Centroid of a Convex n-Dimensional Polyhedron

Computes the center of gravity of a convex polyhedron in any number of dimensions.

Description

USAGE: C = centroid(P)
 
P = Matrix of convex polyhedron vertices: each row is a vertex, and each column is a dimension.
C = Row vector of centroid coordinates. Each column is a dimension.

Notes:
(1) This function computes the centroid by partitioning into simplices and determining the weighted sum of their centroids.
(2) Written in response to a question on comp.soft-sys.matlab

Michael Kleder, Sep 2005

• MATLAB release: MATLAB 7.0.4 (R14SP2)

[Birajashis Pattnaik]

Ohh this is fantastic.

[Glen Lichtwark]

This is a very handy function, thanx.

[fady dawoud]

very nice!! a question though, does the algorithm still work if the points dont form a convex surface.

[The Author]

Answer to Fady Dawoud: If the points do not form a convex polyhedron, then the function gives you an error telling you what happened.

[Roja B]

Hi,

thank you, this is a very useful function. my only problem is when I try to use it in 2-D. how do you think I can fix this?

[The Author]

Answer to Roja B:
As an example in 2-D, try
P=centroid([0 0;1 1;2 0]);
plot([0 1 2 0],[0 1 0 0],...
'b-',P(1),P(2),'r.');

[Charlotte B]

thanks for this function! but what happens with a concave polyhedron? do you have suggestions on how to calculate the center of gravity of these shapes?

[Chris Godau]

Very nice, thank you!
Was just about to write this myself when I found yours.
If your set of points is not convex you can of course use the convex hull:
centroid(P(unique(convhulln(P)),:))

[Raghuram]

For the following p = [0 0; 1 1; 0.6667 0.6667; 0.5 0.8333; 0.1667 0.5] it gives an error saying the polygon is not convex when in fact it is.