There once was a girl named Irene who lived on kerosene
But she started absorbin' a new hydrocarbon
And since then has never Benzene

Concept 2.2 : gluLookAt() vs. Modelling Transformations
=======================================================

Idea:
=====
In the previous concept we posed the question of replacing
gluLookAt() with other transformation commands.  The 
answer to the question is 'Yes'.  We investigate how to do
this in this concept.  gluLookAt() the viewing 
transformation can be replaced by a combination of 
modelling transformations (i.e. translations and 
rotations).

Experiment:
===========
In the template shown above we allow you to use either the
gluLookAt() utility (as in Concept 1.21) or use modelling
transformations.  

1) For the following gluLookAt vlaues can you specify 
   glTranslate() and glRotate() parameters to get the same
   effect?1
   a) gluLookAt(0.0, 3.0, 5.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0);
   b) gluLookAt(0.0, 5.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0);
      Here we are looking at the top face of the cube with 
      the Z axis as our up-vector.
   c) Approximate the effect obtained by the following values
      gluLookAt(9.0, 0.0 , 5.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0);

Come up with your own exercises till you are convinced that 
gluLookAt() is essentially a combination of modelling 
transformations.

Answers:
========
1a)  glTranslatef(0, 0, -5);  glRotatef(45, 1, 0, 0);
1b)  glTranslatef(0, 0, -5);  glRotatef(45, 1, 0, 0);
1c)  glTranslatef(-3, 0, -10); glRotatef(45, 0, -1, 0);

Explanation:
============
Remember when not explicitly specified the camera is 
supposed to be at the origin, pointing down the -ve Z 
axis with (0, 1, 0) as the up-vector.  In this case 
when using the modelling transformations, instead of 
moving the camera (with gluLookAt()) we moved the cube 
away from the camera (with a modelling transformation).  

This duality in the nature of viewing and modelling 
transformations is why you need to think about the effects 
of both types of transformations simultaneously.  This is 
also why modelling and viewing trnasformations are 
combined into the modelview matrix before the 
transformations are applied.