CS 468 -- Winter 2004

Introduction to Computational Topology

by Afra Zomorodian

Wednesdays, 12:30 - 2:00 PM
Starting January 14th
Gates 392

Course Lectures:

The emerging field of computational topology utilizes theory from topology and the power of computing to solving problems in diverse fields. Recent applications include computer graphics, computer-aided design (CAD), and structural biology. In each case, we are interested in understanding the intrinsic shape of some real or abstract space.

The primary goal of the course is to present basic concepts from topology to enable a non-specialist to grasp and participate in current research in computational topology. As such, this course will not be a readings course in computational topology. Rather, it will present mathematics from a computer scientist's point of view. Toward the end of the course, we will examine recent papers in computational topology.

I assume mathematical sophistication and familiarity with programming. However, I do not assume background in topology.

introduction (ps) {1-14-4}
point set topology (ps) [slides] {1-14-4}
surface topology (ps) [slides] + Conway's ZIP {1-21-4}
simplicial complexes (ps) [slides] {1-28-4}
group theory (ps) [slides] {2-04-4}
homotopy (ps) [slides] {2-11-4}
homology (ps) [slides] {2-18-4}
computing homology [slides] {2-25-4}
topology of point cloud data [slides] {3-03-4}
Morse theory [slides] {3-10-4}

Presentations:

Isosurface Topology Simplification by Wood et al. presented by Chand John [slides (ppt)] {3-10-4}
Topology Matching for fully Automatic Similarity Estimation of 3D Shapes by Hilaga et al. presented by Kris Hauser [slides (ppt)] {3-17-4}
Optimally cutting a surface into a disk by Erickson and Har-Peled presented by Nikola Milosavljevic [slides] {3-17-4}

Supplementary Material:

Max Eversion Paper [1977]
Outside In [1994]
The Optiverse [1998]
Thurston, W. P. and Weeks, J. R. The Mathematics of Three-dimensional Manifolds. Scientific American, 251(1), 1984. (Distributed in class)