centroid

Plural: centroids

Noun

• The geometric center of a plane figure or a three-dimensional object.
• the center of mass of an object of uniform density
• The point at which gravitational force (or other universally and uniformly acting force) may be supposed to act on a given rigid, uniformly dense body; the centre of gravity or centre of mass.
• The point of intersection of the three medians of a given triangle; the point whose (Cartesian) coordinates are the arithmetic mean of the coordinates of the three vertices.
• the point whose (Cartesian) coordinates are the arithmetic mean of the coordinates of a given finite set of points.
• An analogue of the centre of gravity of a nonuniform body in which local density is replaced by a specified function (which can take negative values) and the place of the body's shape is taken by the function's domain.
• the arithmetic mean (alternatively, median) position of a cluster of points in a coordinate system based on some application-dependent measure of distance.
• Given a tree of n nodes, either (1) a unique node whose removal would split the tree into subtrees of fewer than n/2 nodes, or (2) either of a pair of adjacent nodes such that removal of the edge connecting them would split the tree into two subtrees of exactly n/2 nodes.

Examples

• He calculated the CENTROID of the remaining letters to optimize his final Scrabble move.
• The centroid of an arbitrary function f is given by #92;frac#123;#92;intxf(x)dx#125;#123;#92;intf(x)dx#125;, where the integrals are calculated over the domain of f.

Synonyms

barycentre, centre of area, centre of gravity, centre of mass, centre of volume, function centroid, geometric centre, geometric centroid, tree centroid

Related Words

barycenter, barycentre, geographical centre