# GeometryProcessing/Spring2009/Schedule

### From VisTrailsWiki

## 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.

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:

Slides:

Further reading:

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

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:

- Advancing Front Methods
- Afront

Required Reading/Notes:

Slides:

## Extra Lecture I -- Jan 23

Lecturer: Carlos

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:

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

Slides:

Further reading:

## 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:

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

Slides:

Further reading:

## 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, 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]

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:

## Mesh Smoothing -- Feb 12

Class Discussion Link: GeometryProcessing/Spring2009/Schedule/Mesh_Smoothing

Lecturer: Claudio/Gustavo

Topics:

- Triangular Mesh Smoothing
- Mesh Denoising

Required Reading/Notes:

[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:

Slides:

Further reading:

## Remeshing II -- Feb 19

Class Discussion Link: GeometryProcessing/Spring2009/Schedule/Remeshing2

Lecturer: Claudio/Gustavo

Topics:

- Triangular Mesh Improvement

Required Reading/Notes:

Slides:

Further reading:

## 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 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]

## Mesh Parameterization II -- Feb 26

Class Discussion Link: GeometryProcessing/Spring2009/Schedule/Mesh_Parametrization2

Lecturer: Claudio/Gustavo

Topics:

- Spherical Parametrization

Required Reading/Notes:

[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:

[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]

[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]

Slides:

Further reading:

## 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]

[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]

## 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]

[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: