Geografic-Information-System/misc/m.transform/m.transform.html

<h2>DESCRIPTION</h2>

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

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

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

<h2>NOTES</h2>

The transformations are:
<p>order=1:
<div class="code"><pre>
    e = [E0 E1][1].[1]
        [E2  0][e] [n]
   
    n = [N0 N1][1].[1]
        [N2  0][e] [n]
</pre></div>

order=2:
<div class="code"><pre>
    e = [E0 E1 E3][1 ] [1 ]
        [E2 E4  0][e ].[n ]
        [E5  0  0][e&sup2;] [n&sup2;]
   
    n = [N0 N1 N3][1 ] [1 ]
        [N2 N4  0][e ].[n ]
        [N5  0  0][e&sup2;] [n&sup2;]
</pre></div>

order=3:
<div class="code"><pre>
    e = [E0 E1 E3 E6][1 ] [1 ]
        [E2 E4 E7  0][e ].[n ]
        [E5 E8  0  0][e&sup2;] [n&sup2;]
        [E9  0  0  0][e&sup3;] [n&sup3;]
   
    n = [N0 N1 N3 N6][1 ] [1 ]
        [N2 N4 N7  0][e ].[n ]
        [N5 N8  0  0][e&sup2;] [n&sup2;]
        [N9  0  0  0][e&sup3;] [n&sup3;]
</pre></div>

["." = dot-product, (AE).N = N'EA.]
<p>In other words, order=1 and order=2 are equivalent to order=3 with
the higher coefficients equal to zero.

<h2>SEE ALSO</h2>

<em>
<a href="i.rectify.html">i.rectify</a>,
<a href="v.rectify.html">v.rectify</a>,
<a href="v.transform.html">v.transform</a>
</em>

<h2>AUTHORS</h2>

Brian J. Buckley<br>
Glynn Clements<br>
Hamish Bowman