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Research project: Geometric Modeling of Developable Surfaces

This research project as described by the list of publications below has a long history, and the hosting institution of this web page (TU Graz) has only contributed a small part. It has been supported by FWF Grant No. P12252 at TU Wien. Work was performed within the National research network S92 "Industrial Geometry", funded by Austrian Science Fund (FWF) in 2005-2010, especially subproject Computational Differential Geometry. From 2012, work on developable surfaces is performed within the framework of the SFB-Transregio programme Discretization in Geometry and Dynamics which is supported by Deutsche Forschungsgemeinschaft in general and by the Austrian Science Fund (FWF, via project I705) in particular.


Developable surfaces are characterized by being unfoldable into the plane without stretching or tearing. For all practical purposes this is the same as being composed of special kinds of ruled surfaces.

We are e.g. concerned with approximation of surfaces by developables, and in the segmention of freeform surfaces into developable strips. From the mathematical viewpoint, a series of curves which have the property that the ruled strips generated by them are developable (a developable strip model) represents a semidiscrete conjugate net, so there is an intimate connection to discrete (actually, semidiscrete) differential geometry.

The property of being developable is highly relevant for manufacturing, which makes such surfaces useful in various applied areas, from mechanican engineering to architecture.