Felix Günther: Smooth polyhedral surfacesIn modern architecture, facades and glass roofs often model smooth shapes but are realized as polyhedral surfaces. Bad approximations may be observed as wiggly meshes, even though the polyhedral mesh is close to a smooth reference surface. So what does it mean for a polyhedral surface to be smooth?
In this talk, which is based on joint work with Caigui Jiang and Helmut Pottmann, we introduce a theory of smooth polyhedral surfaces. A key role is played by the Gaussian normal image. We present a projectively invariant class of polyhedral surfaces that share several properties with their smooth counterparts. Furthermore, we derive suitable notions of tangent planes at vertices and asymptotic directions that are also invariant under projective transformations.