Page 25 - Geometric Modeling and Algebraic Geometry

1 The GAIA Project 19
approaches of GAIA II for finding intersection and self-intersection e.g. using recur-
sive subdivision and the Bernstein basis are natural extensions of the GAIA work.
However, except for the exact methods developed, not much of the code generated
in GAIA II can be directly used.

1.8.4 Micro and nano technology

We followed the suggestion by the reviewers at the second review (June 2004) to
look at micro and nano technology and go to the DATE 2005 exhibition in Munich.
Before this exhibition we tried to understand what the actual needs within nano and
micro technology were. This proved to be a big challenge. Within SINTEF we both
have a micro/nano technology laboratory and people doing ASIC design. First ad-
dressing those running the laboratory we realized that the laboratory was oriented to-
wards production processes and could not answer our questions. Approaching ACIS
designers was more successful. With the current level of circuit miniaturization, the
actual geometry of the circuits due to etching starts to be more important. In the fine
detail corners are not sharp, they are round. Thus to take the actual geometry of the
circuits into consideration for simulation seems to be critical in micro and nano tech-
nology. During our presentation at the University boot of DATE we established two
areas where the GAIA II approach can be used:

• Solution of systems of equations describing the properties of integrated circuits.
• Description of the detailed shape of circuits using piecewise algebraic surfaces.
However, within micro and nano technology there are already groups of math-
ematicians. To be able to address this area we have to establish a common meeting
place, such as a series of workshops may be as a strategic support action in the 7th
framework program.

1.9 Potential impact of the GAIA project

The development of mathematics for CAD has been stagnating since the standard-
ization of CAD-representation in the start of the 1990s, and as the mathematicians
addressing CAD-challenges got fewer. The CAD-vendors have merged to a handful
of dominant world wide CAD-systems. As large user groups do not need handling
of complex surface geometries, the problems of industries in need of improvements
or improved algorithms have been given low priority by the vendors.

1.9.1 Bottleneck before GAIA II: Only rudimentary self-intersection
algorithms
Advance shaped products are to a large extent built by structures of sculptured sur-
faces. The designers like smooth transitions, and love the shape behavior close to