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centroid

noun

Etymology

From centre + -oid. From 1844, used as a replacement for the older terms "centre of gravity" and "centre of mass" in situations described in purely geometrical terms, and subsequently used for further generalisations.

  1. derived from κέντρον
  2. derived from centrum
  3. derived from centre
  4. inherited from center
  5. formed as centroid — “centre + -oid”

Definitions

  1. The point at which gravitational force (or other universally and uniformly acting force)…

    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.

    • operatorname Centroid(𝒳)=(∫xg(x)dx)/(∫g(x)dx)      (6) where the integrals are taken over the whole space ℝⁿ, and g is the characteristic function of the subset, which is 1 inside 𝒳 and 0 outside it [27].

  2. The point of intersection of the three medians of a given triangle

    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.

  3. the point whose (Cartesian) coordinates are the arithmetic mean of the coordinates of a…

    the point whose (Cartesian) coordinates are the arithmetic mean of the coordinates of a given finite set of points.

  4. ›+ 3 more definitions

    1. An analogue of the centre of gravity of a nonuniform body in which local density is…

      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 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.

    2. the arithmetic mean (alternatively, median) position of a cluster of points in a…

      the arithmetic mean (alternatively, median) position of a cluster of points in a coordinate system based on some application-dependent measure of distance.

    3. Given a tree of n nodes, either (1) a unique node whose removal would split the tree into…

      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.

The neighborhood

Derived

bicentroidal, centroidal, centroided, centroider, centroiding, function centroid, geometric centroid, gyrocentroid, intercentroid, quasicentroid

Vish — recursive loop

No curated loop yet for centroid. Loops are being traced one word at a time while the ingestion pipeline matures.

sense glosses and etymology drawn from English Wiktionary · source · CC-BY-SA