tuesday, 5/2

note: this was a fun, gee-whiz lecture to show you the sorts of things
you are now able to do in matlab.  you are not responsible for new
matlab commands shown in this lecture that were not shown earlier,
e.g. you are NOT responsible for $clf$, $treeplot$, $deblank$,
$blanks$, $patch$, $pcolor$, $image$, or $imagesc$.

% ideas from prelim 3, question 1: make a checkerboard

clf;
x = zeros(5, 8);
[h,w] = size(x);
x(1:2:h, 1:2:w) = 1;
x(2:2:h, 2:2:w) = 2;
pcolor(x); % note: pcolor does not draw the last row or last column :(


% prelim 3, question 2: see newsgroup


% prelim 3, question 3: overlapping rectangles

clf;
n = 5; width = ceil(rand(1,n) * 50); height = ceil(rand(1,n) * 50);
left = ceil(rand(1,n) .* (100 - width)); right = left + width;
bottom = ceil(rand(1,n) .* (100 - height)); top = bottom + height;
pixels = zeros(101,101);
for i = 1:n
    pixels(bottom(i):top(i), left(i):right(i)) = pixels(bottom(i):top(i), left(i):right(i)) +1;
    % note: typo during lecture: the $(i)$s above were omitted
end
imagesc(pixels)



% draw a tree

%   9
%  /|\
% 6 7 8
%  /|\ \
% 2 3 4 5
%       |
%       1
%
%  1 2 3 4 5 6 7 8 9
t=[5 7 7 7 8 9 9 9 0]; % t(i) = "parent" of i; 0 means "no parent"
clf;
treeplot(t);



% right justify rectangular array of text

a = strvcat(...
'right justify text in matlab', ...
'matlab trees', ...
'triangle of stars', ...
'overlap rectangle', ...
'exercise 9 -- duplicate birthdays', ...
'dutch national flag');

[h,w] = size(a);
for i = 1:h
    s = deblank(a(i,:));
    a(i,:) = [blanks(w-length(s)) s];
end
a


% exercise 9 -- duplicate birthdays

clf;
npeople = 500; ndays = 365; ntrials = 1000;
counts = zeros(1,ntrials);
for i = 1:ntrials
    days = ceil(rand(1,npeople) * ndays);
    counts(i) = max(full(sparse(1,days,1,1,ndays)));
end
hist(counts, 1:10);


% triangle of stars

clf;

x = [ 15 25 50 ];
y = [ 10 40 60 ];

x = x - min(x) + 1; y = y - min(y) + 1; % shift coord to be >= 1
patch(x,y,'r'); pause
width = max(x); height = max(y);
xs = 1:width; xs = xs(ones(1,height),:);
ys = (1:height)'; ys = ys(:,ones(1,width));
inside = ones(height,width);
for i = 1:3
    clf; hold on
    v = [x ; y]; 
    w = v(:,i); v(:,i) = []; % save and delete i-th vertex
    % want equation Ax + By + C = for line through points in V
    A = v(2,2) - v(2,1);
    B = v(1,2) - v(1,1); B = -B;
    C = - (v(1) * A + v(2) * B);
    side = (A * xs + B * ys + C <= 0) == (A * w(1) + B * w(2) + C <= 0);
    inside = inside & side;
    pcolor(side);
    plot([x x(1)], [y y(1)], 'r')
    pause % wait for user to press a key
end
stars = ' *';
inside = stars(inside+1);
disp(flipud(inside)) % draw, making increasing y/row go up, not down