Path: utzoo!utgpu!jarvis.csri.toronto.edu!mailrus!csd4.milw.wisc.edu!leah!rsb584
From: rsb584@leah.Albany.Edu (Raymond S Brand)
Newsgroups: comp.graphics
Subject: Re: Computational geometry
Message-ID: <1810@leah.Albany.Edu>
Date: 29 Apr 89 20:10:36 GMT
References: <2053@incas.UUCP> <5397@cs.utexas.edu>
Organization: his computer
Lines: 49

In article <5397@cs.utexas.edu>, atc@cs.utexas.edu (Alvin T. Campbell III) writes:
> In article <2053@incas.UUCP> mdoerr@incas.UUCP (Michael Doerr) writes:
> >
> >	How does one determine _reliabely_ (!!!) the winding sense (clockwise
> >	or counter-clockwise) of the sides of an arbitrary polygon?
> >
> 
> I recently had to solve the winding-sense problem myself.
> I am glad to see other people have had to deal with it as well.
> 
[ ... ]
> 
> Now for the method.  Assume that we have a polygon with n 
> vertices, numbered v1, v2, ..., vn.  First, we find the vertex,
> vtop, with the largest y-coordinate.  The angle of the polygon
> at this vertex is guaranteed to be convex.  Now we take the 
> cross-product of the vectors (vaft, vtop) and (vtop, vbef),
> where vaft is the vertex following vtop, and vbef is the vertex
> preceding vtop. If the cross-product is negative, the vertices
> are counter-clockwise.  Otherwise, the vertices are clockwise.
> 
[ ... ]
> -- 
> 				A. T. Campbell, III
> 				CS Department, University of Texas
> 				atc@cs.utexas.edu

I believe that a figure-8 is a permited shape in the original question, but
that shape can lead to different answers from your method depending on the
orientation of the figure-8.


-------------------------------------------------------------------------
Raymond S. Brand                 rsbx@beowulf.uucp
3A Pinehurst Ave.                rsb584@leah.albany.edu
Albany NY  12203                 FidoNet 1:7729/255 (518-489-8968)
(518)-482-8798                   BBS: (518)-489-8968

-------------------------------------------------------------------------
Raymond S. Brand                 rsbx@beowulf.uucp
3A Pinehurst Ave.                rsb584@leah.albany.edu
Albany NY  12203                 FidoNet 1:7729/255 (518-489-8968)
(518)-482-8798                   BBS: (518)-489-8968

-------------------------------------------------------------------------
Raymond S. Brand                 rsbx@beowulf.uucp
3A Pinehurst Ave.                rsb584@leah.albany.edu
Albany NY  12203                 FidoNet 1:7729/255 (518-489-8968)
(518)-482-8798                   BBS: (518)-489-8968