By Tor Dokken (auth.), Bert Jüttler, Ragni Piene (eds.)
The ?elds of Geometric Modeling and Algebraic Geometry, notwithstanding heavily - lated, are routinely represented through virtually disjoint scienti?c groups. either ?elds care for gadgets de?ned by means of algebraic equations, however the items are studied in numerous methods. whereas algebraic geometry has built extraordinary - sults for knowing the theoretical nature of those items, geometric modeling makes a speciality of functional purposes of digital shapes de?ned by means of algebraic equations. lately, even if, interplay among the 2 ?elds has prompted new learn. for example, algorithms for fixing intersection difficulties have bene?ted from c- tributions from the algebraic aspect. The workshop sequence on Algebraic Geometry and Geometric Modeling (Vilnius 1 2 2002 , great 2004 ) and on Computational equipment for Algebraic Spline Surfaces three (Kefermarkt 2003 , Oslo 2005) have supplied a discussion board for the interplay among the 2 ?elds. the current quantity offers revised papers that have grown out of the 2005 Oslo workshop, which used to be aligned with the ?nal evaluate of the ecu venture GAIA II, entitled Intersection algorithms for geometry dependent IT-applications four utilizing approximate algebraic equipment (IST 2001-35512) .