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From: "FDR " <gene.bunin@epfl.ch>
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Subject: Re: How to check whether the curve is concave?
Date: Fri, 18 Nov 2011 22:18:11 +0000 (UTC)
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"Marco Wu" wrote in message <j6d0co$2qn$1@newscl01ah.mathworks.com>...
> But it seems like you ignore the fact that there could be more than one Y value for the same X, if I convert the pol2cart coordinate. The 2nd order derivative should only work for unique Y value for giving any given X.


I don't know if this will be of any use, but I just submitted a file that checks convexity/concavity of a data set. It doesn't handle very large data sets (yet), but if you want to take < 100 sample points and verify their convexity/concavity within a tolerance (probably very small tolerance if you assume no noise), then it might do what you want.

http://www.mathworks.com/matlabcentral/fileexchange/33811

The convex hull approach is probably not that bad, either, though.