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4.9 | 15 ratings Rate this file 105 Downloads (last 30 days) File Size: 38.9 KB File ID: #319 Version: 1.2
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H.J. Sommer (view profile)


09 Oct 1998 (Updated )

POLYGEOM computes area, centroid location, area moments of inertia and perimeter of closed polygons.

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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.


This file inspired Co Blade: Software For Analysis And Design Of Composite Blades.

MATLAB release MATLAB 5.2 (R10)
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Comments and Ratings (19)
28 Sep 2016 sue142857  
19 Aug 2016 Javier Sarmiento

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

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:n-1]);
yime1 = y([n 1:n-1]);

a = 1/2*sum(xime1.*y-x.*yime1);
Ixx = 1/12*sum((yime1.^2+yime1.*y+y.^2).*(xime1.*y-x.*yime1));
Iyy = 1/12*sum((xime1.^2+xime1.*x+x.^2).*(xime1.*y-x.*yime1));
if (a<0) a=-a; Ixx=-Ixx; Iyy=-Iyy; end

04 Dec 2014 Nele Gerrits

Does it also work for an arbitrarily shaped form?

Comment only
29 Jan 2013 charlie

Excellent program.

Question: Is J = Iuu + Ivv valid only for circular cross sections?

01 Oct 2011 Steve Tweddell

Excellent function, a real time saver

14 Apr 2011 Richard Crozier  
14 Apr 2011 Richard Crozier

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

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

Comment only
23 Feb 2011 Raghuram

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.

Comment only
08 Jun 2009 Stefan Berger

This prog is wonderful, just what I needed. If you have time please improve it to handle the third dimension!!

29 Nov 2008 Xu

Xu (view profile)

29 Nov 2008 Xu

Xu (view profile)

Can't download ZIP instead of m file only?

Comment only
15 Apr 2008 Alice Huang  
04 Dec 2006 Pooya S

Nice package

22 Mar 2006 Jim Price

Yes, yes, yes --- this is an extremely useful and well-done script. Should be a part of the regular Matlab so that users can most easily find it. Thank You!!

31 Oct 2005 Alfonso Rojas

Very useful program, clean and well-commented code. Tried it with Matlab
v 7.0.1 (R14), and it works fine. Excellent.

30 Aug 2005 Chinmay Pangarkar

Super!!! I get all geometry of my arbitrary cells using this code. Thank you H.J. Sommer!!

07 Apr 2005 Thor I. Fossen

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:)

23 Jan 2004 Finlay Scott

Very useful for getting the perimeter of cyclic predator-prey ecological systems

10 Sep 2003 Elvis Dieguez

Excellent program! Saved me lots of time trying to calculate the area surveyed by a moving wheeled sensor system.

12 Jan 2005

Provides positive area for CW or CCW vertex sequence.

30 Nov 2008 1.2

derivation and test routine added to ZIP on 08.11.30

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