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Discrete conformal mappings and Riemann surfaces

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If you have a question about this talk, please contact Shahar Hadar.

The general idea of discrete differential geometry is to find and investigate discrete models that exhibit properties and structures characteristic of 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 establish a connection between conformal geometry for triangulated surfaces, the geometry of ideal hyperbolic polyhedra and discrete uniformization of Riemann surfaces. Applications in geometry processing and computer graphics will be demonstrated. Fragments from a new movie “conform!” will be shown.

This talk is part of the Theoretical Physics Colloquium series.

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