[comp.theory] SIMPLICITY TEST for polygons

krishna@cs.tamu.edu (Krishna Kumar) (01/22/91)

Can anyone out there tell me what the current status of the following
problem is ?

INPUT : A polygon P
QN    : Is P simple (i.e Do any two edges of P intersect other than at a vertex)

Preparata and Shamos describe an O( nlogn ) algorithm. Has anything better
been done recently? Alternatively is there a non-trivial lower
bound known for the problem?

Krishna Kumar
Dept. of Computer Science
Texas A&M University
College Station, TX 77840

eppstein@wormwood.ics.uci.edu (David Eppstein) (01/23/91)

In article <11430@helios.TAMU.EDU> krishna@cs.tamu.edu (Krishna Kumar) writes:
> Can anyone out there tell me the current status of the following problem?
>
> INPUT : A polygon P
> QN    : Is P simple (Do any two edges of P intersect other than at a vertex)

This can be done in linear time -- compute the convex hull, triangulate
the interior and the "indentations" between the polygon and its hull
using Chazelle's algorithm, and test if you really have a triangulation
of a convex region.

Of course if you're looking for a practical algorithm, this is not the way...
--
David Eppstein    UC Irvine, Info & Computer Science    eppstein@ics.uci.edu