Page 13 - Geometric Modeling and Algebraic Geometry

1 The GAIA Project 7
Sophia Antipolis in France was contacted. An application for an IST FET Open As-
sessment project was made also including the CAD-company think3. The proposal
was successful, and in October 2000 the project IST 1999-290010 – GAIA – Applica-
tion of approximate algebraic geometry in industrial computer aided geometry was
started.
The final review of the assessment project in October 2001 was successful, and
the project consortium was invited to propose a full FET-Open Project. Also this
proposal was successful, and July 1st 2002 the project IST-2001-35512 – GAIA II –
Intersection algorithms for geometry based IT-applications using approximate alge-
braic methods started. The full project ended on September 30th 2005. The budgets
of the phases of project have been:

• GAIA assessment phase: Budget: 175 000 EURO, with financial contribution
from the European Union of 100 000 EURO.
• GAIA II project phase: Budget: 2 300 000 EURO, with financial contribution
from the European Union of 1 500 000 EURO.
Among the project partners we find one CAD-company, one industrial research
institute, and four university groups:
• SINTEF ICT, Department of Applied Mathematics, Norway, has been the
project coordinator, and focused on work within approximate implicitization,
recursive intersection algorithms and recursive self-intersection algorithms. For
more information on SINTEF see: http://www.sintef.no/math/.
• think3 SPA, Italy and France, is a CAD-system developer, and had as their
main role to supply industrial level examples of challenging CAD-intersection
and self-intersections, to integrate developed intersection algorithms into a pro-
totype version of their system thinkdesign, and finally to test and assess the pro-
totype algorithms developed in the project. For more information on think3 see:
http://www.think3.com/.
• University of Nice Sophia Antipolis (UNSA), France, developed in close co-
operation with INRIA exact intersection algorithms and a triangulation based
reference method for surface intersection and self-intersection. For more infor-
mation on UNSA and INRIA see: http://www-sop.inria.fr/galaad/.
• University of Cantabria, Spain, worked on combined numeric and exact inter-
section algorithms. For more information see: http://www.unican.es/.
• Johannes Kepler University, Austria, focused on new approaches to approxi-
mate implicitization and testing of approximate implicitization algorithms. For
more information on this partner see: http://www.ag.jku.at/.
• University of Oslo, Norway, has focused on classification of algebraic curves
and surfaces and their singularities. For more information on the University of
Oslo see: http://www.cma.uio.no/.
Based on state-of-the-art reports, research reports and software prototypes we
have tried to establish a common mathematical understanding of different approaches
and tools. As the project partners come from an axis spanning from fairly theoretical
classical algebraic geometry to computer aided geometric design and CAD-system