Definitions
from The American Heritage® Dictionary of the English Language, 4th Edition
 n. See center of mass.
 n. The point in a system of masses each of whose coordinates is a weighted mean of coordinates of the same dimension of points within the system, the weights being determined by the density function of the system.
from Wiktionary, Creative Commons Attribution/ShareAlike License
 n. 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 coordinates of the centroid are the average (arithmetic mean) of the coordinates 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.
from the GNU version of the Collaborative International Dictionary of English
 n. The center of mass, inertia, or gravity of a body or system of bodies.
from The Century Dictionary and Cyclopedia
 n. In mathematics, the center of mass. See center.
 n. In kinematics, same as centrode. Reauleaux.
 n. A point of emphasis or increased energy in a series of speechsounds, or in any series of impulses. Also used attributively.
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
 n. the center of mass of an object of uniform density
Etymologies
Sorry, no etymologies found.
Examples

The third is the centroid, which is the intersection of the lines that go from the vertex to the midpoints of opposing lines.

For each signature, we calculated the gene expression centroid of the two groups of breast tumors (as determined in the original publications), and then correlated each centroid with cell line expression of the respective signature genes.

Search the Discussion Group history for "centroid," and you'll find lots of entries, many on nearly the same question.

Situated in a tightly packed urban neighborhood, this limited space outdoor sculpture garden inherits a large tree, and uses this sole arboreal presence to establish a gravitational pattern of grooves that are focused towards the tree's centroid.

Vertical circulation always maintains a close connection to the diagrammatic and structural centroid of the building.

The framers of Illinois deliberately chose to put the capital in a small town near the transportation centroid of the new state.

In 1767 Leonhard Euler proved that for all triangles the orthocenter, the circumcenter, the centroid and the center of the midcircle are always on the same line.

Each turtle moves towards the centroid of the others, accelerating at a rate inversely proportional to its distance from that point — except when the distance is below a certain small threshhold, it just coasts.
hughstimson.org » Blog Archive » Simple Chaos: A Three Body Problem

For example a robin would be closer to the centroid of the shape than an emu.

That centroid step is indeed the sort of discretization I meant.
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