Newsgroups: comp.graphics
Path: utzoo!utgpu!watserv1!watcgl!pfbertnd
From: pfbertnd@watcgl.waterloo.edu (Philippe F. Bertrand)
Subject: Re: Polygon orientation test ?
Message-ID: <1990Oct28.160039.19901@watcgl.waterloo.edu>
Organization: University of Waterloo
References: <4158.272311a1@cc.curtin.edu.au> <1728@wet.UUCP>
Date: Sun, 28 Oct 90 16:00:39 GMT
Lines: 24

In article <1728@wet.UUCP> smiller@wet.UUCP (Gregory Shane Miller) writes:
>
>Note saying, given any three points from a polygon, eval this 3x3
>matrix (eg. find det of the 3x3 matrix).  If returns the twice the
>signed area of the three points (eg a triangle).  The sign of the
>result tells whether it's oriented CW or CCW.

This algorithm only works on concave polygons!  ie it will not work for
(0,0), (1,1), (0,2), (2,2), (2,0)  = square with a chunk removed
your algorithm using the first 3 points will return CCW when in fact it is CW

This is important for hidden surface algorithms in 3D where a face of an object
has all the perspective and view operations performed on it resulting in a 
2D polygon.  If all faces originally appear CW when they are facing you, hidden
surfaces will be CCW after the view transformations.

Previously posted solutions appeared correct.
>
>G. Shane Miller [ smiller@wet.UUCP ]  Von Neumann eat your heart out!

- Philip F. Bertrand                            pfbertrand@violet.waterloo.edu 
Computer Graphics Lab,                         or pfbertnd@watcgl.waterloo.edu 
Department of Computer Science, University of Waterloo
Waterloo, Canada  N2L 3G1