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GeometryProcessing/Spring2009/Schedule/Spectral Processing4

2009-02-05T17:30:17Z

Loos: New page: * Brad Loos Okay, what is isometry, as in ''symmetries of a shape which are invariant up to isometry''. Is there a more technical definition than just something that is the same about a s...

* Brad Loos

Okay, what is isometry, as in ''symmetries of a shape which are invariant up to isometry''. Is there a more technical definition than just something that is the same about a shape even if you rotate/scale/animate it?

GeometryProcessing/Spring2009/Schedule

2009-01-31T02:25:04Z

Loos: /* Extra Lecture I -- Jan 23 */

== Introduction to Geometry Processing -- Jan 13 ==

Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/Introduction_to_Geometry_Processing]]

Lecturer: Gustavo

Topics: Course Overview

Slides: [http://www.vistrails.org/images/Introduction.pdf Introduction.pdf]

== Surface Representations -- Jan 15 ==

Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/Surface_Representations]]

Lecturer: Gustavo

Topics:

* Implicit and Parametric Surfaces
* Representing/Manipulating Implicit Surfaces - CAGD
* Representing/Manipulating Parametric Surfaces - Splines
* Piecewise Linear Approximations - Topological Data Structures

Required Reading/Notes:

[GM], Chapters 2 and 3.

Slides:

Animations:

Further reading:

Martti Mäntylä. An Introduction to Solid Modeling. Computer Science Press, College Park, MD, 1988.

[http://www.gvu.gatech.edu/~jarek/papers/CornerTable.pdf Edgebreaker on a Corner Table: A Simple Technique for Representing and Compressing Triangulated Surfaces]

[http://cg.www.techfak.uni-bielefeld.de/publications/papers/openmesh.pdf OpenMesh – a generic and efﬁcient polygon mesh data structure]

[http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4055948 Edge-Based Data Structures for Solid Modeling in Curved-Surface Environments]

== Surface Generation and/or Extraction I -- Jan 20 ==

Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/Surface_Generation_Extraction1]]

Lecturer: Carlos

Topics:

* Capturing Methods
** Marching Cubes/Tetrahedra
** Dual Contouring

Required Reading/Notes:

[[http://portal.acm.org/ft_gateway.cfm?id=37422&type=pdf&coll=GUIDE&dl=GUIDE&CFID=15556705&CFTOKEN=70616554 William E. Lorensen and Harvey E. Cline. MARCHING CUBES: A High Resolution 3D Surface Construction Algorithm, Computer Graphics, 1987]]

Slides: [http://www.sci.utah.edu/~cscheid/lectures/090120.pdf PDF File]

Further reading:

[http://www.sci.utah.edu/~csilva/papers/vis2008b.pdf Carlos A. Dietrich et al. Edge Groups: An Approach to Understanding the Mesh Quality of Marching Methods, IEEE TVCG, 2008]

[http://www.cs.sfu.ca/~torsten/Publications/Papers/tvcg06_hamish.pdf Hamish Carr, Torsten Moller, and Jack Snoeyink. Artifacts Caused By Simplicial Subdivision, IEEE TVCG, 2006]

[http://graphics.ethz.ch/teaching/scivis_common/Literature/Newman06.pdf Newman and Yi. A survey of the marching cubes algorithm. Computers and Graphics, 2006]

[http://www.cse.ohio-state.edu/~wenger/publications/isomesh.pdf Raman and Wenger. Quality isosurface Generation Using an Extended Marching Cubes Lookup Table. Eurovis 2008]

[http://www.cs.berkeley.edu/~jrs/papers/elemj.pdf Shewchuk. What Is a Good Linear Finite Element? Interpolation, Conditioning, Anisotropy, and Quality Measures]

[http://portal.acm.org/ft_gateway.cfm?id=566586&type=pdf&coll=GUIDE&dl=GUIDE&CFID=15556907&CFTOKEN=76114820 Tao Ju, Frank Losasso, Scott Schaefer, Joe Warren. Dual Contouring of Hermite Data, SIGGRAPH 2002]

== Surface Generation and/or Extraction II -- Jan 22 ==

Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/Surface_Generation_Extraction2]]

Lecturer: Carlos

Topics:

* Element quality in isosurface extraction
** Finish discussion of SnapMC, Macet, Edge Groups (Tet Stuffing?)
* Feature preservation
** Extended Marching Cubes
* "Adaptive" methods
** Dual Contouring
* Advancing Front Methods
** Afront

Required Reading/Notes:

[http://portal.acm.org/citation.cfm?id=383265 Feature sensitive surface extraction from volume data Feature Sensitive Surface Extraction from Volume Data, SIGGRAPH 2001]

[http://portal.acm.org/ft_gateway.cfm?id=566586&type=pdf&coll=GUIDE&dl=GUIDE&CFID=15556907&CFTOKEN=76114820 Tao Ju, Frank Losasso, Scott Schaefer, Joe Warren. Dual Contouring of Hermite Data, SIGGRAPH 2002]

[http://www.sci.utah.edu/~csilva/papers/tvcg2006acr.pdf John Schreiner, Carlos E. Scheidegger, and Claudio T. Silva. High-Quality Extraction of Isosurfaces from Regular and Irregular Grids, IEEE TVCG, 2006]

Slides:

== Extra Lecture I -- Jan 23 ==

Lecturer: Carlos

Topics: Software libraries for geometry processing

Location: Jones Conference Room. WEB 3840
Time: 3:30PM

This will be a fairly short meeting to help you get acquainted to the software we will be using for the first assignment. You will be using trimesh2, a lightweight c++ library for triangle meshes from Szymon Rusinkiewicz: http://www.cs.princeton.edu/~smr/

it is trivial to compile trimesh2 on Linux and Mac OS X. I have no experience with Windows, but I'll gladly try to help if you bring your laptop to class. if you're an enrolled student, you can get Visual Studio for free [https://software.utah.edu/osl/index.shop here]

Website with many mesh files: [http://shapes.aim-at-shape.net/index.php Aim@Shape shape repository]

Stanford 3D repository

Bilateral Mesh Denoising. Fleishman, Drori, Cohen-Or. SIGGRAPH 2003. [http://www.sci.utah.edu/~shachar/Publications/bmd03.pdf pdf version of paper]

''Building on Windows:''

Brad has created two Visual Studio Solution files (2005 & 2008) that students can use if they want (I assume one of the profs will take this down if they don't like it). The files have been tested locally on his machine and at least compile and allow all the utilities (MeshAlign, MeshCat, MeshCC, MeshFilter, MeshMake, MeshShade, MeshView) print out proper command line usage when run with no parameters.

Once you have built the solution you should find a bin and a libs subdirectory that contain Debug and/or Release directories that should contain the binary/library files respectively.

Brad would really rather not troubleshoot these files if you can't get them to work, but thought that perhaps some students might have some use for them anyway.

The files can be found here

* [http://www.cs.utah.edu/~loos/courses/cs6968/trimesh2-2.8-vs2005.zip trimesh2-2.8 VS 2005]
* [http://www.cs.utah.edu/~loos/courses/cs6968/trimesh2-2.8-vs2008.zip trimesh2-2.8 VS 2008]

== Spectral Processing I -- Jan 27 ==

Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/Spectral_Processing1]]

Lecturer: Claudio/Gustavo

Topics:

* Laplacian Mesh Matrix
** Eigenvalues and Eigenvectors/Eigenfunctions
** Geometry and Laplacian Matrix

Required Reading/Notes:

[[http://mesh.caltech.edu/ee148/refs/Taubin-star-eg00.pdf G. Taubin. Geometric Signal Processing on Polygonal Meshes, EUROGRAPHICS ’2000 STAR – State of The Art Report, 2000]]

[[https://guinness.cs.stevens-tech.edu/~quynh/courses/cs638-papers/taubin_surf_fairing.pdf G. Taubin. A signal processing approach to fair surface design, 1995]]

[[http://alice.loria.fr/publications/papers/2008/ManifoldHarmonics/MH-EG.pdf B. Vallet and B. Lévy. Spectral Geometry Processing with Manifold Harmonics, EUROGRAPHICS 2008]]

Slides:

Further reading:

[[http://142.58.111.29/~haoz/pubs/zhang_eg07star_spectral.pdf Hao Zhang Oliver van Kaick Ramsay Dyer. Spectral Methods for Mesh Processing and Analysis, EUROGRAPHICS 2007 STAR – State of The Art Report, 2007]]

== Spectral Processing II -- Jan 29 ==

Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/Spectral_Processing2]]

Lecturer: Claudio/Gustavo

Topics:

* Laplacian Eigenfunctions
** Properties
** Visualization
** Interaction

Required Reading/Notes:

[[http://alice.loria.fr/publications/papers/2006/SMI_Laplacian/SMI_Laplacian.pdf Bruno Levy. Laplace-Beltrami Eigenfunctions Towards an algorithm that “understands” geometry, SMI, 2006]]

[[http://page.mi.fu-berlin.de/wardetzk/pub/laplacian.pdf M. Wardetzky et al. Discrete Laplace Operators: No free lunch, SGP, 2007]]

[[ftp://ftp.gdv.uni-hannover.de/papers/reuter2006-shape_dna.pdf M Reuter et al. Laplace–Beltrami spectra as ‘Shape-DNA’ of surfaces and solids, CAD, 2007]]

Slides:

Further reading:

[[ftp://ftp.gdv.uni-hannover.de/papers/reuter2006-shape_dna.pdf Martin Reuter, Franz-Erich Wolter, Niklas Peinecke. Laplace–Beltrami spectra as ‘Shape-DNA’ of surfaces and solids, Computer-Aided Design, 2006]]

Fan R. K. Chung. Spectral Graph Theory (CBMS Regional Conference Series in Mathematics, No. 92),
American Mathematical Society, 1997

== Spectral Processing III -- Feb 3 ==

Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/Spectral_Processing3]]

Lecturer: Claudio/Gustavo

Topics:

* Spectral Mesh Segmentation

Required Reading/Notes:

[[http://142.58.111.29/~lrong/personal/docs/05_vmv_spectcut.pdf Hao Zhang, Rong Liu. Mesh Segmentation via Recursive and Visually Salient Spectral Cuts, 2005]]

[[http://www.cs.sfu.ca/~haoz/pubs/liu_zhang_eg07.pdf Rong Liu and Hao Zhang. Mesh Segmentation via Spectral Embedding and Contour Analysis, EUROGRAPHICS, 2007]]

[[http://fas.sfu.ca/~haoz/pubs/liu_zhang_pg04.pdf Rong Liu, Hao Zhang. Segmentation of 3D Meshes through Spectral Clustering, 2004]]

Slides:

Further reading:

[[http://www-ee.technion.ac.il/~ayellet/Ps/SMI06.pdf Mesh segmentation – A comparative study, SMI, 2006]]

== Spectral Processing IV -- Feb 5 ==

Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/Spectral_Processing4]]

Lecturer: Claudio/Gustavo

Topics:

* Shape Symmetries
* Spectral Quadrangulation

Required Reading/Notes:

[[http://graphics.stanford.edu/projects/lgl/papers/osg-giss-08/osg-giss-08.pdf Maks Ovsjanikov, Jian Sun, Leonidas Guibas. Global Intrinsic Symmetries of Shapes, SGP, 2008]]

[[http://www.pascucci.org/pdf-papers/SIGGRAPH-06.pdf S. Dong, P.-T. Bremer, M. Garland, V. Pascucci, John C.Hart. Spectral Surface Quadrangulation, SIGGRAPH, 2006]]

[[http://www.graphics.rwth-aachen.de/uploads/media/kobbelt_2008_asia.pdf J. Huang, M. Zhang, J. Ma, X. Liu, L. Kobbelt, H. Bao. Spectral Quadrangulation with Orientation and Alignment Control, SIGGRAPH Asia, 2008]]

Slides:

== Mesh Decimation -- Feb 10 ==

Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/Mesh_Decimation]]

Lecturer: Claudio/Gustavo

Topics:

* Triangular Mesh Simplification

Required Reading/Notes:

[[http://www1.cs.columbia.edu/~cs4162/html05s/garland97.pdf Michael Garland, Paul S. Heckbert, Surface Simpliﬁcation Using Quadric Error Metrics, 1997]]

[[http://vims.cis.udel.edu/~jeab/research/papers/simplification/cignoni97comparison.pdf P. Cignoni, C. Montani, R. Scopigno. A comparison of mesh simplification algorithms, 1997]]

Slides:

Further reading:

[[http://graphics.cs.uiuc.edu/~garland/papers/qtheory.pdf Paul S. Heckbert, Michael Garland. Optimal triangulation and quadric-based surface simpliﬁcation, Computational Geometry, 1999]

== Mesh Smoothing -- Feb 12 ==

Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/Mesh_Smoothing]]

Lecturer: Claudio/Gustavo

Topics:

* Triangular Mesh Smoothing
* Mesh Denoising

Required Reading/Notes:

[[http://geometry.caltech.edu/pubs/JDD03.pdf Thouis R. Jones, Fredo Durand, Mathieu Desbrun. Non-iterative, feature-preserving mesh smoothing,ACM TOG, 2003]]

