3D point sets. In: Proc. First Hungarian Conference on Computer Graphics and Geometry, Budapest, 70–75
Borouchaki H (2000) Simplification de maillage basee sur la distance de Hausdorff. Comptes Rendus de l’Académie des Sciences, 329(1):641–646
Mezentsev A (2004) MezGen-unstructured hybrid Delaunay mesh generator with effective boundary recovery. http://cadmesh.homeunix.com/andrey/Mezgen.html
Weatherill N, Hassan O (1994) Efficient three-dimensional Delaunay triangulation with automatic point creation and imposed boundary constraints. Int J Numer Meth Engng 37:2005–2039
George P, Hecht F, Saltel E (1991) Automatic mesh generator with specified boundary. Comp Meth Appl Mechan Engng 92:269–288
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Mezentsev, A.A., Munjiza, A., Latham, JP. (2005). Unstructured Computational Meshes for Subdivision Geometry of Scanned Geological Objects. In: Hanks, B.W. (eds) Proceedings of the 14th International Meshing Roundtable. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-29090-7_5
Download citation
DOI: https://doi.org/10.1007/3-540-29090-7_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-25137-8
Online ISBN: 978-3-540-29090-2
eBook Packages: EngineeringEngineering (R0)