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Temporal Curves
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I found this way to find a path through some points I called a temporal curve. If anyone's interested I can explain how I solve for the constants matrix for different numbers of points...,
My question is what are the types of points geogabra uses called, The formula above works in any number of dimensions but I don't know how to explain that the same formula for t is applied to each coordinate axis the way geogabra does curves, I'm just missing some vocabulary to look up online to use when explaining this idea...
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Create points A,B,C,D,E, then
https://www.geogebra.org/m/k4X3MSgf
hello
it is clear for me that both methods make the same curve. In attached file I see that the calculus has the difference in t
in blue t=0,1,2,3,4
in red t=1,2,3,4,5
saludos
the two methods recalculate the coeficients. moving the A point is clear. more, the calculus are equivalent
I can explain it better in spanish. you solve a matricial equation with a Vandermonde matrix and Zbynek use polynomial[] (Lagrange's polynomial). the picture from wikipedia can illustrate this fact. see the red marks.
This is a part 2 showing you can change the left row vector to a different basis... They have to be at least linearly independent, not sure any other restrictions...
here's a file for the 2nd curve
hello
Some multiplication rules.,.
if you use f4(t),f3(t),f2(t),f1(t),f0(t) you only need the inverse of matrix M being M the matrix
I do not remember the order of this calculus
ceartainly GG repeat the calculus for each Fit[] command but I do not know if the calculus is longer in time
saludos
hello
I think you can do the same steps in CAS of GG, defining each equation with substitute[], solving them with solved[] and creating the curve
but I tink that GG has its own style so I think this is the simpler steps for doing the curve
the calculus of inverse spend a time
https://www.geogebra.org/m/zt7uMnZ7
saludos
just to show this works with surfaces too!
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