% MS-E2170 Simulation
% Exercise 1.1: Estimate area of a polygon using Monte Carlo simulation
% b) What is your estimate for the area of P? Define a 1-delta confidence 
%    interval for the estimate with delta = 0.05.
% c) Compare your solution to the actual area of the polygon.
%
% Fill the '<your_code_here>' with your own input.
%
% Created: 2018-02-19 Heikki Puustinen


%% Initialization

% Sample size: 
N = <your_code_here>;

% Define the x- and y-coordinate values of the polygon.
px = [0.2, 0.4, 0.8, 0.5];
py = [0, 0.25, 0, 1];

% Define the surrounding rectangle.
rx = [0, 0, 1, 1];
ry = [0, 1, 1, 0];


%% Simulation

% We use the area estimation function area_mc.
% V = estimated area
% Ci = confidence interval [lower, upper]
[V, Ci] = area_mc(<your_code_here>);


%% Results

fprintf('Results:\n')

% Actual area of the polygon.
area = polyarea(px,py);

% Display estimated area (%.5f = float with 5 digits after the
% decimal point). You can also use 'display' function.
fprintf('Estimated area: %.5f \n', V)

% Display confidence intervals
fprintf('Confidence interval: [%.5f, %.5f]\n', Ci(1),Ci(2))

% Display actual area
fprintf('Actual area: %.5f \n',area)