Discrete Curvature

Theory and Applications


A colloquium on discrete curvature

Relative discrete curvatures and self-supporting structures

Helmut Pottmann

Slides are availble by following the link.

Relative discrete curvatures of polyhedral meshes can be based on mesh parallelism and its dual in the sense of isotropic geometry. We will provide an overview of the main results on this type of discrete curvatures. As a potential application, we show that the self-supporting property of a structure can be expressed with help of relative discrete curvatures of that structure with respect to the discrete Airy stress potential. This leads us to explicit constructions of remarkable types of self-supporting polyhedral meshes and allows us to remesh self-supporting shapes by self-supporting quad meshes with planar faces. Their architectural realization can be steel/glass constructions with low moments in nodes.

This is joint work with A. Bobenko, M. Hobinger, Y. Liu, E. Vouga and J. Wallner.

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