This page http://new.math.uiuc.edu/oldnew/math428 was last updated 18apr19 by
gfrancis@uiuc.edu.
## 2000 Course: Topics in Geometry

# Math 428G1/351G1 : GEOMETRICAL GRAPHICS

Lawson's Snails. Crossed stereo left two, straight stereo right two images.
Professor
George Francis

3:00 - 5:00 pm MWF

UIMATH.grafiXlab -- 102 Altgeld Hall, and

NCSA
Renaissance Experimental Lab
(REL)
-- 3414 Beckman Institute

We treat the geometrical basis of computer graphics, emphasizing
real-time interactive computer animation
(RTICA)
and its use in computational science and engineering
(CSE)
applications, in particular, for
mathematical visualization.
We will use Unix (Irix and Linux) workstations in the
Renaissance Experimental Lab (REL) of the NCSA to program
short RTICAs in C/C++/Java, using the OpenGL graphics library.
We will use the
CAVE totally immersive virtual environment.

Topics include the structure of the OpenGL graphical pipeline, the
polyhedral encoding of surfaces as triangular meshes, the geometry of
linear and aerial perspective (ligh and shade), the representation of
the 3-D affine group in 4-D homogeneous coordinates, the algebra
of 3-D rotations in terms of unit quaternions, projective spaces and
their Euclidean, spherical and Minkowski (hyperbolic) metrics. We
will explore non-Euclidean splines and morphing techniques, real time
interactive texture mapping, and other advanced graphics techniques
for innovative mathematical application.

Prospective students should have a good spatial intuition,
some artistic abilities or ambitions, a solid grounding in
linear algebra and 3-D calculus. In addition, it is advisable
that students either already have a good command of C/Unix
and be prepared to learn some higher geometry,
OR program fluently in some language but already have a
strong geometrical background. Students will be expected to
share their expertise with their colleagues.
Credit is based on active participation in the tutorials,
timely submission of documented programming assignments,
and the completion of a substantial semester
projects
appropriate to the course and tailored to the proficiency
of the student.

The .dvi and .ps files for the early chapters of the
M428 classnotes
are on the web. They are "old" but possibly useful. On some browsers you
can just click on the .ps files and read them on line without downloading
them first.