[[http://www-stat.stanford.edu/~idrori/BMD.pdf Shachar Fleishman, Iddo Drori, Daniel Cohen-Or. Bilateral Mesh Denoising, ACM TOG, 2003]]

[[http://portal.acm.org/citation.cfm?id=218473&dl= G. Taubin. A Signal Processing Approach To Fair Surface Design, 1995]]

Slides:

Further reading:

[[http://www.mpi-sb.mpg.de/~belyaev/papers/ik03bo.ps.gz A comparison of mesh smoothing methods]]

== Remeshing I -- Feb 17 ==

Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/Remeshing1]]

Lecturer: Claudio/Gustavo

Topics:

* Triangular Mesh Improvement

Required Reading/Notes:

[[http://portal.acm.org/citation.cfm?id=882373 V. Surazhsky and C. Gotsman. Explicit surface remeshing. Proceedings of the Symposium on Mesh Processing, 2003]]

Slides:

Further reading:

[[http://www.cs.technion.ac.il/~gotsman/AmendedPubl/Pierre/remeshing_survey.pdf Pierre Alliez, Giuliana Ucelli, Craig Gotsman and Marco Attene. Recent Advances in Remeshing of Surfaces, 2005]]

[[http://www.imr.sandia.gov/papers/imr11/surazhsky.pdf Vitaly Surazhsky, Craig Gotsman. High Quality Compatible Triangulations,11th International Meshing Roundtable, 2002]]

== Remeshing II -- Feb 19 ==

Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/Remeshing2]]

Lecturer: Claudio/Gustavo

Topics:

* Triangular Mesh Improvement

Required Reading/Notes:

[[http://ieeexplore.ieee.org/search/wrapper.jsp?arnumber=1199601 P. Alliez , E. Colin de Verdiere, O. Devillers, and M. Isenburg. Isotropic surface remeshing. In Proceedings of Shape Modeling International, 2003]]

Slides:

Further reading:

[[http://www.imr.sandia.gov/papers/imr11/surazhsky.pdf Vitaly Surazhsky, Craig Gotsman. High Quality Compatible Triangulations,11th International Meshing Roundtable, 2002]]

[[ftp://ftp-sop.inria.fr/prisme/ECG/Reports/Month30/ECG-TR-304100-01.pdf Vitaly Surazhsky, Pierre Alliez, Craig Gotsman. Isotropic Remeshing of Surfaces: a Local Parameterization Approach, ECG Technical Report No. : ECG-TR-304100-01, 2003]]

== Mesh Parameterization I -- Feb 24 ==
Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/Mesh_Parametrization1]]

Lecturer: Claudio/Gustavo

Topics:

* Planar Parametrization

Required Reading/Notes:

[[http://heim.ifi.uio.no/~michaelf/papers/mean_value.pdf M. Floater. Mean value coordinates, Computer Aided Geometric Design, 2003]]

[[http://www.multires.caltech.edu/teaching/courses/cs101.3.spring02/cs101_files/resources/Parameterization/Floater.pdf M. Floater. Parametrization and smooth approximation of surface triangulations, Computer Aided Geometric Design, 1997]]

[[http://jjcao1231.googlepages.com/Intrinsic_Parameterizations_of_Surface_Meshes_02.pdf M Desbrun, M Meyer, P Alliez. Intrinsic Parameterizations of Surface Meshes, CGF, 2002]]

Slides:

Further reading:

[[http://www.cs.jhu.edu/~misha/Fall07/Papers/Tutte63.pdf W.T. Tutte. How to draw a graph,Proc. London Math. Soc, 1963]]

[[http://vcg.isti.cnr.it/Publications/2005/FH05/survey_mingle04.pdf MS Floater, K Hormann. Surface parameterization: a tutorial and survey, 2005]]

[[http://www.cs.ubc.ca/~sheffa/papers/param_survey06.pdf A Sheffer, E Praun, K Rose. Mesh Parameterization Methods and Their Applications, 2006]]

[[https://graphics.stanford.edu/courses/cs468-03-fall/Papers/floater_triangulation.pdf M. Floater, M Reimers. Meshless parameterization and surface reconstruction, Computer Aided Geometric Design, 2001]]

== Mesh Parameterization II -- Feb 26 ==
Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/Mesh_Parametrization2]]

Lecturer: Claudio/Gustavo

Topics:

* Spherical Parametrization

Required Reading/Notes:

[[http://www.cs.sfu.ca/~torsten/GL/PAPERS/sphere2.pdf C. Gotsman, X. Gu, A. Sheffer. Fundamentals of spherical parameterization for 3D meshes, ACM TOG, 2003]]

[[http://kucg.korea.ac.kr/seminar/2003/src/PA-03-19.pdf E Praun, H Hoppe. Spherical parametrization and remeshing, 2003]]

Slides:

== Quad meshing I -- Mar 3 ==
Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/quadmesh1]]

Lecturer: Claudio/Gustavo/Joel

Topics:

Required Reading/Notes:

Slides:

Further reading:

== Quad meshing II -- Mar 5 ==
Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/quadmesh2]]

Lecturer: Claudio/Gustavo/Joel

Topics:

Required Reading/Notes:

Slides:

Further reading:

== Quad meshing III -- Mar 10 ==
Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/quadmesh3]]

Lecturer: Claudio/Gustavo/Joel

Topics:

Required Reading/Notes:

Slides:

Further reading:

== Quad meshing IV -- Mar 12 ==
Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/quadmesh4]]

Lecturer: Claudio/Gustavo/Joel

Topics:

Required Reading/Notes:

Slides:

Further reading:

== Mar 17 (Spring Break) ==
== Mar 19 (Spring Break) ==

== Mesh Compression -- Mar 24 ==
Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/Compression]]

Lecturer: Claudio/Gustavo

Topics:

* Geometrical Mesh Compression
* Spectral Mesh Compression

Required Reading/Notes:

[[http://ieeexplore.ieee.org/search/wrapper.jsp?arnumber=764870 J. Rossignac. Edgebreaker: Connectivity compression for triangle meshes. IEEE Transactions on Visualization and Computer Graphics, 5(1):47–61, January-March 1999]]

[[http://www.mpi-sb.mpg.de/~karni/publications/spectral.pdf Z Karni, C Gotsman. Spectral compression of mesh geometry, 2000]]

Slides:

Further reading:

[[http://portal.acm.org/ft_gateway.cfm?id=274365&type=pdf&coll=GUIDE&dl=GUIDE&CFID=15500980&CFTOKEN=61929152 G Taubin, J Rossignac. Geometric compression through topological surgery - ACM TOG, 1998]]

[[http://www.cs.unc.edu/~isenburg/research/papers/il-sm-05.pdf Martin Isenburg, Peter Lindstrom. Streaming Meshes, Proceedings of Visualization 2005]]

[[http://www.gvu.gatech.edu/%7Ejarek/papers/Compression.pdf Jarek Rossignac. 3D Mesh Compression, Chapter in the Visualization Handbook. Academic Press. Eds. C. Hansen and C. Johnson. 2004]]

[[http://www.cs.northwestern.edu/~pren/paperpool/ig-ooccgpm-03.pdf M Isenburg, S Gumhold. Out-of-core compression for gigantic polygon meshes, SIGGRAPH, 2003]]

== Mesh Editing -- Mar 26 ==
Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/MeshEditing]]

Lecturer: Claudio/Gustavo

Topics:

* Multiresolution approach
* Laplacian Mesh Editing
* Poisson-based mesh editing

Required Reading/Notes:

[[http://www.cs.bell-labs.com/who/wim/papers/sig97.pdf D Zorin, P Schroder, W Sweldens. Interactive multiresolution mesh editing, SIGGRAPH, 2007]]

[[http://research.microsoft.com/asia/dload_files/group/ig/2004/poisson.pdf Y Yu, K Zhou, D Xu, X Shi, H Bao, B Guo, HY Shum. Mesh editing with poisson-based gradient field manipulation, SIGGRAPH, 2004]]

[[http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=1314505&isnumber=29137 Y Lipman, O Sorkine, D Cohen-Or, D Levin, C Rossi, H Seidel. Differential coordinates for interactive mesh editing, Shape Modeling Applications, 2004]]

Slides:

Further reading:

[[http://portal.acm.org/citation.cfm?id=1073204.1073324 A Nealen, O Sorkine, M Alexa, D Cohen-Or. A sketch-based interface for detail-preserving mesh editing, SIGGRAPH, 2005]]

[[http://graphics.stanford.edu/courses/cs468-05-fall/Papers/p479-lipman.pdf Y Lipman, O Sorkine, D Levin, D Cohen-Or. Linear rotation-invariant coordinates for meshes, SIGGRAPH, 2005]]

== Mesh Repair -- Mar 31 ==
Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/MeshRepair]]

Lecturer: Claudio/Gustavo

Topics:

* Repairing Polygonal Soup
* Hole filling
* Surface Completion

Required Reading/Notes:

[[http://portal.acm.org/ft_gateway.cfm?id=1015815&type=pdf&coll=GUIDE&dl=GUIDE&CFID=16049617&CFTOKEN=45512742 T. Ju. Robust repair of polygonal models, SIGGRAPH, 2004]]

[[http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=1024098&isnumber=22019 J Davis, SR Marschner, M Garr, M Levoy. Filling holes in complex surfaces using volumetric diffusion, 2002]]

[[http://portal.acm.org/ft_gateway.cfm?id=1015814&type=pdf&coll=GUIDE&dl=GUIDE&CFID=16050250&CFTOKEN=44199354 A Sharf, M Alexa, D Cohen-Or. Context-based surface completion, SIGGRAPH, 2004]]

Slides:

Further reading:

[[http://www.cs.ubc.ca/labs/imager/tr/2005/Vlad_MCompletion/sgp05.pdf V Kraevoy, A Sheffer. Template-based mesh completion, SGP, 2005]]

[[http://graphics.stanford.edu/courses/cs468-05-fall/Papers/p896-shen.pdf C Shen, JF O'Brien, JR Shewchuk. Interpolating and approximating implicit surfaces from polygon soup, SIGGRAPH, 2004]]

== Discrete Exterior Calculus I -- Apr 2 ==
Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/DEC1]]

Lecturer: Claudio/Gustavo

Topics:

* Differential Forms in Euclidean Spaces
* Manifolds and Tangent Space
* Differential Forms on Manifolds

Required Reading/Notes:

* Loring W. Tu. An Introduction to Manifolds, Springer, 2008.

Slides:

Further reading:

* D. Bachman. A geometric Approach to Differential Forms, Birkhauser, 2006.

== Discrete Exterior Calculus II -- Apr 7 ==
Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/DEC2]]

Lecturer: Claudio/Gustavo

Topics:

* Discrete Differential Geometry
* Discrete Differential Forms

Required Reading/Notes:

[[http://etd.caltech.edu/etd/available/etd-05202003-095403/unrestricted/thesis_hirani.pdf A. Hirani. Discrete Exterior Calculus, 2003]]

[[http://www.multires.caltech.edu/pubs/diffGeoOps.pdf Mark Meyer, Mathieu Desbrun, Peter Schröder, Alan H. Barr. Discrete Differential-Geometry Operators for Triangulated 2-Manifolds]]

[[http://mesh.brown.edu/taubin/pdfs/taubin-iccv95b.pdf Gabriel Taubin. Estimating the Tensor of Curvature of a Surface from a Polyhedral Approximation, 1995]]

[[http://portal.acm.org/ft_gateway.cfm?id=1198662&type=pdf&coll=GUIDE&dl=GUIDE&CFID=15587878&CFTOKEN=77328344 John M. Sullivan. Curvature Measures for Discrete Surfaces, SIGGRAPH, 2005]]

Slides:

== Point-Set Surfaces I -- Apr 9 ==
Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/PSS1]]

Lecturer: Claudio/Gustavo/Carlos

Topics:

Required Reading/Notes:

Slides:

Further reading:

== Point-Set Surfaces II -- Apr 14 ==
Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/PSS2]]

Lecturer: Claudio/Gustavo/Carlos

Topics:

Required Reading/Notes:

Slides:

Further reading:

== Point-Set Surfaces III -- Apr 16 ==
Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/PSS3]]

Lecturer: Claudio/Gustavo/Carlos

Topics:

Required Reading/Notes:

Slides:

Further reading:

== Point-Set Surfaces IV -- Apr 21 ==
Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/PSS4]]

Lecturer: Claudio/Gustavo/Carlos

Topics:

Required Reading/Notes:

Slides:

Further reading:

== Project Presentation -- Apr 23 ==
== Project Presentation -- Apr 28 ==

GeometryProcessing/Spring2009/Schedule

2009-01-29T20:01:35Z

Loos: /* Extra Lecture I -- Jan 23 */

== Introduction to Geometry Processing -- Jan 13 ==

Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/Introduction_to_Geometry_Processing]]

Lecturer: Gustavo

Topics: Course Overview

Slides: [http://www.vistrails.org/images/Introduction.pdf Introduction.pdf]

== Surface Representations -- Jan 15 ==

Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/Surface_Representations]]

Lecturer: Gustavo

Topics:

* Implicit and Parametric Surfaces
* Representing/Manipulating Implicit Surfaces - CAGD
* Representing/Manipulating Parametric Surfaces - Splines
* Piecewise Linear Approximations - Topological Data Structures

Required Reading/Notes:

[GM], Chapters 2 and 3.

