In geometry, the **centroid**, **geometric center**, or **barycenter** of a plane figure or two-dimensional shape *X* is the intersection of all straight lines that divide *X* into two parts of equal moment about the line. Informally, it is the "average" (arithmetic mean) of all points of *X*. The definition extends to any object *X* in *n*-dimensional space: its centroid is the intersection of all hyperplanes that divide *X* into two parts of equal moment.

In physics, the word **centroid** means the geometric center of the object's shape, as above, but **barycenter** may also mean its physical center of mass or the center of gravity, depending on the context. Informally, the center of mass (and center of gravity in a uniform gravitational field) is the average 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.

In geography, the centroid of a region of the Earth's surface, projected radially onto said surface, is known as its geographical center.

Read more about Centroid: Properties

### Other articles related to "centroid, centroids":

... The mean center, or

**centroid**, is the point on which a rigid, weightless map would balance perfectly, if the population members are represented as points of ... Mathematically, the

**centroid**is the point to which the population has the smallest possible sum of squared distances ... If defined in the three-dimensional space, the

**centroid**of points on the Earth's surface is actually inside the Earth ...

... x y z = 2x 2y 2z.) A = 1 0 0 B = 0 1 0 C = 0 0 1 incenter = 1 1 1

**centroid**= bc ca ab = 1/a 1/b 1/c = csc A csc B csc C ... Note that, in general, the incenter is not the same as the

**centroid**the

**centroid**has barycentric coordinates 1 1 1 (these being proportional to actual signed areas of the ...

**Centroid**-

**Centroid**of Cone or Pyramid

... The

**centroid**of a cone or pyramid is located on the line segment that connects the apex to the

**centroid**of the base ... For a solid cone or pyramid, the

**centroid**is 1/4 the distance from the base to the apex ... For a cone or pyramid that is just a shell (hollow) with no base, the

**centroid**is 1/3 the distance from the base plane to the apex ...

... made at the half-way point between the

**centroid**of each texel and the

**centroids**of every surrounding texel for the entire texture ... The result is that each texel

**centroid**will have a Voronoi polygon surrounding it ... This polygon region consists of all points that are closer to its texel

**centroid**than any other

**centroid**...

... In a cyclic quadrilateral, the "area

**centroid**" Ga, the "vertex

**centroid**" Gv, and the intersection P of the diagonals are collinear ...