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				99	<h1>Support the standard GIS objects (DRAFT)</h1>
				100	<div class="section">
				101	<h2><a name="Table_of_Contents"></a><a name="toc" id="toc">Table of Contents</a></h2>
				102	<ul>
				103
				104	<li><a href="#Introduction">Introduction</a></li>
				105	<li><a href="#construction">Construction functions</a></li>
				106	<li><a href="#primitive">Primitive functions</a></li>
				107	<li><a href="#predicate">Spatial Predicate</a></li>
				108	<li><a href="#analysis">Spatial Analysis</a></li>
				109	<li><a href="#aggregate">Spatial Aggregates</a></li>
				110	</ul></div>
				111	<div class="section">
				112	<h2><a name="Introduction" id="Introduction">Introduction</a></h2>
				113	<p>To support standard GIS objects in AsterixDB, you need to use the <tt>geometry</tt> data type as follows.</p>
				114
				115	<div>
				116	<div>
				117	<pre class="source">DROP dataverse GeoJSON if exists;
				118	CREATE dataverse GeoJSON;
				119
				120	USE GeoJSON;
				121
				122	CREATE TYPE GeometryType AS{
				123	id : int,
				124	myGeometry : geometry
				125	};
				126
				127	CREATE DATASET Geometries (GeometryType) PRIMARY KEY id;
				128	</pre></div></div>
				129
				130	<p>Please note that even though the <a class="externalLink" href="http://desktop.arcgis.com/en/arcmap/10.3/manage-data/using-sql-with-gdbs/what-is-an-srid.htm">SRID</a> input is supported for certain functions and is represented internally in the correct manner the serialized result (printed in the output) displays the SRID as 4326 always because of the limitations in Esri API.</p></div>
				131	<div class="section">
				132	<h2><a name="Construction_functions"></a><a name="construction" id="construction">Construction functions</a></h2>
				133	<p>The Geometry datatype can be created by the constructor functions.</p>
				134	<div class="section">
				135	<h3><a name="st_make_point"></a>st_make_point</h3>
				136	<ul>
				137
				138	<li>
				139
				140	<p>Creates a 2D,3DZ or 4D point geometry.</p>
				141	</li>
				142	<li>
				143
				144	<p>Example:</p>
				145	</li>
				146	<li>Create a 2D point at coordinates (x,y) = (-71, 42)</li>
				147	<li>Command:
				148
				149	<div>
				150	<div>
				151	<pre class="source">st_make_point(-71, 42);
				152	</pre></div></div>
				153	</li>
				154	<li>Result:
				155
				156	<div>
				157	<div>
				158	<pre class="source">{"type":"Point","coordinates":[-71,42],"crs":{"type":"name","properties":{"name":"EPSG:4326"}}}
				159	</pre></div></div>
				160	</li>
				161	<li>Example:</li>
				162	<li>Create a 3D point at coordinates (x,y,z) = (1,2,1.59)</li>
				163	<li>Command:
				164
				165	<div>
				166	<div>
				167	<pre class="source">st_make_point(1,2,1.59);
				168	</pre></div></div>
				169	</li>
				170	<li>Result:
				171
				172	<div>
				173	<div>
				174	<pre class="source">{"type":"Point","coordinates":[1,2,1.59],"crs":{"type":"name","properties":{"name":"EPSG:4326"}}}
				175	</pre></div></div>
				176	</li>
				177	</ul></div>
				178	<div class="section">
				179	<h3><a name="st_geom_from_text"></a>st_geom_from_text</h3>
				180	<ul>
				181
				182	<li>
				183
				184	<p>Return a specified ST_Geometry value from Well-Known Text representation (WKT).</p>
				185	</li>
				186	<li>
				187
				188	<p>Example:</p>
				189	</li>
				190	<li>Create a LineString geometry from the WKT format.</li>
				191	<li>Command:
				192
				193	<div>
				194	<div>
				195	<pre class="source">st_geom_from_text("LINESTRING(1 2,3 4,5 6)");
				196	</pre></div></div>
				197	</li>
				198	<li>Result:
				199
				200	<div>
				201	<div>
				202	<pre class="source">{"type":"LineString","coordinates":[[1,2],[3,4],[5,6]],"crs":{"type":"name","properties":{"name":"EPSG:4326"}}}
				203	</pre></div></div>
				204	</li>
				205	<li>Example:</li>
				206	<li>Create a MultiLineString geometry from the WKT format.</li>
				207	<li>Command:
				208
				209	<div>
				210	<div>
				211	<pre class="source">st_geom_from_text('MULTILINESTRING((1 2,3 4,5 6),(7 8,9 10))');
				212	</pre></div></div>
				213	</li>
				214	<li>Result:
				215
				216	<div>
				217	<div>
				218	<pre class="source">{"type":"MultiLineString","coordinates":[[[1,2],[3,4],[5,6]],[[7,8],[9,10]]],"crs":null}
				219	</pre></div></div>
				220	</li>
				221	</ul></div>
				222	<div class="section">
				223	<h3><a name="st_geom_from_wkb"></a>st_geom_from_wkb</h3>
				224	<ul>
				225
				226	<li>
				227
				228	<p>Creates a geometry instance from a Well-Known Binary geometry representation (WKB) and optional SRID.</p>
				229	</li>
				230	<li>
				231
				232	<p>Example:</p>
				233	</li>
				234	<li>Command:
				235
				236	<div>
				237	<div>
				238	<pre class="source">st_geom_from_wkb(hex("010100000000000000000000400000000000001440"));
				239	</pre></div></div>
				240	</li>
				241	<li>Result:
				242
				243	<div>
				244	<div>
				245	<pre class="source">{"type":"Point","coordinates":[2,5],"crs":{"type":"name","properties":{"name":"EPSG:4326"}}}
				246	</pre></div></div>
				247	</li>
				248	</ul></div>
				249	<div class="section">
				250	<h3><a name="st_geom_from_geojson"></a>st_geom_from_geojson</h3>
				251	<ul>
				252
				253	<li>
				254
				255	<p>Creates a geometry instance from its GeoJSON representation</p>
