Re(2): Clockwise or Counter-clockwise

Given 3 2d non-colinear points in sequence, create the 3d vectors v1 = p1->p2 and v2 = p1->p3 on the z0 plane. calculate v3 = v1 X v2. if v3 has positive z then they are in counter-clockwise order, negative z then clockwise.

That only works if the polygon in question is convex, otherwise local orientation says nothing about the polygon's orientation (unless you pick your locale cleverly, of course).

Take the example of a banana-shaped counterclockwise polygon: the interior section will have a "clockwise" orientation.

-- F o x t r o t U n i f o r m Found a typo in this node? /msg me The hell with paco, vote for Erudil!

Comment on Re(2): Clockwise or Counter-clockwise

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Re: Re(2): Clockwise or Counter-clockwise by zengargoyle (Deacon) on Feb 19, 2003 at 06:53 UTC
Given 3 2d non-colinear points in sequence there's no such thing as convex or concave. (that's why i didn't go with 3 or more...) =P	[reply]
Re(4): Clockwise or Counter-clockwise by tall_man (Parson) on Feb 19, 2003 at 14:55 UTC
Given 3 2d non-colinear points in sequence there's no such thing as convex or concave. I think you mean to say that they form a triangle, and all triangles are convex.	[reply]
Re: Re(4): Clockwise or Counter-clockwise by thor (Priest) on Feb 19, 2003 at 16:14 UTC
I think you mean to say that they form a triangle, and all triangles are convex. That is to say that 3 points taken in isolation form a triangle. (all the caveats about non-colinearity apply) Three points on a general 2-D surface will be connected in an ordered fashion with a line (think connect the dots). thor	[reply]