## DESCRIPTION

m.transform is an utility to compute transformation based upon GCPs and output error measurements.

If coordinates are given with the input file option or fed from `stdin`, both the input and the output format is "x y" with one coordinate pair per line. Reverse transform is performed with the -r flag.

The format option determines how control points are printed out. A summary on the control points can be printed with the -s flag. The summary includes maximum deviation observed when transforming GCPs and overall RMS. The format option is ignored when coordinates are given with the input file option.

## NOTES

The transformations are:

order=1:

        e = [E0 E1][1].[1]
            [E2  0][e] [n]

        n = [N0 N1][1].[1]
            [N2  0][e] [n]

order=2:

        e = [E0 E1 E3][1 ] [1 ]
            [E2 E4  0][e ].[n ]
            [E5  0  0][e²] [n²]

        n = [N0 N1 N3][1 ] [1 ]
            [N2 N4  0][e ].[n ]
            [N5  0  0][e²] [n²]

order=3:

        e = [E0 E1 E3 E6][1 ] [1 ]
            [E2 E4 E7  0][e ].[n ]
            [E5 E8  0  0][e²] [n²]
            [E9  0  0  0][e³] [n³]

        n = [N0 N1 N3 N6][1 ] [1 ]
            [N2 N4 N7  0][e ].[n ]
            [N5 N8  0  0][e²] [n²]
            [N9  0  0  0][e³] [n³]

["." = dot-product, (AE).N = N'EA.]

In other words, order=1 and order=2 are equivalent to order=3 with the higher coefficients equal to zero.

## SEE ALSO

i.rectify, v.rectify, v.transform

## AUTHORS

Brian J. Buckley
Glynn Clements
Hamish Bowman

Last changed: $Date$