Page 27 - Geometric Modeling and Algebraic Geometry

1 The GAIA Project 21
Intel, it states that the growth of computing power follows an empirical exponential
law. Moore originally proposed a 12 month doubling and, later, a 24 month period.
Until recently the evolution of the frequency of the CPU has had a close relation
to a doubling every 12, 18 or 24 month. However, in the last years multi-core CPUs
have been introduced. As long as the growth in computational power was related to
the CPU-frequency, old sequential program codes could easily profit from the growth
in computational power. However, with multi-core CPUs the code has to be prepared
for multi-core CPUs to benefit from the performance. Consequently, the era when
old sequential program codes automatically benefit from Moore’s law is coming to
an end. In the coming years reimplementation of algorithms will be necessary to
benefit significantly from Moores law.
The GAIA II results have shown significantly improvements in CAD-function-
ality, but we have also experienced that the 2005 level single-core CPUs are too slow
for efficient industrial use of the results. However, with the ongoing activity within
SINTEF on GPU-acceleration of intersection algorithms and the use of multi-core
CPUs will make accessible sufficient low cost computational resources for industrial
use of the GAIA II results. SINTEF has already started on this work [5] as stated
above, and has addressed IPR-protection by patenting.
The ideas of GAIA II should be combined with GPU-acceleration and multi-core
CPUs. There are indications that visualization and simulation will be central in FP7.
If this is the case GAIA II and the SINTEF GPU-activity can be viewed as preproject
for proposals within FP7.

1.9.4 Future outlook: More use of algebraic representations in CAD

Although we have not found as much results in traditional real algebraic geometry
as expected to be used within CAD, the work on approximate implicitization and ap-
proximate parameterization has opened a bridge between parametric and algebraic
representation that earlier did not exist. We also expect that more efficient visualiza-
tion techniques will be available for algebraic surfaces in the years coming. When
this is in place we expect a much wider use of algebraic geometry both in CAD and
in applications within petroleum and health.

1.9.5 Use of the GAIA II results by other researchers in the area

With the broad range of papers published by GAIA II project partners, most of the
research done within GAIA II is already available to other researchers in the area.
The reference list following contains papers related to the GAIA II project published
by the partners form the start of the GAIA assessment project until the publication
of this book.
Much of the most important software of GAIA II is already available or will be
available for download on the Internet as Open Source (GNU GPL License):

• AXEL library is available at http://www-sop.inria.fr/galaad/.
• Approximate implicitization is available at http://www.sintef.no/math/.