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K. Gavriil:
"Interactive Freeform Architectural Design with Nearly Developables and Cold Bent Glass";
Supervisor, Reviewer: H. Pottmann; E 104 Institut für Diskrete Mathematik und Geometrie, 2020; oral examination: 2020-09-18.

Interactive design of freeform architectural surface panelizations is at the core of this PhD thesis. We provide the computational framework for dealing with two important types of paneling elements. Specifically, we focus on certain types of developable surfaces and cold bent glass panels, all relevant to contemporary freeform architecture. To this end, we initially present a novel method for increasing the developability of a B-spline surface. We use the property that the Gauss image of a developable surface is 1-dimensional and can be locally well approximated by circles. This is cast into an algorithm for thinning the Gauss image by increasing the planarity of the Gauss images of appropriate neighborhoods. A variation of the main method allows us to tackle the problem of paneling a freeform architectural surface with developable panels, in particular enforcing rotational cylindrical, rotational conical and planar panels, which are the main preferred types of developable panels in architecture due to the reduced cost of manufacturing. We are interested in near developability, rather than exact developability, so the optimization approach is sucient. The motivation behind this is the fact that most materials allow for a little bit of stretching and therefore developability needs not be satised to a high degree. One such material is glass which is the main focus of the second panelization problem of this thesis. Toughened glass can withstand higher stresses, and therefore allows initially planar glass panels to be elastically bent and fixed at ambient temperatures to a curved frame. This process is called cold bending and it produces panels that can exhibit double curvature, providing a cost- and energy-efficient alternative of higher optical quality than traditional hot bent glass panels. However, it is very challenging to navigate the design space of cold bent glass panels due to the fragility of the material, which impedes the form-finding for practically feasible and aesthetically pleasing cold bent glass façades. We present an interactive, data-driven approach for designing cold bent glass façades that can be seamlessly integrated into a typical architectural design pipeline. Our method allows non-expert users to interactively edit a parametric surface while providing real-time feedback on the deformed shape and maximum stress of cold bent glass panels. Designs are automatically refined to minimize several fairness criteria while maximal stresses are kept within glass limits. We achieve interactive frame rates by using a differentiable mixture density network trained from more than a million simulations. Given a curved boundary, our regression model is capable of handling multistable configurations and accurately predicting the equilibrium shape of the panel and its corresponding maximal stress. We show predictions are highly accurate and validate our results with a physical realization of a cold bent glass surface. For both applications explored in this work, a plethora of results and examples are provided.

architectural geometry; computational design; fabrication aware design; inverse design; deep learning; mechanical simulation; cold bent glass; developable surface

http://dx.doi.org/10.34726/hss.2020.82428