Centroid

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.

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Other articles related to "centroid, centroids":

Center Of Population - Definitions - Mean Center
... 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 ...
Trilinear Coordinates - Examples
... 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 ...
Locating 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 ...
Texel (graphics)
... 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 ...
Cyclic Quadrilateral - Anticenter and Collinearities
... In a cyclic quadrilateral, the "area centroid" Ga, the "vertex centroid" Gv, and the intersection P of the diagonals are collinear ...