Geometry

Geometry and Computational Design

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KAUST

An important stream of research in computational design aims at digital tools which support users in realizing their design intent in a simple and intuitive way, while simultaneously taking care of key aspects of function and fabrication. Such tools are expected to shorten the product development cycle through a reduction of costly feedback loops between design, engineering and fabrication. The strong coupling between shape generation, function and fabrication is a rich source for the development of new geometric concepts, with an impact to the original applications as well as to geometric theory. This will be illustrated at hand of applications in architecture and fabrication with a mathematical focus on discrete differential geometry and geometric optimization problems.

Geometry and Computational Design of Equilibrium Structures

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B1 L3 R3119

Freeform structures play a prominent role in contemporary architecture. In order to stay within reasonable cost limits, computational shape design has to incorporate aspects of structural analysis and fabrication constraints. The talk discusses solutions to important problems in this area. They concern the design of polyhedral surfaces with nearly rectangular faces, polyhedral surfaces in static equilibrium, the smoothest visual appearance of polyhedral surfaces and the closely related problem of finding material-minimizing forms and structures. From a methodology perspective, there is an interplay of geometry, mechanics and optimization. Classical subjects such as isotropic geometry, a simple Cayley-Klein geometry, play a role as well as most recent developments in discrete differential geometry. We also show how practical requirements have led to new results and open problems in geometry.