- Hex mesh existence proof, "A characterization…"
- Whisker Weaving (WW) basic ideas
- Reliable WW via curve contraction
- WW knives
- Resolving two faces sharing two edges in WW
- All-hex geode-template and fixed coordinates as cubit journal file
- Geode Algorithm
- Choosing corners for mapped meshing
- Interval assignment
- QMG quadtree/octree mesh generator
Dual Hex Meshing, Whisker Weaving
This first paper is informally known as the "hex mesh existence proof"
A Characterization of the Quadrilateral Meshes of a Surface which Admit a Compatible Hexahedral Mesh of the Enclosed Volume
Scott A. Mitchell Proc. 13th Annual Symposium on Theoretical Aspects of Computer Science (STACS `96), Lecture Notes in Computer Science 1046, Springer, pages 465-476, 1996 pdf STACS slides (pdf)
See also David Eppstein’s result: Linear complexity hexahedral mesh generation
Bill Thurston also wrote a newsgroup article outlining a proof that is similar to my paper: "Hexahedral decomposition of polyhedra, sci.math, 25 Oct 1993."
Thurston’s post is saved on David Eppstein’s website:
Geometry in Action email Re: Hexahedral decomposition of polyhedra.
Reliable Whisker Weaving via Curve Contraction
Nathan T. Folwell and Scott A. Mitchell Proc. 7th International Meshing Roundtable `98, 365-378, (1998).
The Whisker Weaving Algorithm: a Connectivity Based Method for Constructing All-hexahedral Finite Element Meshes
Timothy J. Tautges, Ted D. Blacker, Scott A. Mitchell Int. J. Numer. Methods Engrg. 39:19 (1996), pp. 3327-3350 pdf and doi
Progress Report on the Whisker Weaving All-hexahedral Meshing Algorithm
Timothy J. Tautges and Scott A. Mitchell 5th International Conference on Numerical Grid Generation in Computational Field Simulations, Mississippi State University, pp.659-670, April 1996 Sandia Tech Library and UNT
Hexahedral Mesh Generation via the Dual
Steven Benzley, Ted D. Blacker, Scott A. Mitchell, Peter Murdoch, Timothy J. Tautges Proc. 11th Annual Symp. on Computational Geometry, C4-C5 (1995). ACM digital library
Connectivity-Based, All-hexahedral Mesh Generation Method and Apparatus (patent)
Timothy J. Tautges, Scott A. Mitchell, Ted D. Blacker, and Peter Murdoch. Patent US 5,768,1556, 16 June 1998. Sandia Corporation, Albuquerque, NM.
The Spatial Twist Continuum Captures the Global Connectivity of an All-Hexahedral Finite Element Mesh
Peter Murdoch, Steven Benzley, Ted Blacker, and Scott A. Mitchell
Pillowing Doublets: Refining a Mesh to Ensure that Faces Share at Most One Edge
Scott A. Mitchell and Timothy J. Tautges
Proc. 4th International Meshing Roundtable, 231-240 (1995). IMR bibtex
The Spatial Twist Continuum: a Connectivity Based Method for Representing All-hexahedral Finite Element Meshes
Peter Murdoch, Steven Benzley, Ted D. Blacker, and Scott A. Mitchell Finite Elements in Analysis and Design, Volume 28, Number 2, 15 December 1997, Elsevier, pp. 137-149(13)
Whisker Weaving: Invalid Connectivity Resolution and Primal Construction Algorithm
Timothy J. Tautges and Scott A. Mitchell
Proceedings, 4th International Meshing Roundtable, SAND95-2130, Sandia National Laboratories, pp.115-127, October 1995. IMR
Forming and Resolving Wedges in the Spatial Twist Continuum
Ted D. Blacker, Scott A. Mitchell, Timothy J. Tautges, Peter Murdoch, Steven Benzley,
Engineering with Computers 13:35-47 (1997)
pdf and journal site
Dual-based hex meshing, non-Whisker-Weaving
The Graft Tool: an All-hexahedral Transition Algorithm for Creating a Multi-directional Swept Volume Mesh
Steven R. Jankovich, Steven E. Benzley, Jason F. Shepherd, and Scott A. Mitchell Proc. 8th International Meshing Roundtable `99, 387-392 (1999) imr
Method for Generating a Mesh Representation of a Region Characterized by a Trunk and a Branch thereon (patent)
Jason Shepherd, Scott A. Mitchell, Steven R. Jankovich, and Steven E. Benzley. Patent US 7,219,039 B1, 15 May 2007. Sandia Corporation, Albuquerque, NM.
