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3D Mapped Meshing/Hex Meshing

A list of recent publications that interests us

BMSWEEP: Locating Interior Nodes During Sweeping

Staten, Matthew L., Scott A. Canann, and Steve J. Owen

7th International Meshing Roundtable, Sandia National Labs, October 1998

ANSYS Design Development Department ANSYS, Inc. Canonsburg, PA USA

Abstract:BMSweep is a new algorithm used to mesh a class of three-dimensional models with all hexahedral elements. BMSweep is able to mesh volumes that have a topologically constant cross section along a single logical axis. This subset of three-dimensional models is often referred to as two and one half dimensional. General three-dimensional volumes can be meshed with hexahedral elements using BMSweep after first being decomposed into multiple two and one half dimensional volumes.

The algorithm used to determine the location of the interior nodes uses background mesh interpolation. This approach allows the cross section of the volume to curve and twist freely while still allowing sweep to be performed.


All hexahedral mesh generation by Intelligent Local Approach (ILA)

Wada, Y, S. Yoshimura and G. Yagawa

presentation at ANSYS Inc., Pittsburgh PA, July 1998

presentation given at ANSYS Inc., Pittsburgh, PA. Presented by Akio Myoshi Department of Quantum Engineering and Systems Science(QUEST) The University of Tokyo


Automatic remeshing for three-dimensional finite element simulation of welding

Lindgren, L.-E., H.-A. Haggblad, J.M.J. McDill, A.S. Oddy

Computer Methods in Applied Mechanics and Engineering, Elsevier, Vol 147, pp.401-409, 1997

L.-E. Lindgren and H.-A. Haggblad Lulea University of Technology, 971 87 Lulea. Sweden

J.M.J. McDill Carleton University. Ottawa, KIS 5B6. Canada

A.S. Oddy Oddy/McDill Numerical Investigation Sciences Inc.. Ottawa, K1G OW8. Canada

Abstract: Three-dimensional finite element simulation of electron beam welding of a large copper canister has been performed. The use of an automatic remeshing algorithm, based on a graded hexahedral element was found to be effective. With this algorithm the strongly nonlinear thermomechanical effects locally close to the moving heat source can accurately be modelled using a dense element mesh that follows the heat source.

Generating Hexahedron-Dominant Mesh Based on Shrinking-Mapping Method

Min, Weidong

Proceedings, 6th International Meshing Roundtable, Sandia National Laboratories, pp.171-182, October 1997

Department of Computing Science, University of Alberta, Edmonton, Alberta, Canada, T6G 2H1,

Abstract This paper presents an algorithm based on shrunken polyhedron and mapping to mesh a convex polyhedron using mixed elements, with mostly hexahedra, but including some tetrahedra, pyramids, and wedges. It is part of a scheme for automatically meshing an arbitrary SD geometry. The scheme first decomposes a 3D geometry into a set of convex polyhedra. Then the boundary quadrilateral meshes of these convex polyhedra are formed. For every convex polyhedron, the algorithm proposed in this paper generates shrunken polyhedra one by one and uses hexahedron, wedge, pyramid and tetrahedron to fill between two adjacent polyhedra. The 2D boundary meshes of a convex polyhedron are mapped to the boundary polygons of the shrunken polyhedron. The mixed hexahedron mesh is generated based on the mapping relations and on the ending cases for the 2D meshes without direct mapping relation.

Pyramid Elements for Maintaining Tetrahedra to Hexahedra Conformability

Owen, Steven J., Scott A. Canann and Sunil Saigal

AMD-Vol. 220 Trends in Unstructured Mesh Generation, ASME, pp.123-129, July 1997

Department of Civil and Environmental Engineering, Carnegie Mellon University and ANSYS Inc. 275 Technology Drive. Cannonsburg PA. USA 15317

presented at The 1997 Joint ASME/ASCE/SES Summer Meeting June 29-July 2, 1997 Northwestern University Evanston Illinois

Abstract A method is proposed whereby an existing non-conforming, mixed hexahedra-tetrahedra element mesh, is altered to conform by the insertion and formation of five-node or thirteen-node pyramids. Local tetrahedral transformations are performed to provide the topology enabling the merging of two adjacent tetrahedra into one pyramid. Local smoothing and cleanup operations improve the quality of the transition region. Other methods for the creation of transition pyramid elements are also discussed. Results show superior performance of the resulting elements in a commercial finite element code over non-conforming interface conditions.

An Immersive Environment for Exploration of CUBIT Meshes

Pavlakos, Constantine J., Jake S. Jones and Scott A. Mitchell

Proceedings, 6th International Meshing Roundtable, Sandia National Laboratories, pp.47-48, October 1997

Sandia National Laboratories PO. Box 5800, Albuquerque, NM 87185 Web:,,

Abstract This work explores the use of immersive technologies, such as those used in synthetic virtual environments (commonly referred to as virtual reality, or VR), in enhancing the mesh-generation process for 3-dimensional (3D) models. The objective is to enable interaction with meshes, either complete or under construction, in a highly visual and intuitive manner, allowing a much greater understanding of the mesh, as well as allowing interactive feedback to the mesh generation process. This capability is particularly useful for examining mesh quality and mesh topology in certain spatial localities where the automated mesher may have produced certain complexities or anomalies.

This work partners with Sandia's CUBIT mesh generation research, and explores the use of capabilities developed for Sandia's Multi-dimensional User-oriented Synthetic Environment (MUSE). We have successfully implemented a prototype system for viewing and understanding CUBIT meshes which led one CUBIT developer to comment: "A capability like this on the desktop would increase our productivity by a factor of 4 or 5 for looking at meshes." The system has been linked to CUBIT (using sockets), so, in addition to being able to import meshes from a file, it is possible to import meshes directly from CUBIT, while the meshing system is actively generating a mesh. This further enables mesh editing and/or other feedback while the meshing algorithm is running - to date, we have only begun to explore this aspect by demonstrating the ability to move nodes spatially in the mesh. While the prototype system has been demonstrated with a high-end, equipment-rich VR system, the software is also running on a lower-end desktop system for which we are currently working to enable certain VR features, such as stereo, head-tracking, and use of a space-ball for input. Other current work includes an effort to enhance the system for use with relatively large meshes - the initial prototype worked very well for very small meshes, but experimentation with certain real application meshes has mandated a need to investigate other approaches, particularly of a hierarchical or selective nature, for allowing high-performance manipulation and exploration of such meshes.

Functionality of the prototype system includes: the ability to differentiate between nodes in the mesh which belong to different numbers of elements; the ability to turn on/off mesh edges (i.e. to see only nodes, or nodes and edges); the ability to displa y node identifiers with the nodes; the ability to highlight specific elements in the me sh for visual scrutiny; the ability to "tether" to (i.e. visually focus attention to) a specific node, which also highlights the edges of all elements which contain the node; the ability to grab and move nodes in the mesh; and the ability to interact with all of t hese features in a fully stereoscopic environment, supported by advanced human-computer interface capabilities. We are also currently implementing a capability which would enable CUBIT researchers working on the "WhiskerWeaving" algorithm to explore a resulting mesh together with associated sheet diagrams, highlighting certain primaldual relationships. To accommodate larger meshes, we provide a couple-of simplified ways to look at a global mesh space (colored bounding boxes for each element block or display of exterior faces only) together with mechanisms for pickin- -a certain locality for detailed display and scrutiny - for example, one approach use s a movable transparent sphere to select a spherical portion of the global mesh space for detailed display.

Our presentation will include a description of the prototype system, a discussion of lessons learned, and a video segment showing a live session of the prototype in use.

Hexahedral Mesh Generation by Medial Surface Subdivision: Part II. Solids with Flat and Concave Edges

Price, M.A., and C.G. Armstrong

International Journal for Numerical Methods in Engineering, John Wiley & Sons, Vol 40, pp.111-136, January 1997

Summary :A method is presented for the subdivision of a large class of solids into simple subregions suitable for automatic finite element meshing with hexahedral elements. The medial surface subdivision technique described previously in the literature is us ed as tha basis for this work and is extended here to cover solids which have flat and concave edges. Problems where the medial surface is degenerated are also addressed.

The HexTet Hex-Dominant Automesher: An Interim Progress Report

Tuchinsky, Philip M. and Brett W. Clark

Proceedings, 6th International Meshing Roundtable, Sandia National Laboratories, pp.183-194, October 1997

Dr. Philip M. Tuchinsky Ford Research Laboratory Ford Motor Company Mail Drop 2122 SRL P.0. Box 2053 Dearborn, Ml 48121 USA

Brett W. Clark Datalogics. Inc. 276 East 950 South Orem, UT 84058 USA formerly at Sandia National Laboratories

Abstract HexTet is an automesher for general solid bodies. It meshes inward from an allquadfilatemi surface mesh, using an advancing-front "plastering" algorithm to create hexahedmi elements. HexTet fills as much of the volume as ft can, but leaves void regions where ft cannot hex-mesh further. It a partial hex mesh results, the remaining void regions are separated into polyhedra and each void- bounding quadrilateral face is diagonally split into two triangles. The resulting triangle-mes hed polyhedral voids are then filled with tetrahedral elements to complete the mixed-element mesh. HexTet is implemented in the Ford Automesher and Sandia Cubit meshing tools. It robustly meshes many simpler solids. Research and development continues to improve its robustness with increasingly complex problems. This is a progress report.