Slides:

Animations:

Further reading:

Martti Mäntylä. An Introduction to Solid Modeling. Computer Science Press, College Park, MD, 1988.

[http://www.gvu.gatech.edu/~jarek/papers/CornerTable.pdf Edgebreaker on a Corner Table: A Simple Technique for Representing and Compressing Triangulated Surfaces]

[http://cg.www.techfak.uni-bielefeld.de/publications/papers/openmesh.pdf OpenMesh – a generic and efﬁcient polygon mesh data structure]

[http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4055948 Edge-Based Data Structures for Solid Modeling in Curved-Surface Environments]

== Surface Generation and/or Extraction I -- Jan 20 ==

Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/Surface_Generation_Extraction1]]

Lecturer: Carlos

Topics:

* Capturing Methods
** Marching Cubes/Tetrahedra
** Dual Contouring

Required Reading/Notes:

[[http://portal.acm.org/ft_gateway.cfm?id=37422&type=pdf&coll=GUIDE&dl=GUIDE&CFID=15556705&CFTOKEN=70616554 William E. Lorensen and Harvey E. Cline. MARCHING CUBES: A High Resolution 3D Surface Construction Algorithm, Computer Graphics, 1987]]

Slides: [http://www.sci.utah.edu/~cscheid/lectures/090120.pdf PDF File]

Further reading:

[http://www.sci.utah.edu/~csilva/papers/vis2008b.pdf Carlos A. Dietrich et al. Edge Groups: An Approach to Understanding the Mesh Quality of Marching Methods, IEEE TVCG, 2008]

[http://www.cs.sfu.ca/~torsten/Publications/Papers/tvcg06_hamish.pdf Hamish Carr, Torsten Moller, and Jack Snoeyink. Artifacts Caused By Simplicial Subdivision, IEEE TVCG, 2006]

[http://graphics.ethz.ch/teaching/scivis_common/Literature/Newman06.pdf Newman and Yi. A survey of the marching cubes algorithm. Computers and Graphics, 2006]

[http://www.cse.ohio-state.edu/~wenger/publications/isomesh.pdf Raman and Wenger. Quality isosurface Generation Using an Extended Marching Cubes Lookup Table. Eurovis 2008]

[http://www.cs.berkeley.edu/~jrs/papers/elemj.pdf Shewchuk. What Is a Good Linear Finite Element? Interpolation, Conditioning, Anisotropy, and Quality Measures]

[http://portal.acm.org/ft_gateway.cfm?id=566586&type=pdf&coll=GUIDE&dl=GUIDE&CFID=15556907&CFTOKEN=76114820 Tao Ju, Frank Losasso, Scott Schaefer, Joe Warren. Dual Contouring of Hermite Data, SIGGRAPH 2002]

== Surface Generation and/or Extraction II -- Jan 22 ==

Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/Surface_Generation_Extraction2]]

Lecturer: Carlos

Topics:

* Element quality in isosurface extraction
** Finish discussion of SnapMC, Macet, Edge Groups (Tet Stuffing?)
* Feature preservation
** Extended Marching Cubes
* "Adaptive" methods
** Dual Contouring
* Advancing Front Methods
** Afront

Required Reading/Notes:

[http://portal.acm.org/citation.cfm?id=383265 Feature sensitive surface extraction from volume data Feature Sensitive Surface Extraction from Volume Data, SIGGRAPH 2001]

[http://portal.acm.org/ft_gateway.cfm?id=566586&type=pdf&coll=GUIDE&dl=GUIDE&CFID=15556907&CFTOKEN=76114820 Tao Ju, Frank Losasso, Scott Schaefer, Joe Warren. Dual Contouring of Hermite Data, SIGGRAPH 2002]

[http://www.sci.utah.edu/~csilva/papers/tvcg2006acr.pdf John Schreiner, Carlos E. Scheidegger, and Claudio T. Silva. High-Quality Extraction of Isosurfaces from Regular and Irregular Grids, IEEE TVCG, 2006]

Slides:

== Extra Lecture I -- Jan 23 ==

Lecturer: Carlos

Topics: Software libraries for geometry processing

Location: Jones Conference Room. WEB 3840
Time: 3:30PM

This will be a fairly short meeting to help you get acquainted to the software we will be using for the first assignment. You will be using trimesh2, a lightweight c++ library for triangle meshes from Szymon Rusinkiewicz: http://www.cs.princeton.edu/~smr/

it is trivial to compile trimesh2 on Linux and Mac OS X. I have no experience with Windows, but I'll gladly try to help if you bring your laptop to class. if you're an enrolled student, you can get Visual Studio for free [https://software.utah.edu/osl/index.shop here]

''Building on Windows:''

Brad has created two Visual Studio Solution files (2005 & 2008) that students can use if they want (I assume one of the profs will take this down if they don't like it). The files have been tested locally on his machine and at least compile and allow all the utilities (MeshAlign, MeshCat, MeshCC, MeshFilter, MeshMake, MeshShade, MeshView) print out proper command line usage when run with no parameters.

Once you have built the solution you should find a bin and a libs subdirectory that contain Debug and/or Release directories that should contain the binary/library files respectively.

Brad would really rather not troubleshoot these files if you can't get them to work, but thought that perhaps some students might have some use for them anyway.

The files can be found here

* [http://www.cs.utah.edu/~loos/courses/cs6968/trimesh2-2.8-vs2005.zip trimesh2-2.8 VS 2005]
* [http://www.cs.utah.edu/~loos/courses/cs6968/trimesh2-2.8-vs2008.zip trimesh2-2.8 VS 2008]

'''NOTE:''' The programs seem to load and modify meshes all right, although when I use MeshShade to color a model then try to view it in MeshView, the model isn't colored (I don't know if this is a bug or not).

Website with many mesh files: [http://shapes.aim-at-shape.net/index.php Aim@Shape shape repository]

Stanford 3D repository

Bilateral Mesh Denoising. Fleishman, Drori, Cohen-Or. SIGGRAPH 2003. [http://www.sci.utah.edu/~shachar/Publications/bmd03.pdf pdf version of paper]

== Spectral Processing I -- Jan 27 ==

Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/Spectral_Processing1]]

Lecturer: Claudio/Gustavo

Topics:

* Laplacian Mesh Matrix
** Eigenvalues and Eigenvectors/Eigenfunctions
** Geometry and Laplacian Matrix

Required Reading/Notes:

[[http://mesh.caltech.edu/ee148/refs/Taubin-star-eg00.pdf G. Taubin. Geometric Signal Processing on Polygonal Meshes, EUROGRAPHICS ’2000 STAR – State of The Art Report, 2000]]

[[https://guinness.cs.stevens-tech.edu/~quynh/courses/cs638-papers/taubin_surf_fairing.pdf G. Taubin. A signal processing approach to fair surface design, 1995]]

[[http://alice.loria.fr/publications/papers/2008/ManifoldHarmonics/MH-EG.pdf B. Vallet and B. Lévy. Spectral Geometry Processing with Manifold Harmonics, EUROGRAPHICS 2008]]

Slides:

Further reading:

[[http://142.58.111.29/~haoz/pubs/zhang_eg07star_spectral.pdf Hao Zhang Oliver van Kaick Ramsay Dyer. Spectral Methods for Mesh Processing and Analysis, EUROGRAPHICS 2007 STAR – State of The Art Report, 2007]]

== Spectral Processing II -- Jan 29 ==

Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/Spectral_Processing2]]

Lecturer: Claudio/Gustavo

Topics:

* Laplacian Eigenfunctions
** Properties
** Visualization
** Interaction

Required Reading/Notes:

[[http://alice.loria.fr/publications/papers/2006/SMI_Laplacian/SMI_Laplacian.pdf Bruno Levy. Laplace-Beltrami Eigenfunctions Towards an algorithm that “understands” geometry, SMI, 2006]]

[[http://page.mi.fu-berlin.de/wardetzk/pub/laplacian.pdf M. Wardetzky et al. Discrete Laplace Operators: No free lunch, SGP, 2007]]

[[ftp://ftp.gdv.uni-hannover.de/papers/reuter2006-shape_dna.pdf M Reuter et al. Laplace–Beltrami spectra as ‘Shape-DNA’ of surfaces and solids, CAD, 2007]]

Slides:

Further reading:

[[ftp://ftp.gdv.uni-hannover.de/papers/reuter2006-shape_dna.pdf Martin Reuter, Franz-Erich Wolter, Niklas Peinecke. Laplace–Beltrami spectra as ‘Shape-DNA’ of surfaces and solids, Computer-Aided Design, 2006]]

Fan R. K. Chung. Spectral Graph Theory (CBMS Regional Conference Series in Mathematics, No. 92),
American Mathematical Society, 1997

== Spectral Processing III -- Feb 3 ==

Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/Spectral_Processing3]]

Lecturer: Claudio/Gustavo

Topics:

* Spectral Mesh Segmentation

Required Reading/Notes:

[[http://142.58.111.29/~lrong/personal/docs/05_vmv_spectcut.pdf Hao Zhang, Rong Liu. Mesh Segmentation via Recursive and Visually Salient Spectral Cuts, 2005]]

[[http://www.cs.sfu.ca/~haoz/pubs/liu_zhang_eg07.pdf Rong Liu and Hao Zhang. Mesh Segmentation via Spectral Embedding and Contour Analysis, EUROGRAPHICS, 2007]]

[[http://fas.sfu.ca/~haoz/pubs/liu_zhang_pg04.pdf Rong Liu, Hao Zhang. Segmentation of 3D Meshes through Spectral Clustering, 2004]]

Slides:

Further reading:

[[http://www-ee.technion.ac.il/~ayellet/Ps/SMI06.pdf Mesh segmentation – A comparative study, SMI, 2006]]

== Spectral Processing IV -- Feb 5 ==

Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/Spectral_Processing4]]

Lecturer: Claudio/Gustavo

Topics:

* Shape Symmetries
* Spectral Quadrangulation

Required Reading/Notes:

[[http://graphics.stanford.edu/projects/lgl/papers/osg-giss-08/osg-giss-08.pdf Maks Ovsjanikov, Jian Sun, Leonidas Guibas. Global Intrinsic Symmetries of Shapes, SGP, 2008]]

[[http://www.pascucci.org/pdf-papers/SIGGRAPH-06.pdf S. Dong, P.-T. Bremer, M. Garland, V. Pascucci, John C.Hart. Spectral Surface Quadrangulation, SIGGRAPH, 2006]]

[[http://www.graphics.rwth-aachen.de/uploads/media/kobbelt_2008_asia.pdf J. Huang, M. Zhang, J. Ma, X. Liu, L. Kobbelt, H. Bao. Spectral Quadrangulation with Orientation and Alignment Control, SIGGRAPH Asia, 2008]]

Slides:

== Mesh Decimation -- Feb 10 ==

Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/Mesh_Decimation]]

Lecturer: Claudio/Gustavo

Topics:

* Triangular Mesh Simplification

Required Reading/Notes:

[[http://www1.cs.columbia.edu/~cs4162/html05s/garland97.pdf Michael Garland, Paul S. Heckbert, Surface Simpliﬁcation Using Quadric Error Metrics, 1997]]

[[http://vims.cis.udel.edu/~jeab/research/papers/simplification/cignoni97comparison.pdf P. Cignoni, C. Montani, R. Scopigno. A comparison of mesh simplification algorithms, 1997]]

Slides:

Further reading:

[[http://graphics.cs.uiuc.edu/~garland/papers/qtheory.pdf Paul S. Heckbert, Michael Garland. Optimal triangulation and quadric-based surface simpliﬁcation, Computational Geometry, 1999]

== Mesh Smoothing -- Feb 12 ==

Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/Mesh_Smoothing]]

Lecturer: Claudio/Gustavo

Topics:

* Triangular Mesh Smoothing
* Mesh Denoising

Required Reading/Notes:

[[http://geometry.caltech.edu/pubs/JDD03.pdf Thouis R. Jones, Fredo Durand, Mathieu Desbrun. Non-iterative, feature-preserving mesh smoothing,ACM TOG, 2003]]

[[http://www-stat.stanford.edu/~idrori/BMD.pdf Shachar Fleishman, Iddo Drori, Daniel Cohen-Or. Bilateral Mesh Denoising, ACM TOG, 2003]]

[[http://portal.acm.org/citation.cfm?id=218473&dl= G. Taubin. A Signal Processing Approach To Fair Surface Design, 1995]]

Slides:

Further reading:

[[http://www.mpi-sb.mpg.de/~belyaev/papers/ik03bo.ps.gz A comparison of mesh smoothing methods]]

== Remeshing I -- Feb 17 ==

Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/Remeshing1]]

Lecturer: Claudio/Gustavo

Topics:

* Triangular Mesh Improvement

Required Reading/Notes:

[[http://portal.acm.org/citation.cfm?id=882373 V. Surazhsky and C. Gotsman. Explicit surface remeshing. Proceedings of the Symposium on Mesh Processing, 2003]]

Slides:

