<P> In mathematics and physics, the centroid or geometric center of a plane figure is the arithmetic mean ("average") position of all the points in the shape . The definition extends to any object in n - dimensional space: its centroid is the mean position of all the points in all of the coordinate directions . Informally, it is the point at which a cutout of the shape could be perfectly balanced on the tip of a pin . </P> <P> While in geometry the term "barycenter" is a synonym for "centroid", in astrophysics and astronomy, barycenter is the center of mass of two or more bodies which are orbiting each other . In physics, the center of mass is the arithmetic mean of all points weighted by the local density or specific weight . If a physical object has uniform density, then its center of mass is the same as the centroid of its shape . </P>

Is centroid the same as center of gravity