pgLatLon

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Added update script to version 0.7 and make version 0.7 default
author jbe
date Mon Sep 26 09:56:29 2016 +0200 (2016-09-26)
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1 <html><head><title>pgLatLon v0.6 documentation</title></head><body>
2 <h1>pgLatLon v0.6 documentation</h1>
4 <p>pgLatLon is a spatial database extension for the PostgreSQL object-relational
5 database management system providing geographic data types and spatial indexing
6 for the WGS-84 spheroid.</p>
8 <p>While many other spatial databases still use imprecise bounding boxes for
9 many operations, pgLatLon aims to support more precise calculations for all
10 implemented geographic operators. Efficient indexing of geographic objects
11 is provided using space-filling fractal curves. Optimizations on bit level
12 (including logarithmic compression) allow for a highly memory-efficient
13 non-overlapping index suitable for huge datasets.</p>
15 <p>pgLatLon is a lightweight solution as it only depends on PostgreSQL itself (and
16 a C compiler for building).</p>
18 <p>Unlike competing spatial extensions for PostgreSQL, pgLatLon is available under
19 the permissive MIT/X11 license to avoid problems with viral licenses like the
20 GPLv2/v3.</p>
22 <h2>Installation</h2>
24 <h3>Automatic installation</h3>
26 <p>Prerequisites:</p>
28 <ul>
29 <li>Ensure that the <code>pg_config</code> binary is in your path (shipped with PostgreSQL).</li>
30 <li>Ensure that GNU Make is available (either as <code>make</code> or <code>gmake</code>).</li>
31 </ul>
33 <p>Then simply type:</p>
35 <pre><code>make install
36 </code></pre>
38 <h3>Manual installation</h3>
40 <p>It is also possible to compile and install the extension without GNU Make as
41 follows:</p>
43 <pre><code>cc -Wall -O2 -fPIC -shared -I `pg_config --includedir-server` -o latlon-v0006.so latlon-v0006.c
44 cp latlon-v0006.so `pg_config --pkglibdir`
45 cp latlon.control `pg_config --sharedir`/extension/
46 cp latlon--*.sql `pg_config --sharedir`/extension/
47 </code></pre>
49 <h3>Loading the extension</h3>
51 <p>After installation, you can create a database and load the extension as
52 follows:</p>
54 <pre><code>% createdb test_database
55 % psql test_database
56 psql (9.5.4)
57 Type "help" for help.
59 test_database=# CREATE EXTENSION latlon;
60 </code></pre>
62 <h3>Updating</h3>
64 <p>Before updating your database cluster to a new version of pgLatLon, you may
65 want to uninstall the old by calling "<code>make uninstall</code>" in the unpacked source
66 code directory of your old pgLatLon version. You may also manually delete the
67 <code>latlon-v????.so</code> files from your PostgreSQL library directory and the
68 <code>latlon.control</code> and <code>latlon--*.sql</code> files from your PostgreSQL extension
69 directory.</p>
71 <p>The new version can be installed as described above. For altering an existing
72 database to use the installed new version (mandatory if you removed the old
73 version), execute the following SQL command in the respective databases:</p>
75 <pre><code>ALTER EXTENSION latlon UPDATE;
76 </code></pre>
78 <p>If the update contains modifications to operator classes, it may be necessary
79 to drop all indices on geographic data types first (you will get an error
80 message in this case). These indices can be re-created after the update.</p>
82 <p>Note that taking several update steps at once (e.g. updating from version 0.2
83 directly to version 0.4) requires the intermediate versions to be installed
84 (i.e. in this example version 0.3 would need to be installed). Whenever you
85 install or uninstall an intermediate or old version, make sure to afterwards
86 re-install the latest pgLatLon version to ensure that the <code>latlon.control</code> file
87 is available and points to the latest version.</p>
89 <p>If the update contains modifications to the internal data representation
90 format, an update path might not be available. In this case, create a dump of
91 your database, delete your database, and restore it from your dump.</p>
93 <p>Be sure to always keep backups of all your data before attempting to update.</p>
95 <h2>Reference</h2>
97 <h3>1. Types</h3>
99 <p>pgLatLon provides four geographic types: <code>epoint</code>, <code>ebox</code>, <code>ecircle</code>, and
100 <code>ecluster</code>.</p>
102 <h4><code>epoint</code></h4>
104 <p>A point on the Earth spheroid (WGS-84).</p>
