Calculate area of polygon recursively - matlab

Question

I had to calculate any polygon given cordinates of point in 'x-vector','y-vector' (only thing I know is the cordinates are ordered clockwise and polygons like hourglass are not included).
I tried writing this code:
function [areaofit] = Polygarea(xs,ys,cor,prevsum)
if(length(xs)~=length(ys))
disp('dimentions error!please try again');
end
if(nargin==2)
cor=1;
prevsum=0;
end
if(cor==length(xs)-1)
areaofit=prevsum;
figure(1);
fill(xs,ys,'r');
title(['Area = ' num2str(areaofit)]);
end
if(cor~=length(xs)-1)
mat=[xs(1) ys(1) 1;zeros(2,3)];
for k=2:3
mat(k,1)=xs(cor+k-1);
mat(k,2)=ys(cor+k-1);
mat(k,3)=1;
end
farea=prevsum+abs(det(mat))/2;
Polygarea(xs,ys,cor+1,farea);
end
The function does work with any convex polygon but there are concave polygons it does work with (like 'stars' e.g ). What can be improved in my solution? thanks

Answer 1

I think you need to modify this line:
farea=prevsum+abs(det(mat))/2;
to
farea=prevsum+det(mat)/2;
Like this, the concavities in your polygon will add or subtract areas according to what direction they sweep the 0..2π range. To ensure final positive values for your area, there should be something like areaofit=abs(prevsum);