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How to create a spline x>y (not t>x, t>y)?
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I would like to create spline curve between several points that is x>y. Reason for that is, I would like to show the derivative (d/dx) of that spline (I would like to move the points and the derivative changes the same time).
It seems there is no general purpose invert command that allows inverting the x(t) of the spline and substituting into y(t) of the spline.
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I meant to share one work with problem in your post
when I clic in your link I do not know where is the problem
but if you have a curve (x(t),y(t)) you have not get a x>y derivate because the curve can have double points for some t
so I suposse you want ordered points and a(t) function (sometimes a(t) is a curve although the points are ordered)
perhaps this one
I do not understand why the new users does not share their works.
the old user are working in the dark
is this you want?
or did you want to use polynomial[<list of points>]?
saludos
PD: this post https://www.geogebra.org/he... can help you
I'm sorry, I don't understand your problem, I've shared my work: https://www.geogebra.org/s_o
As for this problem, there is nothing to share:
create 5 points AE
do Spline[A,B,C,D,E]
=> Youl'll get a spline function t>x and t>y (like the manual says, like in your file).
I would like to have a function x>y (of course I know this is only possible if x(A)<x(B)<x(C)<x(D)<x(E) ). I have not found any solution on that. A polynomial is not what I would like to have, as it will oscillate.
You're work is similar to what I would like to create: It creates the derivative as a trace of a point during the animation. I would like to be able to move a point and instantly the derivative changes, for that I need a spline function x>y (any other ideas?).
I meant to share one work with problem in your post
when I clic in your link I do not know where is the problem
but if you have a curve (x(t),y(t)) you have not get a x>y derivate because the curve can have double points for some t
so I suposse you want ordered points and a(t) function (sometimes a(t) is a curve although the points are ordered)
perhaps this one
Thank you very much, that trick is exactly what I was looking for!
Final result: https://www.geogebra.org/m/xeFKZTfM
@mathmagic's solution is nice, there is also the command ParametricDerivative[a] to get the derivative function.
Note that the splines that GeoGebra produces are not always functions, see https://www.geogebra.org/he... for details.
I wanted to ask a similar question, this is how I found this thread.
I see now how to create a parametric curve from a spline.
Is there a way to create a function?
Besides the derivative, I would also like to draw the integral function.
Interested to in selfmade splinefunctions
https://www.geogebra.org/m/s5g89mqy
https://www.geogebra.org/m/QW6bURhd
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