106 <p>The text input format is <code>'[N|S]&lt;float&gt; [E|W]&lt;float&gt;'</code>, where each float is in
107 degrees. Note the required white space between the latitude and longitude
108 components. Each floating point number may have a sign, in which case <code>N</code>/<code>S</code>
109 or <code>E</code>/<code>W</code> are switched respectively (e.g. <code>E-5</code> is the same as <code>W5</code>).</p>
111 <p>An <code>epoint</code> may also be created from two floating point numbers by calling
112 <code>epoint(latitude, longitude)</code>, where positive latitudes are used for the
113 northern hemisphere, negative latitudes are used for the southern hemisphere,
114 positive longitudes indicate positions east of the prime meridian, and negative
115 longitudes indicate positions west of the prime meridian.</p>
117 <p>Latitudes exceeding -90 or +90 degrees are truncated to -90 or +90
118 respectively, in which case a warning will be issued. Longitudes exceeding -180
119 or +180 degrees will be converted to values between -180 and +180 (both
120 inclusive) by adding or substracting a multiple of 360 degrees, in which case a
121 notice will be issued.</p>
123 <p>If the latitude is -90 or +90 (south pole or north pole), a longitude value is
124 still stored in the datum, and if a point is on the prime meridian or the
125 180th meridian, the east/west bit is also stored in the datum. In case of the
126 prime meridian, this is done by storing a floating point value of -0 for
127 0 degrees west and a value of +0 for 0 degrees east. In case of the
128 180th meridian, this is done by storing -180 or +180 respectively. The equality
129 operator, however, returns true when the same points on Earth are described,
130 i.e. the longitude is ignored for the poles, and 180 degrees west is considered
131 to be equal to 180 degrees east.</p>
133 <h4><code>ebox</code></h4>
135 <p>An area on Earth demarcated by a southern and northern latitude, and a western
136 and eastern longitude (all given in WGS-84).</p>
138 <p>The text input format is
139 <code>'{N|S}&lt;float&gt; {E|W}&lt;float&gt; {N|S}&lt;float&gt; {E|W}&lt;float&gt;'</code>, where each float is in
140 degrees. The ordering of the four white-space separated blocks is not
141 significant. To include the 180th meridian, one longitude boundary must be
142 equal to or exceed <code>W180</code> or <code>E180</code>, e.g. <code>'N10 N20 E170 E190'</code>.</p>
144 <p>A special value is the empty area, denoted by the text represenation <code>'empty'</code>.
145 Such an <code>ebox</code> does not contain any point.</p>
147 <p>An <code>ebox</code> may also be created from four floating point numbers by calling
148 <code>ebox(min_latitude, max_latitude, min_longitude, max_longitude)</code>, where
149 positive values are used for north and east, and negative values are used for
150 south and west. If <code>min_latitude</code> is strictly greater than <code>max_latitude</code>, an
151 empty <code>ebox</code> is created. If <code>min_longitude</code> is greater than <code>max_longitude</code> and
152 if both longitudes are between -180 and +180 degrees, then the area oriented in
153 such way that the 180th meridian is included.</p>
155 <p>If the longitude span is less than 120 degrees, an <code>ebox</code> may be alternatively
156 created from two <code>epoints</code> in the following way: <code>ebox(epoint(lat1, lon1),
157 epoint(lat2, lon2))</code>. In this case <code>lat1</code> and <code>lat2</code> as well as <code>lon1</code> and
158 <code>lon2</code> can be swapped without any impact.</p>
160 <h4><code>ecircle</code></h4>
162 <p>An area containing all points not farther away from a given center point
163 (WGS-84) than a given radius.</p>
165 <p>The text input format is <code>'{N|S}&lt;float&gt; {E|W}&lt;float&gt; &lt;float&gt;'</code>, where the first
166 two floats denote the center point in degrees and the third float denotes the
167 radius in meters. A radius equal to minus infinity denotes an empty circle
168 which contains no point at all (despite having a center), while a radius equal
169 to zero denotes a circle that includes a single point.</p>
171 <p>An <code>ecircle</code> may also be created by calling <code>ecircle(epoint(...), radius)</code> or
172 from three floating point numbers by calling <code>ecircle(latitude, longitude,
173 radius)</code>.</p>
175 <h4><code>ecluster</code></h4>
177 <p>A collection of points, paths, polygons, and outlines on the WGS-84 spheroid.
178 Each path, polygon, or outline must cover a longitude range of less than
179 180 degrees to avoid ambiguities.</p>
181 <p>The text input format is a white-space separated list of the following items:</p>
183 <ul>
184 <li><code>point ({N|S}&lt;float&gt; {E|W}&lt;float&gt;)</code></li>
185 <li><code>path ({N|S}&lt;float&gt; {E|W}&lt;float&gt; {N|S}&lt;float&gt; {E|W}&lt;float&gt; ...)</code></li>
186 <li><code>outline ({N|S}&lt;float&gt; {E|W}&lt;float&gt; {N|S}&lt;float&gt; {E|W}&lt;float&gt; {N|S}&lt;float&gt; {E|W}&lt;float&gt; ...)</code></li>
187 <li><code>polygon ({N|S}&lt;float&gt; {E|W}&lt;float&gt; {N|S}&lt;float&gt; {E|W}&lt;float&gt; {N|S}&lt;float&gt; {E|W}&lt;float&gt; ...)</code></li>
188 </ul>
190 <p>Paths are open by default (i.e. there is no connection from the last point in
191 the list to the first point in the list). Outlines and polygons, in contrast,
192 are automatically closed (i.e. there is a line segment from the last point in
193 the list to the first point in the list) which means the first point should not
194 be repeated as last point in the list. Polygons are filled, outlines are not.</p>
196 <h3>2. Indices</h3>
198 <p>Two kinds of indices are supported: B-tree and GiST indices.</p>
200 <h4>B-tree indices</h4>
202 <p>A B-tree index can be used for simple equality searches and is supported by the
203 <code>epoint</code>, <code>ebox</code>, and <code>ecircle</code> data types. B-tree indices can not be used for
204 geographic searches.</p>
206 <h4>GiST indices</h4>
208 <p>For geographic searches, GiST indices must be used. The <code>epoint</code>, <code>ecircle</code>,
209 and <code>ecluster</code> data types support GiST indexing. A GiST index for geographic
210 searches can be created as follows:</p>
212 <pre><code>CREATE TABLE tbl (
213 id serial4 PRIMARY KEY,
214 loc epoint NOT NULL );
216 CREATE INDEX name_of_index ON tbl USING gist (loc);
217 </code></pre>
219 <p>GiST indices also support nearest neighbor searches when using the distance
220 operator (<code>&lt;-&gt;</code>) in the ORDER BY clause.</p>
222 <h4>Indices on other data types (e.g. GeoJSON)</h4>
224 <p>Note that further types can be indexed by using an index on an expression with
225 a conversion function. One conversion function provided by pgLatLon is the
226 <code>GeoJSON_to_ecluster(float8, float8, text)</code> function:</p>
228 <pre><code>CREATE TABLE tbl (
229 id serial4 PRIMARY KEY,
230 loc jsonb NOT NULL );
232 CREATE INDEX name_of_index ON tbl USING gist((GeoJSON_to_ecluster("loc")));
233 </code></pre>
235 <p>When using the conversion function in an expression, the index will be used
236 automatically:</p>
238 <pre><code>SELECT * FROM tbl WHERE GeoJSON_to_ecluster("loc") &amp;&amp; 'N50 E10 10000'::ecircle;
239 </code></pre>
241 <h3>3. Operators</h3>
243 <h4>Equality operator <code>=</code></h4>
245 <p>Tests if two geographic objects are equal.</p>
247 <p>The longitude is ignored for the poles, and 180 degrees west is considered to
248 be equal to 180 degrees east.</p>
250 <p>For boxes and circles, two empty objects are considered equal. (Note that a
251 circle is not empty if the radius is zero but only if it is negative infinity,
252 i.e. smaller than zero.) Two circles with a positive infinite radius are also
253 considered equal.</p>
255 <p>Implemented for:</p>
257 <ul>
258 <li><code>epoint = epoint</code></li>
259 <li><code>ebox = ebox</code></li>
260 <li><code>ecircle = ecircle</code></li>
261 </ul>
263 <p>The negation is the inequality operator (<code>&lt;&gt;</code> or <code>!=</code>).</p>
265 <h4>Linear ordering operators <code>&lt;&lt;&lt;</code>, <code>&lt;&lt;&lt;=</code>, <code>&gt;&gt;&gt;=</code>, <code>&gt;&gt;&gt;</code></h4>
267 <p>These operators create an arbitrary (but well-defined) linear ordering of
268 geographic objects, which is used internally for B-tree indexing and merge
269 joins. These operators will usually not be used by an application programmer.</p>
271 <h4>Overlap operator <code>&amp;&amp;</code></h4>
273 <p>Tests if two geographic objects have at least one point in common. Currently
274 implemented for:</p>
276 <ul>
277 <li><code>epoint &amp;&amp; ebox</code></li>
278 <li><code>epoint &amp;&amp; ecircle</code></li>
279 <li><code>epoint &amp;&amp; ecluster</code></li>
280 <li><code>ebox &amp;&amp; ebox</code></li>
281 <li><code>ebox &amp;&amp; ecircle</code></li>
282 <li><code>ebox &amp;&amp; ecluster</code></li>
283 <li><code>ecircle &amp;&amp; ecircle</code></li>
284 <li><code>ecircle &amp;&amp; ecluster</code></li>
285 <li><code>ecluster &amp;&amp; ecluster</code></li>
286 </ul>
288 <p>The <code>&amp;&amp;</code> operator is commutative, i.e. "<code>a &amp;&amp; b</code>" is the same as "<code>b &amp;&amp; a</code>".
289 Each commutation is supported as well.</p>
291 <h4>Lossy overlap operator <code>&amp;&amp;+</code></h4>
293 <p>Tests if two geographic objects may have at least one point in common. Opposed
294 to the <code>&amp;&amp;</code> operator, the <code>&amp;&amp;+</code> operator may return false positives and is
295 currently implemented for:</p>
297 <ul>
298 <li><code>epoint &amp;&amp;+ ecluster</code></li>
299 <li><code>ebox &amp;&amp;+ ecircle</code></li>
300 <li><code>ebox &amp;&amp;+ ecluster</code></li>
301 <li><code>ecircle &amp;&amp;+ ecluster</code></li>
302 <li><code>ecluster &amp;&amp;+ ecluster</code></li>
303 </ul>
305 <p>The <code>&amp;&amp;+</code> operator is commutative, i.e. "<code>a &amp;&amp;+ b</code>" is the same as "<code>b &amp;&amp;+ a</code>".
306 Each commutation is supported as well.</p>
308 <p>Where two data types support both the <code>&amp;&amp;</code> and the <code>&amp;&amp;+</code> operator, the <code>&amp;&amp;+</code>
309 operator computes faster.</p>
311 <h4>Contains operator <code>@&gt;</code></h4>
313 <p>Tests if the object right of the operator is contained in the object left of
314 the operator. Currently implemented for:</p>
316 <ul>
317 <li><code>ebox @&gt; epoint</code> (alias for <code>&amp;&amp;</code>)</li>
318 <li><code>ebox @&gt; ebox</code></li>
319 <li><code>ebox @&gt; ecluster</code></li>
320 <li><code>ecluster @&gt; epoint</code> (alias for <code>&amp;&amp;</code>)</li>
321 <li><code>ecluster @&gt; ebox</code></li>
322 <li><code>ecluster @&gt; ecluster</code></li>
323 </ul>
325 <p>The commutator of <code>@&gt;</code> ("contains") is <code>&lt;@</code> ("is contained in"), i.e.
326 "<code>a @&gt; b</code>" is the same as "<code>b &lt;@ a</code>".</p>
328 <p>Whether the perimeter of an object is taken into account is undefined and may
329 differ between the left and the right hand side of the operator. The current
330 implementation returns true only if an object is contained completely within
331 the other object, not touching its perimeter, paths, outlines, or any singular
332 points.</p>
334 <h4>Distance operator <code>&lt;-&gt;</code></h4>
336 <p>Calculates the shortest distance between two geographic objects in meters (zero
337 if the objects are overlapping). Currently implemented for:</p>
339 <ul>
340 <li><code>epoint &lt;-&gt; epoint</code></li>
341 <li><code>epoint &lt;-&gt; ebox</code></li>
342 <li><code>epoint &lt;-&gt; ecircle</code></li>
343 <li><code>epoint &lt;-&gt; ecluster</code></li>
344 <li><code>ebox &lt;-&gt; ebox</code></li>
345 <li><code>ebox &lt;-&gt; ecircle</code></li>
346 <li><code>ebox &lt;-&gt; ecluster</code></li>
347 <li><code>ecircle &lt;-&gt; ecircle</code></li>
348 <li><code>ecircle &lt;-&gt; ecluster</code></li>
349 <li><code>ecluster &lt;-&gt; ecluster</code></li>
350 </ul>
352 <p>The <code>&lt;-&gt;</code> operator is commutative, i.e. "<code>a &lt;-&gt; b</code>" is the same as "<code>b &lt;-&gt; a</code>".
353 Each commutation is supported as well.</p>
355 <p>For short distances, the result is very accurate (i.e. respects the dimensions
356 of the WGS-84 spheroid). For longer distances in the order of magnitude of
357 Earth's radius or greater, the value is only approximate (but the error is
358 still less than 0.2% as long as no polygons with very long edges are involved).</p>
360 <p>The functions <code>distance(epoint, epoint)</code> and <code>distance(ecluster, epoint)</code> can
361 be used as an alias for this operator.</p>
363 <p>Note: In case of radial searches with a fixed radius, this operator should
364 not be used. Instead, an <code>ecircle</code> should be created and used in combination
365 with the overlap operator (<code>&amp;&amp;</code>). Alternatively, the functions
366 <code>distance_within(epoint, epoint, float8)</code> or <code>distance_within(ecluster, epoint,
367 float8)</code> can be used for fixed-radius searches.</p>
369 <h3>4. Functions</h3>
371 <h4><code>center(circle)</code></h4>
373 <p>Returns the center of an <code>ecircle</code> as an <code>epoint</code>.</p>
375 <h4><code>distance(epoint, epoint)</code></h4>
377 <p>Calculates the distance between two <code>epoint</code> datums in meters. This function is
378 an alias for the distance operator <code>&lt;-&gt;</code>.</p>
380 <p>Note: In case of radial searches with a fixed radius, this function should not be
381 used. Use <code>distance_within(epoint, epoint, float8)</code> instead.</p>
383 <h4><code>distance(ecluster, epoint)</code></h4>
385 <p>Calculates the distance from an <code>ecluster</code> to an <code>epoint</code> in meters. This
386 function is an alias for the distance operator <code>&lt;-&gt;</code>.</p>
388 <p>Note: In case of radial searches with a fixed radius, this function should not be
389 used. Use <code>distance_within(epoint, epoint, float8)</code> instead.</p>
391 <h4><code>distance_within(</code>variable <code>epoint,</code> fixed <code>epoint,</code> radius <code>float8)</code></h4>
393 <p>Checks if the distance between two <code>epoint</code> datums is not greater than a given
394 value (search radius).</p>
396 <p>Note: In case of radial searches with a fixed radius, the first argument must
397 be used for the table column, while the second argument must be used for the
398 search center. Otherwise an existing index cannot be used.</p>
400 <h4><code>distance_within(</code>variable <code>ecluster,</code> fixed <code>epoint,</code> radius <code>float8)</code></h4>
402 <p>Checks if the distance from an <code>ecluster</code> to an <code>epoint</code> is not greater than a
403 given value (search radius).</p>
405 <h4><code>ebox(</code>latmin <code>float8,</code> latmax <code>float8,</code> lonmin <code>float8,</code> lonmax <code>float8)</code></h4>
407 <p>Creates a new <code>ebox</code> with the given boundaries.
408 See "1. Types", subsection <code>ebox</code> for details.</p>
410 <h4><code>ebox(epoint, epoint)</code></h4>
412 <p>Creates a new <code>ebox</code>. This function may only be used if the longitude
413 difference is less than or equal to 120 degrees.
414 See "1. Types", subsection <code>ebox</code> for details.</p>
416 <h4><code>ecircle(epoint, float8)</code></h4>
418 <p>Creates an <code>ecircle</code> with the given center point and radius.</p>
420 <h4><code>ecircle(</code>latitude <code>float8,</code> longitude <code>float8,</code> radius <code>float8)</code></h4>
422 <p>Creates an <code>ecircle</code> with the given center point and radius.</p>
424 <h4><code>ecluster_concat(ecluster, ecluster)</code></h4>
426 <p>Combines two clusters to form a new <code>ecluster</code> by uniting all entries of both
427 clusters. Note that two overlapping areas of polygons annihilate each other
428 (which may be used to create polygons with holes).</p>
430 <h4><code>ecluster_concat(ecluster[])</code></h4>
432 <p>Creates a new <code>ecluster</code> that unites all entries of all clusters in the passed
433 array. Note that two overlapping areas of polygons annihilate each other (which
434 may be used to create polygons with holes).</p>
436 <h4><code>ecluster_create_multipoint(epoint[])</code></h4>
438 <p>Creates a new <code>ecluster</code> which contains multiple points.</p>
440 <h4><code>ecluster_create_outline(epoint[])</code></h4>
442 <p>Creates a new <code>ecluster</code> that is an outline given by the passed points.</p>
444 <h4><code>ecluster_create_path(epoint[])</code></h4>
446 <p>Creates a new <code>ecluster</code> that is a path given by the passed points.</p>
448 <h4><code>ecluster_create_polygon(epoint[])</code></h4>
450 <p>Creates a new <code>ecluster</code> that is a polygon given by the passed points.</p>
452 <h4><code>ecluster_extract_outlines(ecluster)</code></h4>
454 <p>Set-returning function that returns the outlines of an <code>ecluster</code> as <code>epoint[]</code>
455 rows.</p>
457 <h4><code>ecluster_extract_paths(ecluster)</code></h4>
459 <p>Set-returning function that returns the paths of an <code>ecluster</code> as <code>epoint[]</code>
460 rows.</p>
462 <h4><code>ecluster_extract_points(ecluster)</code></h4>
464 <p>Set-returning function that returns the points of an <code>ecluster</code> as <code>epoint</code>
465 rows.</p>
467 <h4><code>ecluster_extract_polygons(ecluster)</code></h4>
469 <p>Set-returning function that returns the polygons of an <code>ecluster</code> as <code>epoint[]</code>
470 rows.</p>
472 <h4><code>empty_ebox</code>()</h4>
474 <p>Returns the empty <code>ebox</code>.
475 See "1. Types", subsection <code>ebox</code> for details.</p>
477 <h4><code>epoint(</code>latitude <code>float8,</code> longitude <code>float8)</code></h4>
479 <p>Returns an <code>epoint</code> with the given latitude and longitude.</p>
481 <h4><code>epoint_latlon(</code>latitude <code>float8,</code> longitude <code>float8)</code></h4>
483 <p>Alias for <code>epoint(float8, float8)</code>.</p>
485 <h4><code>epoint_lonlat(</code>longitude <code>float8,</code> latitude <code>float8)</code></h4>
487 <p>Same as <code>epoint(float8, float8)</code> but with arguments reversed.</p>
489 <h4><code>GeoJSON_to_epoint(jsonb, text)</code></h4>
491 <p>Maps a GeoJSON object of type "Point" or "Feature" (which contains a
492 "Point") to an <code>epoint</code> datum. For any other JSON objects, NULL is returned.</p>
494 <p>The second parameter (which defaults to <code>epoint_lonlat</code>) may be set to a name
495 of a conversion function that transforms two coordinates (two <code>float8</code>
496 parameters) to an <code>epoint</code>.</p>
498 <h4><code>GeoJSON_to_ecluster(jsonb, text)</code></h4>
500 <p>Maps a (valid) GeoJSON object to an <code>ecluster</code>. Note that this function
501 does not check whether the JSONB object is a valid GeoJSON object.</p>
503 <p>The second parameter (which defaults to <code>epoint_lonlat</code>) may be set to a name
504 of a conversion function that transforms two coordinates (two <code>float8</code>
505 parameters) to an <code>epoint</code>.</p>
507 <h4><code>max_latitude(ebox)</code></h4>
509 <p>Returns the northern boundary of a given <code>ebox</code> in degrees between -90 and +90.</p>
511 <h4><code>max_longitude(ebox)</code></h4>
513 <p>Returns the eastern boundary of a given <code>ebox</code> in degrees between -180 and +180
514 (both inclusive).</p>
516 <h4><code>min_latitude(ebox)</code></h4>
518 <p>Returns the southern boundary of a given <code>ebox</code> in degrees between -90 and +90.</p>
520 <h4><code>min_longitude(ebox)</code></h4>
522 <p>Returns the western boundary of a given <code>ebox</code> in degrees between -180 and +180
523 (both inclusive).</p>
525 <h4><code>latitude(epoint)</code></h4>
527 <p>Returns the latitude value of an <code>epoint</code> in degrees between -90 and +90.</p>
529 <h4><code>longitude(epoint)</code></h4>
531 <p>Returns the longitude value of an <code>epoint</code> in degrees between -180 and +180
532 (both inclusive).</p>
534 <h4><code>radius(ecircle)</code></h4>
536 <p>Returns the radius of an <code>ecircle</code> in meters.</p>
537 </body></html>

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