x =[2 4 5 3 9 10]
y =[-10 8 4 -5 9 10]
plot(x,y,'*')
[min_y,i] = min(y);
pivot = [x(i),y(i)];
number = i
%getting the angle
x(i) = [];
y(i) = [];
delta_x = x - ones(1,length(x))*pivot(1);
delta_y = y - ones(1,length(y))*pivot(2);
theta = atan2d(delta_y,delta_x);
%sorting without losing the position
c = [];
x_new= [];
y_new = [];
for n = 1:length(theta)
    [min_theta, d] = min(theta);
    c = [c d];
    x_new = [x_new x(d)];
    y_new = [y_new y(d)];
    theta(d) = [1000]; %random value need to be higher than 180 degrees
end
x_new = [pivot(1) x_new pivot(1) x_new(1)];
y_new = [pivot(2) y_new pivot(2) y_new(1)];
%using cross product in this exercise none of the lines are collinear
%If the result is 0, the points are collinear;
%if it is positive, the three points constitute a "left turn" or counter-clockwise orientation,
%otherwise a "right turn" or clockwise orientation (for counter-clockwise numbered points)
%source wiki
n_bad = [];
n_good = [];
x_new
y_new
for n = 1:(length(x_new)-3) %this caused by how the array x_new and y_new contain duplicates
    x_new(n+1)
    cross_product = (x_new(n+1) - x_new(n))*(y_new(n+2)-y_new(n))-((y_new(n+1)-y_new(n))*(x_new(n+2)-x_new(n)))
    if cross_product < 0
        n_bad = [n_bad n+1];
    end
    if cross_product > 0 %this is unnecassaray can be used for skipping making the program faster
        n_good = [n_good n+1]
    end
end
%in case I did something wrong the graph can be plotted here:
figure
x_good = [pivot(1) x_new(n_good) pivot(1)];
y_good = [pivot(2) y_new(n_good) pivot(2)];
plot(x_good,y_good)
%to get the same index as the input
if number>1
    n_good = n_good + 1;
    n = sort([n_good number]);
else
    n = [number n_good];
end
n