1 research outputs found
On the number of radial orderings of planar point sets
Given a set of points in the plane, a \emph{radial ordering} of
with respect to a point (not in ) is a clockwise circular ordering of
the elements in by angle around . If is two-colored, a \emph{colored
radial ordering} is a radial ordering of in which only the colors of the
points are considered. In this paper, we obtain bounds on the number of
distinct non-colored and colored radial orderings of . We assume a strong
general position on , not three points are collinear and not three
lines---each passing through a pair of points in ---intersect in a point of
. In the colored case, is a set of points partitioned
into red and blue points, and is even. We prove that: the number of
distinct radial orderings of is at most and at least
; the number of colored radial orderings of is at most
and at least ; there exist sets of points with
colored radial orderings and sets of points with only
colored radial orderings