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:

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:

M. Mantyla

Slides:

Animations:

Further reading:

[[1]]

Surface Generation and/or Extraction I -- Jan 20

Class Discussion Link: GeometryProcessing/Spring2009/Schedule/Surface_Generation_Extraction1

Lecturer: Gustavo

Topics:

• Capturing Methods
  • Marching Cubes/Tetrahedra
  • Dual Contouring

Required Reading/Notes:

[MARCHING CUBES: A High Resolution 3D Surface Construction Algorithm]

[Dual Contouring of Hermite Data]

Slides:

Further reading:

[Edge Groups: An Approach to Understanding the Mesh Quality of Marching Methods]

[Artifacts Caused By Simplicial Subdivision]

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:

[High-Quality Extraction of Isosurfaces from Regular and Irregular Grids]

Slides:

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:

[Geometric Signal Processing on Polygonal Meshes]

[Spectral Geometry Processing with Manifold Harmonics]

Slides:

Further reading:

[Spectral Methods for Mesh Processing and Analysis]

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:

[Laplace-Beltrami Eigenfunctions Towards an algorithm that “understands” geometry]

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

Slides:

Further reading:

[Laplace–Beltrami spectra as ‘Shape-DNA’ of surfaces and solids]

Spectral Processing III -- Feb 3

Class Discussion Link: GeometryProcessing/Spring2009/Schedule/Spectral_Processing3

Lecturer: Claudio/Gustavo

Topics:

• Spectral Mesh Segmentation

Required Reading/Notes:

[Mesh Segmentation via Recursive and Visually Salient Spectral Cuts]

[Mesh Segmentation via Spectral Embedding and Contour Analysis]

[Segmentation of 3D Meshes through Spectral Clustering]

Slides:

Further reading:

[Mesh segmentation – A comparative study]

Spectral Processing IV -- Feb 5

Class Discussion Link: GeometryProcessing/Spring2009/Schedule/Spectral_Processing4

Lecturer: Claudio/Gustavo

Topics:

• Shape Symmetries
• Spectral Quadrangulation

Required Reading/Notes:

[Global Intrinsic Symmetries of Shapes]

[Spectral Surface Quadrangulation]

[Spectral Quadrangulation]

Slides:

Mesh Decimation -- Feb 10

Class Discussion Link: GeometryProcessing/Spring2009/Schedule/Mesh_Decimation

Lecturer: Claudio

Topics:

Required Reading/Notes:

[Surface Simplification Using Quadric Error Metrics]

[A comparison of mesh simplification algorithms]

Slides:

Further reading:

[Optimal triangulation and quadric-based surface simplification

Typical Class

Class Discussion Link:

Lecturer:

Topics:

Required Reading/Notes:

Slides:

Animations:

Further reading: