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Any command/tool for generating a quadratic surface(quadric) given 9 points?
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Is there any command in 3D to generate the quadratic surface defined by 9 points in space? If not, are you aware of anybody who has written a sketch of this? I can solve the generic equation for a quadric in Mathematica, but that takes quite a bit of time (and accuracy when plugging in values).
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I'm sure I've seen that using GeoGebra's matrix commands (but I can't find it :( )
Hopefully this helps:
https://math.stackexchange....
How's this? Exact for 6 points: https://www.geogebra.org/m/fqfe5trp
(it can be made more efficient if the points only move vertically as M_A will then be constant)
I think you can probably use the SVD command if you want "best fit" through eg 9 points
https://wiki.geogebra.org/e...
Hi Michael,
I made a try to calc quadrik by
f(x,y)=Sum(m3 {x², y², x y, x, y, 1})
can you check the result too?
got a list. why?
BTW
my ipad do not give me the keyboard using online app  had to download the file to work with, great work!
I remember there was a post to this?
I think this is OK for 9 points (maybe you can check against your Mathematica answers to verify)
https://www.geogebra.org/m/dwsk5nwg
Sorry, didn't use enough terms. I've updated https://www.geogebra.org/m/fqfe5trp so it's now exact for 9 points :)
I used the CAS to substitute into the general equation of a quadric the coordinates of the nine points, solve the resulting system of equations and again substitute the solution into the equation. I thus obtained the equation of the quadric, see here the result: https://www.geogebra.org/m/mxpdmt4n
with brute force. but I am afraid the PC crashes
... and much shorter solutions from Zbynek
... and what the original poster actually wants I think from Mathieu :)
https://www.geogebra.org/m/xqkwgcan
awesome
but they fail when (0,0,0) is in quadric (mine too)
this problem was also implementing conic
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