Page 14 - Geometric Modeling and Algebraic Geometry

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developers, a major focus has been on bridging the language and knowledge gaps
between the different mathematical groups involved. All groups have had to invest
time into better understanding the traditional approaches of the other groups.

1.3 Why are CAD-type intersections still a problem for industry?

1.3.1 CAD technology evolution hampered by standardization

In the Workshop on Mathematical Foundations of CAD (Mathematical Sciences Re-
search Institute, Berkeley, CA. June 4-5, 1999) the consensus was that: The single
greatest cause of poor reliability of CAD systems is lack of topologically consistent
surface intersection algorithms. Tom Peters, Computer Science and Engineering,
The University of Connecticut, estimated the cost to be $1 Billion/year. For more in-
formation consult SIAM News, Volume 32, Number 5, June 1999, Closing the Gap
Between CAD Model and Downstream Application, http://www.siam.org/siamnews/
06-99/cadmodel.htm. Too low quality of CAD-intersection forces the industry to re-
sort to expensive workarounds and redesigns to develop new products.
CAD-systems play a central role in most producing industries. The investment in
CAD-model representation of current industrial products is enormous. CAD-models
are important in all stages of the product life-cycle, some products have a short life-
time, while other products are expected to last at least for one decade. Consequently
backward compatibility of CAD-systems with respect to functionality and the abil-
ity to handle “old” CAD-models is extremely important to the industry. Transfer of
CAD-models between systems from different CAD-system vendors is essential to
support a flexible product creation value chain. In the late 1980s the development of
the STEP standard (ISO 10303) Product Data Representation and Exchange started
with the aim to support backward compatibility of CAD-models and CAD-model ex-
change. STEP is now an important component in all CAD-systems and has been an
important component in the globalization of design and production. However, STEP
standardized the geometry processing technology of the 1980s, and the problems
associated with that generation of technology. Due to the CAD-model legacy (the
huge bulk of existing CAD-models) upgraded CAD-technology has to handle exist-
ing models to protect the resources already invested in CAD-models. Consequently
the CAD-customers and CAD-vendors are conservative, and new technology has to
be backward compliant. Improved intersection algorithms have thus to be compliant
with STEP representation of geometry and the traditional approach to CAD coming
from the late 1980s. For research within CAD-type intersection algorithms to be of
interest to producing industries and CAD-vendors backward compatibility and the
legacy of existing CAD-models have not to be forgotten.

1.4 Challenges of CAD-type intersections

If the faces of a CAD-represented volume are all planar, then it is fairly straight-
forward to represent the curves describing the edges with minimal rounding error.