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Polygon Centroid


The positions of the geometric centroid of a planar non-self-intersecting polygon with vertices (x_1,y_1), ..., (x_n,y_n) are

x^_=1/(6A)sum_(i=1)^(n)(x_i+x_(i+1))(x_iy_(i+1)-x_(i+1)y_i)
(1)
y^_=1/(6A)sum_(i=1)^(n)(y_i+y_(i+1))(x_iy_(i+1)-x_(i+1)y_i),
(2)

where A is the polygon area and x_(n+1)=x_1 and y_(n+1)=y_1 (Bourke 1988, Nürnberg 2013).


See also

Geometric Centroid, Polygon, Polygon Area

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References

Bourke, P. "Calculating the Area and Centroid of a Polygon." July 1988. http://paulbourke.net/geometry/polygonmesh/.Nürnberg, R. "Calculating the Area and Centroid of a Polygon in 2D." 2013. https://www.ma.imperial.ac.uk/~rn/centroid.pdf.

Cite this as:

Weisstein, Eric W. "Polygon Centroid." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PolygonCentroid.html

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