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From: Dakota Judo <dakotajudo@mac.com>
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Subject: Re: How to detect turning points in curves...
References: <f76kg0$ic0$1@news.Stanford.EDU> <f76ko9$ilr$1@news.Stanford.EDU>
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In article <f76ko9$ilr$1@news.Stanford.EDU>,
 "Linus Utopia" <linus_utopia@gmail.com> wrote:

> Hi all,
> 
> Please be advised that my curves are not continuous -- they are discrete 
> data points. When I plotted them in Matlab, they are connected and looked 
> like a continous curve. So I am not sure if the second "finite difference" 
> will help..., and accurately...
> 

My first thought would be to polynomial interpolation of 3-5 points at a 
time, then use the second derivative of that polynomial.

I can't say anything about how efficient that would be, or how accurate, 
though.

Peter Claussen


> > 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!
> >
> >
> >
> >
> >
> >