# 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

[GM], Chapters 2 and 3.

Slides:

Animations:

Martti Mäntylä. An Introduction to Solid Modeling. Computer Science Press, College Park, MD, 1988.

## 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

Slides: PDF File

## 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
• Dual Contouring
• Advancing Front Methods
• Afront

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

## 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

Slides:

## Spectral Processing II -- Jan 29

Class Discussion Link: GeometryProcessing/Spring2009/Schedule/Spectral_Processing2

Lecturer: Claudio/Gustavo

Topics:

• Laplacian Eigenfunctions
• Properties
• Visualization
• Interaction

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

Slides:

## Spectral Processing III -- Feb 3

Class Discussion Link: GeometryProcessing/Spring2009/Schedule/Spectral_Processing3

Lecturer: Claudio/Gustavo

Topics:

• Spectral Mesh Segmentation

Slides:

## Spectral Processing IV -- Feb 5

Class Discussion Link: GeometryProcessing/Spring2009/Schedule/Spectral_Processing4

Lecturer: Claudio/Gustavo

Topics:

• Shape Symmetries

Slides:

## Mesh Decimation -- Feb 10

Class Discussion Link: GeometryProcessing/Spring2009/Schedule/Mesh_Decimation

Lecturer: Claudio/Gustavo

Topics:

• Triangular Mesh Simplification

Slides:

## Mesh Smoothing -- Feb 12

Class Discussion Link: GeometryProcessing/Spring2009/Schedule/Mesh_Smoothing

Lecturer: Claudio/Gustavo

Topics:

• Triangular Mesh Smoothing
• Mesh Denoising

Slides:

## Remeshing I -- Feb 17

Class Discussion Link: GeometryProcessing/Spring2009/Schedule/Remeshing1

Lecturer: Claudio/Gustavo

Topics:

• Triangular Mesh Improvement

Slides:

## Remeshing II -- Feb 19

Class Discussion Link: GeometryProcessing/Spring2009/Schedule/Remeshing2

Lecturer: Claudio/Gustavo

Topics:

• Triangular Mesh Improvement

Slides:

## Mesh Parameterization I -- Feb 24

Class Discussion Link: GeometryProcessing/Spring2009/Schedule/Mesh_Parametrization1

Lecturer: Claudio/Gustavo

Topics:

• Planar Parametrization

Slides:

## Mesh Parameterization II -- Feb 26

Class Discussion Link: GeometryProcessing/Spring2009/Schedule/Mesh_Parametrization2

Lecturer: Claudio/Gustavo

Topics:

• Spherical Parametrization

Slides:

## Quad meshing I -- Mar 3

Lecturer: Claudio/Gustavo/Joel

Topics:

Slides:

## Quad meshing II -- Mar 5

Lecturer: Claudio/Gustavo/Joel

Topics:

Slides:

## Quad meshing III -- Mar 10

Lecturer: Claudio/Gustavo/Joel

Topics:

Slides:

## Quad meshing IV -- Mar 12

Lecturer: Claudio/Gustavo/Joel

Topics:

Slides:

## Mesh Compression -- Mar 24

Class Discussion Link: GeometryProcessing/Spring2009/Schedule/Compression

Lecturer: Claudio/Gustavo

Topics:

• Geometrical Mesh Compression
• Spectral Mesh Compression

Slides:

## Mesh Editing -- Mar 26

Class Discussion Link: GeometryProcessing/Spring2009/Schedule/MeshEditing

Lecturer: Claudio/Gustavo

Topics:

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

Slides:

## Mesh Repair -- Mar 31

Class Discussion Link: GeometryProcessing/Spring2009/Schedule/MeshRepair

Lecturer: Claudio/Gustavo

Topics:

• Repairing Polygonal Soup
• Hole filling
• Surface Completion

Slides:

## 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

• Loring W. Tu. An Introduction to Manifolds, Springer, 2008.

Slides:

• 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

Slides:

## Point-Set Surfaces I -- Apr 9

Class Discussion Link: GeometryProcessing/Spring2009/Schedule/PSS1

Lecturer: Claudio/Gustavo/Carlos

Topics:

Slides:

## Point-Set Surfaces II -- Apr 14

Class Discussion Link: GeometryProcessing/Spring2009/Schedule/PSS2

Lecturer: Claudio/Gustavo/Carlos

Topics:

Slides:

## Point-Set Surfaces III -- Apr 16

Class Discussion Link: GeometryProcessing/Spring2009/Schedule/PSS3

Lecturer: Claudio/Gustavo/Carlos

Topics:

Slides:

## Point-Set Surfaces IV -- Apr 21

Class Discussion Link: GeometryProcessing/Spring2009/Schedule/PSS4

Lecturer: Claudio/Gustavo/Carlos

Topics:

Slides: