May 25 – 30 , 2008, Dagstuhl Seminar 08221

Geometric Modeling


Gerald Farin (Arizona State University – Tempe, US)
Stefanie Hahmann (University of Grenoble, FR)
Jörg Peters (University of Florida – Gainesville, US)
Wenping Wang (University of Hong Kong, HK)

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The seminar succeeded in bringing together leading researchers from 17 countries to present and discuss radically different approaches to the challenge of modeling complex geometric phenomena on the computer. Acquisition, representation and analysis of 3-dimensional geometry call for the combination of technically complex and often interdisciplinary approaches that are grounded both in classical mathematics and computer science data structures and theory. Reflecting the dynamics of the field, the meeting included a number of junior researchers.

The presentations ranged from the application of graphics processing units, to graph techniques, to algebraic approaches, discrete geometry, combining clasical spline with new subdivision methods and leveraging the geometry of classical surfaces in areas as far as architecture and medical modeling.

The unique setting and combination of participants revealed and correlated a surprising number of new techniques and insights. New surface fitting methods addressed the intricate problem of resolving the shape where several different primary geometric features merge (the multisided fair surface blending problem), and of representing thicker layers of surfaces (shells)as well as support functions on surfaces to support computations on manifolds.

A key point, both for industrial applications and fundamental scientific inquiery, is the topological correctness of surfaces. In particular, topological and metric guarantees are needed when reconstructing and matching objects or extracting surfaces (geometric processing); for example to avoid singularities and self-intersections. The (highly nonlinear) challenge of not only measuring but of controlling intrinsic geometry was laid out in several talks. While some approaches concentrate on the mathematical challenge, an alternative is to emphasize the interface and human intervention.

For simple geometry, determining geometry from constraints is another viable approach. Subdivision is an intriguing technique to flexibly represent geometry via refinement. This method bridges discrete and spline-based geometry. While key components have matured to the point where a survey talk laid out the fundamental structure, talks exposing work in progress and posing unresolved questions highlighted the need for further work. The detailed findings will appear in two refereed volumes, of full length research papers on Geometric Modeling to be published in a Springer journal.

Fittingly, the workshop was the setting for the John Gregory Award. The award, named after a pioneer of the field, honored the longterm innovative contributions to field of Hartmut Prautzsch, Helmut Pottmann and Tom Sederberg.

The productive meeting and exchange was made possible thanks to the unique setting and atmosphere of Dagstuhl castle whose scientific board gave the opportunity to organize this seminar and whose excellent administration made it possible to focus on work.

Dagstuhl Seminar Series


  • Computer Graphics
  • Modeling


  • Geometry
  • Engineering
  • Volumetric modeling
  • Computer graphics


In the series Dagstuhl Reports each Dagstuhl Seminar and Dagstuhl Perspectives Workshop is documented. The seminar organizers, in cooperation with the collector, prepare a report that includes contributions from the participants' talks together with a summary of the seminar.


Download overview leaflet (PDF).

Dagstuhl's Impact

Please inform us when a publication was published as a result from your seminar. These publications are listed in the category Dagstuhl's Impact and are presented on a special shelf on the ground floor of the library.


Furthermore, a comprehensive peer-reviewed collection of research papers can be published in the series Dagstuhl Follow-Ups.