Silverman's Law: If Murphy's Law can go wrong, it will.

Concept 3.3 : Perspective Projection - 
A call to glFrustum()
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Idea
====
To define the projection (from a 3D world on to our 
computer screen) first the matrix mode is set with 
glMatrixMode(GL_PROJECTION) to be the projection mode.
glFrustum() is used to specify the perspective
projection viewing volume (Concept3.1)
Window II shows the actual frustum used for viewing the
cube rendered in the top window.

Experiment:
===========
a) Increase the near plane distance to 10.  Can you
   explain this?
  
b) Type in 14 as a value for Near Plane and explain
   the result.

c) Lets try one more variation.  Change Left to -5, 
   Bottom to -1, Right to 5, and Top to 1.
 

d) Try different values for the camera position in 
   window I

Answers
=======

a) By increasing the near plane value to 10 from 2
   we bring it 8 units closer to the object.  Remember
   the Near Plane distance is measured from the view
   point.  So now the object appears bigger.

b) Now the near plane value is at -1.  Our cube is
   rendered about the orign.  So our frustum starts 
   inside the cube and what we see is the back inside
   face of the cube ( in red)
 
c) The cube gets elongated along the Y axis, because
   the frustum is expanded in the X direction and shrunk
   in the Y direction. Hence the screwed up aspect ratio.

gluPerspective()
=================
We end this module by briefly discussing gluPerspective()
gluPerspective() is a library routine built on top of 
glFrustum() that is easier to use.  

gluPerspective( fovy, aspect, near, far ).  'fovy' is 
the angle at the apex along y-z plane and 'aspect' is the
width / height of the rectangular top face of the frustum.
'near' and 'far' are as before.

Note:
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On the screen at the bottom use the (x,X), (y, Y),
(z,Z) keys to navigate along the respective axes to
view the frustum from different angles.