Word Finder - centroid

definition

The point at the centre of any shape, sometimes called centre of area or centre of volume. For a triangle, the centroid is the point at which the medians intersect. The co-ordinates of the centroid are the average (arithmetic mean) of the co-ordinates of all the points of the shape. For a shape of uniform density, the centroid coincides with the centre of mass which is also the centre of gravity in a uniform gravitational field.

The ideas of moment and of centroid are extended to geometrical figures, whether solid, superficial or linear.

The centroid of a figure is a point fixed with regard to the figure, and such that its moment with regard to any plane (or, in the case of a plane area or line, with regard to any line in the plane) is the same as if the whole volume, area or length were concentrated at this point.

The centroid is sometimes called the centre of volume, centre of area, or centre of arc. The proof of the existence of the centroid of a figure is the same as the proof of the existence of the centre of gravity of a body.

The mean distance of a plane figure from a line in its plane, or of any figure from a plane, is therefore the same as the distance of the centroid of the figure from the line or plane.

We sometimes require the moments with regard to a line or plane through the centroid.

These formulae also hold for converting moments of a solid figure with regard to a plane into moments with regard to a parallel plane through the centroid; x being the distance between the two planes.

A line through the centroid of a plane figure (drawn in the plane of the figure) is a central line, and a plane through the centroid of a solid figure is a central plane, of the figure.

They may be applied, for instance, to finding the centroid of a semicircle or of the arc of a semicircle.

The " central ordinate " is the ordinate through the centroid of the trapezette (§ 32).

The ordinate through the centroid of the figure is the ' ` central ordinate."

In the case, therefore, of any solid whose cross-section at distance x from one end is a quadratic function of x, the position of the crosssection through the centroid is to be found by determining the position of the centre of gravity of particles of masses proportional to So, S2, and 4S 1, placed at the extremities and the middle of a line drawn from one end of the solid to the other.

If input parameter centroid is set to ` yes ', then X and Y are centroids of photon distributions in the detect cell.

The two-dimensional coordinates of each marker were obtained by calculating the centroid of each marker outline for each digitized video frame.

If you use the option of " residue " then the residue centroid is used throughout the routine.

These can be used to output a ten figure (10 meter) National Grid reference for the zone centroid.

We have generated ensembles of Cα and sidechain centroid models conformations with RAPPER, for each target in the above list.

It can be proved by geometry that (aA-H3B) +yC = aA+(aB+- y C) = (a + 1 3+ 7) P, where P is in fact the centroid of masses a, 13, y placed at A, B, C respectively.

This point is the centroid of the body.

The centroid of a rectangle is its centre, i.e.

The centroid of a hemisphere of radius R, for instance, is the same as the centroid of particles of masses 0, 7rR 2, and 4.