Generalized 3D Paving: An Automated Quadrilateral Surface Mesh Generation Algorithm

Cass, Roger J.

International Journal For Numerical Methods In Engineering, John Wiley & Sons, Vol 39, pp.1475-1489, 1996

Summary: This paper discusses the extension of the paving algorithm for all-quadrilateral mesh generation to arbitrary three-dimensional trimmed surfaces. Methods of calculating angles and projecting elements for generating surfaces are presented. Extensions of t he smoothing algorithms for three-dimensions are set forth. A new connectivity-based mesh cleanup and improvement algorithm is discussed. Advances in the use of scalar sizing functions is presented. These functions better approximate internal mesh densi ty from boundary densities and surface characteristics.

An Automatic Hexahedral Mesh Generation System Based on the Shape-Recognition and Boundary-Fit Methods

Chiba, N., I. Nishigaki, Y. Yamashita, C. Takizawa, K. Fujishiro

5th International Meshing Roundtable, Sandia National Laboratories, pp.281-290, October 1996

Abstract A general-purpose automatic hexahedral mesh generation system for FEA (Finite Element Analysis) was developed based on a shape recognition technique and the boundary-fit method. In this system, a solid model is analyzed and decomposed into single-connected sub-models. Then, other sub-models topologically identical to the original ones are constructed using, only orthogonal angles. Cubes are used to constr uct intermediate models, which reassemble these, and finally, hexahedral meshes are generated by mapping the cubes back onto the original solid model.

A Multiple Source and Target Sweeping Method for Generating All-Hexahedral Finite Element Meshes

Mingwu, Lai, Steven E. Benzley, Greg Sjaardema and Tim Tautges

5th International Meshing Roundtable, Sandia National Laboratories, pp.217-228, October 1996

Abstract This paper presents an algorithm to enhance the capabilities of generating all hexahedral finite element meshes by the sweeping process. Traditional sweeping techniques are very useful and robust. They create meshes by projecting an existing single-surface mesh along a specified trajectory to a specified single target surface . In this process the source surface is meshed by any surface meshing algorithm while the sides that couple the source to the target are limited to a regular mapped quadrilate ral mesh. This process is often called two and one half dimensional meshing. The procedure presented in this paper enhances this traditional technique by developing a projection technique that minimizes mesh distortion; and allows multiple connected surfaces to single target, multiple unconnected surfaces to single target, and multip le unconnected surfaces to multiple unconnected target sweeping.

Automated Hexahedral Mesh Generation by Swept Volume Decomposition and Recomposition

Shih, Bih-Yaw and Hiroshi Sakurai

5th International Meshing Roundtable, Sandia National Laboratories, pp.273-280, October 1996

Abstract :In this paper a method is presented to generate uniform hexahedral meshes automatically. In this method, a solid model with complex geometry is decomposed into swept volumes with simpler geometry. A sweepable face on the solid model is selected as the generator face to generate a swept volume. Each generator face is specified with node density and a quadrilateral mesh is generated from it. Then, the mesh is swept into a hexahedral mesh of the swept volume. Finally, all hexahedral meshes of swept volumes are recomposed into a hexahedral mesh of the original solid model.

Automatic, Quadrilateral and Hexahedral Meshing of Pseudo-Cartesian Geometries using Virtual Subdivision

White, David Roger

Master's Thesis, Brigham Young University, pp.63, June 1996

Author's Homepage:

Download thesis (postscript) from:

Automated Hexahedral Mesh Generation from Biomedical Image Data:Applications in Limb Prosthetics

Zachariah, Santosh G., Joan E. Sanders and George M. Turkiyyah

IEEE Transactions on Rehabilitation Engineering, IEEE, Vol 4, Num 2, pp.91-102, June 1996

Center for Bioengineering and Department of Civil Engineering. University of Washington. Seattle, WA USA.

Abstract A general method to generate hexahedral meshes for finite element analysis of residua l limbs and similar biomedical geometries is presented. The method utilizes skeleton-based subdivision of cross-sectional domains to produce simple subdomains in which structured meshes are easily generated. Application to a below-knee residual limb and external prosthetic socket is described. The residual limb was modeled as consisting of bones, soft tissue, and skin. The prosthetic socket model comprised a socket wall with an inner liner. The geometries of these structures were defined usin g axial cross-sectional contour data from X-ray computed tomography, optical scanning, and mechanical surface digitization. A tubular surface representation, usin g B-splines to define the directrix and generator, is shown to be convenient for definition of the structure geometries. Conversion of cross-sectional data to the compact tubular surface representation is direct, and the analytical representation simplifies geometric querying and numerical optimization within the mesh generation algorithms. The element meshes remain geometrically accurate since boundary nodes are constrained to lie on the tubular surfaces. Several element meshes of increasing mesh density were generated for two residual limbs and prosthetic sockets. Convergence testing demonstrated that approximately 19 elements are required along a circumference of the residual limb surface for a simple linear elastic model. A model with the fibula absent compared with the same geometry with the fibula present showed differences suggesting higher distal stresses in the absence of the fibula. Automated hexahedral mesh generation algorithms for sliced data represent an advancement in prosthetic stress analysis since they allow rapid modeling of any give n residual limb and optimization of mesh parameters.

