MATLAB >> center of mass fucntion

by NBT » Wed, 18 Jan 2006 23:34:28 GMT

what is the function to calculate center of mass or
centroid of a 2d object.

MATLAB >> center of mass fucntion

by noob » Wed, 18 Jan 2006 23:52:58 GMT

do you have the coordinates of each point on the object? what about
the weight of each point? if you have those, then its just a trivial
sum (the definition of centroid).

MATLAB >> center of mass fucntion

by NBT » Thu, 19 Jan 2006 00:00:18 GMT

I have the coord. of each point, actually it is b/w nonsymatical
image taht I try to find the center of the image.
How I go about to use sum. I get rusted on the math stuff.

MATLAB >> center of mass fucntion

by ellieandrogerxyzzy » Thu, 19 Jan 2006 04:49:08 GMT

In your problem, NBT, it is important to distinguish between two
possibilities. One is that you consider your points to be mass points and
you want the simple center of mass of the points themselves. If all the
points have the same mass, then, as Noob indicated, it is a simple matter
of taking the means of the x and y coordinates.

However, if what you want is the area centroid of the entire interior
region surrounded by a polygon running through the points, that is a very
different problem. Here is a function I gave someone else on CSSM some
time ago. I have reason to believe there are some functions in MathWorks'
File Exchange that do the same thing, but anyway here it is:

function [x0,y0,a] = centroid(x,y)

% x and y must be non-scalar column vectors of the
% same length defining a polygonal region in clockwise
% sequence. a is returned with the polygon's area, and
% (x0,y0) with the coordinates of the polygon's centroid.
% Note: with counterclockwise order, x0 and y0 are
% still correct but a is the negative of the area.
% RAS - 1/17/05

n = length(x);
x2 = [x(2:n);x(1)];
y2 = [y(2:n);y(1)];
a = 1/2*sum(x2.*y-x.*y2);
x0 = 1/6*sum((x2.*y-x.*y2).*(x+x2))/a;
y0 = 1/6*sum((x2.*y-x.*y2).*(y+y2))/a;

(Remove "xyzzy" and ".invalid" to send me email.)
Roger Stafford

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