Industrial Geometry

Industrial geometry is based on computational techniques which originated in various areas of applied geometry. To give a few examples, the methods of Computer Aided Geometric Design form the mathematical foundation of the powerful CAD technologies available today. Computer Vision provides methods for inspecting and analyzing images and videos. Image processing is used to reconstruct geometric features from digital image data, such as X-ray or computer tomography images. Computational Geometry provides efficient algorithms for solving fundamental geometrical problems. Robot kinematics deals with geometric problems which occur in connection with robot mechanical systems.

In recent years, these different areas of research have started to become increasingly interconnected, and begun even to merge. A driving force in this process is the increasing complexity of applications, where one field of research alone would be insufficient to achieve useful results. Novel technologies for acquisition and processing of data lead to new and increasingly challenging problems, whose solution requires the combination of techniques from different branches of applied geometry.

• Initializing a close cooperation between Austrian research groups working in areas which are important for Industrial Geometry.
• Building up an internationally leading research team in Industrial geometry by doing joint research on the many projects which have been identified by the members of our team.
• Development of new methods for the solution of important Industrial geometry problems.
• Developing new university course material in central areas of Industrial geometry, thereby introducing young researchers to Industrial geometry, which is necessary for growth and continuing excellence of this research area.
• Creating an international scientific community for Industrial Geometry.
• Defining and emphasizing new directions for geometry education in Austria, which draws from a long tradition of constructive geometry.
• Strengthening Industrial Mathematics as an already existing area of excellence in the Austrian research landscape.

One of the main goals of the proposed NRN is the initialization of a close cooperation between different research groups working in various areas of Industrial Geometry. The structure of the present proposal reflects this by showing the close interrelation of the research problems we intend to study. The fact that the majority of such problems has its origin in one of those areas and has been formulated within the related theoretical background does not disagree with this viewpoint.

In view of the wide range of different topics involved, ranging from classical geometry to robotics and computational geometry, the combined knowledge of all groups participating in this NRN will be needed for its successful implementation. Specific relations and expected synergies between the sub-projects are described in detail within each subproject. Please refer to project pages for more details.