Industrial Geometry

Summary

This subproject focuses on the communication and exchange of ideas and knowledge within the research network. In order to facilitate this scientific exchanges, we organized a series of internal seminars and international workshops, and we run the project website.

At the internal seminars, talks about the ongoing research activities were presented by the collaborators in this research network. In addition, the team of this subproject has prepared tutorials about fundamental aspects of the various fields of expertise which are present in this network. The aim of this activity was to transfer knowledge between the different research groups within the network.

A major goal has been to collect these and continuing themes in a textbook on industrial geometry. Additionally a novel textbook on geometry for architecture has been supported. It covers fundamental and classical material and proceeds to advanced and modern topics in geometry which are close to present research topics in geometric optimization and discrete differential geometry.

Status seminars

In order to facilitate the scientific exchange between the participating groups, we organized a sequence of status seminars. The investigators and collaborators of the network participated in these events.

• The kick-off meeting took place in Obergurgl in April 2005.
• The first status seminar was held as a 3-day workshop in Graz/St. Martin, in November 2005.
• The second status seminar took place at Strobl in June 2006 (4 days).
• The third status seminar was held as a 2-day extension of the international workshop on Level Set methods and Image Processing. It took place in Obergurgl in September 2006.
• The fourth status seminar took place during 2 days in March 2007, and was held at St. Martin (Graz). It served 3 main purposes.
• A fifth status seminar took place in March 2008. It was again held at Strobl. This event served as the kick-off meeting for the continuation of the network activities.
• A sixth status seminar is scheduled for April 2009. It will again be held at Strobl.

International workshops

We organized several workshops for participants from all over the world. These workshops were dedicated to special topics which are under investigation within the FSP.

• A five-day international workshop on "Variational, PDE, and Level Set Methods", which was mainly organized by the Innsbruck group, took place in Obergurgl in September 2006. Several of the invited papers will appear shortly in a special issue of Computing.
• A workshop focusing on the interaction of Geometric Modeling and Computational geometry, which was jointly organized by the groups in Linz and Graz, was held in the monastery Stift Vorau, in November 2006. In addition to 8 lectures by invited speakers, several talks of participants in this network were given.
• A workshop on "Computational Methods for Algebraic Spline Surfaces" has jointly been organized by B. Jüttler (Linz), M. Peternell (Vienna) and J. Schicho (Linz). This workshop took place in the second week of September 2007 at Strobl.
• Immediately after this event, a workshop on " Polyhedral Surfaces and Industrial Applications" took place at Strobl. It has jointly been organized by A. Bobenko (Berlin), K. Polthier (Berlin), H. Pottmann (Vienna) and J. Wallner (Graz).

Web Site and Technical Report Series

Tutorials - Knowledge transfer

Fundamental material for lectures from classical geometry, curves and surfaces in CAGD, computational geometry and geometric optimization has been collected. Part of them have been presented at introductory lectures at the status seminars. These short courses aim at transferring knowledge between the different research groups within the research network and help the researchers to get to know methods and techniques from the various fields of science coming together in industrial geometry.

More precisely, 4 tutorials were developed and presented at the four status seminars:

• Classical geometry on curves and surfaces in CAGD
• Fundamentals of computational geometry
• Image processing
• Discrete differential geometry

Each of them was jointly prepared by the team of subproject 1 and one of the participating groups in the FSP (Linz, Graz, Innsbruck and Vienna, respectively).
These introductory lectures were considered as the best possibility to distribute the various knowledge present at the different research groups among all participating researchers. Most of the short course materials, which includes several matlab and CGAL demo programs for free form curves and surfaces and computational geometry tasks, are available at the homepage of the research network.

Case studies and comparison of methods

For our work on distance functions, and on approximation with spheres, see the detailed report.

Compilation of lecture notes and textbooks

In the first two years of the funding period, major effort was dedicated to compile lecture notes for a course entitled Industrial Geometry, already being taught at the TU Vienna. Test implementations for registration algorithms with and without known correspondences have been performed. A further topic has been the reconstruction of developable surfaces from point clouds. Two diploma theses have been supervised.

Most work of the last year is dedicated to support the finalization of a novel textbook on geometry and its applications in architecture. The content of this monograph reaches from a fundamental introduction to advanced methods and current research topics, mainly in discrete differential geometry. Figures for the introductory part and test implementations for the advanced topics have been provided.

A detailed report of the first funding period is available here. See also the list of Publications.