Further reading:

[[http://www.cs.technion.ac.il/~gotsman/AmendedPubl/Pierre/remeshing_survey.pdf Pierre Alliez, Giuliana Ucelli, Craig Gotsman and Marco Attene. Recent Advances in Remeshing of Surfaces, 2005]]

[[http://www.imr.sandia.gov/papers/imr11/surazhsky.pdf Vitaly Surazhsky, Craig Gotsman. High Quality Compatible Triangulations,11th International Meshing Roundtable, 2002]]

== Remeshing II -- Feb 19 ==

Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/Remeshing2]]

Lecturer: Claudio/Gustavo

Topics:

* Triangular Mesh Improvement

Required Reading/Notes:

[[http://ieeexplore.ieee.org/search/wrapper.jsp?arnumber=1199601 P. Alliez , E. Colin de Verdiere, O. Devillers, and M. Isenburg. Isotropic surface remeshing. In Proceedings of Shape Modeling International, 2003]]

Slides:

Further reading:

[[http://www.imr.sandia.gov/papers/imr11/surazhsky.pdf Vitaly Surazhsky, Craig Gotsman. High Quality Compatible Triangulations,11th International Meshing Roundtable, 2002]]

[[ftp://ftp-sop.inria.fr/prisme/ECG/Reports/Month30/ECG-TR-304100-01.pdf Vitaly Surazhsky, Pierre Alliez, Craig Gotsman. Isotropic Remeshing of Surfaces: a Local Parameterization Approach, ECG Technical Report No. : ECG-TR-304100-01, 2003]]

== Mesh Parameterization I -- Feb 24 ==
Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/Mesh_Parametrization1]]

Lecturer: Claudio/Gustavo

Topics:

* Planar Parametrization

Required Reading/Notes:

[[http://heim.ifi.uio.no/~michaelf/papers/mean_value.pdf M. Floater. Mean value coordinates, Computer Aided Geometric Design, 2003]]

[[http://www.multires.caltech.edu/teaching/courses/cs101.3.spring02/cs101_files/resources/Parameterization/Floater.pdf M. Floater. Parametrization and smooth approximation of surface triangulations, Computer Aided Geometric Design, 1997]]

[[http://jjcao1231.googlepages.com/Intrinsic_Parameterizations_of_Surface_Meshes_02.pdf M Desbrun, M Meyer, P Alliez. Intrinsic Parameterizations of Surface Meshes, CGF, 2002]]

Slides:

Further reading:

[[http://www.cs.jhu.edu/~misha/Fall07/Papers/Tutte63.pdf W.T. Tutte. How to draw a graph,Proc. London Math. Soc, 1963]]

[[http://vcg.isti.cnr.it/Publications/2005/FH05/survey_mingle04.pdf MS Floater, K Hormann. Surface parameterization: a tutorial and survey, 2005]]

[[http://www.cs.ubc.ca/~sheffa/papers/param_survey06.pdf A Sheffer, E Praun, K Rose. Mesh Parameterization Methods and Their Applications, 2006]]

[[https://graphics.stanford.edu/courses/cs468-03-fall/Papers/floater_triangulation.pdf M. Floater, M Reimers. Meshless parameterization and surface reconstruction, Computer Aided Geometric Design, 2001]]

== Mesh Parameterization II -- Feb 26 ==
Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/Mesh_Parametrization2]]

Lecturer: Claudio/Gustavo

Topics:

* Spherical Parametrization

Required Reading/Notes:

[[http://www.cs.sfu.ca/~torsten/GL/PAPERS/sphere2.pdf C. Gotsman, X. Gu, A. Sheffer. Fundamentals of spherical parameterization for 3D meshes, ACM TOG, 2003]]

[[http://kucg.korea.ac.kr/seminar/2003/src/PA-03-19.pdf E Praun, H Hoppe. Spherical parametrization and remeshing, 2003]]

Slides:

== Quad meshing I -- Mar 3 ==
Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/quadmesh1]]

Lecturer: Claudio/Gustavo/Joel

Topics:

Required Reading/Notes:

Slides:

Further reading:

== Quad meshing II -- Mar 5 ==
Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/quadmesh2]]

Lecturer: Claudio/Gustavo/Joel

Topics:

Required Reading/Notes:

Slides:

Further reading:

== Quad meshing III -- Mar 10 ==
Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/quadmesh3]]

Lecturer: Claudio/Gustavo/Joel

Topics:

Required Reading/Notes:

Slides:

Further reading:

== Quad meshing IV -- Mar 12 ==
Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/quadmesh4]]

Lecturer: Claudio/Gustavo/Joel

Topics:

Required Reading/Notes:

Slides:

Further reading:

== Mar 17 (Spring Break) ==
== Mar 19 (Spring Break) ==

== Mesh Compression -- Mar 24 ==
Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/Compression]]

Lecturer: Claudio/Gustavo

Topics:

* Geometrical Mesh Compression
* Spectral Mesh Compression

Required Reading/Notes:

[[http://ieeexplore.ieee.org/search/wrapper.jsp?arnumber=764870 J. Rossignac. Edgebreaker: Connectivity compression for triangle meshes. IEEE Transactions on Visualization and Computer Graphics, 5(1):47–61, January-March 1999]]

[[http://www.mpi-sb.mpg.de/~karni/publications/spectral.pdf Z Karni, C Gotsman. Spectral compression of mesh geometry, 2000]]

Slides:

Further reading:

[[http://portal.acm.org/ft_gateway.cfm?id=274365&type=pdf&coll=GUIDE&dl=GUIDE&CFID=15500980&CFTOKEN=61929152 G Taubin, J Rossignac. Geometric compression through topological surgery - ACM TOG, 1998]]

[[http://www.cs.unc.edu/~isenburg/research/papers/il-sm-05.pdf Martin Isenburg, Peter Lindstrom. Streaming Meshes, Proceedings of Visualization 2005]]

[[http://www.gvu.gatech.edu/%7Ejarek/papers/Compression.pdf Jarek Rossignac. 3D Mesh Compression, Chapter in the Visualization Handbook. Academic Press. Eds. C. Hansen and C. Johnson. 2004]]

[[http://www.cs.northwestern.edu/~pren/paperpool/ig-ooccgpm-03.pdf M Isenburg, S Gumhold. Out-of-core compression for gigantic polygon meshes, SIGGRAPH, 2003]]

== Mesh Editing -- Mar 26 ==
Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/MeshEditing]]

Lecturer: Claudio/Gustavo

Topics:

* Multiresolution approach
* Laplacian Mesh Editing
* Poisson-based mesh editing

Required Reading/Notes:

[[http://www.cs.bell-labs.com/who/wim/papers/sig97.pdf D Zorin, P Schroder, W Sweldens. Interactive multiresolution mesh editing, SIGGRAPH, 2007]]

[[http://research.microsoft.com/asia/dload_files/group/ig/2004/poisson.pdf Y Yu, K Zhou, D Xu, X Shi, H Bao, B Guo, HY Shum. Mesh editing with poisson-based gradient field manipulation, SIGGRAPH, 2004]]

[[http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=1314505&isnumber=29137 Y Lipman, O Sorkine, D Cohen-Or, D Levin, C Rossi, H Seidel. Differential coordinates for interactive mesh editing, Shape Modeling Applications, 2004]]

Slides:

Further reading:

[[http://portal.acm.org/citation.cfm?id=1073204.1073324 A Nealen, O Sorkine, M Alexa, D Cohen-Or. A sketch-based interface for detail-preserving mesh editing, SIGGRAPH, 2005]]

[[http://graphics.stanford.edu/courses/cs468-05-fall/Papers/p479-lipman.pdf Y Lipman, O Sorkine, D Levin, D Cohen-Or. Linear rotation-invariant coordinates for meshes, SIGGRAPH, 2005]]

== Mesh Repair -- Mar 31 ==
Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/MeshRepair]]

Lecturer: Claudio/Gustavo

Topics:

* Repairing Polygonal Soup
* Hole filling
* Surface Completion

Required Reading/Notes:

[[http://portal.acm.org/ft_gateway.cfm?id=1015815&type=pdf&coll=GUIDE&dl=GUIDE&CFID=16049617&CFTOKEN=45512742 T. Ju. Robust repair of polygonal models, SIGGRAPH, 2004]]

[[http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=1024098&isnumber=22019 J Davis, SR Marschner, M Garr, M Levoy. Filling holes in complex surfaces using volumetric diffusion, 2002]]

[[http://portal.acm.org/ft_gateway.cfm?id=1015814&type=pdf&coll=GUIDE&dl=GUIDE&CFID=16050250&CFTOKEN=44199354 A Sharf, M Alexa, D Cohen-Or. Context-based surface completion, SIGGRAPH, 2004]]

Slides:

Further reading:

[[http://www.cs.ubc.ca/labs/imager/tr/2005/Vlad_MCompletion/sgp05.pdf V Kraevoy, A Sheffer. Template-based mesh completion, SGP, 2005]]

[[http://graphics.stanford.edu/courses/cs468-05-fall/Papers/p896-shen.pdf C Shen, JF O'Brien, JR Shewchuk. Interpolating and approximating implicit surfaces from polygon soup, SIGGRAPH, 2004]]

== Discrete Exterior Calculus I -- Apr 2 ==
Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/DEC1]]

Lecturer: Claudio/Gustavo

Topics:

* Differential Forms in Euclidean Spaces
* Manifolds and Tangent Space
* Differential Forms on Manifolds

Required Reading/Notes:

* Loring W. Tu. An Introduction to Manifolds, Springer, 2008.

Slides:

Further reading:

* D. Bachman. A geometric Approach to Differential Forms, Birkhauser, 2006.

== Discrete Exterior Calculus II -- Apr 7 ==
Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/DEC2]]

Lecturer: Claudio/Gustavo

Topics:

* Discrete Differential Geometry
* Discrete Differential Forms

Required Reading/Notes:

[[http://etd.caltech.edu/etd/available/etd-05202003-095403/unrestricted/thesis_hirani.pdf A. Hirani. Discrete Exterior Calculus, 2003]]

[[http://www.multires.caltech.edu/pubs/diffGeoOps.pdf Mark Meyer, Mathieu Desbrun, Peter Schröder, Alan H. Barr. Discrete Differential-Geometry Operators for Triangulated 2-Manifolds]]

[[http://mesh.brown.edu/taubin/pdfs/taubin-iccv95b.pdf Gabriel Taubin. Estimating the Tensor of Curvature of a Surface from a Polyhedral Approximation, 1995]]

[[http://portal.acm.org/ft_gateway.cfm?id=1198662&type=pdf&coll=GUIDE&dl=GUIDE&CFID=15587878&CFTOKEN=77328344 John M. Sullivan. Curvature Measures for Discrete Surfaces, SIGGRAPH, 2005]]

Slides:

== Point-Set Surfaces I -- Apr 9 ==
Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/PSS1]]

Lecturer: Claudio/Gustavo/Carlos

Topics:

Required Reading/Notes:

Slides:

Further reading:

== Point-Set Surfaces II -- Apr 14 ==
Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/PSS2]]

Lecturer: Claudio/Gustavo/Carlos

Topics:

Required Reading/Notes:

Slides:

Further reading:

== Point-Set Surfaces III -- Apr 16 ==
Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/PSS3]]

Lecturer: Claudio/Gustavo/Carlos

Topics:

Required Reading/Notes:

Slides:

Further reading:

== Point-Set Surfaces IV -- Apr 21 ==
Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/PSS4]]

Lecturer: Claudio/Gustavo/Carlos

Topics:

Required Reading/Notes:

Slides:

Further reading:

== Project Presentation -- Apr 23 ==
== Project Presentation -- Apr 28 ==

GeometryProcessing/Spring2009/Schedule/Spectral Processing2

2009-01-29T18:18:01Z

Loos: New page: * Brad I found a link to the [http://books.google.com/books?id=YUc38_MCuhAC&dq=Spectral+Graph+Theory&printsec=frontcover&source=bn&hl=en&sa=X&oi=book_result&resnum=4&ct=result#PPP1,M1 Spe...

* Brad

I found a link to the [http://books.google.com/books?id=YUc38_MCuhAC&dq=Spectral+Graph+Theory&printsec=frontcover&source=bn&hl=en&sa=X&oi=book_result&resnum=4&ct=result#PPP1,M1 Spectral Graph Theory] reading but it's 230 pages long. Is it really necessary to read it?

GeometryProcessing/Spring2009/Schedule

2009-01-28T08:42:31Z

Loos: /* Extra Lecture I -- Jan 23 */

== Introduction to Geometry Processing -- Jan 13 ==

Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/Introduction_to_Geometry_Processing]]

Lecturer: Gustavo

Topics: Course Overview

Slides: [http://www.vistrails.org/images/Introduction.pdf Introduction.pdf]

== Surface Representations -- Jan 15 ==

Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/Surface_Representations]]

Lecturer: Gustavo

Topics:

* Implicit and Parametric Surfaces
* Representing/Manipulating Implicit Surfaces - CAGD
* Representing/Manipulating Parametric Surfaces - Splines
* Piecewise Linear Approximations - Topological Data Structures

Required Reading/Notes:

[GM], Chapters 2 and 3.

