Coupling evolving level sets with curves and surfaces

Industrial geometry is based on computational techniques which originated in various branches of applied geometry. For instance, the methods of Computer Aided Geometric Design form the mathematical foundation of the powerful CAD technology which is available today. Computer Vision provides methods for inspecting and analyzing video images. The tools of image processing are used to reconstruct geometrical features from digital image data, such as X-ray or computer tomography images. Computational Geometry provides efficient algorithms for solving fundamental geometrical problems. Until recently, these different branches of applied geometry have been developed by fairly disjoint and independent scientific communities. The wide background of problems and applications led to a great diversity of approaches and produced a wealth of available techniques. Now, the different branches of applied geometry have matured and provide solutions for certain well--defined classes of problems. During the last years, the different fields and communities have started to become increasingly interconnected, and begun even to merge. This process is driven by the increasing complexity of the applications, where techniques from only one field are generally not sufficient to arrive at useful results. The new technological possibilities of data acquisition and processing lead to a new and more challenging class of problems. The FWF Joint Research Programme "Industrial Geometry" will integrate and combine the different branches of application-oriented geometric research. It is necessary to look at central problems of industrial geometry from different viewpoints, to gain new tools and insight and to perform the work together within the same big project. The following research groups will take part in this project: Oswin Aichholzer/Franz Aurenhammer (TU Graz, www.igi.tugraz.at/oaich), Manfred Husty (Innsbruck, techmath.uibk.ac.at/geometrie), Otmar Scherzer (Innsbruck, www1-c703.uibk.ac.at/infmath}, Bert Jüttler (Speaker, Linz, www.ag.jku.at), Helmut Pottmann (Co-Speaker, TU Vienna, www.geometrie.tuwien.ac.at/ig).