Name: 

  Collaborators: 

  Due date: Sept 11, 2012, 11:59pm

  To handin: Create a folder in your CS account called 
  cs440.  Inside of that directory create a directory called
  handin.  Leave your completed .cpp file in your handin directory.
  Make sure not to change it after the due date - I will check 
  the "last modified" time on the file.  

  File permissions: make sure that your handin directory is not 
  publicly readable.  Use "chmod og-rx handin" and 
  "chomd og-rx handin/*" to make the directory and files
  so they are not readable by others.  I can still read your files
  because I have admin/root access.

  Task: Complete the following.  If you use any programs for any of these, 
  then include the source code, calling each program hw4SOMETHING.WHATEVER

  Grading: 15 Points


* Problem 1 *
Consider the following transformations.
T: translate object's x, y, z coordinates by 1, 2, 3.
S: scale object's x, y, z coordinates by factors of 2, 3, 4.
R: rotate object about the vector (1, 1, 0) by 90 degrees.

1.a Write down 4x4 matrices for each of these transformations.  Do it in a 
way that shows your work and shows how you got the matrices.

1.b Compute each of the compositions RT, TR, ST, TS.  Use a computer 
for the calculation if you like (I would).  

1.c Which of the pairs of transformations (S and T, S and R, R and T)
are commutative, and why?



* Problem 2 *
Suppose you have a 1920 x 1080 screen and your OpenGL scene shows:
two parallel lines going up the height of the screen at 4/10 the width and 
6/10 the width, and 
two parallel lines going across the width of the screen at 4/10 the height
and 6/10 the width.

Give the following that could have resulted in this image:
* eye coordinates and viewing direction/orientation,
* perspective or orthographic projection,
* location of projection screen,
* field of view (if perspective projection),
* dimensions of projection screen (if orthographic projection),
* coordinates of lines, expressed in world coordinates.



* Problem 3 *
Suppose you have the following scene and screen.
* 1x1x1 cube centered at (1, 0, 0).
* radius 2 sphere centered at (1, 0, -3).
* 1x1x1 cube centered at (-1, 0, -3).
* eye at (0,0,5), projection screen at z=3, field of view = 60 deg vertically total (30 deg up, 30 deg down)
* computer screen that is 1920 x 1080.

3a. Give a description/picture/image of what the scene would look like.  Use
a computer if you like.  Show your work.

3b. Along with your description/picture/image give the screen coordinates
where the vertices of the cube centered at (-1, 0, -3) will end up.  
Show your work how you get those screen coordinates.  Use computer assistance
if you want, but you need to show "why" the vertices end up at those
screen coordinates.



* Problem 4 *
Project idea.  Look around, think, etc. for a project idea.  Explain why 
you would want to do this project, and list any resources you found that 
might help.  One suggestion is to look at other graphics course webpages
for what they have done.  Note that you do not need to pick something you 
think you could do now.  You can assume I'd figure it out and provide 
assistance and a general framework to use.  Give links to any references.