Sattinger's Law: 
It works better if you plug it in

Concept 2.1 : The Viewing Transformation
======================================

Idea
====
The camera is positioned in OpenGL using the gluLookAt() 
command:
gluLookAt(eyex, eyey, eyez, centerx, centery, centerz, 
          upx, upy, upz);
The first three specify the position of the camera, the
next three the direction in which it is pointing, the 
last three define the up-vector

In the default position the camera is at the origin, is 
looking down the negative z-axis (i.e. into the screen) 
and has the positive y-axis as straight up.

Experiments:
============
1) Try the following values for the parameters described above.
a) gluLookAt(0.0, 3.0, 5.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0);
b) gluLookAt(3.0, 3.0, 5.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0); 
c) gluLookAt(0.0, 0.0, 10.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0);
   The screen goes blank!  Why?

2)  Vary the parameters and reexecute the code.  What is 
    the color of the left face of the cube?

3)  Vary the positions to see the color of the back
    of the cube.

4)  Press the Reset button.  Set the Up X, Up Y, and Up Z 
    values as below.  What happens and why?
	Up X = 1
	Up Y = 1
	Up Z = 0

Answers:
========
1c) We see nothing, because the up vector is parallel to
    the viewing direction.  Typically an upvector 
    perpendicular to the viewing direction will work fine.
2)  Green.  Try gluLookAt(-4, 4, 5, 0, 0, 0, 0, 1, 0) 
3)  Red.  Try gluLookAt(2, 2, -5, 0, 0, 0, 0, 1, 0)
4)  Our image seems to be flipped by a 45 degree angle.  
    Imagine that now we have a camera 10 units along the 
    +ve Z direction, aimed at the orign, but the camera 
    itself is tilted 45 degrees along the XY plane.

Question:
=========
If you were not allowed use the gluLookAt() utility could 
you use any other transformation commands instead?
Hint: In the default positon the camera is at the origin
looking down the negative z-axis.
We shall answer this question in the next concept.