				256	</li>
				257	<li>
				258
				259	<p>Example:</p>
				260	</li>
				261	<li>Command:
				262
				263	<div>
				264	<div>
				265	<pre class="source">st_geom_from_geojson({"type":"Point","coordinates":[2,5],"crs":{"type":"name","properties":{"name":"EPSG:4326"}}});
				266	</pre></div></div>
				267	</li>
				268	<li>
				269
				270	<p>Result:</p>
				271
				272	<div>
				273	<div>
				274	<pre class="source">{"type":"Point","coordinates":[2,5],"crs":{"type":"name","properties":{"name":"EPSG:4326"}}}
				275	</pre></div></div>
				276	</li>
				277	</ul></div>
				278	<div class="section">
				279	<h3><a name="st_make_envelope"></a>st_make_envelope</h3>
				280	<ul>
				281
				282	<li>
				283
				284	<p>Creates a rectangular Polygon formed from the given minimums and maximums. Input values must be in SRS specified by the SRID.</p>
				285	</li>
				286	<li>
				287
				288	<p>Example:</p>
				289	</li>
				290	<li>Command:
				291
				292	<div>
				293	<div>
				294	<pre class="source">st_make_envelope(10, 10, 11, 11, 4326);
				295	</pre></div></div>
				296	</li>
				297	<li>Result:
				298
				299	<div>
				300	<div>
				301	<pre class="source">{"type":"Polygon","coordinates":[[[10,10],[11,10],[11,11],[10,11],[10,10]]],"crs":{"type":"name","properties":{"name":"EPSG:4326"}}}
				302	</pre></div></div>
				303	</li>
				304	</ul></div></div>
				305	<div class="section">
				306	<h2><a name="Primitive_functions"></a><a name="primitive" id="primitive">Primitive functions</a></h2>
				307	<p>There are primitive functions that take as input geometry/es and return a primitive type.</p>
				308	<div class="section">
				309	<h3><a name="st_area"></a>st_area</h3>
				310	<ul>
				311
				312	<li>
				313
				314	<p>Return the area of the surface if it is a Polygon or MultiPolygon. For geometry, a 2D Cartesian area is determined with units specified by the SRID. For geography, area is determined on a curved surface with units in square meters.</p>
				315	</li>
				316	<li>
				317
				318	<p>Example:</p>
				319	</li>
				320	<li>Command:
				321
				322	<div>
				323	<div>
				324	<pre class="source">st_area(st_geom_from_text('POLYGON((7 2,4 9,3 6,2.6 7,8 16))'));
				325	</pre></div></div>
				326	</li>
				327	<li>Result:
				328
				329	<div>
				330	<div>
				331	<pre class="source">26.500000000000007
				332	</pre></div></div>
				333	</li>
				334	</ul></div>
				335	<div class="section">
				336	<h3><a name="st_coord_dim"></a>st_coord_dim</h3>
				337	<ul>
				338
				339	<li>
				340
				341	<p>Return the coordinate dimension of the Geometry value.</p>
				342	</li>
				343	<li>
				344
				345	<p>Example:</p>
				346	</li>
				347	<li>Command:
				348
				349	<div>
				350	<div>
				351	<pre class="source">st_coord_dim(st_make_point(1,2));
				352	</pre></div></div>
				353	</li>
				354	<li>Result:
				355
				356	<div>
				357	<div>
				358	<pre class="source">2
				359	</pre></div></div>
				360	</li>
				361	</ul></div>
				362	<div class="section">
				363	<h3><a name="st_dimension"></a>st_dimension</h3>
				364	<ul>
				365
				366	<li>
				367
				368	<p>Return the inherent dimension of this Geometry object, which must be less than or equal to the coordinate dimension.</p>
				369	</li>
				370	<li>
				371
				372	<p>Example:</p>
				373	</li>
				374	<li>Command:
				375
				376	<div>
				377	<div>
				378	<pre class="source">st_dimension(st_geom_from_text('GEOMETRYCOLLECTION(LINESTRING(1 1,0 0),POINT(0 0))'));
				379	</pre></div></div>
				380	</li>
				381	<li>Result:
				382
				383	<div>
				384	<div>
				385	<pre class="source">1
				386	</pre></div></div>
				387	</li>
				388	</ul></div>
				389	<div class="section">
				390	<h3><a name="geometry_type"></a>geometry_type</h3>
				391	<ul>
				392
				393	<li>
				394
				395	<p>Return the type of the geometry as a string. Eg: ‘LINESTRING’, ‘POLYGON’, ‘MULTIPOINT’, etc.</p>
				396	</li>
				397	<li>
				398
				399	<p>Example:</p>
				400	</li>
				401	<li>Command:
				402
				403	<div>
				404	<div>
				405	<pre class="source">geometry_type(st_geom_from_text('LINESTRING(77.29 29.07,77.42 29.26,77.27 29.31,77.29 29.07)'));
				406	</pre></div></div>
				407	</li>
				408	<li>Result:
				409
				410	<div>
				411	<div>
				412	<pre class="source">"LineString"
				413	</pre></div></div>
				414	</li>
				415	</ul></div>
				416	<div class="section">
				417	<h3><a name="st_m"></a>st_m</h3>
				418	<ul>
				419
				420	<li>
				421
				422	<p>Return the M coordinate of the point, or NULL if not available. Input must be a point.</p>
				423	</li>
				424	<li>
				425
				426	<p>Example:</p>
				427	</li>
				428	<li>Command:
				429
				430	<div>
				431	<div>
				432	<pre class="source">st_m(st_make_point(1, 2, 3, 4));
				433	</pre></div></div>
				434	</li>
				435	<li>Result:
				436
				437	<div>
				438	<div>
				439	<pre class="source">4.0
				440	</pre></div></div>
				441	</li>
				442	</ul></div>
				443	<div class="section">
				444	<h3><a name="st_n_points"></a>st_n_points</h3>
				445	<ul>
				446
				447	<li>
				448
				449	<p>Return the number of points (vertexes) in a geometry.</p>
				450	</li>
				451	<li>
				452
				453	<p>Example:</p>
				454	</li>
				455	<li>Command:
				456
				457	<div>
