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Someone placed this comment in the article, which is not where it belongs. I am moving it here: I think this item makes a mistake yet. For the conferenced item is about the relation between three points, and the author of this item extend it to general case. The mistake is appearred at this time. If we choose points F, G, H as the investigated points, we would get a different result by the author's way. Unfortunately, I do not have a correct way to assure the orientation of a simple closed curve either.
Now, to address the comment. The article specifically mentions that the middle point you select must be on the convex hull of the polygon. Point G is not on the convex hull. So, yes, you would get a different, incorrect result if you select a middle point which is not on the convex hull, or if you select collinear points. James Monroe (talk) 00:11, 29 January 2010 (UTC)