Slides:

Animations:

Further reading:

Martti Mäntylä. An Introduction to Solid Modeling. Computer Science Press, College Park, MD, 1988.

[http://www.gvu.gatech.edu/~jarek/papers/CornerTable.pdf Edgebreaker on a Corner Table: A Simple Technique for Representing and Compressing Triangulated Surfaces]

[http://cg.www.techfak.uni-bielefeld.de/publications/papers/openmesh.pdf OpenMesh – a generic and efﬁcient polygon mesh data structure]

[http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4055948 Edge-Based Data Structures for Solid Modeling in Curved-Surface Environments]

== Surface Generation and/or Extraction I -- Jan 20 ==

Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/Surface_Generation_Extraction1]]

Lecturer: Carlos

Topics:

* Capturing Methods
** Marching Cubes/Tetrahedra
** Dual Contouring

Required Reading/Notes:

[[http://portal.acm.org/ft_gateway.cfm?id=37422&type=pdf&coll=GUIDE&dl=GUIDE&CFID=15556705&CFTOKEN=70616554 William E. Lorensen and Harvey E. Cline. MARCHING CUBES: A High Resolution 3D Surface Construction Algorithm, Computer Graphics, 1987]]

Slides: [http://www.sci.utah.edu/~cscheid/lectures/090120.pdf PDF File]

Further reading:

[http://www.sci.utah.edu/~csilva/papers/vis2008b.pdf Carlos A. Dietrich et al. Edge Groups: An Approach to Understanding the Mesh Quality of Marching Methods, IEEE TVCG, 2008]

[http://www.cs.sfu.ca/~torsten/Publications/Papers/tvcg06_hamish.pdf Hamish Carr, Torsten Moller, and Jack Snoeyink. Artifacts Caused By Simplicial Subdivision, IEEE TVCG, 2006]

[http://graphics.ethz.ch/teaching/scivis_common/Literature/Newman06.pdf Newman and Yi. A survey of the marching cubes algorithm. Computers and Graphics, 2006]

[http://www.cse.ohio-state.edu/~wenger/publications/isomesh.pdf Raman and Wenger. Quality isosurface Generation Using an Extended Marching Cubes Lookup Table. Eurovis 2008]

[http://www.cs.berkeley.edu/~jrs/papers/elemj.pdf Shewchuk. What Is a Good Linear Finite Element? Interpolation, Conditioning, Anisotropy, and Quality Measures]

[http://portal.acm.org/ft_gateway.cfm?id=566586&type=pdf&coll=GUIDE&dl=GUIDE&CFID=15556907&CFTOKEN=76114820 Tao Ju, Frank Losasso, Scott Schaefer, Joe Warren. Dual Contouring of Hermite Data, SIGGRAPH 2002]

== Surface Generation and/or Extraction II -- Jan 22 ==

Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/Surface_Generation_Extraction2]]

Lecturer: Carlos

Topics:

* Element quality in isosurface extraction
** Finish discussion of SnapMC, Macet, Edge Groups (Tet Stuffing?)
* Feature preservation
** Extended Marching Cubes
* "Adaptive" methods
** Dual Contouring
* Advancing Front Methods
** Afront

Required Reading/Notes:

[http://portal.acm.org/citation.cfm?id=383265 Feature sensitive surface extraction from volume data Feature Sensitive Surface Extraction from Volume Data, SIGGRAPH 2001]

[http://portal.acm.org/ft_gateway.cfm?id=566586&type=pdf&coll=GUIDE&dl=GUIDE&CFID=15556907&CFTOKEN=76114820 Tao Ju, Frank Losasso, Scott Schaefer, Joe Warren. Dual Contouring of Hermite Data, SIGGRAPH 2002]

[http://www.sci.utah.edu/~csilva/papers/tvcg2006acr.pdf John Schreiner, Carlos E. Scheidegger, and Claudio T. Silva. High-Quality Extraction of Isosurfaces from Regular and Irregular Grids, IEEE TVCG, 2006]

Slides:

== Extra Lecture I -- Jan 23 ==

Lecturer: Carlos

Topics: Software libraries for geometry processing

Location: Jones Conference Room. WEB 3840
Time: 3:30PM

This will be a fairly short meeting to help you get acquainted to the software we will be using for the first assignment. You will be using trimesh2, a lightweight c++ library for triangle meshes from Szymon Rusinkiewicz: http://www.cs.princeton.edu/~smr/

it is trivial to compile trimesh2 on Linux and Mac OS X. I have no experience with Windows, but I'll gladly try to help if you bring your laptop to class. if you're an enrolled student, you can get Visual Studio for free [https://software.utah.edu/osl/index.shop here]

''Building on Windows:''

Brad has created two Visual Studio Solution files (2005 & 2008) that students can use if they want (I assume one of the profs will take this down if they don't like it). The files have been tested locally on his machine and at least compile and allow all the utilities (MeshAlign, MeshCat, MeshCC, MeshFilter, MeshMake, MeshShade, MeshView) print out proper command line usage when run with no parameters.

Once you have built the solution you should find a bin and a libs subdirectory that contain Debug and/or Release directories that should contain the binary/library files respectively.

Brad would really rather not troubleshoot these files if you can't get them to work, but thought that perhaps some students might have some use for them anyway.

The files can be found here

* [http://www.cs.utah.edu/~loos/courses/cs6968/trimesh2-2.8-vs2005.zip trimesh2-2.8 VS 2005]
* [http://www.cs.utah.edu/~loos/courses/cs6968/trimesh2-2.8-vs2008.zip trimesh2-2.8 VS 2008]

'''NOTE:''' As I wasn't able to make it to the extra lecture, perhaps one of the profs can give me some examples to try, so I can find out if these programs really work. There were a lot of double->float conversion warnings that make me worry a bit. Also, I wouldn't send this code outside this class as I copied a getopt implementation from somewhere off the net (I don't remember where anymore).

Website with many mesh files: [http://shapes.aim-at-shape.net/index.php Aim@Shape shape repository]

Stanford 3D repository

Bilateral Mesh Denoising. Fleishman, Drori, Cohen-Or. SIGGRAPH 2003. [http://www.sci.utah.edu/~shachar/Publications/bmd03.pdf pdf version of paper]

== Spectral Processing I -- Jan 27 ==

Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/Spectral_Processing1]]

Lecturer: Claudio/Gustavo

Topics:

* Laplacian Mesh Matrix
** Eigenvalues and Eigenvectors/Eigenfunctions
** Geometry and Laplacian Matrix

Required Reading/Notes:

[[http://mesh.caltech.edu/ee148/refs/Taubin-star-eg00.pdf G. Taubin. Geometric Signal Processing on Polygonal Meshes, EUROGRAPHICS ’2000 STAR – State of The Art Report, 2000]]

[[https://guinness.cs.stevens-tech.edu/~quynh/courses/cs638-papers/taubin_surf_fairing.pdf G. Taubin. A signal processing approach to fair surface design, 1995]]

[[http://alice.loria.fr/publications/papers/2008/ManifoldHarmonics/MH-EG.pdf B. Vallet and B. Lévy. Spectral Geometry Processing with Manifold Harmonics, EUROGRAPHICS 2008]]

Slides:

Further reading:

[[http://142.58.111.29/~haoz/pubs/zhang_eg07star_spectral.pdf Hao Zhang Oliver van Kaick Ramsay Dyer. Spectral Methods for Mesh Processing and Analysis, EUROGRAPHICS 2007 STAR – State of The Art Report, 2007]]

== Spectral Processing II -- Jan 29 ==

Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/Spectral_Processing2]]

Lecturer: Claudio/Gustavo

Topics:

* Laplacian Eigenfunctions
** Properties
** Visualization
** Interaction

Required Reading/Notes:

[[http://alice.loria.fr/publications/papers/2006/SMI_Laplacian/SMI_Laplacian.pdf Bruno Levy. Laplace-Beltrami Eigenfunctions Towards an algorithm that “understands” geometry, SMI, 2006]]

Fan R. K. Chung. Spectral Graph Theory (CBMS Regional Conference Series in Mathematics, No. 92),
American Mathematical Society, 1997

Slides:

Further reading:

[[ftp://ftp.gdv.uni-hannover.de/papers/reuter2006-shape_dna.pdf Martin Reuter, Franz-Erich Wolter, Niklas Peinecke. Laplace–Beltrami spectra as ‘Shape-DNA’ of surfaces and solids, Computer-Aided Design, 2006]]

== Spectral Processing III -- Feb 3 ==

Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/Spectral_Processing3]]

Lecturer: Claudio/Gustavo

Topics:

* Spectral Mesh Segmentation

Required Reading/Notes:

[[http://142.58.111.29/~lrong/personal/docs/05_vmv_spectcut.pdf Hao Zhang, Rong Liu. Mesh Segmentation via Recursive and Visually Salient Spectral Cuts, 2005]]

[[http://www.cs.sfu.ca/~haoz/pubs/liu_zhang_eg07.pdf Rong Liu and Hao Zhang. Mesh Segmentation via Spectral Embedding and Contour Analysis, EUROGRAPHICS, 2007]]

[[http://fas.sfu.ca/~haoz/pubs/liu_zhang_pg04.pdf Rong Liu, Hao Zhang. Segmentation of 3D Meshes through Spectral Clustering, 2004]]

Slides:

Further reading:

[[http://www-ee.technion.ac.il/~ayellet/Ps/SMI06.pdf Mesh segmentation – A comparative study, SMI, 2006]]

== Spectral Processing IV -- Feb 5 ==

Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/Spectral_Processing4]]

Lecturer: Claudio/Gustavo

Topics:

* Shape Symmetries
* Spectral Quadrangulation

Required Reading/Notes:

[[http://graphics.stanford.edu/projects/lgl/papers/osg-giss-08/osg-giss-08.pdf Maks Ovsjanikov, Jian Sun, Leonidas Guibas. Global Intrinsic Symmetries of Shapes, SGP, 2008]]

[[http://www.pascucci.org/pdf-papers/SIGGRAPH-06.pdf S. Dong, P.-T. Bremer, M. Garland, V. Pascucci, John C.Hart. Spectral Surface Quadrangulation, SIGGRAPH, 2006]]

[[http://www.graphics.rwth-aachen.de/uploads/media/kobbelt_2008_asia.pdf J. Huang, M. Zhang, J. Ma, X. Liu, L. Kobbelt, H. Bao. Spectral Quadrangulation with Orientation and Alignment Control, SIGGRAPH Asia, 2008]]

Slides:

== Mesh Decimation -- Feb 10 ==

Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/Mesh_Decimation]]

Lecturer: Claudio/Gustavo

Topics:

* Triangular Mesh Simplification

Required Reading/Notes:

[[http://www1.cs.columbia.edu/~cs4162/html05s/garland97.pdf Michael Garland, Paul S. Heckbert, Surface Simpliﬁcation Using Quadric Error Metrics, 1997]]

[[http://vims.cis.udel.edu/~jeab/research/papers/simplification/cignoni97comparison.pdf P. Cignoni, C. Montani, R. Scopigno. A comparison of mesh simplification algorithms, 1997]]

Slides:

Further reading:

[[http://graphics.cs.uiuc.edu/~garland/papers/qtheory.pdf Paul S. Heckbert, Michael Garland. Optimal triangulation and quadric-based surface simpliﬁcation, Computational Geometry, 1999]

== Mesh Smoothing -- Feb 12 ==

Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/Mesh_Smoothing]]

Lecturer: Claudio/Gustavo

Topics:

* Triangular Mesh Smoothing
* Mesh Denoising

Required Reading/Notes:

[[http://geometry.caltech.edu/pubs/JDD03.pdf Thouis R. Jones, Fredo Durand, Mathieu Desbrun. Non-iterative, feature-preserving mesh smoothing,ACM TOG, 2003]]

[[http://www-stat.stanford.edu/~idrori/BMD.pdf Shachar Fleishman, Iddo Drori, Daniel Cohen-Or. Bilateral Mesh Denoising, ACM TOG, 2003]]

[[http://portal.acm.org/citation.cfm?id=218473&dl= G. Taubin. A Signal Processing Approach To Fair Surface Design, 1995]]

Slides:

Further reading:

[[http://www.mpi-sb.mpg.de/~belyaev/papers/ik03bo.ps.gz A comparison of mesh smoothing methods]]

== Remeshing I -- Feb 17 ==

Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/Remeshing1]]

Lecturer: Claudio/Gustavo

Topics:

* Triangular Mesh Improvement

Required Reading/Notes:

[[http://portal.acm.org/citation.cfm?id=882373 V. Surazhsky and C. Gotsman. Explicit surface remeshing. Proceedings of the Symposium on Mesh Processing, 2003]]

Slides:

Further reading:

[[http://www.cs.technion.ac.il/~gotsman/AmendedPubl/Pierre/remeshing_survey.pdf Pierre Alliez, Giuliana Ucelli, Craig Gotsman and Marco Attene. Recent Advances in Remeshing of Surfaces, 2005]]

[[http://www.imr.sandia.gov/papers/imr11/surazhsky.pdf Vitaly Surazhsky, Craig Gotsman. High Quality Compatible Triangulations,11th International Meshing Roundtable, 2002]]

