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From: "Linus Utopia" <linus_utopia@gmail.com>
Newsgroups: comp.soft-sys.matlab,sci.math,sci.stat.math,sci.stat.consult,sci.stat.edu
Subject: How to detect turning points in curves...
Date: Thu, 12 Jul 2007 21:26:39 -0400
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How to detect turning points in curves

Hi all,

If you take a look at the following plot,

http://img63.imageshack.us/img63/5050/gggyt1.jpg

You will agree with me that there are two turning points.

But is there a systematic way to let computer detect the turning points 
automatically and programmatically?

Please be advised that the second turn isn't neccessarily turning down, it 
can also possibly go up...

And in real-world applications, the turn can be more smooth and round, but 
still, naked eyes should be able to find the turning points easily.

My program has to do a classification:

All the good curves should first go down, and then either make no turns; or 
make a turn, and stay vertically flat and slightly up, going from the left 
to the right.

There should be no second turn (up or down). If there is the second turn, 
then that's the bad curves.

My program needs to decern the good curves from bad curves.

I cranked a few algorithms but they don't work well. Are there systematic 
methods of handling this?

Thanks a lot!