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From: "John D'Errico" <woodchips@rochester.rr.com>
Newsgroups: comp.soft-sys.matlab
Subject: Re: Spline ,Histopolation or Histospline - Matlab
Date: Wed, 8 Jul 2009 16:11:24 +0000 (UTC)
Organization: John D'Errico (1-3LEW5R)
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"Paul Meissner" <magnesit@gmx.at> wrote in message <h32fct$aut$1@fred.mathworks.com>...
> Hello,
> 
> I have a very tricky problem, I want to create an interpolation of a Step-Function. The problem is that the interpolation should keep the condition of area-preserving for every single step. This sounds like a histopolation, does it? Using Google (search: histopolation, histospline) had shown many theoretical abstracts but no Matlab-code. I found only a code-example for Mathematica but at all this is not working for me. (The spline is to "nervous"(rippled) for making a good interpolation)  
> 
> I hope you can give me an advice, how to make such an interpolation in Matlab. I would also be happy if you know a software which is able to do such an interpolation.
> 
> Best regards,
> Paul M.

So instead of using the spline to interpolate specific
data points, you wish to find a piecewise cubic (C1?
C2?) that reproduces the area in each interval?

Should be doable. The spline is linear in its parameters.
There will be a minimum energy configuration that
satisfies the areal constraints. I already have such a
constraint in my slm tools, but only for the overall
area of the curve.

John