The Discrete Charm of Geometry by Alexander Bobenko

Explore the fascinating world of discrete geometry in this captivating lecture by Alexander Bobenko from the Technical University of Berlin. Delve into the foundations of a new branch of mathematics that underpins real-world applications, from contemporary architecture to computer-generated imagery. Discover the concept of structure-preserving discretizations through simple examples, including toy spinning tops, elastic rods, smoke rings, and vortex lines in fluids. Witness how discrete geometric structures can model and approximate continuous shapes and processes, blurring the line between continuous and discrete models in geometry and dynamical systems theory. Learn about conformal texture mappings in computer graphics, free-form glass and steel structures, and animations used in Hollywood movies. Enjoy excerpts from the award-winning computer-animated film "conform!" and gain insights into the beauty and practicality of this emerging mathematical field.

Introduction
Discretization
Art
Geometric Integration
Metric Integration
Practical Applications
Elastic Rods
Elastic Curves
Discrete Analogs
Discrete Tangent Flow
Discrete Smokering Flow
Discrete Differential Geometry
Structure
Constructions
Mathematical surfaces
Curved glass
Flat maps
World map
Map projection
Stereographic projection
Mercatos map
Conformal maps
Informal maps