Find the centers of multiple polygons

I have an nx3 matrix that holds the locations for the vertices of a chain of hexagonal shapes (images 1, 2).

Side-note: The coordinates for the vertices of these hexagons are not in any logical order within the matrix. The coordinates were retrieved from an STL file which may be the reason why.

I'm trying to find the centroid of each of these hexagons and index those six points to its respective centroid. Once I've indexed these, I plan on writing some more code to manipulate the six points farther away from their respective centroids - making the hexagons larger and making my structure thicker [ they are currently too thin ] (image 3).

My problem is the centroid and indexing part. I've tried clustering the hexagons into n/6 clusters using the k-means and subclust functions, but there're always points that do not fall in the center of a hexagon (image 4).

Would anyone know what I should try?

[I've also attached the matrix, in case you would like to play around with the data as well.]

Answer 1

[Image Analyst]

Isn't the centroid of a perfect hexagon just the mean of the x and y coordinates of the vertices?

xCentroid = mean(xVertices);
yCentroid = mean(yVertices);

Just do that for every hexagon and you'll have all the centroids.

[Jeremy]

That part I do get, but the matrix itself isn't in any particular order (which I failed to mention; sorry!!), which makes singling out any one hexagon's coordinates difficult as well as finding the centroid of that hexagon and indexing those hexagon vertices to that centroid, if that makes sense.

I'm trying out other statistical clustering methods to pick out the hexagons and then apply the code you suggested. Thanks!

[Image Analyst]

So it's just a random assortment of vertices where the hexagon groupings only become apparent after all the dots have been plotted?

[Jeremy]

Yes. The data was imported from an STL file, where I presume the random ordering is necessary to construct mesh/surface type objects. Any ideas?

[Image Analyst]

Nope.