Cleave and Fill Tool: An All-hexahedral Refinement Algorithm for Swept Meshes
Michael Borden, Steven Benzley, Scott A. Mitchell, David R. White and Ray MeyersProc. 9th International Meshing Roundtable, Sandia National Laboratories, pp. 69-76, October 2000
The All-hex Geode-template for Conforming a Diced Tetrahedral Mesh to any Diced Hexahedral Mesh
Scott A. Mitchell Proc. 7th International Meshing Roundtable `98, 295-305 (1998), and Engineering with Computers, 15: 228-235.
paper with erroneous mesh node coordinates. Fixed coordinates as txt file and cubit journal file.
The Geode Algorithm: Combining Hex/tet Plastering, Dicing and Transition Elements for Automatic, All-hex Mesh Generation
Robert W. Leland, Darryl J. Melander, Ray W. Meyers, Scott A. Mitchell, Timothy J. Tautges Proc. 7th International Meshing Roundtable `98, 515-521 (1998).
Interval assignment and structured cubical meshing
Methods for Multisweep Automation
Jason Shepherd, Scott A. Mitchell, Patrick Knupp, and David White
Proc. 9th International Meshing Roundtable, pp. 77-87, October 2000
High Fidelity Interval Assignment
Scott A. Mitchell Proc. 6th International Meshing Roundtable `97, 33-44 (1997), and International Journal of Computational Geometry and Applications, Vol. 10, No. 4 (2000) 399-415.
Integration of Mesh Optimization with 3D All-Hex Mesh Generation, LDRD Subcase 3504340000, Final Report
Patrick Knupp and Scott A. Mitchell, SAND99-2852, Unlimited Release, November 1999. tech report and local mirror, also black&white and ps bibtex
A Global Optimization Approach to Quadrilateral Meshing
Joseph Jung, Clark Dohrmann, Walter Witkowski, Paul Wolfenberger, Walter Gerstle, Scott A. Mitchell, Malcolm Panthaki, and Daniel Segalman Proc. 6th International Meshing Roundtable `97, 155-167 (1997).
Interval Assignment for Volumes with Holes
Jason Shepherd, Steven Benzley and Scott A. Mitchell International Journal for Numerical Methods in Engineering, John Wiley, Vol 49, Num 1, pp. 277-288, 2000
pdf and Sandia Tech Library and OSTI and IJNME and doi
Choosing Corners of Rectangles for Mapped Meshing
Scott A. Mitchell Proc. Thirteenth annual symposium on Computational Geometry, 87-93 (1997)
ACM digital library and citeseer
A Method for Controlling Skew on Linked Surfaces
R. A. Kerr, S. E. Benzley, D. R. White, S. Mitchell Proc. 8th International Meshing Roundtable `99, 377- 385 (1999) pdf and imr bibtex
An Immersive Environment for Exploration of CUBIT Meshes
C. J. Pavlakos, J. S. Jones, and S. A. Mitchell Proc. 6th International Meshing Roundtable `97, 47-65 (1997).
An Aspect Ratio Bound for Triangulating a d-Grid Cut by a Hyperplane
Scott A. Mitchell and Steven A. VavasisProc. 12th Annual Symposium on Computational Geometry, (1996) 48-57
Courses, demos, and user manuals
A Technical History of Hexahedral Mesh Generation
Scott A. Mitchell 11th International Meshing Roundtable, short course, 15 Sept 2002.
abstract powerpoint slides
Cubit software demonstration
Department of Energy, Accelerated Strategic Computing Initiative (ASCI), SC2000 Research Exhibitor Booth R1124, Supercomputing 2000.
Mesh Generation for High Performance Computing. Part II: Mesh Generation for Massively Parallel-Based Analysis
Scott Mitchell, Patrick Knupp, and Timothy J. Tautges Tutorial S6B, Supercomputing 2000.
CUBIT Mesh Generation Enviroment Users Manual, vol. 1
Ted D. Blacker, Steven Benzley, Steven Jankovich, Robert Kerr, Jason Kraftcheck, Robert Kerr, Patrick Knupp, Robert Leland, Darryl Melander, Ray Meyers, Scott A. Mitchell, Jason Shepard, Timothy J. Tautges, and David WhiteSandia National Laboratories, Albuquerque, NM, 1994. SAND94-1100.