				458	<div>
				459	<pre class="source">st_n_points(st_geom_from_text('LINESTRING(77.29 29.07,77.42 29.26,77.27 29.31,77.29 29.07)'));
				460	</pre></div></div>
				461	</li>
				462	<li>Result:
				463
				464	<div>
				465	<div>
				466	<pre class="source">4
				467	</pre></div></div>
				468	</li>
				469	</ul></div>
				470	<div class="section">
				471	<h3><a name="st_n_rings"></a>st_n_rings</h3>
				472	<ul>
				473
				474	<li>
				475
				476	<p>If the geometry is a polygon or multi-polygon return the number of rings.</p>
				477	</li>
				478	<li>
				479
				480	<p>Example:</p>
				481	</li>
				482	<li>Command:
				483
				484	<div>
				485	<div>
				486	<pre class="source">st_n_rings(st_geom_from_text('POLYGON((10.689 -25.092, 34.595 -20.170, 38.814 -35.639, 13.502 -39.155, 10.689 -25.092))'));
				487	</pre></div></div>
				488	</li>
				489	<li>Result:
				490
				491	<div>
				492	<div>
				493	<pre class="source">1
				494	</pre></div></div>
				495	</li>
				496	</ul></div>
				497	<div class="section">
				498	<h3><a name="st_num_geometries"></a>st_num_geometries</h3>
				499	<ul>
				500
				501	<li>
				502
				503	<p>If geometry is a GEOMETRYCOLLECTION (or MULTI*) return the number of geometries, for single geometries will return 1, otherwise return NULL.</p>
				504	</li>
				505	<li>
				506
				507	<p>Example:</p>
				508	</li>
				509	<li>Command:
				510
				511	<div>
				512	<div>
				513	<pre class="source">st_num_geometries(st_geom_from_text('LINESTRING(77.29 29.07,77.42 29.26,77.27 29.31,77.29 29.07)'));
				514	</pre></div></div>
				515	</li>
				516	<li>Result:
				517
				518	<div>
				519	<div>
				520	<pre class="source">1
				521	</pre></div></div>
				522	</li>
				523	<li>Example:</li>
				524	<li>Command:
				525
				526	<div>
				527	<div>
				528	<pre class="source">st_num_geometries(st_geom_from_text('GEOMETRYCOLLECTION(MULTIPOINT(-2 3 , -2 2), LINESTRING(5 5 ,10 10), POLYGON((-7 4.2,-7.1 5,-7.1 4.3,-7 4.2)))'));
				529	</pre></div></div>
				530	</li>
				531	<li>Result:
				532
				533	<div>
				534	<div>
				535	<pre class="source">3
				536	</pre></div></div>
				537	</li>
				538	</ul></div>
				539	<div class="section">
				540	<h3><a name="st_num_interiorRings"></a>st_num_interiorRings</h3>
				541	<ul>
				542
				543	<li>
				544
				545	<p>Return the number of interior rings of a polygon geometry.</p>
				546	</li>
				547	<li>
				548
				549	<p>Example:</p>
				550	</li>
				551	</ul>
				552	<p><img src="../images/linestring.png" alt="Image of interiorRings" /> * Command:</p>
				553
				554	<div>
				555	<div>
				556	<pre class="source"> st_num_interior_rings(st_geom_from_text("POLYGON ((35 10, 45 45, 15 40, 10 20, 35 10),(20 30, 35 35, 30 20, 20 30))"));
				557	</pre></div></div>
				558
				559	<ul>
				560
				561	<li>Result:
				562
				563	<div>
				564	<div>
				565	<pre class="source">1
				566	</pre></div></div>
				567	</li>
				568	</ul></div>
				569	<div class="section">
				570	<h3><a name="st_x"></a>st_x</h3>
				571	<ul>
				572
				573	<li>
				574
				575	<p>Return the X coordinate of the point, or NULL if not available. Input must be a point.</p>
				576	</li>
				577	<li>
				578
				579	<p>Example:</p>
				580	</li>
				581	<li>Command:
				582
				583	<div>
				584	<div>
				585	<pre class="source">st_x(st_make_point(1, 2, 3, 4));
				586	</pre></div></div>
				587	</li>
				588	<li>Result:
				589
				590	<div>
				591	<div>
				592	<pre class="source">1.0
				593	</pre></div></div>
				594	</li>
				595	</ul></div>
				596	<div class="section">
				597	<h3><a name="st_y"></a>st_y</h3>
				598	<ul>
				599
				600	<li>
				601
				602	<p>Return the Y coordinate of the point, or NULL if not available. Input must be a point.</p>
				603	</li>
				604	<li>
				605
				606	<p>Example:</p>
				607	</li>
				608	<li>Command:
				609
				610	<div>
				611	<div>
				612	<pre class="source">st_y(st_make_point(1, 2, 3, 4));
				613	</pre></div></div>
				614	</li>
				615	<li>Result:
				616
				617	<div>
				618	<div>
				619	<pre class="source">1.0
				620	</pre></div></div>
				621	</li>
				622	</ul></div>
				623	<div class="section">
				624	<h3><a name="st_x_max"></a>st_x_max</h3>
				625	<ul>
				626
				627	<li>
				628
				629	<p>Return X maximum of a bounding box 2d or 3d or a geometry.</p>
				630	</li>
				631	<li>
				632
				633	<p>Example:</p>
				634	</li>
				635	<li>Command:
				636
				637	<div>
				638	<div>
				639	<pre class="source">st_x_max(st_geom_from_text('POLYGON((10.689 -25.092, 34.595 -20.170, 38.814 -35.639, 13.502 -39.155, 10.689 -25.092))'));
				640	</pre></div></div>
				641	</li>
				642	<li>Result:
				643
				644	<div>
				645	<div>
				646	<pre class="source">38.814
				647	</pre></div></div>
				648	</li>
				649	</ul></div>
				650	<div class="section">
				651	<h3><a name="st_x_min"></a>st_x_min</h3>
				652	<ul>
				653
				654	<li>Return X minimum of a bounding box 2d or 3d or a geometry.</li>
				655	</ul></div>
				656	<div class="section">
				657	<h3><a name="st_y_max"></a>st_y_max</h3>
				658	<ul>
				659
				660	<li>Return Y maximum of a bounding box 2d or 3d or a geometry.</li>
				661	</ul></div>
				662	<div class="section">
				663	<h3><a name="st_y_min"></a>st_y_min</h3>
				664	<ul>
