An Efficient Geometrical Model for Meshing Applications in Heterogeneous Environments

This paper introduces a new neutral hybrid discrete (in the limit continuous) solid CAD model for meshing applications within the Integrated Computational Environments, based on subdivision surfaces. The model uses the Boundary Representation for the CAD model topology and the Butterfly Interpolating subdivision scheme for definition of underlying curves and surfaces. It is automatically derived from the original solid model, based on parametric surfaces, using a fast loop-traversal approach for identification of geometrical discontinuities. A curvature-based sizing function is introduced for generation of an optimal control mesh for subdivision surfaces. A new hybrid CAD model has significantly fewer faces, uses robust discrete structure, which simplifies computational meshing and geometrical model transfer within the heterogeneous components of computational environments.

[1]  Chi King Lee Automatic metric 3D surface mesh generation using subdivision surface geometrical model. Part 2 : mesh generation algorithm and examples , 2003 .

[2]  Steven E. Benzley,et al.  GENERALIZED 3-D PAVING : AN AUTOMATED QUADRILATERAL SURFACE MESH GENERATION ALGORITHM , 1996 .

[3]  Denis Zorin,et al.  Interpolating Subdivision for Meshes of Arbitary Topology , 1996 .

[4]  Rao V. Garimella,et al.  Proceedings of the 17th International Meshing Roundtable , 2008 .

[5]  K. Schweizerhof,et al.  Iterative mesh generation for FE‐computations on free form surfaces , 1997 .

[6]  Chi King Lee,et al.  Automatic metric 3D surface mesh generation using subdivision surface geometrical model. Part 1: Construction of underlying geometrical model , 2003 .

[7]  A. She SURFACE PARAMETERIZATION FOR MESHING BY TRIANGULATION FLATTENING , 2000 .

[8]  Charles T. Loop,et al.  Smooth Subdivision Surfaces Based on Triangles , 1987 .

[9]  Timothy J. Baker Identification and Preservation of Surface Features , 2004, IMR.

[10]  David R. White,et al.  Mesh‐based geometry , 2003 .

[11]  Rainald Lohner,et al.  Surface Gridding from Discrete Data , 1995 .

[12]  Pascal J. Frey,et al.  About Surface Remeshing , 2000, IMR.

[13]  Aristides A. G. Requicha,et al.  Solid modeling and beyond , 1992, IEEE Computer Graphics and Applications.

[14]  John-Paul Latham,et al.  Unstructured Computational Meshes for Subdivision Geometry of Scanned Geological Objects , 2005, IMR.

[15]  D. Struik Lectures on classical differential geometry , 1951 .

[16]  N. Dyn,et al.  A butterfly subdivision scheme for surface interpolation with tension control , 1990, TOGS.

[17]  L. Piegl,et al.  Curve and surface constructions using rational B-splines , 1987 .

[18]  H. Borouchaki,et al.  Interpolating and meshing 3D surface grids , 2003 .

[19]  Andrea A. diSessa,et al.  A Principled Design for an Integrated Computational Environment , 1985, Hum. Comput. Interact..

[20]  Timothy J. Tautges,et al.  Volume Decomposition and Feature Recognition for Hexahedral Mesh Generation , 1999, IMR.

[21]  Peter Schröder,et al.  Interpolating Subdivision for meshes with arbitrary topology , 1996, SIGGRAPH.

[22]  E. Sturler,et al.  Surface Parameterization for Meshing by Triangulation Flattenin , 2000 .

[23]  Kenji Shimada,et al.  Polygon crawling: feature edge extraction from a general polygonal surface for mesh generation , 2009, Engineering with Computers.

[24]  Joe Walsh,et al.  Accessing CAD Geometry for Mesh Generation , 2003, IMR.

[25]  Andrey A. Mezentsev,et al.  Methods and Algorithms of Automated CAD Repair for Incremental Surface Meshing , 1999, IMR.