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: 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.

Edgebreaker on a Corner Table: A Simple Technique for Representing and Compressing Triangulated Surfaces

OpenMesh – a generic and efficient polygon mesh data structure

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:

[William E. Lorensen and Harvey E. Cline. MARCHING CUBES: A High Resolution 3D Surface Construction Algorithm, Computer Graphics, 1987]

Slides: PDF File

Further reading:

Carlos A. Dietrich et al. Edge Groups: An Approach to Understanding the Mesh Quality of Marching Methods, IEEE TVCG, 2008

Hamish Carr, Torsten Moller, and Jack Snoeyink. Artifacts Caused By Simplicial Subdivision, IEEE TVCG, 2006

Newman and Yi. A survey of the marching cubes algorithm. Computers and Graphics, 2006

Raman and Wenger. Quality isosurface Generation Using an Extended Marching Cubes Lookup Table. Eurovis 2008

Shewchuk. What Is a Good Linear Finite Element? Interpolation, Conditioning, Anisotropy, and Quality Measures

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:

Feature sensitive surface extraction from volume data Feature Sensitive Surface Extraction from Volume Data, SIGGRAPH 2001

Tao Ju, Frank Losasso, Scott Schaefer, Joe Warren. Dual Contouring of Hermite Data, SIGGRAPH 2002

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 here

Website with many mesh files: Aim@Shape shape repository

Stanford 3D repository

Bilateral Mesh Denoising. Fleishman, Drori, Cohen-Or. SIGGRAPH 2003. 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

• trimesh2-2.8 VS 2005
• 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:

[G. Taubin. Geometric Signal Processing on Polygonal Meshes, EUROGRAPHICS ’2000 STAR – State of The Art Report, 2000]

[G. Taubin. A signal processing approach to fair surface design, 1995]

[B. Vallet and B. Lévy. Spectral Geometry Processing with Manifold Harmonics, EUROGRAPHICS 2008]

Slides: [PDF file]

Further reading:

[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:

[Bruno Levy. Laplace-Beltrami Eigenfunctions Towards an algorithm that “understands” geometry, SMI, 2006]

[M. Wardetzky et al. Discrete Laplace Operators: No free lunch, SGP, 2007]

[M Reuter et al. Laplace–Beltrami spectra as ‘Shape-DNA’ of surfaces and solids, CAD, 2007]

Slides: PDF file

Further reading:

[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:

[G. Taubin. A signal processing approach to fair surface design, 1995]

[Hao Zhang, Rong Liu. Mesh Segmentation via Recursive and Visually Salient Spectral Cuts, 2005]

[Rong Liu and Hao Zhang. Mesh Segmentation via Spectral Embedding and Contour Analysis, EUROGRAPHICS, 2007]

[Rong Liu, Hao Zhang. Segmentation of 3D Meshes through Spectral Clustering, 2004]

Slides:

Further reading:

[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:

[R. Rustamov, Laplace-Beltrami Eigenfunctions for Deformation Invariant Shape Representation, SPG, 2007]

[S. Takahashi et al., Spectral-Based Group Formation Control]

Slides:

Further Reading:

[Maks Ovsjanikov, Jian Sun, Leonidas Guibas. Global Intrinsic Symmetries of Shapes, SGP, 2008]

[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:

Michael Garland, Paul S. Heckbert, Surface Simplification Using Quadric Error Metrics, 1997

P. Cignoni, C. Montani, R. Scopigno. A comparison of mesh simplification algorithms, 1997

Slides: Simplification

Further reading:

Paul S. Heckbert, Michael Garland. Optimal triangulation and quadric-based surface simplification, Computational Geometry, 1999

Quadric-Based Simplication in Any Dimension

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:

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:

Pierre Alliez, Giuliana Ucelli, Craig Gotsman and Marco Attene. Recent Advances in Remeshing of Surfaces, 2005

Vitaly Surazhsky, Craig Gotsman. High Quality Compatible Triangulations,11th International Meshing Roundtable, 2002

Potentially useful links:

• Genus Defintion [1]

• Voronoi Diagramms [2]

• Centroidal Voronoi Tessellations [3]

• Delaunay Triangulation [4]

• Image Halftoning [5] [6]

• Slides from another lecture about remeshing [7]

• Remeshing apllication [8]

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:

• quadrilateral meshing slides

Further reading:

• An Incremental Approach Feature Aligned Quad-Dominant Remeshing
• Paving and Plastering: A New Idea for all Hexahedral Mesh Generation
• qMorph: An Indirect Approach to Advancing Front Quad Meshing
• Quadrilateral Meshing with Anisotropy and Directionality Control via Close Packing of Rectangular Cells
• Anisotropic Polygonal Remeshing
• 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:

• Fair Morse Functions For Extracting The Topological Structure of a Surface Mesh
• Spectral Surface Quadrangulation
• Spectral Quadrangulation with Orientation and Alignment Control

Slides:

• quadrilateral meshing slides 2

Further reading:

• Designing Quadrangulations with Discrete Harmonic Forms
• Periodic Global Parameterizations
• Mesh Parameterization and Their Applications
• 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:

• Quadrilateral Mesh Simplification
• Automatic Semi-Regular Mesh Construction from Adaptive Distance Fields

Slides:

• quadrilateral meshing slides 3

Further reading:

• 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:

[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:

[Vitaly Surazhsky, Craig Gotsman. High Quality Compatible Triangulations,11th International Meshing Roundtable, 2002]

[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
• Manasi: Eikonal solver for meshes

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:

Mesh Compression -- Mar 24

Class Discussion Link: GeometryProcessing/Spring2009/Schedule/Compression

Lecturer: Claudio/Gustavo

Topics:

• Geometrical Mesh Compression
• Spectral Mesh Compression

Required Reading/Notes:

[J. Rossignac. Edgebreaker: Connectivity compression for triangle meshes. IEEE Transactions on Visualization and Computer Graphics, 5(1):47–61, January-March 1999]

[Z Karni, C Gotsman. Spectral compression of mesh geometry, 2000]

Slides:

Further reading:

[G Taubin, J Rossignac. Geometric compression through topological surgery - ACM TOG, 1998]

[Martin Isenburg, Peter Lindstrom. Streaming Meshes, Proceedings of Visualization 2005]

[Jarek Rossignac. 3D Mesh Compression, Chapter in the Visualization Handbook. Academic Press. Eds. C. Hansen and C. Johnson. 2004]

[M Isenburg, S Gumhold. Out-of-core compression for gigantic polygon meshes, SIGGRAPH, 2003]

Mesh Parameterization -- Apr 2

Class Discussion Link: GeometryProcessing/Spring2009/Schedule/Mesh_Parametrization1

Lecturer: Claudio/Gustavo

Topics:

• Intro to parameterization
• Differential geometry concepts
• Parameterization with barycentric coordinates

Required Reading/Notes:

[M. Floater. Mean value coordinates, Computer Aided Geometric Design, 2003]

[M. Floater. Parametrization and smooth approximation of surface triangulations, Computer Aided Geometric Design, 1997]

[M Desbrun, M Meyer, P Alliez. Intrinsic Parameterizations of Surface Meshes, CGF, 2002]

Slides:

We covered the slides available here: SIGGRAPH 2007 course reflecting the topics listed above.

Further reading:

[W.T. Tutte. How to draw a graph,Proc. London Math. Soc, 1963]

[MS Floater, K Hormann. Surface parameterization: a tutorial and survey, 2005]

[A Sheffer, E Praun, K Rose. Mesh Parameterization Methods and Their Applications, 2006]

[M. Floater, M Reimers. Meshless parameterization and surface reconstruction, Computer Aided Geometric Design, 2001]

Discrete Exterior Calculus I -- Apr 7

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.
• [[9]] A.N. Hirani, Discrete Exterior Calculus, Thesis, 2003]]

Slides:

Further reading:

• [A.N. Nong et al., Discrete Exterior Calculus and Its Implementation, Tech. Rep., 2003]

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

• [10]

Discrete Exterior Calculus II -- Apr 9

Class Discussion Link: GeometryProcessing/Spring2009/Schedule/DEC2

Lecturer: Claudio/Gustavo

Topics:

• Discrete Differential Geometry
• Discrete Differential Forms

Required Reading/Notes:

[A. Hirani. Discrete Exterior Calculus, 2003]

[Mark Meyer, Mathieu Desbrun, Peter Schröder, Alan H. Barr. Discrete Differential-Geometry Operators for Triangulated 2-Manifolds]

[Gabriel Taubin. Estimating the Tensor of Curvature of a Surface from a Polyhedral Approximation, 1995]

[John M. Sullivan. Curvature Measures for Discrete Surfaces, SIGGRAPH, 2005]

Slides:

Point-Set Surfaces I -- Apr 14

Class Discussion Link: GeometryProcessing/Spring2009/Schedule/PSS1

Lecturer: Claudio/Gustavo/Carlos

Topics:

Required Reading/Notes:

Slides:

Further reading:

Point-Set Surfaces II -- Apr 16

Class Discussion Link: GeometryProcessing/Spring2009/Schedule/PSS2

Lecturer: Claudio/Gustavo/Carlos

Topics:

Required Reading/Notes:

Slides:

Further reading:

Point-Set Surfaces III -- Apr 21

Class Discussion Link: GeometryProcessing/Spring2009/Schedule/PSS3

Lecturer: Claudio/Gustavo/Carlos

Topics:

Required Reading/Notes:

Slides:

Further reading:

Point-Set Surfaces IV -- Apr 23

Class Discussion Link: GeometryProcessing/Spring2009/Schedule/PSS4

Lecturer: Claudio/Gustavo/Carlos

Topics:

Required Reading/Notes:

Slides:

Further reading:

Mesh Editing -- TBS

Class Discussion Link: GeometryProcessing/Spring2009/Schedule/MeshEditing

Lecturer: Claudio/Gustavo

Topics:

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

Required Reading/Notes:

[D Zorin, P Schroder, W Sweldens. Interactive multiresolution mesh editing, SIGGRAPH, 2007]

[Y Yu, K Zhou, D Xu, X Shi, H Bao, B Guo, HY Shum. Mesh editing with poisson-based gradient field manipulation, SIGGRAPH, 2004]

[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:

[A Nealen, O Sorkine, M Alexa, D Cohen-Or. A sketch-based interface for detail-preserving mesh editing, SIGGRAPH, 2005]

[Y Lipman, O Sorkine, D Levin, D Cohen-Or. Linear rotation-invariant coordinates for meshes, SIGGRAPH, 2005]

Mesh Repair -- TBS

Class Discussion Link: GeometryProcessing/Spring2009/Schedule/MeshRepair

Lecturer: Claudio/Gustavo

Topics:

• Repairing Polygonal Soup
• Hole filling
• Surface Completion

Required Reading/Notes:

[T. Ju. Robust repair of polygonal models, SIGGRAPH, 2004]

[J Davis, SR Marschner, M Garr, M Levoy. Filling holes in complex surfaces using volumetric diffusion, 2002]

[A Sharf, M Alexa, D Cohen-Or. Context-based surface completion, SIGGRAPH, 2004]

Slides:

Further reading:

[V Kraevoy, A Sheffer. Template-based mesh completion, SGP, 2005]

[C Shen, JF O'Brien, JR Shewchuk. Interpolating and approximating implicit surfaces from polygon soup, SIGGRAPH, 2004]