<!-- doc/src/sgml/earthdistance.sgml -->

<sect1 id="earthdistance" xreflabel="earthdistance">
 <title>earthdistance</title>

 <indexterm zone="earthdistance">
  <primary>earthdistance</primary>
 </indexterm>

 <para>
  The <filename>earthdistance</filename> module provides two different approaches to
  calculating great circle distances on the surface of the Earth. The one
  described first depends on the <filename>cube</filename> module (which
  <emphasis>must</emphasis> be installed before <filename>earthdistance</filename> can be
  installed). The second one is based on the built-in <type>point</type> data type,
  using longitude and latitude for the coordinates.
 </para>

 <para>
  In this module, the Earth is assumed to be perfectly spherical.
  (If that's too inaccurate for you, you might want to look at the
  <application><ulink url="http://postgis.net/">PostGIS</ulink></application>
  project.)
 </para>

 <sect2>
  <title>Cube-based Earth Distances</title>

  <para>
   Data is stored in cubes that are points (both corners are the same) using 3
   coordinates representing the x, y, and z distance from the center of the
   Earth.  A domain <type>earth</type> over <type>cube</type> is provided, which
   includes constraint checks that the value meets these restrictions and
   is reasonably close to the actual surface of the Earth.
  </para>

  <para>
   The radius of the Earth is obtained from the <function>earth()</function>
   function. It is given in meters. But by changing this one function you can
   change the module to use some other units, or to use a different value of
   the radius that you feel is more appropriate.
  </para>

  <para>
   This package has applications to astronomical databases as well.
   Astronomers will probably want to change <function>earth()</function> to return a
   radius of <literal>180/pi()</literal> so that distances are in degrees.
  </para>

  <para>
   Functions are provided to support input in latitude and longitude (in
   degrees), to support output of latitude and longitude, to calculate
   the great circle distance between two points and to easily specify a
   bounding box usable for index searches.
  </para>

  <para>
   The provided functions are shown
   in <xref linkend="earthdistance-cube-functions">.
  </para>

  <table id="earthdistance-cube-functions">
   <title>Cube-based Earthdistance Functions</title>
   <tgroup cols="3">
    <thead>
     <row>
      <entry>Function</entry>
      <entry>Returns</entry>
      <entry>Description</entry>
     </row>
    </thead>
    <tbody>
     <row>
      <entry><function>earth()</function><indexterm><primary>earth</primary></indexterm></entry>
      <entry><type>float8</type></entry>
      <entry>Returns the assumed radius of the Earth.</entry>
     </row>
     <row>
      <entry><function>sec_to_gc(float8)</function><indexterm><primary>sec_to_gc</primary></indexterm></entry>
      <entry><type>float8</type></entry>
      <entry>Converts the normal straight line
       (secant) distance between two points on the surface of the Earth
       to the great circle distance between them.
      </entry>
     </row>
     <row>
      <entry><function>gc_to_sec(float8)</function><indexterm><primary>gc_to_sec</primary></indexterm></entry>
      <entry><type>float8</type></entry>
      <entry>Converts the great circle distance between two points on the
       surface of the Earth to the normal straight line (secant) distance
       between them.
      </entry>
     </row>
     <row>
      <entry><function>ll_to_earth(float8, float8)</function><indexterm><primary>ll_to_earth</primary></indexterm></entry>
      <entry><type>earth</type></entry>
      <entry>Returns the location of a point on the surface of the Earth given
       its latitude (argument 1) and longitude (argument 2) in degrees.
      </entry>
     </row>
     <row>
      <entry><function>latitude(earth)</function><indexterm><primary>latitude</primary></indexterm></entry>
      <entry><type>float8</type></entry>
      <entry>Returns the latitude in degrees of a point on the surface of the
       Earth.
      </entry>
     </row>
     <row>
      <entry><function>longitude(earth)</function><indexterm><primary>longitude</primary></indexterm></entry>
      <entry><type>float8</type></entry>
      <entry>Returns the longitude in degrees of a point on the surface of the
       Earth.
      </entry>
     </row>
     <row>
      <entry><function>earth_distance(earth, earth)</function><indexterm><primary>earth_distance</primary></indexterm></entry>
      <entry><type>float8</type></entry>
      <entry>Returns the great circle distance between two points on the
       surface of the Earth.
      </entry>
     </row>
     <row>
      <entry><function>earth_box(earth, float8)</function><indexterm><primary>earth_box</primary></indexterm></entry>
      <entry><type>cube</type></entry>
      <entry>Returns a box suitable for an indexed search using the cube
       <literal>@&gt;</literal>
       operator for points within a given great circle distance of a location.
       Some points in this box are further than the specified great circle
       distance from the location, so a second check using
       <function>earth_distance</function> should be included in the query.
      </entry>
     </row>
    </tbody>
   </tgroup>
  </table>

 </sect2>

 <sect2>
  <title>Point-based Earth Distances</title>

  <para>
   The second part of the module relies on representing Earth locations as
   values of type <type>point</type>, in which the first component is taken to
   represent longitude in degrees, and the second component is taken to
   represent latitude in degrees.  Points are taken as (longitude, latitude)
   and not vice versa because longitude is closer to the intuitive idea of
   x-axis and latitude to y-axis.
  </para>

  <para>
   A single operator is provided, shown
   in <xref linkend="earthdistance-point-operators">.
  </para>

  <table id="earthdistance-point-operators">
   <title>Point-based Earthdistance Operators</title>
   <tgroup cols="3">
    <thead>
     <row>
      <entry>Operator</entry>
      <entry>Returns</entry>
      <entry>Description</entry>
     </row>
    </thead>
    <tbody>
     <row>
      <entry><type>point</type> <literal>&lt;@&gt;</literal> <type>point</type></entry>
      <entry><type>float8</type></entry>
      <entry>Gives the distance in statute miles between
       two points on the Earth's surface.
      </entry>
     </row>
    </tbody>
   </tgroup>
  </table>

  <para>
   Note that unlike the <type>cube</type>-based part of the module, units
   are hardwired here: changing the <function>earth()</function> function will
   not affect the results of this operator.
  </para>

  <para>
   One disadvantage of the longitude/latitude representation is that
   you need to be careful about the edge conditions near the poles
   and near +/- 180 degrees of longitude.  The <type>cube</type>-based
   representation avoids these discontinuities.
  </para>

 </sect2>

</sect1>
