CAGD has broad industrial applications to the design of cars, aircraft, ships, submarines and more. It is used extensively in computer graphics, font design, cartography and meteorology. It is also an essential ingredient in the new family of digital feature films coming out of Hollywood, such as the brand new Disney/Pixar collaboration, "A Bug's Life".
The SIAM Activity Group on Geometric Design sponsors special conferences on CAGD every two years. We presented results of our Spelman investigations of the mathematical basics of CAGD using Maple at the 1995 meeting.
In the 1993-95 period, many seminars in CAGD were conducted jointly with Dr. Jeffrey Ehme, for both faculty and students at Spelman College, thanks to generous funding and expertise provided by Boeing. We used Maple and Matlab to explore the mathematical basics of CAGD, including the specialized Matlab Splines Toolbox. Overall, about 20 students participated in these seminars, some for several semesters in a row.
Five students were engaged in undergraduate research in this area, presenting papers and posters at local and national conferences, and travelling to Seattle (in April 1995) to visit both the Mathematics R&D folks at Boeing and the Graphics/Visualization Lab at the CS/Engineering department at the University of Washington. Ayana Moore ('97) took first prize in the student category for her talk on CAGD at the SIAM-SEAS Regional Meeting at The Citadel, Charleston, South Carolina, March 1995. Ayana is now in the Ph.D. program in Applied Mathematics at the University of Washington.
Our first minicourse on CAGD, based on the paper listed below, was:
The Elements of Computer Aided Geometric Design
Using Maple (two hours), given jointly with Jeffrey Ehme on 18th
November 1995, at the Eighth Annual International Conference on Technology
in Collegiate Mathematics, Houston, Texas.
The mathematical basics of CAGD are very approachable, requiring only the
rudiments of linear algebra and multivariable calculus to get started.
Later on, sophisticated numerical concerns arise, which must be addressed
in any realistic "industrial strength" applications (be they to industry
or computer graphics or anything else).
Publication:
For a distillation of much of the mathematics encountered in Spelman's CAGD seminars, see:
This assumes no prior familiarity with the subject. The first version was written in the last week of July 1995 with the support of Spelman College's Center For Scientific Applications of Mathematics.
Special thanks to Drs. David Mizell, David Ferguson and John Lewis at Boeing
for their encouragement and support over the years.
Workshops/Tutorials:
A two-hour tutorial on ``The Curves
and Surfaces of The Digital Age'' was given at the
International Conference CIMAF 2001 (6th Symposium on Mathematics
and 4th Italo-Latinoamerican Conference on Industrial and Applied
Mathematics) in Havana, Cuba,
19th-23rd March, 2001.
A three-hour MAA student short course on ``The Curves
and Surfaces of The Digital Age'' was given at the
Oklahoma-Arkanasas Section Meeting at Arkansas Technical University,
Russellville, AR, 31st March, 2000.
A four-hour MAA minicourse entitled
``The
Curves and Surfaces of The Digital Age'' was given (jointly
with Jeffrey Ehme)
at the
Joint Mathematical Meetings in Washington, DC, January 2000.
A similar MAA
minicourse was given
at
Mathfest '99 in Providence, RI.
The Curves and Surfaces of
The Digital Age, a three-hour MAA short course, was given jointly
with Jeffrey Ehme, at the 78th Annual MAA Southeastern Section Meeting,
Rhodes College, Memphis, TN, 12th March 1999.
An
invited talk on this subject was given on Saturday 20th March 1999, during
the 16th
Annual Conference on Undergraduate Mathematics at Rose-Hulman
Institute of Technology (in Terre Haute, IN).
(This is http://www.spelman.edu/~colm/cagd.html,
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