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From May 26 to May 30 2008 the Dagstuhl Seminar 08221 "Geometric Modeling" was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general.doi:10.4230/dagsemproc.08221.1 fatcat:6kzt6gvjlrgllifed7yfizkbx4