# centroid

In mathematics and physics, the centroid or geometric center of a two-dimensional region is, informally, the point at which a cardboard cut-out of the region could be perfectly balanced on the tip of a pencil (assuming uniform density and a uniform gravitational field). Formally, the centroid of a plane figure or two-dimensional shape 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.

While in geometry the term barycenter is a synonym for "centroid", in physics "barycenter" may also mean the physical center of mass or the center of gravity, depending on the context. The center of mass (and center of gravity in a uniform gravitational field) 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. Centroid, Wikipedia