I'm trying to find the area and the center of a polygon

I'm trying to find the area and the center of a polygon, made of a set of coordinates, x & y Here is the code I have so far, the results it's giving me are way off, can anyone see the problem?

%Load the polygon points file

load Drawing1.txt;

x = Drawing1(:,1);

y = Drawing1(:,2);

%Calculate the number of rows

Nrows = numel(textread('Drawing1.txt','%1c%*[^\n]'));

%Set initial values

A = 0;

Cx = 0;

Cy = 0;

for k=0:(Nrows-1);

    if k==0

        %End point is the same as point 0

        i=Nrows;
        j=1;
    else
        %Otherwise use the current point
        i=k;
        j=k+1;
    end
    %Calculate centre points of polygons
    A=A+(((x(i)*y(j))-(x(j)*y(i)))*cosd((y(i)+y(j))/2));
    Cx=Cx+((x(i)+x(j))*((x(i)*y(j))-(x(j)*y(i))));
    Cy=Cy+((y(i)+y(j))*((x(i)*y(j))-(x(j)*y(i))));
end

%Apply terms outside summation

A=0.5*A

Cx = (1/(6*A))*Cx

Cy = (1/(6*A))*Cy

Thanks!

Answer 1

[Sean de Wolski]

No reason to reinvent the wheel:

doc polyarea

And here is a function I wrote for centroid calculation:

function [x_bar, y_bar, As] = xycentroid(x,y)
%Function calculates centroid and area of a list of xy points
%SCd 11/24/2010
%
%
%Input Arguments:
%   -x: vector of x coordinates (can be row or column vector)
%   -y: vector of y coordinates (can be row or column vector)
%
%Output Arguments:
%   -x_bar: x location of centroid
%   -y_bar: y location of centroid
%   -A: area of polygon
%

      %Error checking:
      assert(nargin==2,'This function expects 2 and only 2 input arguments');
      assert(all(size(x(:))==size(y(:))),'Input arguments: x & y are expected to be the same length');
      x = x(:);
      y = y(:);

      %Engine:
      A = x(1:end-1).*y(2:end)-x(2:end).*y(1:end-1);
      As = sum(A)/2;
      x_bar = (sum((x(2:end)+x(1:end-1)).*A)*1/6)/As;
      y_bar = (sum((y(2:end)+y(1:end-1)).*A)*1/6)/As;

end

I guess I didn't know about polyarea when I wrote this !

[Justine]

Thank you for your answer, I have just tried this with my coordinate points and it only returns one value, which isn't a center point??

[Sean de Wolski]

You need to call it with three outputs:

[xb yb A] = xycentroid(x,y)

Also note, this is calculating the centroid - which may be slightly different than the center point.

[Pawan G]

Hello Sean de Wolski,

I tried the same code to calculate the centroid of the polygon but the centroid point appears to be outside the polygon. y x and y coordinates of the polygon are x = [-5;-4;-4;-5], y = [-2;-2;1;1]. could you please help me

[Marius Dam]

I found a small error in your code, you forget to evaluate the element x(end) - x(1) therefore leading to a small difference compared to polyarea. I updated the code:

function [x_bar, y_bar, As] = xycentroid(x,y)
%Function calculates centroid and area of a list of xy points
%SCd 11/24/2010
%
%
%Input Arguments:
%   -x: vector of x coordinates (can be row or column vector)
%   -y: vector of y coordinates (can be row or column vector)
%
%Output Arguments:
%   -x_bar: x location of centroid
%   -y_bar: y location of centroid
%   -A: area of polygon
%
      %Error checking:
      assert(nargin==2,'This function expects 2 and only 2 input arguments');
      assert(all(size(x(:))==size(y(:))),'Input arguments: x & y are expected to be the same length');
      x = x(:);
      y = y(:);
      %Engine:
      A = x(1:end).*y([2:end,1])-x([2:end,1]).*y(1:end);
      As = sum(A)/2;
      x_bar = (sum((x([2:end,1])+x(1:end)).*A)*1/6)/As;
      y_bar = (sum((y([2:end,1])+y(1:end)).*A)*1/6)/As;
end

Answer 2

[Matt J]

For convex polygons,

 [~, Area] = convhulln(points);

 center=mean(points);