Subject: Re: Inside or outside of a polyhedron

From: "Andrzej Szymoszek" <[email-masked]>
Date: Wed, 17 Apr 1996 14:23:00 GMT+1

Dear Netters,
  
  Shouldn't be noticed that if you have n points in space, it isn't
 determined what kind of polyhedron you actually have? This is the
 non-convex case. Imagine 4 points in 2D:
 
                           .4
                          3.
                       1.      2.
                       
  You can go 1-2-4-3-1, or 1-3-4-2-1, or 1-3-2-4-1. So the problem is
 in this case quite complicated.
 
  For the "convex" case, staying by 2D (generalization to 3D is 
 straightforward, hopefully :-) I have an idea first to find a gravity
 centre of the polygon. This is the point we are sure it is inside. 
 Then you join g.c. with the point in question- and determine whether
 it crosses the border (point outside) or not (inside).
 
  Andrzej Szymoszek
  [email-masked]