Structure of a quadric

[Grillteller]

Hello,

I'm using the fit-> 2.5D quadric very often and I wonder how it works mathematically. The documentation says that the cloud is first projected on its best fit plane. Does that mean that you take the distances from the original cloud to the plane as z-values for the quadric? Do you calculate the z-value for every point in the cloud ?
After that i get my equation in the form of: a+b.x+c.y+d.x²+e.y²=0. Can i classify my quadric with this equation ? My quadric is for example
z = -0.00466042 + 0.000139516 * x + 3.05407e-05 * y + 0.0336013 * x^2 + 0.00341947 * x*y + 0.010968 * y^2
And isn't there an additional parameter f.x.y in a 2D-quadric?
Is the RMS value the RMS for all point distances from the original cloud to the quadric ?

Best regards,
Grillteller

[daniel]

Actually we only use the best fitting plane (least squares) to guess the 'most flat' dimension of the cloud / quadric. This is why the resulting equation can be 'X = ...' or 'Y = ...' or 'Z = ...'.

And the equation is of the form 'Z = a + b.X + c.Y + d.X^2 + e.X.Y + f.Y^2' (therefore you do have a 'x.y' part, don't you? If no, what version are you using?)

[Grillteller]

Ah, you're right! My personal quadric has the structure e.x.y. Only the documentation says the equation is a+b.x+c.y+d.x²+e.y²=0.

Thanks :)

[daniel]

Thanks for the feedback. I'll fix the documentation.