Orateur: Felix Günther (Unige)
Titre: Smooth polyhedral surfaces
Résumé: In modern architecture, facades and glass roofs often model
smooth shapes but are realized as polyhedral surfaces. In the case of
reflective surfaces it becomes apparent that the polyhedral surface is
not smooth even though it is very close to a smooth reference surface.
But how can we describe smoothness of polyhedral surfaces?
In this talk that is based on a joint work with Caigui Jiang and Helmut
Pottmann, we discuss a theory of smooth polyhedral surfaces. We start
with a close investigation of the normal images of vertex neighborhoods
and end up with a projectively invariant class of polyhedral surfaces
that share several properties with their smooth counterparts. Smooth
polyhedral surfaces are accompanied by suitable notions of normal
vectors, tangent planes, asymptotic directions, and parabolic curves
that are invariant under projective transformations.

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