				665
				666	<li>Return Y minimum of a bounding box 2d or 3d or a geometry.</li>
				667	</ul></div>
				668	<div class="section">
				669	<h3><a name="st_z"></a>st_z</h3>
				670	<ul>
				671
				672	<li>Return the Z coordinate of the point, or NULL if not available. Input must be a point.</li>
				673	</ul></div>
				674	<div class="section">
				675	<h3><a name="st_z_max"></a>st_z_max</h3>
				676	<ul>
				677
				678	<li>Return Z maximum of a bounding box 2d or 3d or a geometry.</li>
				679	</ul></div>
				680	<div class="section">
				681	<h3><a name="st_z_min"></a>st_z_min</h3>
				682	<ul>
				683
				684	<li>Return Z minimum of a bounding box 2d or 3d or a geometry.</li>
				685	</ul></div>
				686	<div class="section">
				687	<h3><a name="st_as_binary"></a>st_as_binary</h3>
				688	<ul>
				689
				690	<li>
				691
				692	<p>Return the Well-Known Binary (WKB) representation of the geometry/geography without SRID meta data.</p>
				693	</li>
				694	<li>
				695
				696	<p>Example:</p>
				697	</li>
				698	<li>Command:
				699
				700	<div>
				701	<div>
				702	<pre class="source">st_as_binary(st_geom_from_geojson({"type":"Point","coordinates":[2,5],"crs":{"type":"name","properties":{"name":"EPSG:4326"}}}));
				703	</pre></div></div>
				704	</li>
				705	<li>Result:
				706
				707	<div>
				708	<div>
				709	<pre class="source">"010100000000000000000000400000000000001440"
				710	</pre></div></div>
				711	</li>
				712	</ul></div>
				713	<div class="section">
				714	<h3><a name="st_as_geojson"></a>st_as_geojson</h3>
				715	<ul>
				716
				717	<li>
				718
				719	<p>Return the geometry as a GeoJSON element.</p>
				720	</li>
				721	<li>
				722
				723	<p>Example:</p>
				724	</li>
				725	<li>Command:
				726
				727	<div>
				728	<div>
				729	<pre class="source">st_as_geojson(st_geom_from_text('POLYGON((10.689 -25.092, 34.595 -20.170, 38.814 -35.639, 13.502 -39.155, 10.689 -25.092))'));
				730	</pre></div></div>
				731	</li>
				732	<li>Result:
				733
				734	<div>
				735	<div>
				736	<pre class="source">"{\"type\":\"Polygon\",\"coordinates\":[[[10.689,-25.092],[13.502,-39.155],[38.814,-35.639],[34.595,-20.17],[10.689,-25.092]]],\"crs\":{\"type\":\"name\",\"properties\":{\"name\":\"EPSG:4326\"}}}"
				737	</pre></div></div>
				738	</li>
				739	</ul></div>
				740	<div class="section">
				741	<h3><a name="st_distance"></a>st_distance</h3>
				742	<ul>
				743
				744	<li>
				745
				746	<p>For geometry type Return the 2D Cartesian distance between two geometries in projected units (based on spatial ref). For geography type defaults to return minimum geodesic distance between two geographies in meters.</p>
				747	</li>
				748	<li>
				749
				750	<p>Example:</p>
				751	</li>
				752	<li>Command:
				753
				754	<div>
				755	<div>
				756	<pre class="source">st_distance(st_geom_from_text('POINT(-72.1235 42.3521)'),st_geom_from_text('LINESTRING(-72.1260 42.45, -72.123 42.1546)'));
				757	</pre></div></div>
				758	</li>
				759	<li>Result:
				760
				761	<div>
				762	<div>
				763	<pre class="source">0.0015056772638282166
				764	</pre></div></div>
				765	</li>
				766	</ul></div>
				767	<div class="section">
				768	<h3><a name="st_length"></a>st_length</h3>
				769	<ul>
				770
				771	<li>
				772
				773	<p>Return the 2D length of the geometry if it is a LineString or MultiLineString. geometry are in units of spatial reference and geography are in meters (default spheroid).</p>
				774	</li>
				775	<li>
				776
				777	<p>Example:</p>
				778	</li>
				779	<li>Command:
				780
				781	<div>
				782	<div>
				783	<pre class="source">st_length(st_geom_from_text('LINESTRING(-72.1260 42.45, -72.1240 42.45666, -72.123 42.1546)'));
				784	</pre></div></div>
				785	</li>
				786	<li>Result:
				787
				788	<div>
				789	<div>
				790	<pre class="source">0.30901547439030225
				791	</pre></div></div>
				792	</li>
				793	</ul></div></div>
				794	<div class="section">
				795	<h2><a name="Spatial_Predicate"></a><a name="predicate" id="predicate">Spatial Predicate</a></h2>
				796	<p>Spatial predicate functions test for a relationship between two geometries and return a Boolean value (true/false).</p>
				797	<div class="section">
				798	<h3><a name="st_intersects"></a>st_intersects</h3>
				799	<ul>
				800
				801	<li>
				802
				803	<p>Return TRUE if the Geometries/Geography “spatially intersect in 2D”.</p>
				804	</li>
				805	<li>
				806
				807	<p>Example:</p>
				808	</li>
				809	<li>Command:
				810
				811	<div>
				812	<div>
				813	<pre class="source">st_intersects(st_geom_from_text('POINT(0 0)'), st_geom_from_text('LINESTRING ( 0 0, 0 2 )'));
				814	</pre></div></div>
				815	</li>
				816	<li>Result:
				817
				818	<div>
				819	<div>
				820	<pre class="source">true
				821	</pre></div></div>
				822	</li>
				823	</ul></div>
				824	<div class="section">
				825	<h3><a name="st_isclosed"></a>st_isclosed</h3>
				826	<ul>
				827
				828	<li>
				829
				830	<p>Return TRUE if the LINESTRING’s start and end points are coincident.</p>
				831	</li>
				832	<li>
				833
				834	<p>Example:</p>
				835	</li>
				836	<li>Command:
				837
				838	<div>
				839	<div>
				840	<pre class="source">st_is_closed(st_geom_from_text('LINESTRING(0 0, 0 1, 1 1, 0 0)'));
