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<section id="cartographic-projection">
<span id="projections-intro"></span><h1>Cartographic projection<a class="headerlink" href="#cartographic-projection" title="Permalink to this headline">¶</a></h1>
<p>The foundation of PROJ is the large number of
<a class="reference internal" href="../operations/projections/index.html"><span class="doc">projections</span></a> available in the library. This section
is devoted to the generic parameters that can be used on any projection in the
PROJ library.</p>
<p>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 <a class="reference internal" href="../operations/projections/index.html"><span class="doc">projections</span></a>.</p>
<blockquote>
<div><table class="docutils align-default">
<colgroup>
<col style="width: 14%" />
<col style="width: 86%" />
</colgroup>
<thead>
<tr class="row-odd"><th class="head"><p>Parameter</p></th>
<th class="head"><p>Description</p></th>
</tr>
</thead>
<tbody>
<tr class="row-even"><td><p>+a</p></td>
<td><p>Semimajor radius of the ellipsoid axis</p></td>
</tr>
<tr class="row-odd"><td><p>+axis</p></td>
<td><p>Axis orientation</p></td>
</tr>
<tr class="row-even"><td><p>+b</p></td>
<td><p>Semiminor radius of the ellipsoid axis</p></td>
</tr>
<tr class="row-odd"><td><p>+ellps</p></td>
<td><p>Ellipsoid name (see <code class="docutils literal notranslate"><span class="pre">proj</span> <span class="pre">-le</span></code>)</p></td>
</tr>
<tr class="row-even"><td><p>+k</p></td>
<td><p>Scaling factor (deprecated)</p></td>
</tr>
<tr class="row-odd"><td><p>+k_0</p></td>
<td><p>Scaling factor</p></td>
</tr>
<tr class="row-even"><td><p>+lat_0</p></td>
<td><p>Latitude of origin</p></td>
</tr>
<tr class="row-odd"><td><p>+lon_0</p></td>
<td><p>Central meridian</p></td>
</tr>
<tr class="row-even"><td><p>+lon_wrap</p></td>
<td><p>Center longitude to use for wrapping (see below)</p></td>
</tr>
<tr class="row-odd"><td><p>+over</p></td>
<td><p>Allow longitude output outside -180 to 180 range, disables
wrapping (see below)</p></td>
</tr>
<tr class="row-even"><td><p>+pm</p></td>
<td><p>Alternate prime meridian (typically a city name, see below)</p></td>
</tr>
<tr class="row-odd"><td><p>+proj</p></td>
<td><p>Projection name (see <code class="docutils literal notranslate"><span class="pre">proj</span> <span class="pre">-l</span></code>)</p></td>
</tr>
<tr class="row-even"><td><p>+units</p></td>
<td><p>meters, US survey feet, etc.</p></td>
</tr>
<tr class="row-odd"><td><p>+vunits</p></td>
<td><p>vertical units.</p></td>
</tr>
<tr class="row-even"><td><p>+x_0</p></td>
<td><p>False easting</p></td>
</tr>
<tr class="row-odd"><td><p>+y_0</p></td>
<td><p>False northing</p></td>
</tr>
</tbody>
</table>
</div></blockquote>
<p>In the sections below most of the parameters are explained in details.</p>
<section id="units">
<h2>Units<a class="headerlink" href="#units" title="Permalink to this headline">¶</a></h2>
<p>Horizontal units can be specified using the <code class="docutils literal notranslate"><span class="pre">+units</span></code> keyword with a symbolic
name for a unit (i.e. <code class="docutils literal notranslate"><span class="pre">us-ft</span></code>). Alternatively the translation to meters can be
specified with the <code class="docutils literal notranslate"><span class="pre">+to_meter</span></code> keyword (i.e. 0.304800609601219 for US feet). The
<code class="docutils literal notranslate"><span class="pre">-lu</span></code> argument to <strong class="program">cs2cs</strong> or <strong class="program">proj</strong> 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.</p>
<p>Vertical (Z) units can be specified using the <code class="docutils literal notranslate"><span class="pre">+vunits</span></code> keyword with a
symbolic name for a unit (i.e. <code class="docutils literal notranslate"><span class="pre">us-ft</span></code>). Alternatively the translation to
meters can be specified with the <code class="docutils literal notranslate"><span class="pre">+vto_meter</span></code> keyword (i.e. 0.304800609601219
for US feet). The <code class="docutils literal notranslate"><span class="pre">-lu</span></code> argument to <strong class="program">cs2cs</strong> or <strong class="program">proj</strong> 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.</p>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p><strong class="program">proj</strong> does not handle vertical units at all and hence the
<code class="docutils literal notranslate"><span class="pre">+vto_meter</span></code> argument will be ignored.</p>
</div>
<p>Scaling of output units can be done by applying the <code class="docutils literal notranslate"><span class="pre">+k_0</span></code> argument. The
returned coordinates are scaled by the value assigned with the <code class="docutils literal notranslate"><span class="pre">+k_0</span></code>
parameter.</p>
</section>
<section id="false-easting-northing">
<h2>False Easting/Northing<a class="headerlink" href="#false-easting-northing" title="Permalink to this headline">¶</a></h2>
<p>Virtually all coordinate systems allow for the presence of a false easting
(<code class="docutils literal notranslate"><span class="pre">+x_0</span></code>) and northing (<code class="docutils literal notranslate"><span class="pre">+y_0</span></code>). 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.</p>
</section>
<section id="longitude-wrapping">
<h2>Longitude Wrapping<a class="headerlink" href="#longitude-wrapping" title="Permalink to this headline">¶</a></h2>
<p>By default PROJ wraps output longitudes in the range -180 to 180. The <code class="docutils literal notranslate"><span class="pre">+over</span></code>
switch can be used to disable the default wrapping which is done at a low level
in <code class="docutils literal notranslate"><span class="pre">pj_inv()</span></code>. This is particularly useful with projections like the
<a class="reference internal" href="../operations/projections/eqc.html"><span class="doc">equidistant cylindrical</span></a>
where it would be desirable for X values past -20000000 (roughly) to continue
past -180 instead of wrapping to +180.</p>
<p>The <code class="docutils literal notranslate"><span class="pre">+lon_wrap</span></code> option can be used to provide an alternative means of doing
longitude wrapping within <code class="docutils literal notranslate"><span class="pre">pj_transform()</span></code>. The argument to this option is a
center longitude. So <code class="docutils literal notranslate"><span class="pre">+lon_wrap=180</span></code> means wrap longitudes in the range 0 to
360. Note that <code class="docutils literal notranslate"><span class="pre">+over</span></code> does <strong>not</strong> disable <code class="docutils literal notranslate"><span class="pre">+lon_wrap</span></code>.</p>
</section>
<section id="prime-meridian">
<h2>Prime Meridian<a class="headerlink" href="#prime-meridian" title="Permalink to this headline">¶</a></h2>
<p>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.</p>
<p>Currently prime meridian declarations are only utilized by the
<code class="docutils literal notranslate"><span class="pre">pj_transform()</span></code> API call, not the <code class="docutils literal notranslate"><span class="pre">pj_inv()</span></code> and <code class="docutils literal notranslate"><span class="pre">pj_fwd()</span></code> calls.
Consequently the user utility <strong class="program">cs2cs</strong> does honour prime meridians but
the <strong class="program">proj</strong> user utility ignores them.</p>
<p>The following predeclared prime meridian names are supported. These can be
listed using with <code class="docutils literal notranslate"><span class="pre">cs2cs</span> <span class="pre">-lm</span></code>.</p>
<blockquote>
<div><table class="docutils align-default">
<colgroup>
<col style="width: 41%" />
<col style="width: 59%" />
</colgroup>
<thead>
<tr class="row-odd"><th class="head"><p>Meridian</p></th>
<th class="head"><p>Longitude</p></th>
</tr>
</thead>
<tbody>
<tr class="row-even"><td><p>greenwich</p></td>
<td><p>0dE</p></td>
</tr>
<tr class="row-odd"><td><p>lisbon</p></td>
<td><p>9d07’54.862”W</p></td>
</tr>
<tr class="row-even"><td><p>paris</p></td>
<td><p>2d20’14.025”E</p></td>
</tr>
<tr class="row-odd"><td><p>bogota</p></td>
<td><p>74d04’51.3”E</p></td>
</tr>
<tr class="row-even"><td><p>madrid</p></td>
<td><p>3d41’16.48”W</p></td>
</tr>
<tr class="row-odd"><td><p>rome</p></td>
<td><p>12d27’8.4”E</p></td>
</tr>
<tr class="row-even"><td><p>bern</p></td>
<td><p>7d26’22.5”E</p></td>
</tr>
<tr class="row-odd"><td><p>jakarta</p></td>
<td><p>106d48’27.79”E</p></td>
</tr>
<tr class="row-even"><td><p>ferro</p></td>
<td><p>17d40’W</p></td>
</tr>
<tr class="row-odd"><td><p>brussels</p></td>
<td><p>4d22’4.71”E</p></td>
</tr>
<tr class="row-even"><td><p>stockholm</p></td>
<td><p>18d3’29.8”E</p></td>
</tr>
<tr class="row-odd"><td><p>athens</p></td>
<td><p>23d42’58.815”E</p></td>
</tr>
<tr class="row-even"><td><p>oslo</p></td>
<td><p>10d43’22.5”E</p></td>
</tr>
</tbody>
</table>
</div></blockquote>
<p>Example of use. The location <code class="docutils literal notranslate"><span class="pre">long=0</span></code>, <code class="docutils literal notranslate"><span class="pre">lat=0</span></code> in the greenwich based lat/long
coordinates is translated to lat/long coordinates with Madrid as the prime
meridian.</p>
<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>cs2cs +proj=latlong +datum=WGS84 +to +proj=latlong +datum=WGS84 +pm=madrid
0 0
3d41'16.48"E 0dN 0.000
</pre></div>
</div>
</section>
<section id="axis-orientation">
<h2>Axis orientation<a class="headerlink" href="#axis-orientation" title="Permalink to this headline">¶</a></h2>
<p>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:</p>
<ul class="simple">
<li><p>“e” - Easting</p></li>
<li><p>“w” - Westing</p></li>
<li><p>“n” - Northing</p></li>
<li><p>“s” - Southing</p></li>
<li><p>“u” - Up</p></li>
<li><p>“d” - Down</p></li>
</ul>
<p>They can be combined in +axis in forms like:</p>
<ul class="simple">
<li><p><code class="docutils literal notranslate"><span class="pre">+axis=enu</span></code> - the default easting, northing, elevation.</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">+axis=neu</span></code> - northing, easting, up - useful for “lat/long” geographic
coordinates, or south orientated transverse mercator.</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">+axis=wnu</span></code> - westing, northing, up - some planetary coordinate systems
have “west positive” coordinate systems</p></li>
</ul>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>The <code class="docutils literal notranslate"><span class="pre">+axis</span></code> argument does not work with the <strong class="program">proj</strong> command line
utility.</p>
</div>
</section>
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