== Remeshing II -- Feb 19 ==

Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/Remeshing2]]

Lecturer: Claudio/Gustavo

Topics:

* Triangular Mesh Improvement

Required Reading/Notes:

[[http://ieeexplore.ieee.org/search/wrapper.jsp?arnumber=1199601 P. Alliez , E. Colin de Verdiere, O. Devillers, and M. Isenburg. Isotropic surface remeshing. In Proceedings of Shape Modeling International, 2003]]

Slides:

Further reading:

[[http://www.imr.sandia.gov/papers/imr11/surazhsky.pdf Vitaly Surazhsky, Craig Gotsman. High Quality Compatible Triangulations,11th International Meshing Roundtable, 2002]]

[[ftp://ftp-sop.inria.fr/prisme/ECG/Reports/Month30/ECG-TR-304100-01.pdf Vitaly Surazhsky, Pierre Alliez, Craig Gotsman. Isotropic Remeshing of Surfaces: a Local Parameterization Approach, ECG Technical Report No. : ECG-TR-304100-01, 2003]]

== Mesh Parameterization I -- Feb 24 ==
Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/Mesh_Parametrization1]]

Lecturer: Claudio/Gustavo

Topics:

* Planar Parametrization

Required Reading/Notes:

[[http://heim.ifi.uio.no/~michaelf/papers/mean_value.pdf M. Floater. Mean value coordinates, Computer Aided Geometric Design, 2003]]

[[http://www.multires.caltech.edu/teaching/courses/cs101.3.spring02/cs101_files/resources/Parameterization/Floater.pdf M. Floater. Parametrization and smooth approximation of surface triangulations, Computer Aided Geometric Design, 1997]]

[[http://jjcao1231.googlepages.com/Intrinsic_Parameterizations_of_Surface_Meshes_02.pdf M Desbrun, M Meyer, P Alliez. Intrinsic Parameterizations of Surface Meshes, CGF, 2002]]

Slides:

Further reading:

[[http://www.cs.jhu.edu/~misha/Fall07/Papers/Tutte63.pdf W.T. Tutte. How to draw a graph,Proc. London Math. Soc, 1963]]

[[http://vcg.isti.cnr.it/Publications/2005/FH05/survey_mingle04.pdf MS Floater, K Hormann. Surface parameterization: a tutorial and survey, 2005]]

[[http://www.cs.ubc.ca/~sheffa/papers/param_survey06.pdf A Sheffer, E Praun, K Rose. Mesh Parameterization Methods and Their Applications, 2006]]

[[https://graphics.stanford.edu/courses/cs468-03-fall/Papers/floater_triangulation.pdf M. Floater, M Reimers. Meshless parameterization and surface reconstruction, Computer Aided Geometric Design, 2001]]

== Mesh Parameterization II -- Feb 26 ==
Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/Mesh_Parametrization2]]

Lecturer: Claudio/Gustavo

Topics:

* Spherical Parametrization

Required Reading/Notes:

[[http://www.cs.sfu.ca/~torsten/GL/PAPERS/sphere2.pdf C. Gotsman, X. Gu, A. Sheffer. Fundamentals of spherical parameterization for 3D meshes, ACM TOG, 2003]]

[[http://kucg.korea.ac.kr/seminar/2003/src/PA-03-19.pdf E Praun, H Hoppe. Spherical parametrization and remeshing, 2003]]

Slides:

== Quad meshing I -- Mar 3 ==
Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/quadmesh1]]

Lecturer: Claudio/Gustavo/Joel

Topics:

Required Reading/Notes:

Slides:

Further reading:

== Quad meshing II -- Mar 5 ==
Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/quadmesh2]]

Lecturer: Claudio/Gustavo/Joel

Topics:

Required Reading/Notes:

Slides:

Further reading:

== Quad meshing III -- Mar 10 ==
Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/quadmesh3]]

Lecturer: Claudio/Gustavo/Joel

Topics:

Required Reading/Notes:

Slides:

Further reading:

== Quad meshing IV -- Mar 12 ==
Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/quadmesh4]]

Lecturer: Claudio/Gustavo/Joel

Topics:

Required Reading/Notes:

Slides:

Further reading:

== Mar 17 (Spring Break) ==
== Mar 19 (Spring Break) ==

== Mesh Compression -- Mar 24 ==
Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/Compression]]

Lecturer: Claudio/Gustavo

Topics:

* Geometrical Mesh Compression
* Spectral Mesh Compression

Required Reading/Notes:

[[http://ieeexplore.ieee.org/search/wrapper.jsp?arnumber=764870 J. Rossignac. Edgebreaker: Connectivity compression for triangle meshes. IEEE Transactions on Visualization and Computer Graphics, 5(1):47–61, January-March 1999]]

[[http://www.mpi-sb.mpg.de/~karni/publications/spectral.pdf Z Karni, C Gotsman. Spectral compression of mesh geometry, 2000]]

Slides:

Further reading:

[[http://portal.acm.org/ft_gateway.cfm?id=274365&type=pdf&coll=GUIDE&dl=GUIDE&CFID=15500980&CFTOKEN=61929152 G Taubin, J Rossignac. Geometric compression through topological surgery - ACM TOG, 1998]]

[[http://www.cs.unc.edu/~isenburg/research/papers/il-sm-05.pdf Martin Isenburg, Peter Lindstrom. Streaming Meshes, Proceedings of Visualization 2005]]

[[http://www.gvu.gatech.edu/%7Ejarek/papers/Compression.pdf Jarek Rossignac. 3D Mesh Compression, Chapter in the Visualization Handbook. Academic Press. Eds. C. Hansen and C. Johnson. 2004]]

[[http://www.cs.northwestern.edu/~pren/paperpool/ig-ooccgpm-03.pdf M Isenburg, S Gumhold. Out-of-core compression for gigantic polygon meshes, SIGGRAPH, 2003]]

== Mesh Editing -- Mar 26 ==
Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/MeshEditing]]

Lecturer: Claudio/Gustavo

Topics:

* Multiresolution approach
* Laplacian Mesh Editing
* Poisson-based mesh editing

Required Reading/Notes:

[[http://www.cs.bell-labs.com/who/wim/papers/sig97.pdf D Zorin, P Schroder, W Sweldens. Interactive multiresolution mesh editing, SIGGRAPH, 2007]]

[[http://research.microsoft.com/asia/dload_files/group/ig/2004/poisson.pdf Y Yu, K Zhou, D Xu, X Shi, H Bao, B Guo, HY Shum. Mesh editing with poisson-based gradient field manipulation, SIGGRAPH, 2004]]

[[http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=1314505&isnumber=29137 Y Lipman, O Sorkine, D Cohen-Or, D Levin, C Rossi, H Seidel. Differential coordinates for interactive mesh editing, Shape Modeling Applications, 2004]]

Slides:

Further reading:

[[http://portal.acm.org/citation.cfm?id=1073204.1073324 A Nealen, O Sorkine, M Alexa, D Cohen-Or. A sketch-based interface for detail-preserving mesh editing, SIGGRAPH, 2005]]

[[http://graphics.stanford.edu/courses/cs468-05-fall/Papers/p479-lipman.pdf Y Lipman, O Sorkine, D Levin, D Cohen-Or. Linear rotation-invariant coordinates for meshes, SIGGRAPH, 2005]]

== Mesh Repair -- Mar 31 ==
Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/MeshRepair]]

Lecturer: Claudio/Gustavo

Topics:

* Repairing Polygonal Soup
* Hole filling
* Surface Completion

Required Reading/Notes:

[[http://portal.acm.org/ft_gateway.cfm?id=1015815&type=pdf&coll=GUIDE&dl=GUIDE&CFID=16049617&CFTOKEN=45512742 T. Ju. Robust repair of polygonal models, SIGGRAPH, 2004]]

[[http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=1024098&isnumber=22019 J Davis, SR Marschner, M Garr, M Levoy. Filling holes in complex surfaces using volumetric diffusion, 2002]]

[[http://portal.acm.org/ft_gateway.cfm?id=1015814&type=pdf&coll=GUIDE&dl=GUIDE&CFID=16050250&CFTOKEN=44199354 A Sharf, M Alexa, D Cohen-Or. Context-based surface completion, SIGGRAPH, 2004]]

Slides:

Further reading:

[[http://www.cs.ubc.ca/labs/imager/tr/2005/Vlad_MCompletion/sgp05.pdf V Kraevoy, A Sheffer. Template-based mesh completion, SGP, 2005]]

[[http://graphics.stanford.edu/courses/cs468-05-fall/Papers/p896-shen.pdf C Shen, JF O'Brien, JR Shewchuk. Interpolating and approximating implicit surfaces from polygon soup, SIGGRAPH, 2004]]

== Discrete Exterior Calculus I -- Apr 2 ==
Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/DEC1]]

Lecturer: Claudio/Gustavo

Topics:

* Differential Forms in Euclidean Spaces
* Manifolds and Tangent Space
* Differential Forms on Manifolds

Required Reading/Notes:

* Loring W. Tu. An Introduction to Manifolds, Springer, 2008.

Slides:

Further reading:

* D. Bachman. A geometric Approach to Differential Forms, Birkhauser, 2006.

== Discrete Exterior Calculus II -- Apr 7 ==
Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/DEC2]]

Lecturer: Claudio/Gustavo

Topics:

* Discrete Differential Geometry
* Discrete Differential Forms

Required Reading/Notes:

[[http://etd.caltech.edu/etd/available/etd-05202003-095403/unrestricted/thesis_hirani.pdf A. Hirani. Discrete Exterior Calculus, 2003]]

[[http://www.multires.caltech.edu/pubs/diffGeoOps.pdf Mark Meyer, Mathieu Desbrun, Peter Schröder, Alan H. Barr. Discrete Differential-Geometry Operators for Triangulated 2-Manifolds]]

[[http://mesh.brown.edu/taubin/pdfs/taubin-iccv95b.pdf Gabriel Taubin. Estimating the Tensor of Curvature of a Surface from a Polyhedral Approximation, 1995]]

[[http://portal.acm.org/ft_gateway.cfm?id=1198662&type=pdf&coll=GUIDE&dl=GUIDE&CFID=15587878&CFTOKEN=77328344 John M. Sullivan. Curvature Measures for Discrete Surfaces, SIGGRAPH, 2005]]

Slides:

== Point-Set Surfaces I -- Apr 9 ==
Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/PSS1]]

Lecturer: Claudio/Gustavo/Carlos

Topics:

Required Reading/Notes:

Slides:

Further reading:

== Point-Set Surfaces II -- Apr 14 ==
Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/PSS2]]

Lecturer: Claudio/Gustavo/Carlos

Topics:

Required Reading/Notes:

Slides:

Further reading:

== Point-Set Surfaces III -- Apr 16 ==
Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/PSS3]]

Lecturer: Claudio/Gustavo/Carlos

Topics:

Required Reading/Notes:

Slides:

Further reading:

== Point-Set Surfaces IV -- Apr 21 ==
Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/PSS4]]

Lecturer: Claudio/Gustavo/Carlos

Topics:

Required Reading/Notes:

Slides:

Further reading:

== Project Presentation -- Apr 23 ==
== Project Presentation -- Apr 28 ==

GeometryProcessing/Spring2009/Schedule

2009-01-28T08:41:58Z

Loos: /* Extra Lecture I -- Jan 23 */

== Introduction to Geometry Processing -- Jan 13 ==

Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/Introduction_to_Geometry_Processing]]

Lecturer: Gustavo

Topics: Course Overview

Slides: [http://www.vistrails.org/images/Introduction.pdf Introduction.pdf]

== Surface Representations -- Jan 15 ==

Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/Surface_Representations]]

Lecturer: Gustavo

Topics:

* Implicit and Parametric Surfaces
* Representing/Manipulating Implicit Surfaces - CAGD
* Representing/Manipulating Parametric Surfaces - Splines
* Piecewise Linear Approximations - Topological Data Structures

Required Reading/Notes:

[GM], Chapters 2 and 3.

Slides:

Animations:

Further reading:

Martti Mäntylä. An Introduction to Solid Modeling. Computer Science Press, College Park, MD, 1988.

