Syllabus for MA595-CGV 6jan12
This list of lesson titles, resources and topic is subject to
changes. Please consult often. "W1" means Wednesday of week 1.
W1 "What is the Name of this Course"
Administrivia: calendar, website, logins, infosheet, AD passwords.
Resources: Francis, "A Topological Picturebook", Springer PB, 2006.
Official webpage http://new.math.uiuc.edu/math595.
Google.
Expectations: grades, portfolio, journal, tutorials, projects.
Lesson of the Day:
* Survey of Course.
* Tutorial time 4-5pm (?)
* Possible tutorial topics.
* Questions and answers.
F1 "Abbreviated History of Mathematical Illustration"
Chinese and Euclid's proof of the Pythagorean theorem,
Alberti's Veil: From D"urer's Nude to Projective Geometry.
Descriptive geometry, computer graphics, constructive solid
geometry, virtual reality.
Stereolithography: From 19th century plaster models to
contemporary 3D Printers.
Visuals: Powerpoint slides and whiteboard drawings.
* Ben Grosser's stop action video of printing John Sullivan's
3D model "Minimal Flower 3" and Morse Theory.
* Beau Janzen's video of Thales' measurement of the earth.
M2 "Touring the Topological Picturebook"
References:
* George Francis, "The Topological Picturebook", Springer Verlag,
1987 hardback, Paperback with corrected figures 2007.
Also in Russian, Mir, 1991, and Japanese, PB 2006.
* http://new.math.uiuc.edu/netmath403/403/perspective/index.html
* Jeff Weeks, "The Shape of Space", Dekker, (1985), 2002.
Topics:
Linear and aerial perpective (Chapter 3).
Blackboard drawing with chalk (Chapter 2).
Line drawings on paper napkins and vellum (Chapter 5).
Illustrating "Conway's ZIP Proof" with ink drawings in
the appendix, Weeks, Dekker 2nd edition, 2002.
Gains and losses in replacing hand drawing with computer
drawing with the mouse : MacPaint, Paint and iPaint.
Visuals:
* Powerpoint slides and whiteboard drawing.
Lab: Apple's "Grapher" and DPgraph for Windows.
W2 "Putting on the Geometrical Puppetshow"
References: http://new.math.uiuc.edu/puppetshow
Topics:
* Is this any way for a grown mathematician to spend his time?
* How many theorems have been proved using mathematical visualization?
* Bourbaki wasn't the first mathematical iconoclast.
* To explain is to satisfy the curiosity of the questioner.
But what if they're not curious to begin with?
* From the laptop to Immersive Virtual Environments (IVEs)
* A sociology of mathviz.
Visuals:
* Video "Air on the Dirac Strings" with Lou Kauffman and Dan Sandin.
This illustrates the action of the quaternions on 3D rotations.
* Video of the "Etruscan Venus" with Francois Ap`ery and Donna Cox.
* Real-Time Interactive Computer Animatiam (RTICA) of the homotopy.
The romboy homotopy connects four classical surfaces:
Steiner's Roman surface, Boy's surface, Etruscan Venus, Idaszak's IDA.
F2 "Metarealistic Rendering of Real-time Interactive Computer Animations"
Part I (more later.)
References:
"Mathematics and Culture II", M. Emmer ed., p125-145, Springer, 2005
Penultimate prepublication draft:
http:www.math.uiuc.edu/~gfrancis/public/mrtica13may.pdf
John Hart, webstite for
https://agora.cs.illinois.edu/display/cs519sp09/Scientific+Visualization
Topics:
* What is a real-time interactive computer animation (RTICA)?
* How meta-realistic rendering (MRR) differs from
non-photorealistic rendering (NPR).
* Why MRR is not just VR.
* Topological homotopy and morphing.
* Homotopies by dimensions R^n x I -> R^p
- projections n > p
- morphing n = p
- insertions n < p
* Homotopies by complexity:
- motions = isometries
- articulatations = scene graphs
- distortions = warping
- deformations = continuous pointwise dislocation
- the geometry underlying the OpenGL pipeline
- Concepts of alibi, alias and place in coordinate systems
- The mysteries of the associative law of matrix multiplication.
- Apprehending the 4th dimension by direct visualization (4D-viz)
+ decorations (e.g. glyphs as 4D icons)
+ charting (conformal projection, Mercator's projection)
+ shadows (dimension lowering projections, Plato's Cave)
+ slices (3D cross-sections of 4D structures, 4D labyrinth)
- Appreciating the 4th dimension for its practicality (4D-fx)
in visualizing 3D phenomena like
+ designing smooth camera paths = quaternionic splining
+ special and general realativity = gravitational lensing
Visuals: RTICA on the lab computers.
M3 No Class (Senate)
W3 "Virtual Environments/Megabuck Videogames"
F3 Fieldtrip to the Illinois Simulator Laboratory (ISL) for demos in
in immersive virtual environments and simulators.
M4 "Collaborative Research: how to sneak some math into science."
Topics:
* Renaissance teams and the Etruscan Venus.
* SIGGRAPH, Supercomputing, and Planetariums.
* Projects that were raptured.
* Projects that were left behind.
W4 "The Optiverse and Earlier Sphere Eversions."
Topics:
* The sphere eversion problem as a paradigm for mathviz.
* Werner Boy's curvatura integra (1900)
* Whitney-Graustein theorem (1937)
* S. Smale's eversion corollary (1958)
* ... followed by 50 years of visualization:
Shapiro, Thom, Morin, Phillips, Max, Apery, Thurston, Sullivan
F4 "Quasicrystals" with artist Tony Robbins and many students.
DeBruijn proposed two methods for realizing quasicrystals
as 3D-projections of sub-lattices of the 6D unit lattice. A 3D
packing by 2 kinds of rhombohedra is quasicrystalline if it
displays icosahedral symmetry locally, but is aperiodic globally.
In this collaboration with mathematical artist Tony Robbin, and
a succession of REU students we use deBruij's "method by duals"
to create real-time interactive CAVE animations.
M5 "Solved and Unsolved Problems in Geometrical Visualization"
W5 "Geometry Viewers, Graphics Packages, Languages and Libraries."
F5 "Seminar in Lieu of a Midterm" for this 8 week course.
The subsequent half of the course is devoted to seminars and special topics
as chosen by, and given by students. Possible topics are OpenGL programming.
More will be listed for a vote.