				841	</pre></div></div>
				842	</li>
				843	<li>Result:
				844
				845	<div>
				846	<div>
				847	<pre class="source">true
				848	</pre></div></div>
				849	</li>
				850	</ul></div>
				851	<div class="section">
				852	<h3><a name="st_iscollection"></a>st_iscollection</h3>
				853	<ul>
				854
				855	<li>
				856
				857	<p>Return TRUE if the argument is a collection (MULTI*, GEOMETRYCOLLECTION, …)</p>
				858	</li>
				859	<li>
				860
				861	<p>Example:</p>
				862	</li>
				863	<li>Command:
				864
				865	<div>
				866	<div>
				867	<pre class="source">st_is_collection(st_geom_from_text('MULTIPOINT EMPTY'));
				868	</pre></div></div>
				869	</li>
				870	<li>Result:
				871
				872	<div>
				873	<div>
				874	<pre class="source">true
				875	</pre></div></div>
				876	</li>
				877	</ul></div>
				878	<div class="section">
				879	<h3><a name="st_is_empty"></a>st_is_empty</h3>
				880	<ul>
				881
				882	<li>
				883
				884	<p>Return true if this Geometry is an empty geometrycollection, polygon, point etc.</p>
				885	</li>
				886	<li>
				887
				888	<p>Example:</p>
				889	</li>
				890	<li>Command:
				891
				892	<div>
				893	<div>
				894	<pre class="source">st_is_empty(st_geom_from_text('POLYGON EMPTY'));
				895	</pre></div></div>
				896	</li>
				897	<li>Result:
				898
				899	<div>
				900	<div>
				901	<pre class="source">true
				902	</pre></div></div>
				903	</li>
				904	</ul></div>
				905	<div class="section">
				906	<h3><a name="st_is_ring"></a>st_is_ring</h3>
				907	<ul>
				908
				909	<li>
				910
				911	<p>Return TRUE if this LINESTRING is both closed and simple.</p>
				912	</li>
				913	<li>
				914
				915	<p>Example:</p>
				916	</li>
				917	<li>Command:
				918
				919	<div>
				920	<div>
				921	<pre class="source">st_is_ring(st_geom_from_text('LINESTRING(0 0, 0 1, 1 1, 1 0, 0 0)'));
				922	</pre></div></div>
				923	</li>
				924	<li>Result:
				925
				926	<div>
				927	<div>
				928	<pre class="source">true
				929	</pre></div></div>
				930	</li>
				931	</ul></div>
				932	<div class="section">
				933	<h3><a name="st_is_simple"></a>st_is_simple</h3>
				934	<ul>
				935
				936	<li>
				937
				938	<p>Return (TRUE) if this Geometry has no anomalous geometric points, such as self intersection or self tangency.</p>
				939	</li>
				940	<li>
				941
				942	<p>Example:</p>
				943	</li>
				944	<li>Command:
				945
				946	<div>
				947	<div>
				948	<pre class="source">st_is_simple(st_geom_from_text('LINESTRING(1 1,2 2,2 3.5,1 3,1 2,2 1)'));
				949	</pre></div></div>
				950	</li>
				951	<li>Result:
				952
				953	<div>
				954	<div>
				955	<pre class="source">false
				956	</pre></div></div>
				957	</li>
				958	</ul></div>
				959	<div class="section">
				960	<h3><a name="st_contains"></a>st_contains</h3>
				961	<ul>
				962
				963	<li>
				964
				965	<p>Return true if and only if no points of B lie in the exterior of A, and at least one point of the interior of B lies in the interior of A.</p>
				966	</li>
				967	<li>
				968
				969	<p>Example:</p>
				970	</li>
				971	<li>Command:
				972
				973	<div>
				974	<div>
				975	<pre class="source">st_contains(st_geom_from_text('LINESTRING(1 1,-1 -1,2 3.5,1 3,1 2,2 1)'), st_make_point(-1, -1));
				976	</pre></div></div>
				977	</li>
				978	<li>Result:
				979
				980	<div>
				981	<div>
				982	<pre class="source">true
				983	</pre></div></div>
				984	</li>
				985	</ul></div>
				986	<div class="section">
				987	<h3><a name="st_crosses"></a>st_crosses</h3>
				988	<ul>
				989
				990	<li>
				991
				992	<p>Return TRUE if the supplied geometries have some, but not all, interior points in common.</p>
				993	</li>
				994	<li>
				995
				996	<p>Example:</p>
				997	</li>
				998	<li>Command:
				999
				1000	<div>
				1001	<div>
				1002	<pre class="source">st_crosses(st_geom_from_text('LINESTRING(1 1,2 2,3 3,4 4, 5 5,6 6)'), st_geom_from_text('LINESTRING(0 2,1 2,2 2,3 2,4 2,5 2)'));
				1003	</pre></div></div>
				1004	</li>
				1005	<li>Result:
				1006
				1007	<div>
				1008	<div>
				1009	<pre class="source">true
				1010	</pre></div></div>
				1011	</li>
				1012	</ul></div>
				1013	<div class="section">
				1014	<h3><a name="st_disjoint"></a>st_disjoint</h3>
				1015	<ul>
				1016
				1017	<li>
				1018
				1019	<p>Return TRUE if the Geometries do not “spatially intersect” - if they do not share any space together.</p>
				1020	</li>
				1021	<li>
				1022
				1023	<p>Example:</p>
				1024	</li>
				1025	<li>Command:
				1026
				1027	<div>
				1028	<div>
				1029	<pre class="source">st_disjoint(st_geom_from_text('LINESTRING(1 1,2 2,3 3,4 4, 5 5,6 6)'), st_geom_from_text('POINT(0 0)'));
				1030	</pre></div></div>
				1031	</li>
				1032	<li>Result:
				1033
				1034	<div>
				1035	<div>
				1036	<pre class="source">true
				1037	</pre></div></div>
				1038	</li>
				1039	</ul></div>
				1040	<div class="section">
				1041	<h3><a name="st_equals"></a>st_equals</h3>
				1042	<ul>
				1043
				1044	<li>
				1045
				1046	<p>Return true if the given geometries represent the same geometry. Directionality is ignored.</p>
				1047	</li>
				1048	<li>
				1049
				1050	<p>Example:</p>
				1051	</li>
				1052	<li>Command:
				1053
				1054	<div>
				1055	<div>
				1056	<pre class="source">st_equals(st_geom_from_text('LINESTRING(0 0, 10 10)'), st_geom_from_text('LINESTRING(0 0, 5 5, 10 10)'));
				1057	</pre></div></div>
				1058	</li>
				1059	<li>Result:
				1060
				1061	<div>
				1062	<div>
				1063	<pre class="source">true
				1064	</pre></div></div>
				1065	</li>
				1066	</ul></div>
				1067	<div class="section">
				1068	<h3><a name="st_overlaps"></a>st_overlaps</h3>
				1069	<ul>
				1070
				1071	<li>
				1072
				1073	<p>Return TRUE if the Geometries share space, are of the same dimension, but are not completely contained by each other.</p>
				1074	</li>
				1075	<li>
				1076
				1077	<p>Example:</p>
				1078	</li>
				1079	<li>Command:
				1080
				1081	<div>
				1082	<div>
				1083	<pre class="source">st_overlaps(st_geom_from_text('LINESTRING(1 1,2 2,3 3,4 4, 5 5,6 6)'), st_geom_from_text('LINESTRING(0 2,1 2,2 2,3 3,4 2,5 2)'));
				1084	</pre></div></div>
				1085	</li>
				1086	<li>Result:
				1087
				1088	<div>
				1089	<div>
				1090	<pre class="source">true
				1091	</pre></div></div>
				1092	</li>
				1093	</ul></div>
				1094	<div class="section">
				1095	<h3><a name="st_relate"></a>st_relate</h3>
				1096	<ul>
				1097
				1098	<li>
				1099
				1100	<p>Return true if this Geometry is spatially related to anotherGeometry, by testing for intersections between the Interior, Boundary and Exterior of the two geometries as specified by the values in the intersectionMatrixPattern.</p>
				1101	</li>
				1102	<li>
				1103
				1104	<p>Example:</p>
				1105	</li>
				1106	<li>Command:
				1107
				1108	<div>
				1109	<div>
				1110	<pre class="source">st_relate(st_geom_from_text('LINESTRING(1 2, 3 4)'), st_geom_from_text('LINESTRING(5 6, 7 8)'), "FF1FF0102");
				1111	</pre></div></div>
				1112	</li>
				1113	<li>Result:
				1114
				1115	<div>
				1116	<div>
				1117	<pre class="source">true
				1118	</pre></div></div>
				1119	</li>
				1120	</ul></div>
				1121	<div class="section">
				1122	<h3><a name="st_touches"></a>st_touches</h3>
				1123	<ul>
				1124
				1125	<li>
				1126
				1127	<p>Return TRUE if the geometries have at least one point in common, but their interiors do not intersect.</p>
				1128	</li>
				1129	<li>
				1130
				1131	<p>Example:</p>
				1132	</li>
				1133	<li>Command:
				1134
				1135	<div>
				1136	<div>
				1137	<pre class="source">st_touches(st_geom_from_text('LINESTRING(0 0, 1 1, 0 2)'), st_geom_from_text('POINT(0 2)'));
				1138	</pre></div></div>
				1139	</li>
				1140	<li>Result:
				1141
				1142	<div>
				1143	<div>
				1144	<pre class="source">true
				1145	</pre></div></div>
				1146	</li>
				1147	</ul></div>
				1148	<div class="section">
				1149	<h3><a name="st_within"></a>st_within</h3>
				1150	<ul>
				1151
				1152	<li>Return true if the geometry A is completely inside geometry B.</li>
				1153	</ul></div></div>
				1154	<div class="section">
				1155	<h2><a name="Spatial_Analysis"></a><a name="analysis" id="analysis">Spatial Analysis</a></h2>
				1156	<p>Spatial analysis functions take as input one or more geometries and return a geometry as output.</p>
				1157	<div class="section">
				1158	<h3><a name="st_union"></a>st_union</h3>
				1159	<ul>
				1160
				1161	<li>
				1162
				1163	<p>Return a geometry that represents the point set union of the Geometries.</p>
				1164	</li>
				1165	<li>
				1166
				1167	<p>Example:</p>
				1168	</li>
				1169	<li>Command:
				1170
				1171	<div>
				1172	<div>
				1173	<pre class="source">st_union(st_geom_from_text('LINESTRING(0 0, 1 1, 0 2)'), st_geom_from_text('POINT(0 2)'));
				1174	</pre></div></div>
				1175	</li>
				1176	<li>Result:
				1177
				1178	<div>
				1179	<div>
				1180	<pre class="source">{"type":"LineString","coordinates":[[0,0],[1,1],[0,2]],"crs":{"type":"name","properties":{"name":"EPSG:4326"}}}
				1181	</pre></div></div>
				1182	</li>
				1183	</ul></div>
				1184	<div class="section">
				1185	<h3><a name="st_boundary"></a>st_boundary</h3>
				1186	<ul>
				1187
				1188	<li>
				1189
				1190	<p>Return the closure of the combinatorial boundary of this Geometry.</p>
				1191	</li>
				1192	<li>
				1193
				1194	<p>Example:</p>
				1195	</li>
				1196	<li>Command:
				1197
				1198	<div>
				1199	<div>
				1200	<pre class="source">st_boundary(st_geom_from_text('POLYGON((1 1,0 0, -1 1, 1 1))'));
				1201	</pre></div></div>
				1202	</li>
				1203	<li>Result:
				1204
				1205	<div>
				1206	<div>
				1207	<pre class="source">{"type":"MultiLineString","coordinates":[[[1,1],[-1,1],[0,0],[1,1]]],"crs":null}
				1208	</pre></div></div>
				1209	</li>
				1210	</ul></div>
				1211	<div class="section">
				1212	<h3><a name="st_end_point"></a>st_end_point</h3>
				1213	<ul>
				1214
				1215	<li>
				1216
				1217	<p>Return the last point of a LINESTRING or CIRCULARLINESTRING geometry as a POINT.</p>
				1218	</li>
				1219	<li>
				1220
				1221	<p>Example:</p>
				1222	</li>
				1223	<li>Command:
				1224
				1225	<div>
				1226	<div>
				1227	<pre class="source">st_end_point(st_geom_from_text('LINESTRING(1 1, 2 2, 3 3)'));
				1228	</pre></div></div>
				1229	</li>
				1230	<li>Result:
				1231
				1232	<div>
				1233	<div>
				1234	<pre class="source">{"type":"Point","coordinates":[3,3],"crs":{"type":"name","properties":{"name":"EPSG:4326"}}}
				1235	</pre></div></div>