[http://www.gvu.gatech.edu/~jarek/papers/CornerTable.pdf Edgebreaker on a Corner Table: A Simple Technique for Representing and Compressing Triangulated Surfaces]

[http://cg.www.techfak.uni-bielefeld.de/publications/papers/openmesh.pdf OpenMesh – a generic and efﬁcient polygon mesh data structure]

[http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4055948 Edge-Based Data Structures for Solid Modeling in Curved-Surface Environments]

== Surface Generation and/or Extraction I -- Jan 20 ==

Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/Surface_Generation_Extraction1]]

Lecturer: Carlos

Topics:

* Capturing Methods
** Marching Cubes/Tetrahedra
** Dual Contouring

Required Reading/Notes:

[[http://portal.acm.org/ft_gateway.cfm?id=37422&type=pdf&coll=GUIDE&dl=GUIDE&CFID=15556705&CFTOKEN=70616554 William E. Lorensen and Harvey E. Cline. MARCHING CUBES: A High Resolution 3D Surface Construction Algorithm, Computer Graphics, 1987]]

Slides: [http://www.sci.utah.edu/~cscheid/lectures/090120.pdf PDF File]

Further reading:

[http://www.sci.utah.edu/~csilva/papers/vis2008b.pdf Carlos A. Dietrich et al. Edge Groups: An Approach to Understanding the Mesh Quality of Marching Methods, IEEE TVCG, 2008]

[http://www.cs.sfu.ca/~torsten/Publications/Papers/tvcg06_hamish.pdf Hamish Carr, Torsten Moller, and Jack Snoeyink. Artifacts Caused By Simplicial Subdivision, IEEE TVCG, 2006]

[http://graphics.ethz.ch/teaching/scivis_common/Literature/Newman06.pdf Newman and Yi. A survey of the marching cubes algorithm. Computers and Graphics, 2006]

[http://www.cse.ohio-state.edu/~wenger/publications/isomesh.pdf Raman and Wenger. Quality isosurface Generation Using an Extended Marching Cubes Lookup Table. Eurovis 2008]

[http://www.cs.berkeley.edu/~jrs/papers/elemj.pdf Shewchuk. What Is a Good Linear Finite Element? Interpolation, Conditioning, Anisotropy, and Quality Measures]

[http://portal.acm.org/ft_gateway.cfm?id=566586&type=pdf&coll=GUIDE&dl=GUIDE&CFID=15556907&CFTOKEN=76114820 Tao Ju, Frank Losasso, Scott Schaefer, Joe Warren. Dual Contouring of Hermite Data, SIGGRAPH 2002]

== Surface Generation and/or Extraction II -- Jan 22 ==

Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/Surface_Generation_Extraction2]]

Lecturer: Carlos

Topics:

* Element quality in isosurface extraction
** Finish discussion of SnapMC, Macet, Edge Groups (Tet Stuffing?)
* Feature preservation
** Extended Marching Cubes
* "Adaptive" methods
** Dual Contouring
* Advancing Front Methods
** Afront

Required Reading/Notes:

[http://portal.acm.org/citation.cfm?id=383265 Feature sensitive surface extraction from volume data Feature Sensitive Surface Extraction from Volume Data, SIGGRAPH 2001]

[http://portal.acm.org/ft_gateway.cfm?id=566586&type=pdf&coll=GUIDE&dl=GUIDE&CFID=15556907&CFTOKEN=76114820 Tao Ju, Frank Losasso, Scott Schaefer, Joe Warren. Dual Contouring of Hermite Data, SIGGRAPH 2002]

[http://www.sci.utah.edu/~csilva/papers/tvcg2006acr.pdf John Schreiner, Carlos E. Scheidegger, and Claudio T. Silva. High-Quality Extraction of Isosurfaces from Regular and Irregular Grids, IEEE TVCG, 2006]

Slides:

== Extra Lecture I -- Jan 23 ==

Lecturer: Carlos

Topics: Software libraries for geometry processing

Location: Jones Conference Room. WEB 3840
Time: 3:30PM

This will be a fairly short meeting to help you get acquainted to the software we will be using for the first assignment. You will be using trimesh2, a lightweight c++ library for triangle meshes from Szymon Rusinkiewicz: http://www.cs.princeton.edu/~smr/

it is trivial to compile trimesh2 on Linux and Mac OS X. I have no experience with Windows, but I'll gladly try to help if you bring your laptop to class. if you're an enrolled student, you can get Visual Studio for free [https://software.utah.edu/osl/index.shop here]

''Building on Windows:''

Brad has created two Visual Studio Solution files (2005 & 2008) that students can use if they want (I assume one of the profs will take this down if they don't like it). The files have been tested locally on his machine and at least compile and allow all the utilities (MeshAlign, MeshCat, MeshCC, MeshFilter, MeshMake, MeshShade, MeshView) print out proper command line usage when run with no parameters.

Once you have built the solution you should find a bin and a libs subdirectory that contain Debug and/or Release directories that should contain the binary/library files respectively.

Brad would really rather not troubleshoot these files if you can't get them to work, but thought that perhaps some students might have some use for them anyway.

The files can be found here

* [http://www.cs.utah.edu/~loos/courses/cs6968/trimesh2-2.8-vs2005.zip VS 2005]
* [http://www.cs.utah.edu/~loos/courses/cs6968/trimesh2-2.8-vs2008.zip VS 2008]

'''NOTE:''' As I wasn't able to make it to the extra lecture, perhaps one of the profs can give me some examples to try, so I can find out if these programs really work. There were a lot of double->float conversion warnings that make me worry a bit. Also, I wouldn't send this code outside this class as I copied a getopt implementation from somewhere off the net (I don't remember where anymore).

Website with many mesh files: [http://shapes.aim-at-shape.net/index.php Aim@Shape shape repository]

Stanford 3D repository

Bilateral Mesh Denoising. Fleishman, Drori, Cohen-Or. SIGGRAPH 2003. [http://www.sci.utah.edu/~shachar/Publications/bmd03.pdf pdf version of paper]

== Spectral Processing I -- Jan 27 ==

Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/Spectral_Processing1]]

Lecturer: Claudio/Gustavo

Topics:

* Laplacian Mesh Matrix
** Eigenvalues and Eigenvectors/Eigenfunctions
** Geometry and Laplacian Matrix

Required Reading/Notes:

[[http://mesh.caltech.edu/ee148/refs/Taubin-star-eg00.pdf G. Taubin. Geometric Signal Processing on Polygonal Meshes, EUROGRAPHICS ’2000 STAR – State of The Art Report, 2000]]

[[https://guinness.cs.stevens-tech.edu/~quynh/courses/cs638-papers/taubin_surf_fairing.pdf G. Taubin. A signal processing approach to fair surface design, 1995]]

[[http://alice.loria.fr/publications/papers/2008/ManifoldHarmonics/MH-EG.pdf B. Vallet and B. Lévy. Spectral Geometry Processing with Manifold Harmonics, EUROGRAPHICS 2008]]

Slides:

Further reading:

[[http://142.58.111.29/~haoz/pubs/zhang_eg07star_spectral.pdf Hao Zhang Oliver van Kaick Ramsay Dyer. Spectral Methods for Mesh Processing and Analysis, EUROGRAPHICS 2007 STAR – State of The Art Report, 2007]]

== Spectral Processing II -- Jan 29 ==

Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/Spectral_Processing2]]

Lecturer: Claudio/Gustavo

Topics:

* Laplacian Eigenfunctions
** Properties
** Visualization
** Interaction

Required Reading/Notes:

[[http://alice.loria.fr/publications/papers/2006/SMI_Laplacian/SMI_Laplacian.pdf Bruno Levy. Laplace-Beltrami Eigenfunctions Towards an algorithm that “understands” geometry, SMI, 2006]]

Fan R. K. Chung. Spectral Graph Theory (CBMS Regional Conference Series in Mathematics, No. 92),
American Mathematical Society, 1997

Slides:

Further reading:

[[ftp://ftp.gdv.uni-hannover.de/papers/reuter2006-shape_dna.pdf Martin Reuter, Franz-Erich Wolter, Niklas Peinecke. Laplace–Beltrami spectra as ‘Shape-DNA’ of surfaces and solids, Computer-Aided Design, 2006]]

== Spectral Processing III -- Feb 3 ==

Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/Spectral_Processing3]]

Lecturer: Claudio/Gustavo

Topics:

* Spectral Mesh Segmentation

Required Reading/Notes:

[[http://142.58.111.29/~lrong/personal/docs/05_vmv_spectcut.pdf Hao Zhang, Rong Liu. Mesh Segmentation via Recursive and Visually Salient Spectral Cuts, 2005]]

[[http://www.cs.sfu.ca/~haoz/pubs/liu_zhang_eg07.pdf Rong Liu and Hao Zhang. Mesh Segmentation via Spectral Embedding and Contour Analysis, EUROGRAPHICS, 2007]]

[[http://fas.sfu.ca/~haoz/pubs/liu_zhang_pg04.pdf Rong Liu, Hao Zhang. Segmentation of 3D Meshes through Spectral Clustering, 2004]]

Slides:

Further reading:

[[http://www-ee.technion.ac.il/~ayellet/Ps/SMI06.pdf Mesh segmentation – A comparative study, SMI, 2006]]

== Spectral Processing IV -- Feb 5 ==

Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/Spectral_Processing4]]

Lecturer: Claudio/Gustavo

Topics:

* Shape Symmetries
* Spectral Quadrangulation

Required Reading/Notes:

[[http://graphics.stanford.edu/projects/lgl/papers/osg-giss-08/osg-giss-08.pdf Maks Ovsjanikov, Jian Sun, Leonidas Guibas. Global Intrinsic Symmetries of Shapes, SGP, 2008]]

[[http://www.pascucci.org/pdf-papers/SIGGRAPH-06.pdf S. Dong, P.-T. Bremer, M. Garland, V. Pascucci, John C.Hart. Spectral Surface Quadrangulation, SIGGRAPH, 2006]]

[[http://www.graphics.rwth-aachen.de/uploads/media/kobbelt_2008_asia.pdf J. Huang, M. Zhang, J. Ma, X. Liu, L. Kobbelt, H. Bao. Spectral Quadrangulation with Orientation and Alignment Control, SIGGRAPH Asia, 2008]]

Slides:

== Mesh Decimation -- Feb 10 ==

Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/Mesh_Decimation]]

Lecturer: Claudio/Gustavo

Topics:

* Triangular Mesh Simplification

Required Reading/Notes:

[[http://www1.cs.columbia.edu/~cs4162/html05s/garland97.pdf Michael Garland, Paul S. Heckbert, Surface Simpliﬁcation Using Quadric Error Metrics, 1997]]

[[http://vims.cis.udel.edu/~jeab/research/papers/simplification/cignoni97comparison.pdf P. Cignoni, C. Montani, R. Scopigno. A comparison of mesh simplification algorithms, 1997]]

Slides:

Further reading:

[[http://graphics.cs.uiuc.edu/~garland/papers/qtheory.pdf Paul S. Heckbert, Michael Garland. Optimal triangulation and quadric-based surface simpliﬁcation, Computational Geometry, 1999]

== Mesh Smoothing -- Feb 12 ==

Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/Mesh_Smoothing]]

Lecturer: Claudio/Gustavo

Topics:

* Triangular Mesh Smoothing
* Mesh Denoising

Required Reading/Notes:

[[http://geometry.caltech.edu/pubs/JDD03.pdf Thouis R. Jones, Fredo Durand, Mathieu Desbrun. Non-iterative, feature-preserving mesh smoothing,ACM TOG, 2003]]

[[http://www-stat.stanford.edu/~idrori/BMD.pdf Shachar Fleishman, Iddo Drori, Daniel Cohen-Or. Bilateral Mesh Denoising, ACM TOG, 2003]]

[[http://portal.acm.org/citation.cfm?id=218473&dl= G. Taubin. A Signal Processing Approach To Fair Surface Design, 1995]]

Slides:

Further reading:

[[http://www.mpi-sb.mpg.de/~belyaev/papers/ik03bo.ps.gz A comparison of mesh smoothing methods]]

== Remeshing I -- Feb 17 ==

Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/Remeshing1]]

Lecturer: Claudio/Gustavo

Topics:

* Triangular Mesh Improvement

Required Reading/Notes:

[[http://portal.acm.org/citation.cfm?id=882373 V. Surazhsky and C. Gotsman. Explicit surface remeshing. Proceedings of the Symposium on Mesh Processing, 2003]]

Slides:

Further reading:

[[http://www.cs.technion.ac.il/~gotsman/AmendedPubl/Pierre/remeshing_survey.pdf Pierre Alliez, Giuliana Ucelli, Craig Gotsman and Marco Attene. Recent Advances in Remeshing of Surfaces, 2005]]

[[http://www.imr.sandia.gov/papers/imr11/surazhsky.pdf Vitaly Surazhsky, Craig Gotsman. High Quality Compatible Triangulations,11th International Meshing Roundtable, 2002]]

== Remeshing II -- Feb 19 ==

Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/Remeshing2]]

Lecturer: Claudio/Gustavo

Topics:

* Triangular Mesh Improvement

Required Reading/Notes:

[[http://ieeexplore.ieee.org/search/wrapper.jsp?arnumber=1199601 P. Alliez , E. Colin de Verdiere, O. Devillers, and M. Isenburg. Isotropic surface remeshing. In Proceedings of Shape Modeling International, 2003]]

Slides:

Further reading:

[[http://www.imr.sandia.gov/papers/imr11/surazhsky.pdf Vitaly Surazhsky, Craig Gotsman. High Quality Compatible Triangulations,11th International Meshing Roundtable, 2002]]

[[ftp://ftp-sop.inria.fr/prisme/ECG/Reports/Month30/ECG-TR-304100-01.pdf Vitaly Surazhsky, Pierre Alliez, Craig Gotsman. Isotropic Remeshing of Surfaces: a Local Parameterization Approach, ECG Technical Report No. : ECG-TR-304100-01, 2003]]

== Mesh Parameterization I -- Feb 24 ==
Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/Mesh_Parametrization1]]

Lecturer: Claudio/Gustavo

Topics:

