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Institute of Geometry

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Research project: Computational Differential Geometry

This research area has been explored within the framework of the the National Research Network Industrial Geometry, funded by FWF in 2008-2011. Currently we are exploring Semidiscrete Surfaces (FWF-Project I705, 2012-2016) which is part of the SFB-Transregio Discretization in Geometry and Dynamics, which is funded by DFG and in part by FWF.

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Computational Differential Geometry means methods of both numerical and discrete mathematics with the purpose of investigating and modeling curves and surfaces. The main theme of this research project is the robust analysis of differential properties of surfaces, the creation of discrete and semi-discrete models of freeform surfaces, and the study of geometric properties of such models. It is only recently that the wealth of interesting geometry connected to applications in, say, architecture, has come to the attention of mathematicians, and presumably only a small part of it has been investigated.

We are investigating topics of Discrete Differential Geometry: discrete curvatures based on parallel meshes, quad-based and hex-based discrete surfaces, Christoffel duality, and others. New lines of research of semi-discrete surfaces and inverse problems in connection with integral invariants.

The list of publications below also includes work performed before the runtime of the above-mentioned grants.

Publications