[GRASSLIST:6864] polynomial orders - which method

[Maciek Sieczka]

Hi

BTW that i.rectify is being discussed. Could somebody please tell me how the
3 orders of polynom in i.rectify compare to the following 5 rectification
methods used in SuperEditPro? Which order of polymnon is an equivalent of
which method (if it is that simple)? I need to know it in order to be able
to compare outputs of i.rectify and SuperEditPro. I also heard of other
commercial programs which use the same naming convention and would like to
know how i.rectify's "orders" compare to this "methods".

Rectification methods listed in the SuperEditPro manual:

Isotropic linear (Helmert) model - requires at least two correction vectors.
x' = a10 + a1 x + a2 y
y' = a20 - a2 x + a1 y

Anisotropic linear (affine) model - requires at least three correction
vectors.
x' = a10 + a11 x + a12 y
y' = a20 + a21 x + a22 y

Bilinear model - requires at least four correction vectors.
x' = a10 + a11 x + a12 y + a13 xy
y' = a20 + a21 x + a22 y + a23 xy

Biquadratic model - requires at least nine correction vectors.
x' = a10 + a11 x + a12 y + a13 xy + a14 x2 + a15 y2 +
a16 x2y + a17 xy2 + a18 x2y2
y' = a20 + a21 x + a22 y + a23 xy + a24 x2 + a25 y2 +
a26 x2y + a27 xy2 + a28 x2y2

Bicubic model - requires at least 16 correction vectors.
x' = a10 + a11 x + a12 y + a13 xy + a14 x2 + a15 y2 +
a16 x2y + a17 xy2 + a18x2y2+a19 x3 + a1,10 x3y +
     a1,11 x3y2 + a1,12 x3y3 + a1,13 x2y3 + a1,14 xy3 + a1,15 y3
y' = a20 + a21 x + a22 y + a23 xy + a24 x2 + a25 y2 +
a26 x2y + a27 xy2 + a28 x2y2 + a29 x3 + a2,10 x3y +
     a2,11 x3y2 + a2,12 x3y3 + a2,13 x2y3 + a2,14 xy3 + a2,15 y3

As far as I understand for now "Helmert model" is not present in i.rectify,
"affine model" is the 1st order of polynom. What about 2nd and 3rd order?

I know my question sounds lame but I was never very into maths.

Maciek