Alan J. Anders	aanders@ucsd.edu
Final Project

Description: 
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  The project consists of a strange scene in space with earth as the center of
focus. Around the earth is first the Moebius strip that contains a balling rolling on
its surface (it's a one sided figure in three space!) in a sinusoidal fashion on the
width of the strip. Then there is a trefoil knot tube (a topological knot, even
though probably the most trivial) with an animated shrinking and growing green torus
that orients itself around the tube. Similarly, there is a trefoil knot path made up
of lines where a texture mapped cube follows upon. 
  For the last two features, there is a rotating planet which acts like the sun
since it is a light source. And also there are randomly scattered texture stars that 
are always facing the viewer from any position.


Features: (Check the pic2.jpg, it really tells the most!)
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-Textures						(planets, stars)
	The stars, planets and cube moon all use textures which are easily figured 
using the s,t coordinates.

-Animation, Moving lights				(ball, torus, moon cube thing)
	The torus shrinks and grows positioning itself along the tube. See vectors 
below. Also the dark planet moves giving light to the scene.

-Billboarding						(orientation of stars)
	The stars are all oriented towards the viewer using spherical coordinates.

-Space Curves, Tangent, Normal, Binormal Vectors	(trefoil knot, moebius strip)
	The torus and cube moon are really the move complex since they use the normal
and binormal vectors of the parametric space curve that describes the trefoil knot.
These help orient the figures as they move along the tube or path. Oh and the 

-Randomized Jittering & stochastic sampling algorithm	(distribution of stars)
	To give a good distribution of stars, each star has a position on the unit
circle which is in some "neighborhood", then randomly orientated along the zaxis, and
giving a random scaling. And although there are only a few star bitmaps, it gives the
illusion of an animated scene.

-Parametric Equations of 3D Objects
	Both the Moebius Strip and Trefoil Knot are parameterized to give their shape.


Controls: (The standard stuff...)
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up,down    - rotate along azimuth
left,right - rotate along theta
w          - wireframe mode
f          - toggle smooth/flat shading
s/S        - Slow down or speed up animation


Links: 
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Möebius Strip - http://mathworld.wolfram.com/MoebiusStrip.html
Trefoil Knot - http://mathworld.wolfram.com/TrefoilKnot.html
Tubes! - http://mathworld.wolfram.com/Tube.html