CS 686


PROJECT 4		                Due Date: Noon Tuesday 12/13/2005

     This project affords students the opportunity to apply the knowledge
gained in this course on programming SVGA devices, to create a ray-traced 
image of a mathematically defined object in 3-dimensional space.



                        PROJECT STATEMENT

     Select one of the quadratic equations in three variables x, y, z (as
shown on the back this page) describing a (non-degenerate) curved surface 
in space, and choose a position in space from which a viewer can see this 
object, illuminated by at least two distinct point-sources of light.  Use
your knowledge of linear algebra, calculus, and SVGA graphics programming      
to create a C++ program that will employ ray-tracing principles to render
the image of your curved surface in a photorealistic manner.  (Do NOT use
a sphere, because we have already done that example in class; your curved
surface should be either a paraboloid, an ellipsoid, or a hyperboloid.) 

     You may, at your option, include one or more additional objects such
as a planar surface, a background curtain or other decorative effects, if
doing so will produce a more interesting scene (and will not detract from
the main emphasis on your selected quadratic surface).  Additional credit
is awarded for inclusion of features that go beyond the basic assignment.
NOTE: It is probable that you will need to employ rules from calculus for
computing the normal-vector to a curved surface at any given point (i.e., 
the so-called "partial derivatives" with respect to x, y, and z).


                            WHAT TO SUBIT

     You will need to give your Instructor a printout of the C++ program
source-code that you write--along with a printed copy of a 'README' file
which explains the objects in your ray-traced scene (their locations and
your quadric surface's equation), along with any other remarks a reader
would need in order to easily understand your program-code.  These paper
printouts should be delivered to the Instructor's mailbox in HRN-208 (as
usual) by the project deadline, and should show YOUR NAME on each.  Also
you should copy any computer files you create to your /submit directory,
as usual, so that the Instructor can re-compile and execute your program
for the purpose of testing and grading it.  (Failure to submit essential 
pieces of this project, binaries or hardcopies, will result in a zero on
this assignment.)

     You are allowed to discuss this project with the course Instructor,
or with aother student who is taking this course; but you must write the
actual code you submit yourself, to be sure you understand its ideas and
can explain any algorithms you use to your Instructor when questioned.   

________________________________________________________________________
Allan B. Cruse         University of San Francisco             Fall 2005