Computational Geometry is a relatively young and very active field of research in the intersection of mathematics and theoretical computer science. Studying algorithms and data structures have been main objectives of this growing discipline. Although geometric graphs are structures defined by geometric properties, like x- and y-coordinates, they have a highly discrete nature. Straight lines spanned by a finite set of discrete points give rise to simple and memory efficient data structures. While not loosing the geometric information, geometric graphs additionally provide combinatorial context (like neighborhood information) that is sufficient for many applications and allows for very efficient and stable algorithms. Moreover, for many problems the geometric information is not needed for their solution. In these cases, point sets, geometric in principle, can be stored and used in a purely combinatorial way. A simple example is the construction of the convex hull of a point set, which is an intrinsic task of countless algorithms. For this it is sufficient to know for any triple a,b,c of points whether c is to the left or to the right of the straight line spanned by a and b. A data structure that stores this information is the so called order type.

In the context of industrial applications, the complex problems cannot be solved satisfactorily by using methods from a single branch of applied geometry. Instead, a combination of different approaches will often be needed. Therefore, the different fields of Applied Geometry, such as

• Computational Geometry,
• Computer Aided Geometric Design,
• Image Processing,
• Computer Vision,
• Kinematics and Robotics

have started to become increasingly interconnected and begun even to merge.The proposed research in this FSP aims at creating an Austrian research community in this new and emerging field of Industrial Geometry.