"Automating Node And Element Assignments On Conforming Four-Sided Sections Defining A Domain For Mapping Quadrilateral Elements",

Computers and Structures, Pergamon, Vol 62, Num 2, pp.373-380, 1997 keywords: interval assignment mapped meshing quadrilateral

Barker, D.E. and S.A. Lantz


"Knowledge System Approach to Automated Two-Dimensional Quadrilateral Mesh Generation",

Computers in Engineering, ASME, Vol 3, pp.153-162, 1988 keywords: knowledge system mapped meshing primitive decomposition quadrilateral transfinite mapping

Blacker, T. D., J. L. Mitchiner, L. R. Phillips, and Y. T. Lin


"The Cooper Tool",

5th International Meshing Roundtable, Sandia National Laboratories, pp.13-30, October 1996 keywords: cooper hexahedron mapped sweeping

Blacker, Ted


"New Method for Graded Mesh Generation of Quadrilateral Finite Elements",

Computers and Structures, Pergammon, Vol 59, Num 5, pp.823-829, 1996 keywords: geometry decomposition mapped meshing quadrilateral set theory templates

Cheng, Gengdong and Hua Li


"An Automatic Hexahedral Mesh Generation System Based on the Shape-Recognition and Boundary-Fit Methods",

5th International Meshing Roundtable, Sandia National Laboratories, pp.281-290, October 1996 keywords: boundary fit decomposition hexahedron mapping shape recognition sweeping

Chiba, N., I. Nishigaki, Y. Yamashita, C. Takizawa, K. Fujishiro


"Mapping Methods for Generating Three-Dimensional Meshes",

Computers In Mechanical Engineering, CIME Research Supplement, pp.67-72, August 1982 keywords: hexahedron mapped quadrilateral

Cook, W.A. and W.R. Oakes


"A New Method for Creating Grid Abstractions for Complex Configurations", 31st Aerospace Sciences Meeting & Exhibit, Reno, NV, AIAA-93-0428, January 1993 keywords: block structuring mapped meshing

Dannenhoffer, John F. III


"Automatic Finite Element Mesh Transitioning with Hexahedron Elements"

, Dissertation, Brigham Young University, Vol 4, pp.92, August 1989 keywords: hexahedron mapped meshing primitives templates

Esmaeilian, Said


"Generalized Method of Decomposing Solid Geometry into Hexahedron Finite Elements",

Proceedings, 4th International Meshing Roundtable, Sandia National Laboratories, pp.141-152, October 1995 keywords: automated mesh generation hexahedron mapped meshing medial axis spatial decomposition

Holmes, David I.


"Automatic Hexahedral Mesh Generation by Recursive Convex and Swept Volume Decomposition",

Proceedings, 6th International Meshing Roundtable, Sandia National Laboratories, pp.217-231, October 1997 keywords: hexahedron mapped meshing shape recognition volume decomposition

Liu, Shang-Sheng and Rajit Gadh


"A Multiple Source and Target Sweeping Method for Generating All-Hexahedral Finite Element Meshes",

5th International Meshing Roundtable, Sandia National Laboratories, pp.217-228, October 1996 keywords: hexahedron sweeping

Mingwu, Lai, Steven E. Benzley, Greg Sjaardema and Tim Tautges


"Automated Hexahedral Mesh Generation by Swept Volume Decomposition and Recomposition",

5th International Meshing Roundtable, Sandia National Laboratories, pp.273-280, October 1996 keywords: hexahedron sweeping

Shih, Bih-Yaw and Hiroshi Sakurai


"Automated Hexahedral Mesh Generation by Virtual Decomposition",

Proceedings, 4th International Meshing Roundtable, Sandia National Laboratories, pp.165-176, October 1995 keywords: automated mesh generation hexahedron mapped meshing spatial decomposition sweeping

White, David R., Lai Mingwu, Steven E. Benzley, and Gregory D. Sjaardema


"Automatic, Quadrilateral and Hexahedral Meshing of Pseudo-Cartesian Geometries using Virtual Subdivision"

, Master's Thesis, Brigham Young University, pp.63, June 1996 keywords: Cubit hexahedra mapped meshing quadrilateral sub-mapping

White, David Roger