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<title>PROJ.4 - General Parameters</title>
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<body BGCOLOR="#FFFFFF">
<h1>PROJ.4 - General Parameters</h1>
This document attempts to describe a variety of the PROJ.4 parameters
which can be applied to all, or many coordinate system definitions. This
document does not attempt to describe the parameters particular to particular
projection types. Some of these can be found in the GeoTIFF
<a href="http://www.remotesensing.org/geotiff/proj_list/">Projections
Transform List</a>. The definitative documentation for most parameters
is Gerald's original documentation available from the main PROJ.4 page. <p>
<h2><a name="towgs84">towgs84 - Datum transformation to WGS84</a></h2>
Datum shifts can be approximated by 3 parameter spatial translations (in
geocentric space), or 7 parameter shifts (translation + rotation + scaling).
The parameters to describe this can be described using the <b>towgs84</b>
parameter.<p>
In the three parameter case, the three arguments are the translations to the
geocentric location in meters.<p>
For instance, the following demonstrates converting from the Greek GGRS87
datum to WGS84.<p>
<pre>
% cs2cs +proj=latlong +ellps=GRS80 +towgs84=-199.87,74.79,246.62 \
+to +proj=latlong +datum=WGS84
20 35
20d0'5.467"E 35d0'9.575"N 8.570
</pre>
The EPSG database provides this example for transforming from WGS72 to WGS84
using an approximated 7 parameter transformation.<p>
<pre>
% cs2cs +proj=latlong +ellps=WGS72 +towgs84=0,0,4.5,0,0,0.554,0.219 \
+to +proj=latlong +datum=WGS84
4 55
4d0'0.554"E 55d0'0.09"N 3.223
</pre>
The seven parameter case uses <i>delta_x</i>, <i>delta_y</i>, <i>delta_z</i>,
<i>Rx - rotation X</i>, <i>Ry - rotation Y</i>, <i>Rz - rotation Z</i>,
<i>M_BF - Scaling</i>. The three translation parameters are in meters as
in the three parameter case. The rotational parameters are not in physical
units. They are something like the sine of the rotational angle times the
ellipoid axis length, but I don't know the exact details of how to derive
these from a physical description of the rotation. What I do know is that
they match the parameters used for transformation method 9606 in the EPSG
database. The scaling is apparently the scale change in parts per million.<p>
A more complete discussion of the 3 and 7 parameter transformations can be
found in the EPSG database (trf_method's 9603 and 9606). Within PROJ.4
the following calculations are used to apply the <b>towgs84</b> transformation
(going to WGS84). The x, y and z coordinates are in geocentric coordinates.
Three parameter transformation (simple offsets):
<pre>
x[io] = x[io] + defn->datum_params[0];
y[io] = y[io] + defn->datum_params[1];
z[io] = z[io] + defn->datum_params[2];
</pre>
Seven parameter transformation (translation, rotation and scaling):
<pre>
#define Dx_BF (defn->datum_params[0])
#define Dy_BF (defn->datum_params[1])
#define Dz_BF (defn->datum_params[2])
#define Rx_BF (defn->datum_params[3])
#define Ry_BF (defn->datum_params[4])
#define Rz_BF (defn->datum_params[5])
#define M_BF (defn->datum_params[6])
x_out = M_BF*( x[io] - Rz_BF*y[io] + Ry_BF*z[io]) + Dx_BF;
y_out = M_BF*( Rz_BF*x[io] + y[io] - Rx_BF*z[io]) + Dy_BF;
z_out = M_BF*(-Ry_BF*x[io] + Rx_BF*y[io] + z[io]) + Dz_BF;
</pre>
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