The light at the end of the tunnel is the headlight
of an approaching train.

Concept 1.11: Theory of Transformations
======================================

Idea:
=====
OpenGL maintains two matrix stacks that it uses for
rendering.  These are the modelview and projection
matrices.  Shown above are the matrix modes (in red), 
the identity matrix and the transformation commands 
(in blue).

glMatrixMode(GLenum mode); specifies whether the
modelview or projection matrix is to be modified, 
using the arguement GL_MODELVIEW, GL_PROJECTION.

We use the glLoadIdentity() command to clear the 
currently modifiable matrix for future transformation
commands.  Typically, you will call this command 
before specifying projection or viewing transformations
but you might also call it before specifying 
a modelling transformation.

Effect of Transformations on Matrix Stacks
==========================================
Look at the reshape() func where the projection 
matrix gets modified.

Load Identity Matrix       (I)     I
Load Projection Matrix     (P0)    I*P0 = P0

Now change the matrix mode to modelview by calling
glMatrixMode(GL_MODELVIEW);

Lets look at the display() func where the modelview
matrix is further modified. 

Load Identity Matrix         (I)    I 
LookAt                       (M0)   I*M0 = M0
Translate along the y axis   (M1)   M0*M1
Rotate about x axis          (M2)   M0*M1*M2
Translate along z axis       (M3)   M0*M1*M2*M3
Scale the object             (M4)   M0*M1*M2*M3*M4
draw vertex at [a, b, c]            M0*M1*M2*M3*M4*[a,b,c]

The matrices now get applied to the object in reverse order
because of the rules of matrix multiplication.  Final transformed
object is obtained as follows

M0 * (M1 * (M2 * (M3 * (M4 * [a b c] ) ) ) )

This gives the vertices of the object in 3D space.  Our screen
is 2D.  Hence the mapping occurs by multiplying the object
coordinates by the projection matrix P0 from above.

2D coordinates [a,b] = P*(M0*(M1*(M2*(M3*(M4[a,b,c])))))

We will discuss the gluLookAt() command and the projection
command gluPerspective in future concepts.