				1236	</li>
				1237	</ul></div>
				1238	<div class="section">
				1239	<h3><a name="st_envelope"></a>st_envelope</h3>
				1240	<ul>
				1241
				1242	<li>
				1243
				1244	<p>Return a geometry representing the double precision (float8) bounding box of the supplied geometry.</p>
				1245	</li>
				1246	<li>
				1247
				1248	<p>Example:</p>
				1249	</li>
				1250	<li>Command:
				1251
				1252	<div>
				1253	<div>
				1254	<pre class="source">st_envelope(st_geom_from_text('LINESTRING(1 1, 2 2, 3 3)'));
				1255	</pre></div></div>
				1256	</li>
				1257	<li>Result:
				1258
				1259	<div>
				1260	<div>
				1261	<pre class="source">{"type":"Polygon","coordinates":[[[1,1],[3,1],[3,3],[1,3],[1,1]]],"crs":{"type":"name","properties":{"name":"EPSG:4326"}}}
				1262	</pre></div></div>
				1263	</li>
				1264	</ul></div>
				1265	<div class="section">
				1266	<h3><a name="st_exterior_ring"></a>st_exterior_ring</h3>
				1267	<ul>
				1268
				1269	<li>
				1270
				1271	<p>Return a line string representing the exterior ring of the POLYGON geometry. Return NULL if the geometry is not a polygon. Will not work with MULTIPOLYGON.</p>
				1272	</li>
				1273	<li>
				1274
				1275	<p>Example:</p>
				1276	</li>
				1277	<li>Command:
				1278
				1279	<div>
				1280	<div>
				1281	<pre class="source">st_exterior_ring(st_geom_from_text("POLYGON ((35 10, 45 45, 15 40, 10 20, 35 10),(20 30, 35 35, 30 20, 20 30))"));
				1282	</pre></div></div>
				1283	</li>
				1284	<li>Result:
				1285
				1286	<div>
				1287	<div>
				1288	<pre class="source">{"type":"LineString","coordinates":[[35,10],[45,45],[15,40],[10,20],[35,10]],"crs":{"type":"name","properties":{"name":"EPSG:4326"}}}
				1289	</pre></div></div>
				1290	</li>
				1291	</ul></div>
				1292	<div class="section">
				1293	<h3><a name="st_geometry_n"></a>st_geometry_n</h3>
				1294	<ul>
				1295
				1296	<li>
				1297
				1298	<p>Return the 1-based Nth geometry if the geometry is a GEOMETRYCOLLECTION, (MULTI)POINT, (MULTI)LINESTRING, MULTICURVE or (MULTI)POLYGON, POLYHEDRALSURFACE. Otherwise, return NULL.</p>
				1299	</li>
				1300	<li>
				1301
				1302	<p>Example:</p>
				1303	</li>
				1304	<li>Command:
				1305
				1306	<div>
				1307	<div>
				1308	<pre class="source">st_geometry_n(st_geom_from_text('GEOMETRYCOLLECTION(MULTIPOINT(-2 3 , -2 2),LINESTRING(5 5 ,10 10),POLYGON((-7 4.2,-7.1 5,-7.1 4.3,-7 4.2)))'),2);
				1309	</pre></div></div>
				1310	</li>
				1311	<li>Result:
				1312
				1313	<div>
				1314	<div>
				1315	<pre class="source">{"type":"Polygon","coordinates":[[[-7,4.2],[-7.1,5],[-7.1,4.3],[-7,4.2]]],"crs":{"type":"name","properties":{"name":"EPSG:4326"}}}
				1316	</pre></div></div>
				1317	</li>
				1318	</ul></div>
				1319	<div class="section">
				1320	<h3><a name="st_interior_ring_n"></a>st_interior_ring_n</h3>
				1321	<ul>
				1322
				1323	<li>
				1324
				1325	<p>Return the Nth interior linestring ring of the polygon geometry. Return NULL if the geometry is not a polygon or the given N is out of range.</p>
				1326	</li>
				1327	<li>
				1328
				1329	<p>Example:</p>
				1330	</li>
				1331	<li>Command:
				1332
				1333	<div>
				1334	<div>
				1335	<pre class="source">st_interior_ring_n(st_geom_from_text("POLYGON ((35 10, 45 45, 15 40, 10 20, 35 10),(20 30, 35 35, 30 20, 20 30))"), 0);
				1336	</pre></div></div>
				1337	</li>
				1338	<li>Result:
				1339
				1340	<div>
				1341	<div>
				1342	<pre class="source">{"type":"LineString","coordinates":[[20,30],[35,35],[30,20],[20,30]],"crs":{"type":"name","properties":{"name":"EPSG:4326"}}}
				1343	</pre></div></div>
				1344	</li>
				1345	</ul></div>
				1346	<div class="section">
				1347	<h3><a name="st_point_n"></a>st_point_n</h3>
				1348	<ul>
				1349
				1350	<li>
				1351
				1352	<p>Return the Nth point in the first LineString or circular LineString in the geometry. Negative values are counted backwards from the end of the LineString. Return NULL if there is no linestring in the geometry.</p>
				1353	</li>
				1354	<li>
				1355
				1356	<p>Example:</p>
				1357	</li>
				1358	<li>Command:
				1359
				1360	<div>
				1361	<div>
				1362	<pre class="source">st_point_n(st_geom_from_text("LINESTRING(1 1, 2 2, 3 3)"), 1);
				1363	</pre></div></div>
				1364	</li>
				1365	<li>Result:
				1366
				1367	<div>
				1368	<div>
				1369	<pre class="source">{"type":"Point","coordinates":[2,2],"crs":{"type":"name","properties":{"name":"EPSG:4326"}}}
				1370	</pre></div></div>
				1371	</li>
				1372	</ul></div>
				1373	<div class="section">
				1374	<h3><a name="st_start_point"></a>st_start_point</h3>
				1375	<ul>
				1376
				1377	<li>
				1378
				1379	<p>Return the first point of a LINESTRING geometry as a POINT.</p>
				1380	</li>
				1381	<li>
				1382
				1383	<p>Example:</p>
				1384	</li>
				1385	<li>Command:
				1386
				1387	<div>
				1388	<div>
				1389	<pre class="source">st_start_point(st_geom_from_text("LINESTRING(1 1, 2 2, 3 3)"));
				1390	</pre></div></div>
				1391	</li>
				1392	<li>Result:
				1393
				1394	<div>
				1395	<div>
				1396	<pre class="source">{"type":"Point","coordinates":[1,1],"crs":{"type":"name","properties":{"name":"EPSG:4326"}}}
				1397	</pre></div></div>
				1398	</li>
				1399	</ul></div>
				1400	<div class="section">
