Computer Graphics                                                  Homework 2
CS417/CS418 Fall 1998                        Due Wednesday, February 17, 1999

+ Make sure you've turned in the waiver and its requested e-mail. 
+ Hand in each question SEPARATELY.
+ Make sure your names are legible and easily spotted
  on the front page of each part. 
+ As always in this class,
  you are graded on correctness \emph{and also clarity and conciseness}. 
+ Write legibly & sign & date the following (fill blanks appropriately): 
    ``I, ____, CUID# ____, wrote up this assignment;
    my partner is ____, CUID# ____.'' 
+ E-mail how many total hours this homework takes you
  by midnight, Friday, February 19.

===============================================================================
CS417 part
===============================================================================

1. Complete the function below, using a z-buffer for hidden surface removal.

-------------------------------------------------------------------------------
function [pixel] = drawspheres(c,r,ka,kd,ks,n,ambient,l,lc)
% [pixel] = drawspheres(c,r,ka,kd,ks,n,l,lc):
%     return an image pixel (with integer world and view coordinates)
%     just large enough to show all the spheres under the specified lights.
%
%     the i-th sphere has center c(1:3,i), radius r(i),
%     ambient coefficient ka(i), diffuse coefficients kd(1:3,i),
%     specular coefficient ks(i), specular exponent n(i)
%     (the ambient coefficients for each r,g,b component are ka(i)*kd(1:3,i)).
%
%     the ambient light has color ambient(1:3)
%
%     the j-th light travels in direction l(1:3,j), with color lc(1:3,j)

y = c(2,:); y = [y-r y+r]; ybias = 1-min(y); 
x = c(1,:); x = [x-r x+r]; xbias = 1-min(x);
high = ceil(max(y))-floor(min(y))+1;
wide = ceil(max(x))-floor(min(x))+1;

pixel = zeros(high,wide,3)-1; % use -1 to flag background

v = [0 ; 0 ; 1]; % view vector (towards eye)

% fill in each circle with its diffuse color --
% no attempt at lighting or hidden surface removal
% (FIX THIS!)
for i = 1:size(c,2)
    for x = 1:wide
        for y = 1:high
            if (x-xbias-c(1,i))^2 + (y-ybias-c(2,i))^2 <= r(i)^2 
		pixel(y,x,:) = kd(:,i);
            end % if distance^2 <= r^2
        end % for y
    end % for x
end % for i

pixel(pixel<0) = 1; % set background to white
-------------------------------------------------------------------------------

Notes:

+ You may entirely rewrite the loops.
  However, it is not a good idea in this case to eliminate all loops,
  and there are some subtleties.

+ Some things you must do are:
    + given x,y on a sphere, compute the z coordinate
    + compute the normal
    + figure out what to do with negative/positive dot products
    + compute the ambient contribution
    + compute the diffuse contribution
    + compute the reflected vector
    + compute the specular contribution

Turn in your code, and the image from the following 
(it is suggested you store and run it as a script):

    c = [ ...
    20 40  30
    50 30  15
     0 30  20];
    r = [40 15 25];
    ka = [.1 .2 .3];
    kd = [ ...
    .7 0 0
    0 .8 0
    0  0 1];
    ks = [.2 .4 .8];
     n = [1   5  10];
    ambient = [.4 .4 0]';
    l = [ ...
     0 -1 -1
     1 -1  0
    -1 -1 -1];
    lc = [ ...
    1 1 0
    1 0 1
    1 0 1];
    image(drawspheres(c,r,ka,kd,ks,n,ambient,l,lc)); axis equal; axis xy


===============================================================================
CS418 part
===============================================================================

2. Complete the function below.  Turn in your code.

-------------------------------------------------------------------------------
function [hit,where,normal] = raysphere(origin, direction, center, radius)

% [HIT,WHERE,NORMAL] = RAYSPHERE(ORIGIN,DIRECTION,CENTER,RADIUS)
%
% compute the intersection of a ray with a sphere
%
% ORIGIN: 	 start of ray
% DIRECTION:     normalized direction of ray
% CENTER: 	 center of sphere
% RADIUS: 	 radius of sphere
%
% HIT: 		whether ray hits sphere (0 = no, 1 = yes)
% WHERE: 	where the intersection is
% NORMAL:	normalized normal of sphere at intersection
-------------------------------------------------------------------------------