* Planar Parametrization

Required Reading/Notes:

[[http://heim.ifi.uio.no/~michaelf/papers/mean_value.pdf M. Floater. Mean value coordinates, Computer Aided Geometric Design, 2003]]

[[http://www.multires.caltech.edu/teaching/courses/cs101.3.spring02/cs101_files/resources/Parameterization/Floater.pdf M. Floater. Parametrization and smooth approximation of surface triangulations, Computer Aided Geometric Design, 1997]]

[[http://jjcao1231.googlepages.com/Intrinsic_Parameterizations_of_Surface_Meshes_02.pdf M Desbrun, M Meyer, P Alliez. Intrinsic Parameterizations of Surface Meshes, CGF, 2002]]

Slides:

Further reading:

[[http://www.cs.jhu.edu/~misha/Fall07/Papers/Tutte63.pdf W.T. Tutte. How to draw a graph,Proc. London Math. Soc, 1963]]

[[http://vcg.isti.cnr.it/Publications/2005/FH05/survey_mingle04.pdf MS Floater, K Hormann. Surface parameterization: a tutorial and survey, 2005]]

[[http://www.cs.ubc.ca/~sheffa/papers/param_survey06.pdf A Sheffer, E Praun, K Rose. Mesh Parameterization Methods and Their Applications, 2006]]

[[https://graphics.stanford.edu/courses/cs468-03-fall/Papers/floater_triangulation.pdf M. Floater, M Reimers. Meshless parameterization and surface reconstruction, Computer Aided Geometric Design, 2001]]

== Mesh Parameterization II -- Feb 26 ==
Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/Mesh_Parametrization2]]

Lecturer: Claudio/Gustavo

Topics:

* Spherical Parametrization

Required Reading/Notes:

[[http://www.cs.sfu.ca/~torsten/GL/PAPERS/sphere2.pdf C. Gotsman, X. Gu, A. Sheffer. Fundamentals of spherical parameterization for 3D meshes, ACM TOG, 2003]]

[[http://kucg.korea.ac.kr/seminar/2003/src/PA-03-19.pdf E Praun, H Hoppe. Spherical parametrization and remeshing, 2003]]

Slides:

== Quad meshing I -- Mar 3 ==
Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/quadmesh1]]

Lecturer: Claudio/Gustavo/Joel

Topics:

Required Reading/Notes:

Slides:

Further reading:

== Quad meshing II -- Mar 5 ==
Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/quadmesh2]]

Lecturer: Claudio/Gustavo/Joel

Topics:

Required Reading/Notes:

Slides:

Further reading:

== Quad meshing III -- Mar 10 ==
Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/quadmesh3]]

Lecturer: Claudio/Gustavo/Joel

Topics:

Required Reading/Notes:

Slides:

Further reading:

== Quad meshing IV -- Mar 12 ==
Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/quadmesh4]]

Lecturer: Claudio/Gustavo/Joel

Topics:

Required Reading/Notes:

Slides:

Further reading:

== Mar 17 (Spring Break) ==
== Mar 19 (Spring Break) ==

== Mesh Compression -- Mar 24 ==
Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/Compression]]

Lecturer: Claudio/Gustavo

Topics:

* Geometrical Mesh Compression
* Spectral Mesh Compression

Required Reading/Notes:

[[http://ieeexplore.ieee.org/search/wrapper.jsp?arnumber=764870 J. Rossignac. Edgebreaker: Connectivity compression for triangle meshes. IEEE Transactions on Visualization and Computer Graphics, 5(1):47–61, January-March 1999]]

[[http://www.mpi-sb.mpg.de/~karni/publications/spectral.pdf Z Karni, C Gotsman. Spectral compression of mesh geometry, 2000]]

Slides:

Further reading:

[[http://portal.acm.org/ft_gateway.cfm?id=274365&type=pdf&coll=GUIDE&dl=GUIDE&CFID=15500980&CFTOKEN=61929152 G Taubin, J Rossignac. Geometric compression through topological surgery - ACM TOG, 1998]]

[[http://www.cs.unc.edu/~isenburg/research/papers/il-sm-05.pdf Martin Isenburg, Peter Lindstrom. Streaming Meshes, Proceedings of Visualization 2005]]

[[http://www.gvu.gatech.edu/%7Ejarek/papers/Compression.pdf Jarek Rossignac. 3D Mesh Compression, Chapter in the Visualization Handbook. Academic Press. Eds. C. Hansen and C. Johnson. 2004]]

[[http://www.cs.northwestern.edu/~pren/paperpool/ig-ooccgpm-03.pdf M Isenburg, S Gumhold. Out-of-core compression for gigantic polygon meshes, SIGGRAPH, 2003]]

== Mesh Editing -- Mar 26 ==
Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/MeshEditing]]

Lecturer: Claudio/Gustavo

Topics:

* Multiresolution approach
* Laplacian Mesh Editing
* Poisson-based mesh editing

Required Reading/Notes:

[[http://www.cs.bell-labs.com/who/wim/papers/sig97.pdf D Zorin, P Schroder, W Sweldens. Interactive multiresolution mesh editing, SIGGRAPH, 2007]]

[[http://research.microsoft.com/asia/dload_files/group/ig/2004/poisson.pdf Y Yu, K Zhou, D Xu, X Shi, H Bao, B Guo, HY Shum. Mesh editing with poisson-based gradient field manipulation, SIGGRAPH, 2004]]

[[http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=1314505&isnumber=29137 Y Lipman, O Sorkine, D Cohen-Or, D Levin, C Rossi, H Seidel. Differential coordinates for interactive mesh editing, Shape Modeling Applications, 2004]]

Slides:

Further reading:

[[http://portal.acm.org/citation.cfm?id=1073204.1073324 A Nealen, O Sorkine, M Alexa, D Cohen-Or. A sketch-based interface for detail-preserving mesh editing, SIGGRAPH, 2005]]

[[http://graphics.stanford.edu/courses/cs468-05-fall/Papers/p479-lipman.pdf Y Lipman, O Sorkine, D Levin, D Cohen-Or. Linear rotation-invariant coordinates for meshes, SIGGRAPH, 2005]]

== Mesh Repair -- Mar 31 ==
Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/MeshRepair]]

Lecturer: Claudio/Gustavo

Topics:

* Repairing Polygonal Soup
* Hole filling
* Surface Completion

Required Reading/Notes:

[[http://portal.acm.org/ft_gateway.cfm?id=1015815&type=pdf&coll=GUIDE&dl=GUIDE&CFID=16049617&CFTOKEN=45512742 T. Ju. Robust repair of polygonal models, SIGGRAPH, 2004]]

[[http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=1024098&isnumber=22019 J Davis, SR Marschner, M Garr, M Levoy. Filling holes in complex surfaces using volumetric diffusion, 2002]]

[[http://portal.acm.org/ft_gateway.cfm?id=1015814&type=pdf&coll=GUIDE&dl=GUIDE&CFID=16050250&CFTOKEN=44199354 A Sharf, M Alexa, D Cohen-Or. Context-based surface completion, SIGGRAPH, 2004]]

Slides:

Further reading:

[[http://www.cs.ubc.ca/labs/imager/tr/2005/Vlad_MCompletion/sgp05.pdf V Kraevoy, A Sheffer. Template-based mesh completion, SGP, 2005]]

[[http://graphics.stanford.edu/courses/cs468-05-fall/Papers/p896-shen.pdf C Shen, JF O'Brien, JR Shewchuk. Interpolating and approximating implicit surfaces from polygon soup, SIGGRAPH, 2004]]

== Discrete Exterior Calculus I -- Apr 2 ==
Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/DEC1]]

Lecturer: Claudio/Gustavo

Topics:

* Differential Forms in Euclidean Spaces
* Manifolds and Tangent Space
* Differential Forms on Manifolds

Required Reading/Notes:

* Loring W. Tu. An Introduction to Manifolds, Springer, 2008.

Slides:

Further reading:

* D. Bachman. A geometric Approach to Differential Forms, Birkhauser, 2006.

== Discrete Exterior Calculus II -- Apr 7 ==
Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/DEC2]]

Lecturer: Claudio/Gustavo

Topics:

* Discrete Differential Geometry
* Discrete Differential Forms

Required Reading/Notes:

[[http://etd.caltech.edu/etd/available/etd-05202003-095403/unrestricted/thesis_hirani.pdf A. Hirani. Discrete Exterior Calculus, 2003]]

[[http://www.multires.caltech.edu/pubs/diffGeoOps.pdf Mark Meyer, Mathieu Desbrun, Peter Schröder, Alan H. Barr. Discrete Differential-Geometry Operators for Triangulated 2-Manifolds]]

[[http://mesh.brown.edu/taubin/pdfs/taubin-iccv95b.pdf Gabriel Taubin. Estimating the Tensor of Curvature of a Surface from a Polyhedral Approximation, 1995]]

[[http://portal.acm.org/ft_gateway.cfm?id=1198662&type=pdf&coll=GUIDE&dl=GUIDE&CFID=15587878&CFTOKEN=77328344 John M. Sullivan. Curvature Measures for Discrete Surfaces, SIGGRAPH, 2005]]

Slides:

== Point-Set Surfaces I -- Apr 9 ==
Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/PSS1]]

Lecturer: Claudio/Gustavo/Carlos

Topics:

Required Reading/Notes:

Slides:

Further reading:

== Point-Set Surfaces II -- Apr 14 ==
Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/PSS2]]

Lecturer: Claudio/Gustavo/Carlos

Topics:

Required Reading/Notes:

Slides:

Further reading:

== Point-Set Surfaces III -- Apr 16 ==
Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/PSS3]]

Lecturer: Claudio/Gustavo/Carlos

Topics:

Required Reading/Notes:

Slides:

Further reading:

== Point-Set Surfaces IV -- Apr 21 ==
Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/PSS4]]

Lecturer: Claudio/Gustavo/Carlos

Topics:

Required Reading/Notes:

Slides:

Further reading:

== Project Presentation -- Apr 23 ==
== Project Presentation -- Apr 28 ==

GeometryProcessing/Spring2009/Schedule/Spectral Processing1

2009-01-27T20:01:18Z

Loos:

*John Meier
I can't seem to access the link for the second paper in the required reading (G. Taubin. A signal processing approach to fair surface design, 1995). Has anyone else run into this?

* Brad Loos

I got it, but it seems to be almost the exact same paper as the Eurographics 2000 Star Report. Is there supposed to be something we get out of the second paper that wasn't in the first?

GeometryProcessing/Spring2009/Schedule/Surface Generation Extraction1

2009-01-22T05:37:40Z

Loos: /* Questions */

*John Meier
I liked the structure of Tuesday's lecture: 1) the build-up to the topic of marching cubes from marching tets, and 2) examination of the aspects of marching cubes that have been "solved", like how to prevent ambiguous surface extraction by automatically generating the intersection lookup table, and optimizing runtime with structures likes octrees or span spaces. The biggest mental hurdle for me among the lecture topics was the reason for building an octree of an implicit surface from the bottom up as a preprocessing step, which Carlos cleared up well (once the structure is built, it can be queried for any constant). The analogy to sorting an array before searching for elements was intuitive and appreciated.

=== Questions ===

''What steps would take place when using Marching Cubes to extract a surface from an implicit representation?''

(I'm not sure I understood the question, so feel free to tell me I didn't get it) If you already have a volumetric dataset stored as a 3D set of voxels in space, then you can just run Marching Cubes directly on that representation, one voxel being one cube. If what you have is an evaluation formula for each point in space, then you can first evaluate the function in a fixed volumetric grid, giving you the voxels and then running Marching Cubes.

''Guidance Field''

Not sure if this is something we've talked about or are going to talk about, but for an advancing front method to generate iso-surfaces, what's a guidance field? I would assume that it's some sort of function that guides the creation of new triangles, but how? And what's it look like?

GeometryProcessing/Spring2009/Schedule/Surface Generation Extraction1

2009-01-22T05:37:01Z

Loos: /* Questions */

*John Meier
I liked the structure of Tuesday's lecture: 1) the build-up to the topic of marching cubes from marching tets, and 2) examination of the aspects of marching cubes that have been "solved", like how to prevent ambiguous surface extraction by automatically generating the intersection lookup table, and optimizing runtime with structures likes octrees or span spaces. The biggest mental hurdle for me among the lecture topics was the reason for building an octree of an implicit surface from the bottom up as a preprocessing step, which Carlos cleared up well (once the structure is built, it can be queried for any constant). The analogy to sorting an array before searching for elements was intuitive and appreciated.

=== Questions ===

What steps would take place when using Marching Cubes to extract a surface from an implicit representation?

(I'm not sure I understood the question, so feel free to tell me I didn't get it) If you already have a volumetric dataset stored as a 3D set of voxels in space, then you can just run Marching Cubes directly on that representation, one voxel being one cube. If what you have is an evaluation formula for each point in space, then you can first evaluate the function in a fixed volumetric grid, giving you the voxels and then running Marching Cubes.

''Guidance Field''

Not sure if this is something we've talked about or are going to talk about, but for an advancing front method to generate iso-surfaces, what's a guidance field? I would assume that it's some sort of function that guides the creation of new triangles, but how? And what's it look like?