Every polygon has, at a minimum, four distinct "centers": The
barycenter of its vertices. The barycenter of its edges. Its
barycenter as a polygon. A GIS-specific "center" useful for
labeling (usually calculated with undocumented proprietary
methods). (They may accidentally coincide in special cases, but
for "generic" polygons they are distinct points.) A "barycenter"
in general is a "center of mass." The three types differ on
where the mass is presumed located: it either is entirely on the
vertices, spread uniformly on the edges, or spread uniformly
throughout the polygon itself. Simple methods exist to compute
all three barycenters. One approach relies on the basic fact
that the barycenter of the disjoint union of two masses is the
total-mass-weighted average of the barycenters. From this we
easily obtain the following: The barycenter of two (equally
weighted) vertices is their average. This is obtained by
averaging their coordinates separately. Geometrically, it is the
midpoint of the line segment joining