POLYGEOM computes area, centroid location, area moments of inertia and perimeter of closed polygons.
This function is useful for bending/torsion stress analyses, area centroids of models for wind tunnel testing, rotational inertia for dynamics and blob analysis for image processing.
H.J. Sommer (2020). polygeom.m (https://www.mathworks.com/matlabcentral/fileexchange/319polygeomm), MATLAB Central File Exchange. Retrieved .
1.4.0.0  16.12.09 

1.3.0.0  Documentation updated 16.12.09 

1.2.0.0  derivation and test routine added to ZIP on 08.11.30 

1.0.0.0  ZIP includes boundary integral equations and how to handle holes. 

Provides positive area for CW or CCW vertex sequence. 
Inspired: CoBlade: Software for Analysis and Design of Composite Blades
Create scripts with code, output, and formatted text in a single executable document.
It should give Area =0 and the center of the segment
Thank you for this code.
I was wondering if the angles of the principal inertia moments could be state in counterclockwise format, starting at positive X axis direction (from 0 to 180º). If you want this, just add the following code below line 91 of polygeom.m:
%
ang1 = ang1+(ang1 < 0)*pi;
ang2 = ang2+(ang2 < 0)*pi;
%
Function polygeom.
Helpe me please the units are in [m] or [cm].
Wonderfully well written code! I do have a few general questions though. Why take the mean of the coordinate points? The comment says it improves accuracy, but how exactly? Also, most theoretical area approximations used integrals. How do the summations suffice for these integrals? Just curious.
points have to be in neighbouring/sequential. cannot be in random order. use convhull() if in random order.
very good
Thank you so much! It works very fine. I learned about new commands. I would like to know about the references for the Ixx Iyy formulas. Here is a more simple formula in Steger's paper. I'm not sure why the area(a) is in denominator but despite this value it is the same result.
Take a look in formula 36 at http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.29.8765&rep=rep1&type=pdf
Here is a the same example
clear; clc;
x = [ 2.000 0.500 4.830 6.330 ]';
y = [ 4.000 6.598 9.098 6.500 ]';
[ x, ns ] = shiftdim( x );
[ y, ns ] = shiftdim( y );
[ n, c ] = size( x );
xime1 = x([n 1:n1]);
yime1 = y([n 1:n1]);
a = 1/2*sum(xime1.*yx.*yime1);
Ixx = 1/12*sum((yime1.^2+yime1.*y+y.^2).*(xime1.*yx.*yime1));
Iyy = 1/12*sum((xime1.^2+xime1.*x+x.^2).*(xime1.*yx.*yime1));
if (a<0) a=a; Ixx=Ixx; Iyy=Iyy; end
Does it also work for an arbitrarily shaped form?
Excellent program.
Question: Is J = Iuu + Ivv valid only for circular cross sections?
Excellent function, a real time saver
Raghuram, the correct answer is given if you reorder your vertices so they are given clockwise around the outside of the polygon, rather than just specified randomly, e.g,
% Your vertices
% x = [1.0000 0.5000 0.8333 0.5694];
% y = [1.0000 0.1667 0.5000 0.5694] ;
% reordered moving clockwise around the polygon from (0.5, 0.1667)
xy = [0.5, 0.1667;
0.8333, 0.5;
1, 1;
0.5694, 0.5694; ];
x = xy(:,1);
y = xy(:,2);
for i = 1:numel(x)1
line(x(i:i+1), y(i:i+1), [0,0], 'Color', 'b');
hold on
end
line([x(end), x(1)], [y(end), y(1)], [0,0], 'Color', 'b');
[ geom, iner, cpmo ] = polygeom( x, y )
plot(geom(2), geom(3), '+r')
hold off
The outputs are erroneous for the following input:
x = [1.0000 0.5000 0.8333 0.5694]
y = [1.0000 0.1667 0.5000 0.5694]
The centroid is computed as (0.8801,1.1496) which is outside the parallelogram formed by the input points.
This prog is wonderful, just what I needed. If you have time please improve it to handle the third dimension!!
Can't download ZIP instead of m file only?
Nice package
Yes, yes, yes  this is an extremely useful and welldone script. Should be a part of the regular Matlab so that users can most easily find it. Thank You!!
Very useful program, clean and wellcommented code. Tried it with Matlab
v 7.0.1 (R14), and it works fine. Excellent.
Super!!! I get all geometry of my arbitrary cells using this code. Thank you H.J. Sommer!!
Excellent program. Should be standard in Matlab. I have used it compute the centroids for wind and current projected areas as welll as other things:)
Very useful for getting the perimeter of cyclic predatorprey ecological systems
Excellent program! Saved me lots of time trying to calculate the area surveyed by a moving wheeled sensor system.