Triangle centroid

Hello, do you somebody know any simlpe method how to find the triangle centroid (or geometric barycenter) in 3D?

Thanks a lot,

Tom

[Zhenren Yang]

hi, have you get the code that can find the barycenter of 3d (stl,ply)?

Answer 1

[Jonathan Sullivan]

Just average all the coordinates. For example, if you have a vector containing x coordinates and a vector containing y coordinates, you can find it in the following manner.

x = rand(3,1); % x-coordinate
y = rand(3,1); % y-coordinate
x_centroid = mean(x);
y_centroid = mean(y);

[tomas]

Hmm, that's very simple :-)

Thanks

Answer 2

[DGM]

Another example for emphasis:

unzip stepholecube.stl.zip % for the forum

% so you have some triangles in 3D
T = stlread('stepholecube.stl');
[F V] = t2fv(T); % just for cleanliness

% then get the centroids.  you're done
C = mean(permute(reshape(V(F,:),[size(F,1) 3 3]),[1 3 2]),3);

% not sure if that's right? 
% well, the barycenter is at [1 1 1]/3 in barycentric coordinates, so ...
idx = (1:size(T,1)).';
Cref = barycentricToCartesian(T,idx,ones(numel(idx),3)/3);

immse(C,Cref) % they're the same.

ans = 3.3543e-34

Now, would this example have worked in 2012? The calculation of the centroid would work fine, though some of the other tools are anachronistic. That said, you don't actually need them to take the mean. If we were living in 2012, the same demo could still be written:

% so you have some triangles in 3D
[F V] = stlread('stepholecube.stl'); % FEX #22409 (NOT the same function!)

% then get the centroids.  you're done
C = mean(permute(reshape(V(F,:),[size(F,1) 3 3]),[1 3 2]),3);

% not sure if that's right? 
% well, the barycenter is at [1 1 1]/3 in barycentric coordinates, so ...
T = TriRep(F,V);
idx = (1:size(T,1)).';
Cref = baryToCart(T,idx,ones(numel(idx),3)/3);

mean((C(:) - Cref(:)).^2) % they're the same.

ans = 3.3543e-34

For what it's worth, getfacecenters() from FEX #182013 can be used to get other triangle centers, not limited to the centroid. It covers the centroid, incenter, circumcenter, and 8 other centers. It wouldn't have been available in 2012, but it would certainly work in a MATLAB version of the era.