# 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: PDF File

Further reading:

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

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:

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

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

## 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:

[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:

## 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:

[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:

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:

- 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, 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:

- Deformation Invariant Shape Representation
- Cross Mapping

Required Reading/Notes:

[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:

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:

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

Further reading:

Potentially useful links:

- Genus Defintion [1]

- Voronoi Diagramms [2]

- Centroidal Voronoi Tessellations [3]

- Delaunay Triangulation [4]

- 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:

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:

- To be posted...

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

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:

- To be posted...

Further reading:

## Mesh Smoothing -- Feb 26

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 II -- Mar 3

Class Discussion Link: GeometryProcessing/Spring2009/Schedule/Remeshing2

Lecturer: Claudio/Gustavo

Topics:

- Triangular Mesh Improvement

Required Reading/Notes:

Slides:

Further reading:

## Mesh Parameterization I -- Mar 5

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 -- Mar 10

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:

## 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:

[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: