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# PROJ.4 - General Parameters

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 Projections Transform List. The definitative documentation for most parameters is Gerald's original documentation available from the main PROJ.4 page.

## False Easting/Northing

Virtually all coordinate systems allow for the presence of a false easting (+x_0) and northing (+y_0). Note that these values are always expressed in meters even if the coordinate system is some other units. Some coordinate systems (such as UTM) have implicit false easting and northing values.

## pm - Prime Meridian

A prime meridian may be declared indicating the offset between the prime meridian of the declared coordinate system and that of greenwich. A prime meridian is clared using the "pm" parameter, and may be assigned a symbolic name, or the longitude of the alternative prime meridian relative to greenwich.

Currently prime meridian declarations are only utilized by the pj_transform() API call, not the pj_inv() and pj_fwd() calls. Consequently the user utility cs2cs does honour prime meridians but the proj user utility ignores them.

The following predeclared prime meridian names are supported. These can be listed using the cs2cs argument -lm.

       greenwich 0dE
          lisbon 9d07'54.862"W
           paris 2d20'14.025"E
          bogota 74d04'51.3"E
          madrid 3d41'16.48"W
            rome 12d27'8.4"E
            bern 7d26'22.5"E
         jakarta 106d48'27.79"E
           ferro 17d40'W
        brussels 4d22'4.71"E
       stockholm 18d3'29.8"E
          athens 23d42'58.815"E
            oslo 10d43'22.5"E

Example of use. The location long=0, lat=0 in the greenwich based lat/long coordinates is translated to lat/long coordinates with Madrid as the prime meridian.

     cs2cs +proj=latlong +datum=WGS84 +to +proj=latlong +datum=WGS84 +pm=madrid
    0 0                           (input)
    3d41'16.48"E    0dN 0.000     (output)

## towgs84 - Datum transformation to WGS84

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 towgs84 parameter.

In the three parameter case, the three arguments are the translations to the geocentric location in meters.

For instance, the following demonstrates converting from the Greek GGRS87 datum to WGS84.

    % 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

The EPSG database provides this example for transforming from WGS72 to WGS84 using an approximated 7 parameter transformation.

    % 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

The seven parameter case uses delta_x, delta_y, delta_z, Rx - rotation X, Ry - rotation Y, Rz - rotation Z, M_BF - Scaling. 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.

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 towgs84 transformation (going to WGS84). The x, y and z coordinates are in geocentric coordinates. Three parameter transformation (simple offsets):

      x[io] = x[io] + defn->datum_params[0];
      y[io] = y[io] + defn->datum_params[1];
      z[io] = z[io] + defn->datum_params[2];

Seven parameter transformation (translation, rotation and scaling):

      #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;

Note that EPSG method 9607 (coordinate frame rotation) coefficients can be converted to EPSG method 9606 (position vector 7-parameter) supported by PROJ.4 by reversing the sign of the rotation vectors. The methods are otherwise the same.