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<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
<code>stdin</code>, 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][e²] [n²]
n = [N0 N1 N3][1 ] [1 ]
[N2 N4 0][e ]·[n ]
[N5 0 0][e²] [n²]
</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][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]
</pre></div>
["·" = dot-product, (AE)·N = N'EA]
<p>In other words, <em>order=1</em> and <em>order=2</em> are equivalent
to <em>order=3</em> with the higher coefficients equal to zero.
<h2>SEE ALSO</h2>
<em>
<a href="i.ortho.transform.html">i.ortho.transform</a>,
<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
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