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Links to
Class Webpages 2015.
Class Matters 2015.
ISL busroute 2015 for the Fieldtrip
CAVE tours 2015 for the Fieldtrip
Piazza Discussion Forum
PDF of MathViz Powerpoint presented in MA499 6may15
Optiverse Video on YouTube.
Last taught Spring 2012.

MA595 Fall 2015 Course in Geometry:

Professor George Francis
1pm MWF 102 Altgeld Hall
Recommended Text: Francis, A Topological Picturebook, Springer Paper Back, 2006.

We present the geometrical principles of real-time interactive computer animation (RTICA) for mathematical visualization as it is practiced in the classroom, research seminar, and webpages but also in immersive virtual environments from head-mounted displays (Oculus Rift) to the CAVE at the Illinois Simulator Lab (ISL) of the Beckman Institute.

Subject of the Course

Topics include the structure of the OpenGL graphical pipeline, the polyhedral encoding of surfaces as triangular meshes, the geometry of linear and aerial perspective (light and shade), the representation of the 3D group of Euclidean motions in 4D homogeneous coordinates, the algebra of 3D rotations in terms of unit quaternions SU(2), projective spaces and their Euclidean, spherical and hyperbolic metrics.

The course also includes a survey of classical topics including binocular optics and color theory, Haussdorff dimension and fractals, chaos and strange attractors, Wolfram's cellular automata, Barnsley's iterated function systems, Julia and Mandelbrot sets, discrete and continuous logistic equations, and the Lienard-VanderPol dynamical system.

All available topics are online, and students will be invited to request for class elaboration and discussion, those topics of particular interest to them. For their course grade students will create a webpage and give a presentation to the class on a topic of their choosing.

Prerequisites and Practicum

Prospective students should have a good spatial intuition, some artistic abilities or ambitions, and a solid grounding in linear algebra and vector calculus. They may participate in a concurrent tutorial, on useful line and surface graphics tools for the classroom and their dissertation, that may, but does does not require programming.

Students with experience programming in any computer language, such as BASIC, Javascript, C/C++, Python, or Mathematica, may gain 2 additional credits of independent study for a graphics programming project appropriate to the course and tailored to the proficiency of the student. In particular, projects suitable for a virtual environment at ISL are not only supported but strongly encouraged.

Students inexperienced in programming may take an individual study course to learn how to program a mathematical RTICA.