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What is the way to calculate the centroid of polygon? I have a concave polygon of 16 points, and I want know the centroid of that.

thanks

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You've seen this? – J. M. Dec 11 '11 at 14:09
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As for a Mathematica routine: PolygonCentroid[pts_?MatrixQ] := With[{dif = Map[Det, Partition[pts, 2, 1]]}, ((ListConvolve[{1, 1}, #] & /@ Transpose[pts]).dif)/(3 Total[dif])]. Maybe somebody can do better than me... – J. M. Dec 11 '11 at 14:19
thanks but i will be delighted if u could a bit explain me thx – Csabi Dec 11 '11 at 14:22
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Explain what? The formula? The code? You're a bit vague... – J. M. Dec 11 '11 at 14:30

1 Answer

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Label your 16 points $(x_1,y_1)$ through $(x_{16},y_{16})$. Then, according to the Wikipedia article...

$$C = \left(\frac{x_1+x_2+\cdots+x_{16}}{16}, \frac{y_1+y_2+\cdots+y_{16}}{16}\right)$$

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I don't mind giving a quick answer, but please notice that you have not asked a good question. Sure, the wording is fine and the centroid of a polygon does need to be computed, but any research (say, on the Wikipedia page) on your part would have led you to the answer. – The Chaz 2.0 Dec 11 '11 at 15:04
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