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H. Pottmann:
"Form-finding with polyhedral meshes";
Vortrag: SIAM Conference on Industrial and Applied Geometry, Pittsburgh, USA (eingeladen); 12.07.2017.

We discuss interactive modeling of polyhedral meshes for architectural design which combines form, function and fabrication, taking care of user specified constraints such as boundary interpolation, planarity of faces, panel size and shape, statics and last, but not least, cost. Our computational approach can be described as guided exploration of the constraint space whose algebraic structure is simplified by introducing auxiliary variables and ensuring that constraints are at most quadratic. Computationally, we perform a projection onto the constraint space which is biased towards low values of an energy which expresses desirable "soft" properties like fairness. In particular, we present recent research on structures which use the minimal amount of material. There, we encounter remarkable relations to surfaces with minimum total absolute curvature (surface integral of the sum of absolute values of principal curvatures) and to kink angle minimizing polyhedral surfaces.