The more laws and order are made prominent, the more
thieves and robbers there will be -- Lao Tsu

Concept 1.12: Specifying Matrices For Transformation
===================================================

Idea:
=====
Since transformations such as translation, rotation
etc are performed by matrix multiplications, one 
should be able to specify matrices explicitly to 
perform required transformations.

Example Matrices:
=================
The matrix corresponding to translation by the vector
[Dx Dy Dz] is

               1  0  0  Dx
               0  1  0  Dy
T(Dx,Dy,Dz) =  0  0  1  Dz
               0  0  0  1

The matrix corresponding to rotation by an angle 'A' 
about the X axis is

               1  0       0         0
               0  cos(A)  -sin(A)   0
   Rx(A) =     0  sin(A)  cos(A)    0
               0  0       0         1

The matrix corresponding to rotation by an angle 'A'
about the Y axis is

               cos(A)   0  sin(A)  0
               0        1  0       0
   Ry(A) =     -sin(A)  0  cos(A)  0
               0        0  0       1

The matrix corresponding to rotation by an angle 'A'
about the Z axis is 

               cos(A)  -sin(A)  0  0
               sin(A)   cos(A)  0  0 
   Rz(A) =     0        0       1  0
               0        0       0  1

The angle 'A' above is specified in degrees.

The matrix corresponding to scaling about the origin by
the factors Sx, Sy, and Sz (all non-zero) along the
respective coordinate axes is

               Sx  0   0   0
               0   Sy  0   0
S(Sx,Sy,Sz)=   0   0   Sz  0
               0   0   0   1

The matrix corresponding to reflection about the XY plane 
is

               1   0   0   0
               0   1   0   0
S(1, 1, -1) =  0   0  -1   0
               0   0   0   1

Experiment:
===========
glMultMatrix(m) multiplies the current matrix with the one 
specified in 'm'. 'm' points to a 4x4 matrix of floating 
point values stored in column-major order.  Hence for our
example the Translation matrix given by :

                  1   0   0   3
                  0   1   0   0
         Matrix = 0   0   1   0
                  0   0   0   1

woule be specified  as follows:

m = { 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 3, 0, 0, 1}
corresponding to elements [0], [1], [2], ... [15]
Try changing the values of the matrix elements to perform
the following: 

a)  A translation of the cube  3 units along the X axis
b)  A translation of the cube  2 units along the X axis
    3 units along the Y axis and 2 units along the -ve
    Z axis
c)  Perform a rotation of 30 degrees about the X axis
d)  Create a reflection along the XY plane

Answers:
========
a)  m = {1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 3, 0, 0, 1}
b)  m = {1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 2, 3, -2,1}
c)  m = {1, 0, 0, 0, 0, C, S, 0, 0, -S, C, 0, 0, 0, 0, 1}
    where C = cos(30) = 0.8659
    and   S = sin(30) = 0.5001
d)  m = {1, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1}