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]

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

Slides:

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]

Surface Generation and/or Extraction II -- Jan 22

Class Discussion Link: GeometryProcessing/Spring2009/Schedule/Surface_Generation_Extraction2

Lecturer: Gustavo

Topics:

• Advancing Front Methods
  • Afront

Required Reading/Notes:

[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: Claudio

Topics: Software libraries for geometry processing

Location TBD Reading TBD

Spectral Processing I -- Jan 27

Class Discussion Link: GeometryProcessing/Spring2009/Schedule/Spectral_Processing1

Lecturer: Claudio/Gustavo

Topics:

• Laplacian Mesh Matrix
  • Eigenvalues and Eigenvectors/Eigenfunctions
  • Relationship with FFT
  • Geometry and Laplacian Matrix

Required Reading/Notes:

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

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

Slides:

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: Claudio/Gustavo

Topics:

• Laplacian Eigenfunctions
  • Properties
  • Visualization
  • Interaction

Required Reading/Notes:

[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:

[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:

[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: Claudio/Gustavo

Topics:

• Shape Symmetries
• Spectral Quadrangulation

Required Reading/Notes:

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

[S. Dong, P.-T. Bremer, M. Garland, V. Pascucci, John C.Hart. Spectral Surface Quadrangulation, SIGGRAPH, 2006]

[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:

[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:

Further reading:

[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:

[Thouis R. Jones, Fredo Durand, Mathieu Desbrun. Non-iterative, feature-preserving mesh smoothing,ACM TOG, 2003]

[Shachar Fleishman, Iddo Drori, Daniel Cohen-Or. Bilateral Mesh Denoising, ACM TOG, 2003]

[G. Taubin. A Signal Processing Approach To Fair Surface Design, 1995]

Slides:

Further reading:

[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:

[V. Surazhsky and C. Gotsman. Explicit surface remeshing. Proceedings of the Symposium on Mesh Processing, 2003]

Slides:

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]

Remeshing II -- Feb 19

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:

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]

Mesh Parameterization I -- Feb 24

Class Discussion Link: GeometryProcessing/Spring2009/Schedule/Mesh_Parametrization1

Lecturer: Claudio/Gustavo

Topics:

• Planar Parametrization

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:

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]

Mesh Parameterization II -- Feb 26

Class Discussion Link: GeometryProcessing/Spring2009/Schedule/Mesh_Parametrization2

Lecturer: Claudio/Gustavo

Topics:

• Spherical Parametrization

Required Reading/Notes:

[C. Gotsman, X. Gu, A. Sheffer. Fundamentals of spherical parameterization for 3D meshes, ACM TOG, 2003]

[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:

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 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:

[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 -- Mar 31

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]

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:

[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 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: