liquid_feedback_core
diff pgLatLon/README.html @ 529:96ee2db56bec
New PostgreSQL extension "pgLatLon" for geospatial operations and indexing in LiquidFeedback
| author | jbe |
|---|---|
| date | Thu Aug 18 20:19:58 2016 +0200 (2016-08-18) |
| parents | |
| children | 6bc81898fd3b |
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1.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000 1.2 +++ b/pgLatLon/README.html Thu Aug 18 20:19:58 2016 +0200 1.3 @@ -0,0 +1,450 @@ 1.4 +<html><head><title>pgLatLon v0.1 documentation</title></head><body> 1.5 +<h1>pgLatLon v0.1 documentation</h1> 1.6 + 1.7 +<p>pgLatLon is a spatial database extension for the PostgreSQL object-relational 1.8 +database management system providing geographic data types and spatial indexing 1.9 +for the WGS-84 spheroid.</p> 1.10 + 1.11 +<p>While many other spatial databases still use imprecise bounding boxes for many 1.12 +operations, pgLatLon supports more precise geometric calculations for all 1.13 +implemented operators. Efficient indexing of geometric objects is provided 1.14 +using fractal indicies. Optimizations on bit level (including logarithmic 1.15 +compression) allow for a highly memory-efficient non-overlapping index suitable 1.16 +for huge datasets.</p> 1.17 + 1.18 +<p>Unlike competing spatial extensions for PostgreSQL, pgLatLon is available under 1.19 +the permissive MIT/X11 license to avoid problems with viral licenses like the 1.20 +GPLv2/v3.</p> 1.21 + 1.22 +<h2>Installation</h2> 1.23 + 1.24 +<h3>Automatic installation</h3> 1.25 + 1.26 +<p>Prerequisites:</p> 1.27 + 1.28 +<ul> 1.29 +<li>Ensure that the <code>pg_config</code> binary is in your path (shipped with PostgreSQL).</li> 1.30 +<li>Ensure that GNU Make is available (either as <code>make</code> or <code>gmake</code>).</li> 1.31 +</ul> 1.32 + 1.33 +<p>Then simply type:</p> 1.34 + 1.35 +<pre><code>make install 1.36 +</code></pre> 1.37 + 1.38 +<h3>Manual installation</h3> 1.39 + 1.40 +<p>It is also possible to compile and install the extension without GNU Make as 1.41 +follows:</p> 1.42 + 1.43 +<pre><code>cc -Wall -O2 -fPIC -shared -I `pg_config --includedir-server` -o latlon-v0001.so latlon-v0001.c 1.44 +cp latlon-v0001.so `pg_config --pkglibdir` 1.45 +cp latlon.control `pg_config --sharedir`/extension/ 1.46 +cp latlon--0.1.sql `pg_config --sharedir`/extension/ 1.47 +</code></pre> 1.48 + 1.49 +<h3>Loading the extension</h3> 1.50 + 1.51 +<p>After installation, you can create a database and load the extension as 1.52 +follows:</p> 1.53 + 1.54 +<pre><code>% createdb test_database 1.55 +% psql test_database 1.56 +psql (9.5.4) 1.57 +Type "help" for help. 1.58 + 1.59 +test_database=# CREATE EXTENSION latlon; 1.60 +</code></pre> 1.61 + 1.62 +<h2>Reference</h2> 1.63 + 1.64 +<h3>1. Types</h3> 1.65 + 1.66 +<p>pgLatLon provides four geographic types: <code>epoint</code>, <code>ebox</code>, <code>ecircle</code>, and 1.67 +<code>ecluster</code>.</p> 1.68 + 1.69 +<h4><code>epoint</code></h4> 1.70 + 1.71 +<p>A point on the earth spheroid (WGS-84).</p> 1.72 + 1.73 +<p>The text input format is <code>'[N|S]<float> [E|W]<float>'</code>, where each float is in 1.74 +degrees. Note the required white space between the latitude and longitude 1.75 +components. Each floating point number may have a sign, in which case <code>N</code>/<code>S</code> 1.76 +or <code>E</code>/<code>W</code> are switched respectively (e.g. <code>E-5</code> is the same as <code>W5</code>).</p> 1.77 + 1.78 +<p>An <code>epoint</code> may also be created from two floating point numbers by calling 1.79 +<code>epoint(latitude, longitude)</code>, where positive latitudes are used for the 1.80 +northern hemisphere, negative latitudes are used for the southern hemisphere, 1.81 +positive longitudes indicate positions east of the prime meridian, and negative 1.82 +longitudes indicate positions west of the prime meridian.</p> 1.83 + 1.84 +<p>Latitudes exceeding -90 or +90 degrees are truncated to -90 or +90 1.85 +respectively, in which case a warning will be issued. Longitudes exceeding -180 1.86 +or +180 degrees will be converted to values between -180 and +180 (both 1.87 +inclusive) by adding or substracting a multiple of 360 degrees, in which case a 1.88 +notice will be issued.</p> 1.89 + 1.90 +<p>If the latitude is -90 or +90 (south pole or north pole), a longitude value is 1.91 +still stored in the datum, and if a point is on the prime meridian or the 1.92 +180th meridian, the east/west bit is also stored in the datum. In case of the 1.93 +prime meridian, this is done by storing a floating point value of -0 for 1.94 +0 degrees west and a value of +0 for 0 degrees east. In case of the 1.95 +180th meridian, this is done by storing -180 or +180 respectively. The equality 1.96 +operator, however, returns true when the same points on earth are described, 1.97 +i.e. the longitude is ignored for the poles, and 180 degrees west is considered 1.98 +to be equal to 180 degrees east.</p> 1.99 + 1.100 +<h4><code>ebox</code></h4> 1.101 + 1.102 +<p>An area on earth demarcated by a southern and northern latitude, and a western 1.103 +and eastern longitude (all given in WGS-84).</p> 1.104 + 1.105 +<p>The text input format is 1.106 +<code>'{N|S}<float> {E|W}<float> {N|S}<float> {E|W}<float>'</code>, where each float is in 1.107 +degrees. The ordering of the four white-space separated blocks is not 1.108 +significant. To include the 180th meridian, one longitude boundary must be 1.109 +equal to or exceed <code>W180</code> or <code>E180</code>, e.g. <code>'N10 N20 E170 E190'</code>.</p> 1.110 + 1.111 +<p>A special value is the empty area, denoted by the text represenation <code>'empty'</code>. 1.112 +Such an <code>ebox</code> does not contain any point.</p> 1.113 + 1.114 +<p>An <code>ebox</code> may also be created from four floating point numbers by calling 1.115 +<code>ebox(min_latitude, max_latitude, min_longitude, max_longitude)</code>, where 1.116 +positive values are used for north and east, and negative values are used for 1.117 +south and west. If <code>min_latitude</code> is strictly greater than <code>max_latitude</code>, an 1.118 +empty <code>ebox</code> is created. If <code>min_longitude</code> is greater than <code>max_longitude</code> and 1.119 +if both longitudes are between -180 and +180 degrees, then the area oriented in 1.120 +such way that the 180th meridian is included.</p> 1.121 + 1.122 +<p>If the longitude span is less than 120 degrees, an <code>ebox</code> may be alternatively 1.123 +created from two <code>epoints</code> in the following way: <code>ebox(epoint(lat1, lon1), 1.124 +epoint(lat2, lon2))</code>. In this case <code>lat1</code> and <code>lat2</code> as well as <code>lon1</code> and 1.125 +<code>lon2</code> can be swapped without any impact.</p> 1.126 + 1.127 +<h4><code>ecircle</code></h4> 1.128 + 1.129 +<p>An area containing all points not farther away from a given center point 1.130 +(WGS-84) than a given radius.</p> 1.131 + 1.132 +<p>The text input format is <code>'{N|S}<float> {E|W}<float> <float>'</code>, where the first 1.133 +two floats denote the center point in degrees and the third float denotes the 1.134 +radius in meters. A radius equal to minus infinity denotes an empty circle 1.135 +which contains no point at all (despite having a center), while a radius equal 1.136 +to zero denotes a circle that includes a single point.</p> 1.137 + 1.138 +<p>An <code>ecircle</code> may also be created by calling <code>ecircle(epoint(...), radius)</code> or 1.139 +from three floating point numbers by calling <code>ecircle(latitude, longitude, 1.140 +radius)</code>.</p> 1.141 + 1.142 +<h4><code>ecluster</code></h4> 1.143 + 1.144 +<p>A collection of points, paths, polygons, and outlines on the WGS-84 spheroid. 1.145 +Each path, polygon, or outline must cover a longitude range of less than 1.146 +180 degrees to avoid ambiguities.</p> 1.147 + 1.148 +<p>The text input format is a white-space separated list of the following items:</p> 1.149 + 1.150 +<ul> 1.151 +<li><code>point ({N|S}<float> {E|W}<float>)</code></li> 1.152 +<li><code>path ({N|S}<float> {E|W}<float> {N|S}<float> {E|W}<float> ...)</code></li> 1.153 +<li><code>outline ({N|S}<float> {E|W}<float> {N|S}<float> {E|W}<float> {N|S}<float> {E|W}<float> ...)</code></li> 1.154 +<li><code>polygon ({N|S}<float> {E|W}<float> {N|S}<float> {E|W}<float> {N|S}<float> {E|W}<float> ...)</code></li> 1.155 +</ul> 1.156 + 1.157 +<p>Paths are open by default (i.e. there is no connection from the last point in 1.158 +the list to the first point in the list). Outlines and polygons, in contrast, 1.159 +are automatically closed (i.e. there is a line segment from the last point in 1.160 +the list to the first point in the list) which means the first point should not 1.161 +be repeated as last point in the list. Polygons are filled, outlines are not.</p> 1.162 + 1.163 +<h3>2. Indices</h3> 1.164 + 1.165 +<p>Two kinds of indices are supported: B-tree and GiST indices.</p> 1.166 + 1.167 +<h4>B-tree indicies</h4> 1.168 + 1.169 +<p>A B-tree index can be used for simple equality searches and is supported by the 1.170 +<code>epoint</code>, <code>ebox</code>, and <code>ecircle</code> data types. B-tree indices can not be used for 1.171 +geographic searches.</p> 1.172 + 1.173 +<h4>GiST indicies</h4> 1.174 + 1.175 +<p>For geographic searches, GiST indices must be used. The <code>epoint</code>, <code>ecircle</code>, 1.176 +and <code>ecluster</code> data types support GiST indexing. A GiST index for geographic 1.177 +searches can be created as follows:</p> 1.178 + 1.179 +<pre><code>CREATE TABLE tbl ( 1.180 + id serial4 PRIMARY KEY, 1.181 + loc epoint NOT NULL ); 1.182 + 1.183 +CREATE INDEX name_of_index ON tbl USING gist (loc); 1.184 +</code></pre> 1.185 + 1.186 +<p>GiST indicies also support nearest neighbor searches when using the distance 1.187 +operator (<code><-></code>) in the ORDER BY clause.</p> 1.188 + 1.189 +<h4>Indicies on other data types (e.g. GeoJSON)</h4> 1.190 + 1.191 +<p>Note that further types can be indexed by using an index on an expression with 1.192 +a conversion function. One conversion function provided by pgLatLon is the 1.193 +<code>GeoJSON_to_ecluster(float8, float8, text)</code> function:</p> 1.194 + 1.195 +<pre><code>CREATE TABLE tbl ( 1.196 + id serial4 PRIMARY KEY, 1.197 + loc jsonb NOT NULL ); 1.198 + 1.199 +CREATE INDEX name_of_index ON tbl USING gist((GeoJSON_to_ecluster("loc"))); 1.200 +</code></pre> 1.201 + 1.202 +<p>When using the conversion function in an expression, the index will be used 1.203 +automatically:</p> 1.204 + 1.205 +<pre><code>SELECT * FROM tbl WHERE GeoJSON_to_ecluster("loc") && 'N50 E10 10000'::ecircle; 1.206 +</code></pre> 1.207 + 1.208 +<h3>3. Operators</h3> 1.209 + 1.210 +<h4>Equality operator <code>=</code></h4> 1.211 + 1.212 +<p>Tests if two geographic objects are equal.</p> 1.213 + 1.214 +<p>The longitude is ignored for the poles, and 180 degrees west is considered to 1.215 +be equal to 180 degrees east.</p> 1.216 + 1.217 +<p>For boxes and circles, two empty objects are considered equal. (Note that a 1.218 +circle is not empty if the radius is zero but only if it is negative infinity, 1.219 +i.e. smaller than zero.) Two circles with a positive infinite radius are also 1.220 +considered equal.</p> 1.221 + 1.222 +<p>Implemented for:</p> 1.223 + 1.224 +<ul> 1.225 +<li><code>epoint = epoint</code></li> 1.226 +<li><code>ebox = ebox</code></li> 1.227 +<li><code>ecircle = ecircle</code></li> 1.228 +</ul> 1.229 + 1.230 +<p>The negation is the inequality operator (<code><></code> or <code>!=</code>).</p> 1.231 + 1.232 +<h4>Linear ordering operators <code><<<</code>, <code><<<=</code>, <code>>>>=</code>, <code>>>></code></h4> 1.233 + 1.234 +<p>These operators create an arbitrary (but well-defined) linear ordering of 1.235 +geographic objects, which is used internally for B-tree indexing and merge 1.236 +joins. These operators will usually not be used by an application programmer.</p> 1.237 + 1.238 +<h4>Overlap operator <code>&&</code></h4> 1.239 + 1.240 +<p>Tests if two geographic objects have at least one point in common. Currently 1.241 +implemented for:</p> 1.242 + 1.243 +<ul> 1.244 +<li><code>epoint && ebox</code></li> 1.245 +<li><code>epoint && ecircle</code></li> 1.246 +<li><code>epoint && ecluster</code></li> 1.247 +<li><code>ebox && ebox</code></li> 1.248 +<li><code>ecircle && ecircle</code></li> 1.249 +<li><code>ecircle && ecluster</code></li> 1.250 +</ul> 1.251 + 1.252 +<p>The <code>&&</code> operator is commutative, i.e. <code>a && b</code> is the same as <code>b && a</code>. Each 1.253 +commutation is supported as well.</p> 1.254 + 1.255 +<h4>Distance operator <code><-></code></h4> 1.256 + 1.257 +<p>Calculates the shortest distance between two geographic objects in meters (zero 1.258 +if the objects are overlapping). Currently implemented for:</p> 1.259 + 1.260 +<ul> 1.261 +<li><code>epoint <-> epoint</code></li> 1.262 +<li><code>epoint <-> ecircle</code></li> 1.263 +<li><code>epoint <-> ecluster</code></li> 1.264 +<li><code>ecircle <-> ecircle</code></li> 1.265 +<li><code>ecircle <-> ecluster</code></li> 1.266 +</ul> 1.267 + 1.268 +<p>The <code><-></code> operator is commutative, i.e. <code>a <-> b</code> is the same as <code>b <-> a</code>. 1.269 +Each commutation is supported as well.</p> 1.270 + 1.271 +<p>For short distances, the result is very accurate (i.e. respects the dimensions 1.272 +of the WGS-84 spheroid). For longer distances in the order of magnitude of 1.273 +earth's radius or greater, the value is only approximate (but the error is 1.274 +still less than 0.2% as long as no polygons with very long edges are involved).</p> 1.275 + 1.276 +<p>The functions <code>distance(epoint, epoint)</code> and <code>distance(ecluster, epoint)</code> can 1.277 +be used as an alias for this operator.</p> 1.278 + 1.279 +<p>Note: In case of radial searches with a fixed radius, this operator should 1.280 +not be used. Instead, an <code>ecircle</code> should be created and used in combination 1.281 +with the overlap operator (<code>&&</code>). Alternatively, the functions 1.282 +<code>distance_within(epoint, epoint, float8)</code> or <code>distance_within(ecluster, epoint, 1.283 +float8)</code> can be used for fixed-radius searches.</p> 1.284 + 1.285 +<h3>4. Functions</h3> 1.286 + 1.287 +<h4><code>center(circle)</code></h4> 1.288 + 1.289 +<p>Returns the center of an <code>ecircle</code> as an <code>epoint</code>.</p> 1.290 + 1.291 +<h4><code>distance(epoint, epoint)</code></h4> 1.292 + 1.293 +<p>Calculates the distance between two <code>epoint</code> datums in meters. This function is 1.294 +an alias for the distance operator <code><-></code>.</p> 1.295 + 1.296 +<p>Note: In case of radial searches with a fixed radius, this function should not be 1.297 +used. Use <code>distance_within(epoint, epoint, float8)</code> instead.