View source for GeometryProcessing/Spring2009/Schedule

== 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: Gustavo/Claudio 

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: [[http://www.sci.utah.edu/~cscheid/geometry_processing_2009/spectralmesh_p1_p2.pdf PDF file]]

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: Gustavo/Claudio

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: [http://www.sci.utah.edu/~cscheid/geometry_processing_2009/spectralmesh_p1_p2.pdf PDF file]

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: Gustavo/Claudio 

Topics:  

* Smoothing without Shrinkage
* Spectral Mesh Segmentation

Required Reading/Notes: 

[[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://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: Gustavo/Claudio 

Topics:  

* Deformation Invariant Shape Representation
* Cross Mapping

Required Reading/Notes: 

[[http://www.eg.org/EG/DL/WS/SGP/SGP07/225-233.pdf.abstract.pdf R. Rustamov, Laplace-Beltrami Eigenfunctions for Deformation Invariant Shape Representation, SPG, 2007]]

[[http://visual.k.u-tokyo.ac.jp/~shigeo/pdf/eg2009.pdf S. Takahashi et al., Spectral-Based Group Formation Control]]

Slides:

Further Reading:

[[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://142.58.111.29/~haoz/pubs/jain_zhang_smi06.pdf V. Jain and H. Zhang, Robust 3D Shape Correspondence in the Spectral Domain, SMI, 2006]]

== 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: [http://graphics.cs.uiuc.edu/~yuanzhou/class/SciVis2007_simplification Simplification]

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]

[http://portal.acm.org/ft_gateway.cfm?id=1061350&type=pdf&coll=GUIDE&dl=GUIDE&CFID=21204519&CFTOKEN=79519998 Quadric-Based Simplication in Any Dimension] 

[http://www.sci.utah.edu/~csilva/papers/tvcg2007cr Streaming Simplification of Tetrahedral Meshes]


== Remeshing I -- Feb 12 ==

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:  http://www.cs.utah.edu/~csilva/courses/cpsc7960/pdf/remeshing.pdf

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]

Potentially useful links:

*Genus Defintion [http://en.wikipedia.org/wiki/Genus_%28mathematics%29]

*Voronoi Diagramms [http://en.wikipedia.org/wiki/Voronoi_cell]

*Centroidal Voronoi Tessellations [http://orion.math.iastate.edu/gunzburg/voronoi.html]

*Delaunay Triangulation [http://en.wikipedia.org/wiki/Delaunay_triangulation]

*Image Halftoning [http://www.markschulze.net/halftone/] [http://en.wikipedia.org/wiki/Halftone]

*Slides from another lecture about remeshing [http://www.eecs.harvard.edu/~gotsman/geommodel/lectures/2dmesh.pdf]

*Remeshing apllication [http://www.ima.ge.cnr.it/ima/personal/attene/PersonalPage/Remesh/ReMesh.html]

== Quad meshing I -- Feb 17 ==
Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/quadmesh1]]

Lecturer: Claudio/Gustavo/Joel

Topics:  

* Quadrilateral Meshing: motivations and challenges
* Reconstruction techniques: algorithmic survey

 
Required Reading/Notes: 


Slides: 

* [http://www.cs.utah.edu/~jdaniels/courses/quadMesh1.pdf quadrilateral meshing slides]


Further reading:

* [http://www.graphics.rwth-aachen.de/uploads/media/spm08_01.pdf An Incremental Approach Feature Aligned Quad-Dominant Remeshing]
* [https://cfwebprod.sandia.gov/cfdocs/CCIM/docs/Unconstrainedplastering5_12_2005.pdf Paving and Plastering: A New Idea for all Hexahedral Mesh Generation]
* [http://www3.interscience.wiley.com/cgi-bin/fulltext/55001832/PDFSTART qMorph: An Indirect Approach to Advancing Front Quad Meshing]
* [http://www.contrib.andrew.cmu.edu/~sowen/abstracts/Vi749.html Quadrilateral Meshing with Anisotropy and Directionality Control via Close Packing of Rectangular Cells]
* [http://www.geometry.caltech.edu/pubs/ACDLD03.pdf Anisotropic Polygonal Remeshing]
* [http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.1.3074 Direct Anisotropic Quad-Dominant Remeshing]

== Quad meshing II -- Feb 19 ==
Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/quadmesh2]]

Lecturer: Claudio/Gustavo/Joel

Topics:  

* Quadrilateral Reconstruction: continued survey
* Class Discussion: Morse-Smale based algorithms


Required Reading/Notes: 

* [http://graphics.cs.uiuc.edu/~jch/papers/morsecut.pdf Fair Morse Functions For Extracting The Topological Structure of a Surface Mesh]
* [http://www.mgarland.org/papers/ssq.pdf Spectral Surface Quadrangulation]
* [http://www.graphics.rwth-aachen.de/uploads/media/kobbelt_2008_asia_01.pdf Spectral Quadrangulation with Orientation and Alignment Control]


Slides: 

* [http://www.cs.utah.edu/~jdaniels/courses/quadMesh2.pdf quadrilateral meshing slides 2]


Further reading:

* [ftp://ftp-sop.inria.fr/geometrica/alliez/tacd06.pdf Designing Quadrangulations with Discrete Harmonic Forms]
* [http://alice.loria.fr/index.php/publications.html?Paper=TOG_pgp%402006 Periodic Global Parameterizations]
* [http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.84.6655 Mesh Parameterization and Their Applications]
* [http://folk.uio.no/michaelf/papers/surfparam.pdf Surface Parameterization: A Tutorial and Survey]

== Quad meshing III -- Feb 24 ==

This class was canceled due to TopoInVis 2009. Students were advised to see invited talks on Wednesday (Feb 25th).

== Quad meshing III -- Feb 26 ==

Class Discussion Link: [[GeometryProcessing/Spring2009/Schedule/quadmesh3]]

Lecturer: Claudio/Gustavo/Joel

Topics:  

* Quadrilateral Mesh Simplification: global and local operations
* Connectivity-based reconstruction algorithms
* Relationship to hex-based meshing


Required Reading/Notes: 

* [http://portal.acm.org/citation.cfm?id=1409101&dl=GUIDE&coll=GUIDE&CFID=21470734&CFTOKEN=12853505 Quadrilateral Mesh Simplification]
* [http://graphics.cs.uiuc.edu/~ptb/papers/SaintMalo2002_Bremer_et_al.pdf Automatic Semi-Regular Mesh Construction from Adaptive Distance Fields]


Slides: 

* [http://www.cs.utah.edu/~jdaniels/courses/quadMesh3.pdf quadrilateral meshing slides 3]


Further reading:

* [http://www.multires.caltech.edu/pubs/maps.pdf MAPS: Multiresolution Adaptive Parameterization of Surfaces]


== Remeshing II -- Mar 3 ==

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:  http://www.cs.utah.edu/~csilva/courses/cpsc7960/pdf/remeshing.pdf

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]]

== Project Proposal Presentation I -- Mar 5 ==
Students should present the project proposal. Each group should give an overview about the 

problem to be tackled jointly with the solution methodology. The presentations would take 20min in total.

* Matt: Spectral 
* Brad, John: Quad Simplification
* Tiago, Hao: Quad LoD

== Project Proposal Presentation II -- Mar 10 ==

* David: Algebraic Spectral Transform
* Xiaoyue, Cameron, Campbel: Clean Scan
* Andrei: Sketch
* Harsh, Shreeraj: Progressive Stream lines

== Bye week (previously 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:

== Mesh Parameterization I -- Apr 23 ==
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 -- Apr 28 ==
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: