# Cartographic projection¶

The foundation of PROJ is the large number of projections available in the library. This section is devoted to the generic parameters that can be used on any projection in the PROJ library.

Below is a list of PROJ parameters which can be applied to most coordinate system definitions. This table does not attempt to describe the parameters particular to particular projection types. These can be found on the pages documenting the individual projections.

Parameter

Description

+a

Semimajor radius of the ellipsoid axis

+axis

Axis orientation

+b

Semiminor radius of the ellipsoid axis

+ellps

Ellipsoid name (see

`proj -le`

)+k

Scaling factor (deprecated)

+k_0

Scaling factor

+lat_0

Latitude of origin

+lon_0

Central meridian

+lon_wrap

Center longitude to use for wrapping (see below)

+over

Allow longitude output outside -180 to 180 range, disables wrapping (see below)

+pm

Alternate prime meridian (typically a city name, see below)

+proj

Projection name (see

`proj -l`

)+units

meters, US survey feet, etc.

+vunits

vertical units.

+x_0

False easting

+y_0

False northing

In the sections below most of the parameters are explained in details.

## Units¶

Horizontal units can be specified using the `+units`

keyword with a symbolic
name for a unit (i.e. `us-ft`

). Alternatively the translation to meters can be
specified with the `+to_meter`

keyword (i.e. 0.304800609601219 for US feet). The
`-lu`

argument to **cs2cs** or **proj** can be used to list
symbolic unit names. The default unit for projected coordinates is the meter.
A few special projections deviate from this behavior, most notably the
latlong pseudo-projection that returns degrees.

Vertical (Z) units can be specified using the `+vunits`

keyword with a
symbolic name for a unit (i.e. `us-ft`

). Alternatively the translation to
meters can be specified with the `+vto_meter`

keyword (i.e. 0.304800609601219
for US feet). The `-lu`

argument to **cs2cs** or **proj** can
be used to list symbolic unit names. If no vertical units are specified, the
vertical units will default to be the same as the horizontal coordinates.

Note

**proj** does not handle vertical units at all and hence the
`+vto_meter`

argument will be ignored.

Scaling of output units can be done by applying the `+k_0`

argument. The
returned coordinates are scaled by the value assigned with the `+k_0`

parameter.

Input units for parameters that can be understood to be either decimal degrees or radians are interpreted to be decimal degrees by convention.

Explict specification of input units can be accomplished by adding the appropriate suffix to input values.

Suffix

Unit

d

Decimal degrees

D

°

r

Radians

R

Example of use. The longitude of the central meridian `+lon_0=90`

, can also be expressed more explictly
with units of decimal degrees as `+lon_0=90d`

or in radian
units as `+lon_0=1.5708r`

(approximately).

## 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.

## Longitude Wrapping¶

By default PROJ wraps output longitudes in the range -180 to 180. The `+over`

switch can be used to disable the default wrapping which is done at a low level
in `pj_inv()`

. This is particularly useful with projections like the
equidistant cylindrical
where it would be desirable for X values past -20000000 (roughly) to continue
past -180 instead of wrapping to +180.

The `+lon_wrap`

option can be used to provide an alternative means of doing
longitude wrapping within `pj_transform()`

. The argument to this option is a
center longitude. So `+lon_wrap=180`

means wrap longitudes in the range 0 to
360. Note that `+over`

does **not** disable `+lon_wrap`

.

## 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 declared 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 with `cs2cs -lm`

.

Meridian

Longitude

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
3d41'16.48"E 0dN 0.000
```

## Axis orientation¶

Starting in PROJ 4.8.0, the +axis argument can be used to control the axis orientation of the coordinate system. The default orientation is “easting, northing, up” but directions can be flipped, or axes flipped using combinations of the axes in the +axis switch. The values are:

“e” - Easting

“w” - Westing

“n” - Northing

“s” - Southing

“u” - Up

“d” - Down

They can be combined in +axis in forms like:

`+axis=enu`

- the default easting, northing, elevation.`+axis=neu`

- northing, easting, up - useful for “lat/long” geographic coordinates, or south orientated transverse mercator.`+axis=wnu`

- westing, northing, up - some planetary coordinate systems have “west positive” coordinate systems

Note

The `+axis`

argument does not work with the **proj** command line
utility.