% Section 8.8.1/2, Example 8.7, Boyd & Vandenberghe "Convex Optimization"
% Original by Lieven Vandenberghe
% Adapted for CVX by Joelle Skaf - 11/13/05
% (a figure is generated)
%
% Rectangles aligned with the axies need to be place in the smallest
% possible bounding box. No overlap is allowed. Each rectangle to be placed
% can be reconfigured, within some limits. We are given relative
% positioning contrainsts on those rectangles, and minimal required areas.
% In the current problem, 5 rectangles are given

% input data
n = 5;
Amin = [100 100 100 100 100; ...
20  50  80 150 200; ...
180  80  80  80  80; ...
20 150  20 200 110];
r = 1;          % minimum spacing constraints

for iter = 1:4
A = Amin(iter,:);
cvx_begin quiet
variables x(n) y(n) w(n) h(n) W H
minimize ( W + H )
x >= r;
y >= r;
w >= 0;
h >= 0;
x(5) + w(5) + r <= W;    % No rectangles at the right of Rectangle 5
x(1) + w(1) + r <= x(3); % Rectangle 1 is at the left of Rectangle 3
x(2) + w(2) + r <= x(3); % Rectangle 2 is at the left of Rectangle 3
x(3) + w(3) + r <= x(5); % Rectangle 3 is at the left of Rectangle 5
x(4) + w(4) + r <= x(5); % Rectangle 4 is at the left of Rectangle 5
y(4) + h(4) + r <= H;    % No rectangles on top of Rectangle 4
y(5) + h(5) + r <= H;    % No rectangles on top of Rectangle 5
y(2) + h(2) + r <= y(1); % Rectangle 2 is below Rectangle 1
y(1) + h(1) + r <= y(4); % Rectangle 1 is below Rectangle 4
y(3) + h(3) + r <= y(4); % Rectangle 3 is below Rectangle 4
w <= 5*h;                % Aspect ratio constraints
h <= 5*w;
cvx_end
% Plotting
subplot(2,2,iter)
for i=1:n
fill([x(i); x(i)+w(i); x(i)+w(i); x(i)],[y(i);y(i);y(i)+h(i);y(i)+h(i)],0.90*[1 1 1]);
hold on;
text(x(i)+w(i)/2, y(i)+h(i)/2,['B',int2str(i)]);
end
axis([0 W 0 H]);
axis equal; axis off;
end

% print -deps floorplan-opt.eps 