BUILDING DIRECTION FIELDS ON THE MEDIAL OBJECT TO GENERATE 3 D DOMAIN DECOMPOSITIONS FOR HEXAHEDRAL MESHING

In this work, a novel method for creating decompositions of general 3D domains, suitable for hexahedral mesh generation is presented. To accomplish this, frames and cross-fields are generated on top of the medial object of the domain. The geometrical and topological information carried by the medial object, together with the directional information of the frames/crosses help analyze the domain. By generating frames and cross fields on medial vertices, edges and faces based on touching vectors, a directional field is constructed on top of the medial object. Based on it, critical lines in the domain called, singularity lines, are identified. Starting from these, a complete line network is created on the interior of the domain. This network is extruded to the boundary in order to create the boundary of high-quality partitioning surfaces that are used to decompose the domain into regions appropriate for a high-quality hexahedral mesh. Examples are given to validate the method.

[1]  W. J. Gordon,et al.  Construction of curvilinear co-ordinate systems and applications to mesh generation , 1973 .

[2]  Robert E. Smith,et al.  Algebraic grid generation , 1982 .

[3]  Ted D. Blacker,et al.  Paving: A new approach to automated quadrilateral mesh generation , 1991 .

[4]  Scott A. Canann.  Plastering: A new approach to automated, 3-D hexahedral mesh generation , 1992 .

[5]  M. Sabin,et al.  Hexahedral mesh generation by medial surface subdivision: Part I. Solids with convex edges , 1995 .

[6]  M. Price,et al.  Hexahedral Mesh Generation by Medial Surface Subdivision: Part II. Solids with Flat and Concave Edges , 1997 .

[7]  Patrick M. Knupp.  Next-Generation Sweep Tool: A Method for Generating All-Hex Meshes on Two-and-One-Half Dimensional Geometries , 1998, IMR.

[8]  Steven E. Benzley,et al.  Improved many-to-one sweeping. , 2006 .

[9]  Xevi Roca,et al.  A New Procedure to Compute Imprints in Multi-sweeping Algorithms , 2009, IMR.

[10]  T. Blacker,et al.  Unconstrained plastering—Hexahedral mesh generation via advancing‐front geometry decomposition , 2010 .

[11]  Konrad Polthier,et al.  CUBECOVER – Parameterization of 3D Volumes , 2011 .

[12]  Hujun Bao,et al.  Boundary aligned smooth 3D cross-frame field , 2011, ACM Trans. Graph..

[13]  Eugene Zhang,et al.  All‐Hex Mesh Generation via Volumetric PolyCube Deformation , 2011, Comput. Graph. Forum.

[14]  Baining Guo,et al.  All-hex meshing using singularity-restricted field , 2012, ACM Trans. Graph..

[15]  Hujun Bao,et al.  Automatic Frame Field Guided Hexahedral Mesh Generation , 2012 .

[16]  Timothy J. Tautges,et al.  One-to-one sweeping based on harmonic S-T mappings of facet meshes and their cages , 2014, Engineering with Computers.

[17]  Harold J. Fogg,et al.  Automatic generation of multiblock decompositions of surfaces , 2015 .

[18]  William Roshan Quadros,et al.  LayTracks3D: A new approach for meshing general solids using medial axis transform , 2016, Comput. Aided Des..

[19]  Enrico Puppo,et al.  Skeleton‐driven Adaptive Hexahedral Meshing of Tubular Shapes , 2016, Comput. Graph. Forum.

[20]  Franck Ledoux,et al.  Analysis of Non-Meshable Automatically Generated Frame fields. , 2016 .

[21]  Bruno Lévy,et al.  Practical 3D frame field generation , 2016, ACM Trans. Graph..

[22]  Hujun Bao,et al.  All-hex meshing using closed-form induced polycube , 2016, ACM Trans. Graph..

[23]  Franck Ledoux,et al.  Smoothness driven frame field generation for hexahedral meshing , 2016, Comput. Aided Des..

[24]  Yufei Guo,et al.  Hexahedral mesh generation via constrained quadrilateralization , 2017, PloS one.

[25]  J. Solomon,et al.  Boundary Element Octahedral Fields in Volumes , 2017, ACM Trans. Graph..

[26]  Yi Su,et al.  Automatic Blocking of Shapes Using Evolutionary Algorithm , 2018, IMR.

[27]  Heng Liu,et al.  Singularity-constrained octahedral fields for hexahedral meshing , 2018, ACM Trans. Graph..

[28]  Trevor T. Robinson,et al.  Singularities in structured meshes and cross-fields , 2018, Comput. Aided Des..

[29]  Cecil Armstrong,et al.  A Combined Medial Object and Frame Approach to Compute Mesh Singularity Lines (Research note) , 2018 .