				1401	<h3><a name="st_difference"></a>st_difference</h3>
				1402	<ul>
				1403
				1404	<li>
				1405
				1406	<p>Return a geometry that represents that part of geometry A that does not intersect with geometry B.</p>
				1407	</li>
				1408	<li>
				1409
				1410	<p>Example:</p>
				1411	</li>
				1412	<li>Command:
				1413
				1414	<div>
				1415	<div>
				1416	<pre class="source">st_difference(st_geom_from_text("LINESTRING(1 1, 2 2, 3 3)"), st_geom_from_text("POLYGON ((35 10, 45 45, 15 40, 10 20, 35 10),(20 30, 35 35, 30 20, 20 30))"));
				1417	</pre></div></div>
				1418	</li>
				1419	<li>Result:
				1420
				1421	<div>
				1422	<div>
				1423	<pre class="source">{"type":"LineString","coordinates":[[1,1],[2,2],[3,3]],"crs":{"type":"name","properties":{"name":"EPSG:4326"}}}
				1424	</pre></div></div>
				1425	</li>
				1426	</ul></div>
				1427	<div class="section">
				1428	<h3><a name="st_intersection"></a>st_intersection</h3>
				1429	<ul>
				1430
				1431	<li>
				1432
				1433	<p>Return a geometry that represents the shared portion of geomA and geomB.</p>
				1434	</li>
				1435	<li>
				1436
				1437	<p>Example:</p>
				1438	</li>
				1439	<li>Command:
				1440
				1441	<div>
				1442	<div>
				1443	<pre class="source">st_intersection(st_geom_from_text("LINESTRING(1 1,2 2,3 3,4 4, 5 5,6 6)"), st_geom_from_text("LINESTRING(0 2,1 2,2 2,3 3,4 2,5 2)"));
				1444	</pre></div></div>
				1445	</li>
				1446	<li>Result:
				1447
				1448	<div>
				1449	<div>
				1450	<pre class="source">{"type":"LineString","coordinates":[[2,2],[3,3]],"crs":{"type":"name","properties":{"name":"EPSG:4326"}}}
				1451	</pre></div></div>
				1452	</li>
				1453	</ul></div>
				1454	<div class="section">
				1455	<h3><a name="st_sym_difference"></a>st_sym_difference</h3>
				1456	<ul>
				1457
				1458	<li>
				1459
				1460	<p>Return a geometry that represents the portions of A and B that do not intersect. It is called a symmetric difference because ST_SymDifference(A,B) = ST_SymDifference(B,A).</p>
				1461	</li>
				1462	<li>
				1463
				1464	<p>Example:</p>
				1465	</li>
				1466	<li>Command:
				1467
				1468	<div>
				1469	<div>
				1470	<pre class="source">st_sym_difference(st_geom_from_text("LINESTRING(1 1,2 2,3 3,4 4, 5 5,6 6)"), st_geom_from_text("LINESTRING(0 2,1 2,2 2,3 3,4 2,5 2)"));
				1471	</pre></div></div>
				1472	</li>
				1473	<li>Result:
				1474
				1475	<div>
				1476	<div>
				1477	<pre class="source">{"type":"MultiLineString","coordinates":[[[0,2],[1,2],[2,2],[1,1]],[[5,2],[4,2],[3,3],[4,4],[5,5],[6,6]]],"crs":null}
				1478	</pre></div></div>
				1479	</li>
				1480	</ul></div>
				1481	<div class="section">
				1482	<h3><a name="st_polygonize"></a>st_polygonize</h3>
				1483	<ul>
				1484
				1485	<li>
				1486
				1487	<p>Aggregate. Creates a GeometryCollection containing possible polygons formed from the constituent linework of a set of geometries.</p>
				1488	</li>
				1489	<li>
				1490
				1491	<p>Example:</p>
				1492	</li>
				1493	<li>Command:
				1494
				1495	<div>
				1496	<div>
				1497	<pre class="source">st_polygonize([st_geom_from_text("LINESTRING(1 1,2 2,3 3,4 4, 5 5,6 6)"), st_geom_from_text("LINESTRING(0 2,1 2,2 2,3 3,4 2,5 2)")]);
				1498	</pre></div></div>
				1499	</li>
				1500	<li>Result:
				1501
				1502	<div>
				1503	<div>
				1504	<pre class="source">{"type":"GeometryCollection","geometries":[{"type":"LineString","coordinates":[[1,1],[2,2],[3,3],[4,4],[5,5],[6,6]]},{"type":"LineString","coordinates":[[0,2],[1,2],[2,2],[3,3],[4,2],[5,2]]}],"crs":{"type":"name","properties":{"name":"EPSG:4326"}}}
				1505	</pre></div></div>
				1506	</li>
				1507	</ul></div></div>
				1508	<div class="section">
				1509	<h2><a name="Spatial_Aggregates"></a><a name="aggregate" id="aggregate">Spatial Aggregates</a></h2>
				1510	<p>spatial aggregate function which takes as input a set of geometries and return one geometry as the result.</p>
				1511	<div class="section">
				1512	<h3><a name="st_union"></a>st_union</h3>
				1513	<ul>
				1514
				1515	<li>
				1516
				1517	<p>Returns a geometry that represents the point set union of the Geometries.</p>
				1518	</li>
				1519	<li>
				1520
				1521	<p>Example:</p>
				1522	</li>
				1523	<li>Command:
				1524
				1525	<div>
				1526	<div>
				1527	<pre class="source">st_union((SELECT VALUE gbu FROM [st_make_point(1.0,1.0),st_make_point(1.0,2.0)] as gbu));
				1528	</pre></div></div>
				1529	</li>
				1530	<li>Result:
				1531
				1532	<div>
				1533	<div>
				1534	<pre class="source">{"type":"MultiPoint","coordinates":[[1,1],[1,2]],"crs":{"type":"name","properties":{"name":"EPSG:4326"}}}
				1535	</pre></div></div>
				1536	</li>
				1537	</ul></div></div>
				1538	</div>
				1539	</div>
				1540	</div>
				1541	<hr/>
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				1543	<div class="container-fluid">
				1544	<div class="row-fluid">
				1545	<div class="row-fluid">Apache AsterixDB, AsterixDB, Apache, the Apache
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				1547	registered trademarks or trademarks of The Apache Software
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				1549	All other marks mentioned may be trademarks or registered
				1550	trademarks of their respective owners.
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