% MS-E2170 Simulation
% Exercise 1.1: Estimate area of polygon using Monte Carlo simulation
% a) Verify the sampling experiment by constructing a plot of the result.
%
% 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 = [<your_code_here>];
py = [<your_code_here>];

% Define the surrounding rectangle. This is the space where the random 
% points are generated. We use unit rectangle as it's area is easy to 
% calculate.
rx = [0, 0, 1, 1];
ry = [0, 1, 1, 0];

%% Simulation

% Generate 2N random numbers from the uniform distribution U(0,1).
% N for x-coordinate values and N for y-coordinate values.
sx = <your_code_here>;
sy = <your_code_here>;

% Check which points (sx,sy) are inside polygon (px,py). 
% Hint: 'inpolygon' (1: inside, 0: outside).
in = <your_code_here>;


%% Plotting

% Let's create a window so we can plot the results. "fig" is just a name 
% for the handle to the window so we can access it later.
fig = figure('Name','MS-E2170, Exercise 1 a), Monte Carlo Simulation');

% Create an axes (optional but good practice).
ax = axes('Parent',fig);

% Set title
title(ax,'Verification plot')

% Set hold on so that consecutive plots do not clear the axes.
hold(ax,'on'); 

% Plot the polygon. Note that the plot-command does not automatically
% connect the last and the first coordinates so we add the first
% coordinate to the end. 'r' is for 'red'.
plot(ax,[px, px(1)],[py, py(1)],'Color','r')

% Plot the surrounding rectangle (blue).
plot(ax,[rx, rx(1)],[ry, ry(1)],'LineWidth',2,'Color','b') 

% Plot points that are inside the polygon (red dots).
plot(ax,sx(in),sy(in),'r.')

% Plot points that are outside the polygon (blue dots).
plot(ax,sx(~in),sy(~in),'b.')