</p> 1.298 + 1.299 +<h4><code>distance(ecluster, epoint)</code></h4> 1.300 + 1.301 +<p>Calculates the distance from an <code>ecluster</code> to an <code>epoint</code> in meters. This 1.302 +function is an alias for the distance operator <code><-></code>.</p> 1.303 + 1.304 +<p>Note: In case of radial searches with a fixed radius, this function should not be 1.305 +used. Use <code>distance_within(epoint, epoint, float8)</code> instead.</p> 1.306 + 1.307 +<h4><code>distance_within(</code>variable <code>epoint,</code> fixed <code>epoint,</code> radius <code>float8)</code></h4> 1.308 + 1.309 +<p>Checks if the distance between two <code>epoint</code> datums is not greater than a given 1.310 +value (search radius).</p> 1.311 + 1.312 +<p>Note: In case of radial searches with a fixed radius, the first argument must 1.313 +be used for the table column, while the second argument must be used for the 1.314 +search center. Otherwise an existing index cannot be used.</p> 1.315 + 1.316 +<h4><code>distance_within(</code>variable <code>ecluster,</code> fixed <code>epoint,</code> radius <code>float8)</code></h4> 1.317 + 1.318 +<p>Checks if the distance from an <code>ecluster</code> to an <code>epoint</code> is not greater than a 1.319 +given value (search radius).</p> 1.320 + 1.321 +<h4><code>ebox(</code>latmin <code>float8,</code> latmax <code>float8,</code> lonmin <code>float8,</code> lonmax <code>float8)</code></h4> 1.322 + 1.323 +<p>Creates a new <code>ebox</code> with the given boundaries. 1.324 +See "1. Types", subsection <code>ebox</code> for details.</p> 1.325 + 1.326 +<h4><code>ebox(epoint, epoint)</code></h4> 1.327 + 1.328 +<p>Creates a new <code>ebox</code>. This function may only be used if the longitude 1.329 +difference is less than or equal to 120 degrees. 1.330 +See "1. Types", subsection <code>ebox</code> for details.</p> 1.331 + 1.332 +<h4><code>ecircle(epoint, float8)</code></h4> 1.333 + 1.334 +<p>Creates an <code>ecircle</code> with the given center point and radius.</p> 1.335 + 1.336 +<h4><code>ecircle(</code>latitude <code>float8,</code> longitude <code>float8,</code> radius <code>float8)</code></h4> 1.337 + 1.338 +<p>Creates an <code>ecircle</code> with the given center point and radius.</p> 1.339 + 1.340 +<h4><code>ecluster_concat(ecluster, ecluster)</code></h4> 1.341 + 1.342 +<p>Combines two clusters to form a new <code>ecluster</code> by uniting all entries of both 1.343 +clusters. Note that two overlapping areas of polygons annihilate each other 1.344 +(which may be used to create polygons with holes).</p> 1.345 + 1.346 +<h4><code>ecluster_concat(ecluster[])</code></h4> 1.347 + 1.348 +<p>Creates a new <code>ecluster</code> that unites all entries of all clusters in the passed 1.349 +array. Note that two overlapping areas of polygons annihilate each other (which 1.350 +may be used to create polygons with holes).</p> 1.351 + 1.352 +<h4><code>ecluster_create_multipoint(epoint[])</code></h4> 1.353 + 1.354 +<p>Creates a new <code>ecluster</code> which contains multiple points.</p> 1.355 + 1.356 +<h4><code>ecluster_create_outline(epoint[])</code></h4> 1.357 + 1.358 +<p>Creates a new <code>ecluster</code> that is an outline given by the passed points.</p> 1.359 + 1.360 +<h4><code>ecluster_create_path(epoint[])</code></h4> 1.361 + 1.362 +<p>Creates a new <code>ecluster</code> that is a path given by the passed points.</p> 1.363 + 1.364 +<h4><code>ecluster_create_polygon(epoint[])</code></h4> 1.365 + 1.366 +<p>Creates a new <code>ecluster</code> that is a polygon given by the passed points.</p> 1.367 + 1.368 +<h4><code>ecluster_extract_outlines(ecluster)</code></h4> 1.369 + 1.370 +<p>Set-returning function that returns the outlines of an <code>ecluster</code> as <code>epoint[]</code> 1.371 +rows.</p> 1.372 + 1.373 +<h4><code>ecluster_extract_paths(ecluster)</code></h4> 1.374 + 1.375 +<p>Set-returning function that returns the paths of an <code>ecluster</code> as <code>epoint[]</code> 1.376 +rows.</p> 1.377 + 1.378 +<h4><code>ecluster_extract_points(ecluster)</code></h4> 1.379 + 1.380 +<p>Set-returning function that returns the points of an <code>ecluster</code> as <code>epoint</code> 1.381 +rows.</p> 1.382 + 1.383 +<h4><code>ecluster_extract_polygons(ecluster)</code></h4> 1.384 + 1.385 +<p>Set-returning function that returns the polygons of an <code>ecluster</code> as <code>epoint[]</code> 1.386 +rows.</p> 1.387 + 1.388 +<h4><code>empty_ebox</code>()</h4> 1.389 + 1.390 +<p>Returns the empty <code>ebox</code>. 1.391 +See "1. Types", subsection <code>ebox</code> for details.</p> 1.392 + 1.393 +<h4><code>epoint(</code>latitude <code>float8,</code> longitude <code>float8)</code></h4> 1.394 + 1.395 +<p>Returns an <code>epoint</code> with the given latitude and longitude.</p> 1.396 + 1.397 +<h4><code>epoint_latlon(</code>latitude <code>float8,</code> longitude <code>float8)</code></h4> 1.398 + 1.399 +<p>Alias for <code>epoint(float8, float8)</code>.</p> 1.400 + 1.401 +<h4><code>epoint_lonlat(</code>longitude <code>float8,</code> latitude <code>float8)</code></h4> 1.402 + 1.403 +<p>Same as <code>epoint(float8, float8)</code> but with arguments reversed.</p> 1.404 + 1.405 +<h4><code>GeoJSON_to_epoint(jsonb, text)</code></h4> 1.406 + 1.407 +<p>Maps a GeoJSON object of type "Point" or "Feature" (which contains a 1.408 +"Point") to an <code>epoint</code> datum. For any other JSON objects, NULL is returned.</p> 1.409 + 1.410 +<p>The second parameter (which defaults to <code>epoint_lonlat</code>) may be set to a name 1.411 +of a conversion function that transforms two coordinates (two <code>float8</code> 1.412 +parameters) to an <code>epoint</code>.</p> 1.413 + 1.414 +<h4><code>GeoJSON_to_ecluster(jsonb, text)</code></h4> 1.415 + 1.416 +<p>Maps a (valid) GeoJSON object to an <code>ecluster</code>. Note that this function 1.417 +does not check whether the JSONB object is a valid GeoJSON object.</p> 1.418 + 1.419 +<p>The second parameter (which defaults to <code>epoint_lonlat</code>) may be set to a name 1.420 +of a conversion function that transforms two coordinates (two <code>float8</code> 1.421 +parameters) to an <code>epoint</code>.</p> 1.422 + 1.423 +<h4><code>max_latitude(ebox)</code></h4> 1.424 + 1.425 +<p>Returns the northern boundary of a given <code>ebox</code> in degrees between -90 and +90.</p> 1.426 + 1.427 +<h4><code>max_longitude(ebox)</code></h4> 1.428 + 1.429 +<p>Returns the eastern boundary of a given <code>ebox</code> in degrees between -180 and +180 1.430 +(both inclusive).</p> 1.431 + 1.432 +<h4><code>min_latitude(ebox)</code></h4> 1.433 + 1.434 +<p>Returns the southern boundary of a given <code>ebox</code> in degrees between -90 and +90.</p> 1.435 + 1.436 +<h4><code>min_longitude(ebox)</code></h4> 1.437 + 1.438 +<p>Returns the western boundary of a given <code>ebox</code> in degrees between -180 and +180 1.439 +(both inclusive).</p> 1.440 + 1.441 +<h4><code>latitude(epoint)</code></h4> 1.442 + 1.443 +<p>Returns the latitude value of an <code>epoint</code> in degrees between -90 and +90.</p> 1.444 + 1.445 +<h4><code>longitude(epoint)</code></h4> 1.446 + 1.447 +<p>Returns the longitude value of an <code>epoint</code> in degrees between -180 and +180 1.448 +(both inclusive).</p> 1.449 + 1.450 +<h4><code>radius(ecircle)</code></h4> 1.451 + 1.452 +<p>Returns the radius of an <code>ecircle</code> in meters.</p> 1.453 +</body></html>