CS3500 Computer Graphics
			      Spring 2006

			   Home Assignment 6
		     Projection/Normalizing Matrix
			 Due: March 05, 2009

1. Try "man glFrustum" (or the same under OpenGL on diglib). You
   will see the expression for the perspective normalizing matrix under
   the most general situation.

   Derive that matrix in steps. You may follow the steps similar to
   those used for the symmetric view frustum in the class. You may also
   try a new way to derive the matrix.

   Hint: Try to convert it to a symmetric frustum.

2. Compute the perspective normalizing matrix corresponding to the
   following symmetric view frustum: (the canonical view volume has
   the dimensions -1 <= x, y <- +1, 0 <= z <= -1)

	   horizontal field of view: 60 degrees
	   aspect ratio: 4/3  (width / height)
	   near distance: 2 units
	   far distance:  100 units

   Compute the homogenous coordinates and corresponding cartesian
   coordinates after the normalizing transform of the following
   points. Comment on the points if you find them interesting.
   a) (-1.1, 0.8, -2.0)
   b) (2.0, 0.5, -2.0)
   c) (110, -80, -100)
   d) (0.0, 0.0, -51.0)
   e) (10.0, 5.0, -10.0)