DIMENSION++

This project is concerned with geometric partitioning structures in three-dimensional space. Such structures are a versatile tool in storing, processing, and displaying multivariate data, with various applications inside and outside Computer Science. The majority of results available nowadays concern the two-dimensional case. On the other hand, many practical situations lead to problems that are three- dimensional in nature. In this DIMENSION++ project, we intend to join forces to conduct research on 3D problems of this kind. The involved research groups (E. Papadopoulou, Lugano; F. Aurenhammer, Graz; B. Juettler, Linz) have already successfully collaborated on topics in Computational Geometry within the framework of EuroGIGA (initiated by F. Aurenhammer) and in the DACH Project VORONOI++. In fact, our goal is twofold: (1) The theoretical investigation of complex structures such as 3D farthest-site and cluster Voronoi diagrams and 3D straight skeletal structures. These topics show the necessary diverstity for a successful research, and on the other hand are strongly interrelated which promises a (continuing) fruitful cooperation between the involved research groups. (2) The development of practical software for computing these structures using the Computational Geometry Library CGAL. Robust and efficient implementations of 3D geometrical structures are still rare, and the DIMENSION++ project intends to help filling this gap.