Abstract:
We study the behavior of simple, 2D, self-organizing primitives that
interact and move in an unbounded environment to create aggregated
shapes. Each primitive is represented by a disk and a unit point
mass. In order to compare the aggregated shape produced by the
primitives to other shapes, the centers of mass of the two shapes
must be aligned. We present an algorithm for calculating the center
of mass (COM) for a set of point masses that are distributed in an
unbounded 2D environment. The algorithm calculates the centroid for
each coordinate component separately by forming two "orthogonal"
tubes, calculating a center of mass in 3D for each tube and then
projecting the 3D COM back onto the tubes, in order to produce the
2D COM of the points.
