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In this course, we will investigate some of the mathematics needed to
generate computer images. This is the mathematics behind computer
graphics and the mathematics behind CAD/CAM systems. In fact, most
of the mathematics in this course was developed by engineers and computer
scientists, not mathematicians.
For instance, consider the following situation in computer graphics,
how do you create the character below from the Pixar short,
Geri's Game? What information do you need to specify? How much
information do you need to specify? How do you modify the shape of the
character? How do you make him move?
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Geri from Geri's Game
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A wireframe model for a car
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For a second example, consider the problem of designing of a car body,
an airplane wing, an office chair, a keel for a yacht, et cetera (see model
above). This is an example of ab initio design where an object
is to be created to satisfy some functional or aesthetic goals. Frequently,
such objects are designed by defining and redefining the object's shape
and performing appropriate analysis (simulation) until the design criteria
is satisfied.
Some of the questions to be considered in this course are:
What geometric information is needed to create an image on a computer?
How do changes in the information affect the shape of the object?
What do we mean mathematically by the shape of the object?
How does the shape of the object affect its interaction with the
surroundings?
The above question involve serious mathematics, including calculus
and analytic geometry, euclidean geometry, linear algebra (vectors and
matrices), numerical methods, interpolation and approximation theory.
The pre-requisites for this course are MA113 Calculus III and an inquiring
mind (MA 221 or MA 371/373 is recommended for a little linear algebra).
The rest of the mathematics required in the course will be developed as
needed.
Contact Professor Finn at
DAVID.FINN@ROSE-HULMAN.EDU
for more information on the course.
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