This course has two goals - to introduce the participants to the basic concepts of differential geometry of curves and surfaces, and to teach the participants how to preserve the key features of this geometry upon discretization.
The key concept here is that of curvature - a notion that depends strictly on the smooth structure of a manifold. For discrete curves and surfaces the traditional formulas for curvature are inapplicable. The curvature is either not defined or trivial. The challenge is to come up with new notions of curvature that are meaningful and at the same time approximate - or resemble the properties of the traditional differential geometric curvature.
We will first have a look at how to discretize curves, and how to define curvature for these discrete curves. Then we will consider two discretizations of surfaces - quad meshes and triangulations.
Target group: PhD students and postdocs in mathematics and computer science.
Prerequisites: Linear algebra, analysis
Evaluation: Participation, written assignments, problem sets
Teaching format: Lectures and recitations
ECTS: 3 Year: 2021
Track segment(s):
CS-NUM Computer Science - Visual and Numerical Computing
MAT-GEO Mathematics - Geometry and Topology
Teacher(s):
Hana Dal Poz Kourimska
Teaching assistant(s):
If you want to enroll to this course, please click: REGISTER
- Teacher: Hana KOURIMSKA