Discrete conformal mappings, ideal hyperbolic polyhedra, and Ronkin function

03.04.2023 15:00 – 17:00

The general idea of discrete differential geometry is to find and investigate discrete models that exhibit properties and structures characteristic for the corresponding smooth geometric objects. We focus on a discrete notion of conformal equivalence of polyhedral metrics. Two triangulated surfaces are considered discretely conformally equivalent if the edge lengths are related by scale factors associated with the vertices. This simple definition leads to a surprisingly rich theory. We review connections between conformal geometry of triangulated surfaces, the geometry of ideal hyperbolic polyhedra and discrete uniformization of Riemann surfaces. Surprisingly, variational description of discrete conformal mappings is given by Ronkin function on amoeba with three ends. Applications in geometry processing and computer graphics will be demonstrated.

Lieu

Bâtiment: Conseil Général 7-9

Room 6-13, Séminaire "Fables géométriques"

entrée libre