How to obtain a Lagrange interpolation of the parametric equations (not of the Cartesian equation)?

Eliantis shared this question 5 months ago
Answered

Hi,


A lack of technique is present to me in Geogebra.

If I draw in the 2D or 3D coordinate system n points, I need a Lagrange interpolation that Geogebra automatically gives me like this:

https://www.geogebra.org/m/KjPd8tVb


But I want to go more in depth because it is not this interpolation that I need: having drawn n points, I therefore have n X corrdata and n Y corrdata (and n Z corrdata if it is in 3D). of which I wish to obtain successively and automatically 2 Lagrange interpolations (3 if it is in 3D) X_Lagrange (t), Y_lagrange (t) (Z_lagrange (t) if it is in 3D) of the following sets of points x_n (t_n, X_n), y_n (t_n, Y_n) (z_n (t_n, Z_n) if it is in 3D) for n varying from 1 to N.

I could do it myself by rewriting all these points depending on t but I am wondering if a technique in Geogebra can do this automatically.

If yes,which?


thanks

Comments (10)

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1

Do you want https://wiki.geogebra.org/e... ?


If not, please give an example

* input points

* output equation

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1

spline() for 2D???

or

l1 list of points

Polynomial(Zip((k, x(P)), P, l1, k, 1…Length(l1)))

Polynomial(Zip((k, y(P)), P, l1, k, 1…Length(l1)))

Polynomial(Zip((k, z(P)), P, l1, k, 1…Length(l1)))

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1

I forgot this tuto to illustrate my question:

https://rco.fr.nf/index.php...

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1

Polynomial() is the command for lagrange method

Files: foro.ggb
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1

in response to the links given by Michael Borcherds,

1) no Fourier transform appears after drawing.

So I am looking for a tool or a site capable of giving me according to the drawing the Fourrier Transform

Does Geogebra know how to do this?


2) if my drawing is in space, the Fourier Transform will not be sufficient

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1

1) sorry, no


2) you mean in 3D?

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1

2)yes in 3D

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1

in response to mathmagic,what is the entire command without dots

Polynomial(Zip((k, x(P)), P, l1, k, 1…Length(l1))). ?

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1

no entiendo bien. es esto?


Polynomial(Zip((k, x(P)), P, {(-1, 4), (2, 1), (-1, 1), (1, 3), (-2, 2), (3, 3)}, k, 1…6))

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