Konstantinos Gavriil (ESR13)

I am an ITN Marie Skłodowska-Curie Research Fellow at Evolute GmbH and a PhD student at the Applied Geometry group of the Institute of Discrete Mathematics and Geometry at TU Wien, under the supervision of Helmut Pottmann. My BSc is in Mathematics and MSc in Computational Science, both from the University of Athens. The focus of my PhD research is to incorporate various constraint types, such as constraints imposed by material properties, into the abstract geometric modeling design process.

Project: Computational design for architecture.

Supervisor: Helmut Pottmann
Institution: Evolute GmbH, TU Wien, Vienna, Austria

The main initial direction of this PhD is to study geometric modeling under the presence of material constraints. Materials like wood, glass and metal introduce constraints to the abstract geometric modeling of surfaces. The developability of these materials is an example of such a constraint which has been well studied. Additional constraints unique to each material, such as cold bending of glass, the double bending and stretching of metal sheets, and the preferred direction of timber panels can be taken into account. The incorporation of these constraints, induced by the unique properties of each material, to the design process will find immediate applications in areas such as architecture and engineering. At first, different constraint formulations for both material stretching and bending will be studied for both NURBS surfaces, which are the industry standard for geometric modeling, and triangle meshes for the discrete case. Algebraic and nonlinear analysis of these constraints will be carried out, as well as analysis of the error behavior. These constraint formulations will be linked to the existing mechanical property measurements of various materials.

We intend to develop an interactive design tool which allows the user to deform given surfaces from their initial configurations, such that material constraints are maintained within thresholds dictated by the material used. The interactive design tool will be implemented as a plugin to the widespread 3d modeling system Rhinoceros3D. The implementation will make use of an extensive C++ SDK for geometric optimization applications developed at Evolute GmbH. We, also, intend to present this work and any additional progress that will be made to top venues of geometric modeling and geometric computing.

The project will take place at Evolute’s office at Vienna. The PhD will be awarded by TU Wien.

Secondments are planned at INRIA (Sophia-Antipolis, France) and at SINTEF (Oslo, Norway).