Computer Graphics                                                    Homework 6
CS417/CS418 Fall 1998                                Due Friday, April 30, 1999

+ Hand in each question SEPARATELY.  E-mail the bonus.  There is NO CS418 part.

+ Make sure your names are LEGIBLE and EASILY SPOTTED
  at the TOP on the FRONT page of each question.
  (Highlighting/circling helps)

+ You will be graded on correctness and also clarity and conciseness.

+ E-mail how many total hours PER PERSON you spent on this homework
  by midnight, Sunday, May 2.  Feedback on this homework, Prelim 2,
  lecture, the textbooks, office hours, etc. is also appreciated.

################################# CS417 part ##################################

1. (Revised)

   Recall that a map T from view coordinates (x,y,z) to 3D screen
   coordinates (x_s,y_s,z_s) for performing perspective projection onto a
   view plane with view distance d must satisfy (x_s,y_s) = (d/z) * (x,y).

   Suppose we do z-buffering on polygons by interpolating in screen space.

   (a) Formalize mathematically the condition 

       "Using T and linear interpolation
        preserves the relative order of points on rays".

   (b) Give a clear & simple concrete example & computation to show
       that if we use z_s = z then the interpolated z value does not
       match the actual z value.

   (c) Use the fact that using z_s = -1/z yields a map T that maps
       lines in view space to lines to screen space to explain why
       using T and linear interpolation works.

2. Radiosity is intended to be somewhat based on reality, i.e. physics.

   (a) List 2 principles of physics on which it is based.
       (2 assumptions --not physics principles-- are that
       radiosity is constant on each patch and that each patch
       is a perfectly diffuse reflective surface.)

   (b) Briefly explain how these principles affect B and F,
       e.g. write an equation for a principle in terms of B and/or F
       or give an example in terms of some B and/or F illustrating a principle.

3. Consider a scene with only two square patches, an inch apart
   (imagine the top and bottom face of a cube), where
   the top patch A_1 is a light, the bottom patch A_2 is not a light,
   and both patches are reflective (R_1>0, R_2>0).  Fully explain what is
   wrong with the following:

       Since light keeps reflecting off each patch, increasing
       its radiosity, each patch has unbounded radiosity B_1 = B_2 = oo.

#################################### Bonus ####################################

4. (Bonus) Critique each question 1 - 5 on the prelim.  Include as part
   of each critique, 3 similar exam questions:  one that is too easy,
   one that is about right, and one that is too hard.  One of these may
   be the actual prelim question; in this case, write "original
   question" insteed/besides writing out the question.

   You may also comment on the grading.  Note that in general,
   roughly half the points are for the high-level picture, and the
   other half for the details.  Exceptions to this are questions 1 & 5,
   which are essentially all detail.

   This bonus is per person, not per team, and must be e-mailed to
   cs417@cs.cornell.edu.