How to approximate a bezier curve with a polynom f(x) ?

Questions
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1

Hello everybody

I would like to separate a simple bezier curve into multiple parts (compare image) and approximate every part with a polynom of the form f(x) = y

howtoapproximateabeziercurveinseparatedparts.PNG
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If adding a case condition e.g. (if x > 10 AND x < 20 then f(x) = … ) how is it possible to approximate each part with a polynom?

Cheers,
Matt

2

Is this what you are looking for?

3

Dear Mr. Dulgerci

It is a big surprise and pleasure to have gotten your reply!
I appreciate your answer a lot.

After using the function InterpolatingPolynomial[] I am not sure, though, as to whether or not my goals can be reached in mathematica or at all.

Please have a look at the document and tell me whether it is possible to achieve those goals. The interpolation is not giving me a very good fit on the targeted shape (paro2.nb).

Best regards,
Matteo

4

Hi Matteo,

as I understand your problem you just need an interpolation of your 2D data. The idea in this case is to consider the x- and the y-coordinates seperately - see my attachment. Maybe this is helpful.

Regards – Henrik

5

… here just comes an improved version.

Henrik

6

8053re02.png
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5827re04.png
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8

@Henrik
Thanks very much for your answer!
Is there a way to export the point coordinates and the slope values (first differential) of the various points which I see when doubleclicking on the graph?

9

Hi Matteo,

of course you can export all those data (using Export) - see attachment.

Regards – Henrik