Geometric Processing Spring 2016

Course Description: This course introduces the student to wide range of topics and concepts including the foundation of discrete differential geometry on triangulated meshes, surface parameterization, manifold harmonics, Morse theory and computational topology. The course offers both practical and theoretical aspect of geometric processing and geometric computing. The mathematical and theoretical aspects of the course are designed to enhance the understanding of the practical techniques beyond the implementation and to enable the students to understand the advantages and limitations of the presented algorithms.

Class meeting:

T TH, 12:30-1:45 CMC 120

Course Topics : Topics include, but are not limited to,

  • Mesh Data Structure
  • Discrete Differential Geometry: discrete differential operators on triangulated mesh, mean and Gaussian curvatures on triangulated mesh, principal curvatures and directions.
  • Harmonic Functions on triangulated meshes.
  • Surface Parameterization.
  • Mesh Smoothing.
  • Manifold Harmonics.
  • 2-Dimensional PL Morse-Theory

Textbook:

Polygonal Mesh Processing by Mario Botsch, Leif Kobbelt, Mark Pauly, Pierre Alliez, Bruno Levy. Website of the book: http://www.pmp-book.org/

Recommended books :

  • A Sampler of Useful Computational Tools for Applied Geometry, Computer Graphics, and Image Processing by Daniel Cohen and others.
  • Guide to Computational Geometry Processing by J. Andreas Bærentzen, Jens Gravesen, Francois Anton, Henrik Aanæs.

Additional readings from research papers will be announced later in class.

Grading:

Programming assignments
Writing of one of the lectures.
Final project and presentation. The final project is an implementation of an algorithm related to course material.

 

 Lecture Summary Material
Surfaces and their representation

figure_8

Lect_1
 Topology of Surfaces

topology_surfaces

Lect_2
 Parameterization of Surfaces

surface_parametrization

Lect_3
Harmonic Functions

female david first eigen critical points

Lect_4
Discrete Operators on Triangulated Meshes

hat_function

Lect_5
Morse Theory on Triangulated Meshes

Morse

Lect_6