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Geo Functions

This module contains functions that may be applied to geometry data conforming to the Open Geospatial Consortium (OGC) Simple Feature (SF) data model. It is based on the EXPath Geo Module and uses the JTS and GeoTools libraries.

The module supports geometries encoded in GML 2 and GML 3.2. The distinction is determined by the namespace of the input document. Geometries in the namespace http://www.opengis.net/gml/3.2 are processed as GML 3.2 and handled internally by the GeoTools XML parser. All other documents are treated as GML 2 and processed using the JTS GML reader. The GML 2 namespace is http://www.opengis.net/gml.

Functions that return GML elements preserve the input version: if the input geometry is GML 2, results are returned in GML 2; if the input geometry is GML 3.2, results are returned in GML 3.2.

For GML 2 input, the following geometry types are accepted: Point, LineString, LinearRing, Polygon, MultiPoint, MultiLineString, MultiPolygon. All nodes passed to the Geo functions must represent a valid geometry. The geometry type MultiGeometry is not supported. Note: Some operations may still produce a MultiGeometry element as a result (e.g., from set-like operations), even though MultiGeometry is not accepted as an input geometry.

For GML 3.2 input, the following geometry types are accepted: Point, LineString, LinearRing, Polygon, MultiPoint, MultiCurve, MultiSurface, MultiGeometry. All nodes passed to the Geo functions must represent a valid geometry.

Conventions

The module must be installed in the repository before it can be used:

REPO INSTALL https://files.basex.org/modules/expath/geo-12.2.jar

In order to use it, it needs to be imported in the header of the query:

import module namespace geo = 'http://expath.org/ns/geo';

All functions in this module are assigned to the http://expath.org/ns/geo namespace, which in the following is assumed to be bound to the geo prefix.

All errors are assigned to the http://expath.org/ns/error namespace, which is statically bound to the experr prefix.

General Functions

`geo:dimension`

Signature

geo:dimension(
  $geometry  as element(*)
) as xs:integer

Summary Returns the number of dimensions of the supplied geometry $geometry.

Errors

`GEO0001`	The supplied element is not recognized as a valid geometry.
`GEO0002`	The supplied geometry cannot be read by the underlying geometry reader.

Examples

import module namespace geo = 'http://expath.org/ns/geo';
declare namespace gml = 'http://www.opengis.net/gml';

geo:dimension(
  <gml:Point>
    <gml:coordinates>1,2</gml:coordinates>
  </gml:Point>
)

Returns the dimension of a GML Point geometry.

`geo:geometry-type`

Signature

geo:geometry-type(
  $geometry  as element(*)
) as xs:QName

Summary Returns the name of the geometry type of the supplied geometry $geometry. If the geometry is not recognized, an error is raised.

Errors

`GEO0001`	The supplied element is not recognized as a valid geometry.
`GEO0002`	The supplied geometry cannot be read by the underlying geometry reader.

Examples

import module namespace geo = 'http://expath.org/ns/geo';
declare namespace gml = 'http://www.opengis.net/gml';

geo:geometry-type(
  <gml:Point>
    <gml:coordinates>1,2</gml:coordinates>
  </gml:Point>
)

Returns the geometry type name of a GML Point.

`geo:srid`

Signature

geo:srid(
  $geometry  as element(*)
) as xs:integer

Summary

Returns the ID of the Spatial Reference System used by the supplied geometry $geometry. Spatial Reference System information is supported in the simple way defined in the SFS: an SRID is present in each geometry object and can be accessed via basic accessor operations. The SRID is represented as an integer (based on the OpenGIS Simple Features Specifications for SQL).

This differs from the EXPath Geo Module specification, which returns a URI.

Errors

`GEO0001`	The supplied element is not recognized as a valid geometry.
`GEO0002`	The supplied geometry cannot be read by the underlying geometry reader.

Examples

import module namespace geo = 'http://expath.org/ns/geo';
declare namespace gml = 'http://www.opengis.net/gml';

geo:srid(
  <gml:Polygon>
    <outerboundaryIs>
      <gml:LinearRing>
        <coordinates>
          -150,50 -150,60 -125,60 -125,50 -150,50
        </coordinates>
      </gml:LinearRing>
    </outerboundaryIs>
  </gml:Polygon>
)

Returns the SRID of a polygon geometry.

`geo:envelope`

Signature

geo:envelope(
  $geometry  as element(*)
) as element(*)

Summary Returns the gml:Envelope of the supplied geometry $geometry. The envelope is the minimum bounding box of this geometry. If the geometry is empty, an empty Point is returned. If the geometry is a point, a non-empty Point is returned. Otherwise, a Polygon is returned whose points are (minx, miny), (maxx, miny), (maxx, maxy), (minx, maxy), (minx, miny).

Errors

`GEO0001`	The supplied element is not recognized as a valid geometry.
`GEO0002`	The supplied geometry cannot be read by the underlying geometry reader.
`GEO0005`	The output object cannot be written as an element by the underlying geometry writer.

Examples

import module namespace geo = 'http://expath.org/ns/geo';
declare namespace gml = 'http://www.opengis.net/gml';

geo:envelope(
  <gml:LinearRing>
    <gml:coordinates>1,1 20,1 20,20 1,20 1,1</gml:coordinates>
  </gml:LinearRing>
)

Returns the bounding box of a linear ring geometry.

`geo:as-text`

Signature

geo:as-text(
  $geometry  as element(*)
) as xs:string

Summary Returns the WKT (Well-known Text) representation of the supplied geometry $geometry.

Errors

`GEO0001`	The supplied element is not recognized as a valid geometry.
`GEO0002`	The supplied geometry cannot be read by the underlying geometry reader.

Examples

import module namespace geo = 'http://expath.org/ns/geo';
declare namespace gml = 'http://www.opengis.net/gml';

geo:as-text(
  <gml:Point>
    <gml:coordinates>1,2</gml:coordinates>
  </gml:Point>
)

Returns the WKT representation of a point geometry.

`geo:as-binary`

Signature

geo:as-binary(
  $geometry  as element(*)
) as xs:base64Binary

Summary Returns the WKB (Well-known Binary) representation of the supplied geometry $geometry.

Errors

`GEO0001`	The supplied element is not recognized as a valid geometry.
`GEO0002`	The supplied geometry cannot be read by the underlying geometry reader.

Examples

import module namespace geo = 'http://expath.org/ns/geo';
declare namespace gml = 'http://www.opengis.net/gml';

geo:as-binary(
  <gml:Point>
    <gml:coordinates>1,2</gml:coordinates>
  </gml:Point>
)

Returns the WKB representation of a point geometry.

`geo:is-simple`

Signature

geo:is-simple(
  $geometry  as element(*)
) as xs:boolean

Summary Returns whether the supplied geometry $geometry is simple and has no anomalous geometric points (i.e., it does not self-intersect and does not pass through the same point more than once (may be a ring)).

Errors

`GEO0001`	The supplied element is not recognized as a valid geometry.
`GEO0002`	The supplied geometry cannot be read by the underlying geometry reader.

Examples

import module namespace geo = 'http://expath.org/ns/geo';
declare namespace gml = 'http://www.opengis.net/gml';

geo:is-simple(
  <gml:MultiLineString>
    <gml:LineString>
      <gml:coordinates>1,1 0,0 2,1</gml:coordinates>
    </gml:LineString>
    <gml:LineString>
      <gml:coordinates>2,1 3,3 4,4</gml:coordinates>
    </gml:LineString>
  </gml:MultiLineString>
)

Checks if a multilinestring geometry is simple.

`geo:boundary`

Signature

geo:boundary(
  $geometry  as element(*)
) as element(*)?

Summary Returns the boundary of the supplied geometry $geometry, in GML. The result is a sequence of either gml:Point or gml:LinearRing elements as a GeometryCollection object. For a Point or MultiPoint, the boundary is empty, and the empty sequence is returned.

Errors

`GEO0001`	The supplied element is not recognized as a valid geometry.
`GEO0002`	The supplied geometry cannot be read by the underlying geometry reader.
`GEO0005`	The output object cannot be written as an element by the underlying geometry writer.

Examples

import module namespace geo = 'http://expath.org/ns/geo';
declare namespace gml = 'http://www.opengis.net/gml';

geo:boundary(
  <gml:LineString>
    <gml:coordinates>1,1 0,0 2,1</gml:coordinates>
  </gml:LineString>
)

Returns the boundary of a linestring geometry.

`geo:num-geometries`

Signature

geo:num-geometries(
  $geometry  as element(*)
) as xs:integer

Summary

Returns the number of geometries in the geometry collection $geometry, in GML. For geometries that are not collections, 1 is returned.

This implementation is broader than the EXPath specification: it accepts all geometry types, whereas the specification limits the input to collection types (MultiPoint, MultiPolygon, ...).

Errors

`GEO0001`	The supplied element is not recognized as a valid geometry.
`GEO0002`	The supplied geometry cannot be read by the underlying geometry reader.

Examples

import module namespace geo = 'http://expath.org/ns/geo';
declare namespace gml = 'http://www.opengis.net/gml';

geo:num-geometries(
  <gml:MultiLineString>
    <gml:LineString>
      <gml:coordinates>1,1 0,0 2,1</gml:coordinates>
    </gml:LineString>
    <gml:LineString>
      <gml:coordinates>2,1 3,3 4,4</gml:coordinates>
    </gml:LineString>
  </gml:MultiLineString>
)

Returns the number of geometries in a multilinestring.

`geo:geometry-n`

Signature

geo:geometry-n(
  $geometry  as element(*),
  $n         as xs:integer
) as element(*)?

Summary

Returns the Nth geometry in the geometry collection $geometry, in GML. For geometries that are not collections, the geometry itself is returned if $n is 1.

This implementation is broader than the EXPath specification: it accepts all geometry types, whereas the specification limits the input to collection types (MultiPoint, MultiPolygon, ...).

Errors

`GEO0001`	The supplied element is not recognized as a valid geometry.
`GEO0002`	The supplied geometry cannot be read by the underlying geometry reader.
`GEO0004`	The supplied geometry index is out of range.
`GEO0005`	The output object cannot be written as an element by the underlying geometry writer.

Examples

import module namespace geo = 'http://expath.org/ns/geo';
declare namespace gml = 'http://www.opengis.net/gml';

let $line :=
  <gml:MultiLineString>
    <gml:LineString>
      <gml:coordinates>1,1 0,0 2,1</gml:coordinates>
    </gml:LineString>
    <gml:LineString>
      <gml:coordinates>2,1 3,3 4,4</gml:coordinates>
    </gml:LineString>
  </gml:MultiLineString>
return geo:geometry-n($line, 1)

Returns the first geometry of a multilinestring.

`geo:length`

Signature

geo:length(
  $geometry  as element(*)
) as xs:double

Summary Returns the length of the supplied geometry $geometry. If the geometry is a point, 0 is returned.

Errors

`GEO0001`	The supplied element is not recognized as a valid geometry.
`GEO0002`	The supplied geometry cannot be read by the underlying geometry reader.

Examples

import module namespace geo = 'http://expath.org/ns/geo';
declare namespace gml = 'http://www.opengis.net/gml';

let $polygon :=
  <gml:Polygon>
    <gml:outerBoundaryIs>
      <gml:LinearRing>
        <gml:coordinates>1,1 2,1 2,2 1,2 1,1</gml:coordinates>
      </gml:LinearRing>
    </gml:outerBoundaryIs>
  </gml:Polygon>
return geo:length($polygon)

Returns the length of a polygon geometry.

`geo:num-points`

Signature

geo:num-points(
  $geometry  as element(*)
) as xs:integer

Summary

Returns the number of points in the supplied geometry $geometry. It can be used not only for lines, but also for other geometry types such as MultiPolygon. For a Point geometry, 1 is returned.

This differs from the EXPath Geo specification, which limits the input geometry type to lines.

Errors

`GEO0001`	The supplied element is not recognized as a valid geometry.
`GEO0002`	The supplied geometry cannot be read by the underlying geometry reader.

Examples

import module namespace geo = 'http://expath.org/ns/geo';
declare namespace gml = 'http://www.opengis.net/gml';

geo:num-points(
  <gml:LineString>
    <gml:coordinates>2,1 3,3 4,4</gml:coordinates>
  </gml:LineString>
)

Returns the number of points in a linestring.

`geo:area`

Signature

geo:area(
  $geometry  as element(*)
) as xs:double

Summary Returns the area of the supplied geometry $geometry. For points and lines, 0 is returned.

Errors

`GEO0001`	The supplied element is not recognized as a valid geometry.
`GEO0002`	The supplied geometry cannot be read by the underlying geometry reader.

Examples

import module namespace geo = 'http://expath.org/ns/geo';
declare namespace gml = 'http://www.opengis.net/gml';

let $polygon :=
  <gml:Polygon>
    <gml:outerBoundaryIs>
      <gml:LinearRing>
        <gml:coordinates>1,1 2,1 2,2 1,2 1,1</gml:coordinates>
      </gml:LinearRing>
    </gml:outerBoundaryIs>
  </gml:Polygon>
return geo:area($polygon)

Returns the area of a polygon geometry.

`geo:centroid`

Signature

geo:centroid(
  $geometry  as element(*)
) as element(*)

Summary Returns the mathematical centroid of the supplied geometry $geometry, as a gml:Point. Based on the definition, this point is not always located on the surface of the geometry.

Errors

`GEO0001`	The supplied element is not recognized as a valid geometry.
`GEO0002`	The supplied geometry cannot be read by the underlying geometry reader.
`GEO0005`	The output object cannot be written as an element by the underlying geometry writer.

Examples

import module namespace geo = 'http://expath.org/ns/geo';
declare namespace gml = 'http://www.opengis.net/gml';

let $point :=
  <gml:MultiPoint>
    <gml:Point><gml:coordinates>1,1</gml:coordinates></gml:Point>
    <gml:Point><gml:coordinates>10,10</gml:coordinates></gml:Point>
    <gml:Point><gml:coordinates>2,2</gml:coordinates></gml:Point>
  </gml:MultiPoint>
return geo:centroid($point)

Returns the centroid of a multipoint geometry.

`geo:point-on-surface`

Signature

geo:point-on-surface(
  $geometry  as element(*)
) as element(*)

Summary Computes an interior point of the supplied geometry $geometry, as a gml:Point. An interior point is guaranteed to lie in the interior of the Geometry, if it possible to calculate such a point exactly. Otherwise, the point may lie on the boundary of the geometry.

Errors

`GEO0001`	The supplied element is not recognized as a valid geometry.
`GEO0002`	The supplied geometry cannot be read by the underlying geometry reader.
`GEO0005`	The output object cannot be written as an element by the underlying geometry writer.

Examples

import module namespace geo = 'http://expath.org/ns/geo';
declare namespace gml = 'http://www.opengis.net/gml';

geo:point-on-surface(
  <gml:Polygon>
    <gml:outerBoundaryIs>
      <gml:LinearRing>
        <gml:coordinates>1,1 2,1 2,2 1,2 1,1</gml:coordinates>
      </gml:LinearRing>
    </gml:outerBoundaryIs>
  </gml:Polygon>
)

Returns a point on the surface of a polygon geometry.

Spatial Predicate Functions

`geo:equals`

Signature

geo:equals(
  $geometry1  as element(*),
  $geometry2  as element(*)
) as xs:boolean

Summary Returns whether $geometry1 is spatially equal to $geometry2.

Errors

`GEO0001`	The supplied element is not recognized as a valid geometry.
`GEO0002`	The supplied geometry cannot be read by the underlying geometry reader.

Examples

import module namespace geo = 'http://expath.org/ns/geo';
declare namespace gml = 'http://www.opengis.net/gml';

geo:equals(
  <gml:LineString><gml:coordinates>1,1 55,99 2,1</gml:coordinates></gml:LineString>,
  <gml:LineString><gml:coordinates>1,1 1,1 55,99 2,1</gml:coordinates></gml:LineString>
)

Checks if two linestring geometries are spatially equal.

`geo:disjoint`

Signature

geo:disjoint(
  $geometry1  as element(*),
  $geometry2  as element(*)
) as xs:boolean

Summary Returns whether $geometry1 is spatially disjoint from $geometry2 (they have no point in common, they do not intersect each other, and the DE-9IM intersection matrix is FF*FF****).

Errors

`GEO0001`	The supplied element is not recognized as a valid geometry.
`GEO0002`	The supplied geometry cannot be read by the underlying geometry reader.

Examples

import module namespace geo = 'http://expath.org/ns/geo';
declare namespace gml = 'http://www.opengis.net/gml';

let $lines :=
  <gml:MultiLineString>
    <gml:LineString><gml:coordinates>1,1 0,0 2,1</gml:coordinates></gml:LineString>
    <gml:LineString><gml:coordinates>2,1 3,3 4,4</gml:coordinates></gml:LineString>
  </gml:MultiLineString>
let $line :=
  <gml:LineString><gml:coordinates>0,0 2,1 3,3</gml:coordinates></gml:LineString>
return geo:disjoint($lines, $line)

Checks whether a multilinestring and a linestring are disjoint.

`geo:intersects`

Signature

geo:intersects(
  $geometry1  as element(*),
  $geometry2  as element(*)
) as xs:boolean

Summary Returns whether $geometry1 intersects $geometry2. This is true if the two geometries are not disjoint.

Errors

`GEO0001`	The supplied element is not recognized as a valid geometry.
`GEO0002`	The supplied geometry cannot be read by the underlying geometry reader.

Examples

import module namespace geo = 'http://expath.org/ns/geo';
declare namespace gml = 'http://www.opengis.net/gml';

let $lines :=
  <gml:MultiLineString>
    <gml:LineString><gml:coordinates>1,1 0,0 2,1</gml:coordinates></gml:LineString>
    <gml:LineString><gml:coordinates>2,1 3,3 4,4</gml:coordinates></gml:LineString>
  </gml:MultiLineString>
let $line :=
  <gml:LineString><gml:coordinates>0,0 2,1 3,3</gml:coordinates></gml:LineString>
return geo:intersects($lines, $line)

Checks whether a multilinestring and a linestring intersect.

`geo:touches`

Signature

geo:touches(
  $geometry1  as element(*),
  $geometry2  as element(*)
) as xs:boolean

Summary Returns whether $geometry1 spatially touches $geometry2.

Errors

`GEO0001`	The supplied element is not recognized as a valid geometry.
`GEO0002`	The supplied geometry cannot be read by the underlying geometry reader.

Examples

import module namespace geo = 'http://expath.org/ns/geo';
declare namespace gml = 'http://www.opengis.net/gml';

let $line :=
  <gml:LinearRing><gml:coordinates>1,1 2,1 5,3 1,1</gml:coordinates></gml:LinearRing>
let $polygon :=
  <gml:Polygon>
    <gml:outerBoundaryIs>
      <gml:LinearRing><gml:coordinates>1,1 2,1 5,3 1,1</gml:coordinates></gml:LinearRing>
    </gml:outerBoundaryIs>
  </gml:Polygon>
return geo:touches($line, $polygon)

Checks whether a ring touches a polygon.

`geo:crosses`

Signature

geo:crosses(
  $geometry1  as element(*),
  $geometry2  as element(*)
) as xs:boolean

Summary

Returns whether $geometry1 spatially crosses $geometry2, i.e., the geometries have some but not all interior points in common. Returns true if the DE-9IM intersection matrix matches one of the following patterns:

T*T****** (for P/L, P/A, and L/A situations)

T*****T** (for L/P, A/P, and A/L situations)

0******** (for L/L situations)

Errors

`GEO0001`	The supplied element is not recognized as a valid geometry.
`GEO0002`	The supplied geometry cannot be read by the underlying geometry reader.

Examples

import module namespace geo = 'http://expath.org/ns/geo';
declare namespace gml = 'http://www.opengis.net/gml';

let $line :=
  <gml:LinearRing><gml:coordinates>1,1 2,1 5,3 1,1</gml:coordinates></gml:LinearRing>
let $polygon :=
  <gml:Polygon>
    <gml:outerBoundaryIs>
      <gml:LinearRing><gml:coordinates>1,1 2,1 5,3 1,1</gml:coordinates></gml:LinearRing>
    </gml:outerBoundaryIs>
  </gml:Polygon>
return geo:crosses($line, $polygon)

Checks whether a ring crosses a polygon.

`geo:within`

Signature

geo:within(
  $geometry1  as element(*),
  $geometry2  as element(*)
) as xs:boolean

Summary Returns whether $geometry1 is spatially within $geometry2.

Errors

`GEO0001`	The supplied element is not recognized as a valid geometry.
`GEO0002`	The supplied geometry cannot be read by the underlying geometry reader.

Examples

import module namespace geo = 'http://expath.org/ns/geo';
declare namespace gml = 'http://www.opengis.net/gml';

let $line :=
  <gml:LinearRing><gml:coordinates>1,1 2,1 5,3 1,1</gml:coordinates></gml:LinearRing>
let $polygon :=
  <gml:Polygon>
    <gml:outerBoundaryIs>
      <gml:LinearRing><gml:coordinates>1,1 2,1 5,3 1,1</gml:coordinates></gml:LinearRing>
    </gml:outerBoundaryIs>
  </gml:Polygon>
return geo:within($line, $polygon)

Checks whether a ring is within a polygon.

`geo:contains`

Signature

geo:contains(
  $geometry1  as element(*),
  $geometry2  as element(*)
) as xs:boolean

Summary Returns whether $geometry1 spatially contains $geometry2. Returns true if geo:within($geometry2, $geometry1) is true.

Errors

`GEO0001`	The supplied element is not recognized as a valid geometry.
`GEO0002`	The supplied geometry cannot be read by the underlying geometry reader.

Examples

import module namespace geo = 'http://expath.org/ns/geo';
declare namespace gml = 'http://www.opengis.net/gml';

let $point :=
  <gml:Point><gml:coordinates>1,1</gml:coordinates></gml:Point>
let $polygon :=
  <gml:Polygon>
    <gml:outerBoundaryIs>
      <gml:LinearRing><gml:coordinates>1,1 2,1 5,3 1,1</gml:coordinates></gml:LinearRing>
    </gml:outerBoundaryIs>
  </gml:Polygon>
return geo:contains($polygon, $point)

Checks whether a polygon contains a point.

`geo:overlaps`

Signature

geo:overlaps(
  $geometry1  as element(*),
  $geometry2  as element(*)
) as xs:boolean

Summary Returns whether $geometry1 spatially overlaps $geometry2.

Errors

`GEO0001`	The supplied element is not recognized as a valid geometry.
`GEO0002`	The supplied geometry cannot be read by the underlying geometry reader.

Examples

import module namespace geo = 'http://expath.org/ns/geo';
declare namespace gml = 'http://www.opengis.net/gml';

let $polygon1 :=
  <gml:Polygon>
    <gml:outerBoundaryIs>
      <gml:LinearRing>
        <gml:coordinates>1,1 20,1 20,20 30,20 30,30 1,30 1,1</gml:coordinates>
      </gml:LinearRing>
    </gml:outerBoundaryIs>
    <gml:innerBoundaryIs>
      <gml:LinearRing>
        <gml:coordinates>2,2 3,2 3,3 2,3 2,2</gml:coordinates>
      </gml:LinearRing>
    </gml:innerBoundaryIs>
    <gml:innerBoundaryIs>
      <gml:LinearRing>
        <gml:coordinates>10,10 19,10 19,19 10,19 10,10</gml:coordinates>
      </gml:LinearRing>
    </gml:innerBoundaryIs>
  </gml:Polygon>

let $polygon2 :=
  <gml:Polygon>
    <gml:outerBoundaryIs>
      <gml:LinearRing>
        <gml:coordinates>1,1 2,1 5,3 1,1</gml:coordinates>
      </gml:LinearRing>
    </gml:outerBoundaryIs>
  </gml:Polygon>

return geo:overlaps($polygon1, $polygon2)

Checks whether two polygons overlap.

`geo:relate`

Signature

geo:relate(
  $geometry1           as element(*),
  $geometry2           as element(*),
  $intersectionMatrix  as xs:string
) as xs:boolean

Summary

Returns whether the relationships between the boundaries, interiors, and exteriors of $geometry1 and $geometry2 match the pattern specified in $intersectionMatrix. The matrix must have a length of 9 characters.

The values in the DE-9IM matrix can be:

T: the intersection is non-empty
F: the intersection is empty
*: any result
0, 1, 2: expected dimension of the intersection result (point, curve, surface)

Errors

`GEO0001`	The supplied element is not recognized as a valid geometry.
`GEO0002`	The supplied geometry cannot be read by the underlying geometry reader.
`GEO0006`	The supplied intersection matrix is invalid.

Examples

import module namespace geo = 'http://expath.org/ns/geo';
declare namespace gml = 'http://www.opengis.net/gml';

let $point :=
  <gml:Point><gml:coordinates>18,11</gml:coordinates></gml:Point>
let $polygon :=
  <gml:Polygon>
    <gml:outerBoundaryIs>
      <gml:LinearRing>
        <gml:coordinates>10,10 20,10 30,40 20,40 10,10</gml:coordinates>
      </gml:LinearRing>
    </gml:outerBoundaryIs>
  </gml:Polygon>

return geo:relate($point, $polygon, "TF*FFFTT*")

Checks a spatial relationship between a point and a polygon using a DE-9IM matrix pattern.

Analysis Functions

`geo:distance`

Signature

geo:distance(
  $geometry1  as element(*),
  $geometry2  as element(*)
) as xs:double

Summary Returns the shortest distance between $geometry1 and $geometry2, in the units of the spatial reference system of $geometry1. The distance is defined as the distance between a point on each of the geometries.

Errors

`GEO0001`	The supplied element is not recognized as a valid geometry.
`GEO0002`	The supplied geometry cannot be read by the underlying geometry reader.

Examples

import module namespace geo = 'http://expath.org/ns/geo';
declare namespace gml = 'http://www.opengis.net/gml';

let $line :=
  <gml:LinearRing>
    <gml:coordinates>10,400 20,200 30,100 20,100 10,400</gml:coordinates>
  </gml:LinearRing>
let $polygon :=
  <gml:Polygon>
    <gml:outerBoundaryIs>
      <gml:LinearRing>
        <gml:coordinates>10,10 20,10 30,40 20,40 10,10</gml:coordinates>
      </gml:LinearRing>
    </gml:outerBoundaryIs>
  </gml:Polygon>

return geo:distance($line, $polygon)

Returns the distance between a linear ring and a polygon.

`geo:buffer`

Signature

geo:buffer(
  $geometry  as element(*),
  $distance  as xs:double
) as element(*)?

Summary Returns a polygonal geometry representing the buffer of width $distance around the supplied geometry $geometry, in the spatial reference system of the geometry. The buffer of a geometry is the Minkowski sum (or difference) of the geometry with a disc of radius abs($distance). The buffer is constructed using 8 segments per quadrant to approximate curves.

Errors

`GEO0001`	The supplied element is not recognized as a valid geometry.
`GEO0002`	The supplied geometry cannot be read by the underlying geometry reader.
`GEO0005`	The output object cannot be written as an element by the underlying geometry writer.

Examples

import module namespace geo = 'http://expath.org/ns/geo';
declare namespace gml = 'http://www.opengis.net/gml';

let $polygon :=
  <gml:Polygon>
    <gml:outerBoundaryIs>
      <gml:LinearRing>
        <gml:coordinates>10,10 20,10 30,40 20,40 10,10</gml:coordinates>
      </gml:LinearRing>
    </gml:outerBoundaryIs>
  </gml:Polygon>

return geo:buffer($polygon, 3)

Returns a buffer polygon around the supplied polygon geometry.

`geo:convex-hull`

Signature

geo:convex-hull(
  $geometry  as element(*)
) as element(*)?

Summary Returns the convex hull geometry of the supplied geometry $geometry, in GML. The function returns the object of the smallest possible dimension.

Errors

`GEO0001`	The supplied element is not recognized as a valid geometry.
`GEO0002`	The supplied geometry cannot be read by the underlying geometry reader.
`GEO0005`	The output object cannot be written as an element by the underlying geometry writer.

Examples

import module namespace geo = 'http://expath.org/ns/geo';
declare namespace gml = 'http://www.opengis.net/gml';

geo:convex-hull(
  <gml:LinearRing>
    <gml:coordinates>10,400 20,200 30,100 20,100 10,400</gml:coordinates>
  </gml:LinearRing>
)

Returns the convex hull of a linear ring geometry.

`geo:intersection`

Signature

geo:intersection(
  $geometry1  as element(*),
  $geometry2  as element(*)
) as element(*)?

Summary Returns the intersection geometry of $geometry1 and $geometry2, in GML, or the empty sequence if there is no intersection.

Errors

`GEO0001`	The supplied element is not recognized as a valid geometry.
`GEO0002`	The supplied geometry cannot be read by the underlying geometry reader.
`GEO0005`	The output object cannot be written as an element by the underlying geometry writer.

Examples

import module namespace geo = 'http://expath.org/ns/geo';
declare namespace gml = 'http://www.opengis.net/gml';

let $line :=
  <gml:LinearRing>
    <gml:coordinates>10,400 20,200 30,100 20,100 10,400</gml:coordinates>
  </gml:LinearRing>
let $point :=
  <gml:Point><gml:coordinates>1.00,1.00</gml:coordinates></gml:Point>

return geo:intersection($line, $point)

Returns the intersection of a linear ring and a point.

`geo:union`

Signature

geo:union(
  $geometry1  as element(*),
  $geometry2  as element(*)
) as element(*)?

Summary Returns the union geometry of $geometry1 and $geometry2, in GML.

Errors

`GEO0001`	The supplied element is not recognized as a valid geometry.
`GEO0002`	The supplied geometry cannot be read by the underlying geometry reader.
`GEO0005`	The output object cannot be written as an element by the underlying geometry writer.

Examples

import module namespace geo = 'http://expath.org/ns/geo';
declare namespace gml = 'http://www.opengis.net/gml';

let $line :=
  <gml:LinearRing>
    <gml:coordinates>10,400 20,200 30,100 20,100 10,400</gml:coordinates>
  </gml:LinearRing>
let $point :=
  <gml:Point><gml:coordinates>1.00,1.00</gml:coordinates></gml:Point>

return geo:union($line, $point)

Returns the union of a linear ring and a point.

`geo:difference`

Signature

geo:difference(
  $geometry1  as element(*),
  $geometry2  as element(*)
) as element(*)?

Summary Returns the difference of $geometry1 and $geometry2, in GML, or the empty sequence if the difference is empty (i.e., the set of points in $geometry1 that are not included in $geometry2).

Errors

`GEO0001`	The supplied element is not recognized as a valid geometry.
`GEO0002`	The supplied geometry cannot be read by the underlying geometry reader.
`GEO0005`	The output object cannot be written as an element by the underlying geometry writer.

Examples

import module namespace geo = 'http://expath.org/ns/geo';
declare namespace gml = 'http://www.opengis.net/gml';

let $point :=
  <gml:Point><gml:coordinates>1.00,1.00</gml:coordinates></gml:Point>
let $line :=
  <gml:LineString><gml:coordinates>2,1 3,3 4,4</gml:coordinates></gml:LineString>

return geo:difference($point, $line)

Returns the difference of a point and a linestring.

`geo:sym-difference`

Signature

geo:sym-difference(
  $geometry1  as element(*),
  $geometry2  as element(*)
) as element(*)?

Summary Returns the symmetric difference of $geometry1 and $geometry2, in GML, or the empty sequence if the difference is empty (i.e., the set of points that are included in one of the geometries but not in the other).

Errors

`GEO0001`	The supplied element is not recognized as a valid geometry.
`GEO0002`	The supplied geometry cannot be read by the underlying geometry reader.
`GEO0005`	The output object cannot be written as an element by the underlying geometry writer.

Examples

import module namespace geo = 'http://expath.org/ns/geo';
declare namespace gml = 'http://www.opengis.net/gml';

let $point :=
  <gml:Point><gml:coordinates>1.00,1.00</gml:coordinates></gml:Point>
let $line :=
  <gml:LineString><gml:coordinates>2,1 3,3 4,4</gml:coordinates></gml:LineString>

return geo:sym-difference($point, $line)

Returns the symmetric difference of a point and a linestring.

Functions Specific to Geometry Type

`geo:x`

Signature

geo:x(
  $point  as element(*)
) as xs:double

Summary Returns the x coordinate of the supplied point $point. A point must have an x coordinate.

Errors

`GEO0001`	The supplied element is not recognized as a valid geometry.
`GEO0002`	The supplied geometry cannot be read by the underlying geometry reader.

Examples

import module namespace geo = 'http://expath.org/ns/geo';
declare namespace gml = 'http://www.opengis.net/gml';

geo:x(
  <gml:Point><gml:coordinates>1.00,1.00</gml:coordinates></gml:Point>
)

Returns the x coordinate of a point.

`geo:y`

Signature

geo:y(
  $point  as element(*)
) as xs:double

Summary Returns the y coordinate of the supplied point $point. If the point does not have a y coordinate, NaN is returned.

Errors

`GEO0001`	The supplied element is not recognized as a valid geometry.
`GEO0002`	The supplied geometry cannot be read by the underlying geometry reader.

Examples

import module namespace geo = 'http://expath.org/ns/geo';
declare namespace gml = 'http://www.opengis.net/gml';

geo:y(
  <gml:Point><gml:coordinates>1.00,2.00</gml:coordinates></gml:Point>
)

Returns the y coordinate of a point.

`geo:z`

Signature

geo:z(
  $point  as element(*)
) as xs:double

Summary

Returns the z coordinate of the supplied point $point. If the point does not have a z coordinate, NaN is returned.

This differs from the EXPath Geo Module specification, which returns an empty sequence.

Errors

`GEO0001`	The supplied element is not recognized as a valid geometry.
`GEO0002`	The supplied geometry cannot be read by the underlying geometry reader.

Examples

import module namespace geo = 'http://expath.org/ns/geo';
declare namespace gml = 'http://www.opengis.net/gml';

geo:z(
  <gml:Point><gml:coordinates>1.00,1.00,3.00</gml:coordinates></gml:Point>
)

Returns the z coordinate of a point.

`geo:start-point`

Signature

geo:start-point(
  $line  as element(*)
) as element(*)

Summary Returns the starting point of the supplied line $line. The input must be a single line geometry (LineString or LinearRing).

Errors

`GEO0001`	The supplied element is not recognized as a valid geometry.
`GEO0002`	The supplied geometry cannot be read by the underlying geometry reader.
`GEO0003`	The supplied element must be a line; other geometries are not accepted.

Examples

import module namespace geo = 'http://expath.org/ns/geo';
declare namespace gml = 'http://www.opengis.net/gml';

geo:start-point(
  <gml:LineString>
    <gml:coordinates>2,1 3,3 4,4</gml:coordinates>
  </gml:LineString>
)

Returns the start point of a linestring.

`geo:end-point`

Signature

geo:end-point(
  $line  as element(*)
) as element(*)

Summary Returns the ending point of the supplied line $line. The input must be a single line geometry (LineString or LinearRing).

Errors

`GEO0001`	The supplied element is not recognized as a valid geometry.
`GEO0002`	The supplied geometry cannot be read by the underlying geometry reader.
`GEO0003`	The supplied element must be a line; other geometries are not accepted.

Examples

import module namespace geo = 'http://expath.org/ns/geo';
declare namespace gml = 'http://www.opengis.net/gml';

geo:end-point(
  <gml:LineString>
    <gml:coordinates>2,1 3,3 4,4</gml:coordinates>
  </gml:LineString>
)

Returns the end point of a linestring.

`geo:is-closed`

Signature

geo:is-closed(
  $line  as element(*)
) as xs:boolean

Summary Returns whether the supplied line $line forms a closed loop (i.e., the start point and end point are identical). The input must be a line geometry (LineString or LinearRing) or a MultiLineString.

Errors

`GEO0001`	The supplied element is not recognized as a valid geometry.
`GEO0002`	The supplied geometry cannot be read by the underlying geometry reader.
`GEO0003`	The supplied element must be a line; other geometries are not accepted.

Examples

import module namespace geo = 'http://expath.org/ns/geo';
declare namespace gml = 'http://www.opengis.net/gml';

geo:is-closed(
  <gml:LineString>
    <gml:coordinates>2,1 3,3 4,4</gml:coordinates>
  </gml:LineString>
)

Checks whether a linestring is closed.

`geo:is-ring`

Signature

geo:is-ring(
  $line  as element(*)
) as xs:boolean

Summary Returns whether the supplied line $line is a ring (i.e., a single closed loop). The input must be a single line geometry (LineString or LinearRing).

Errors

`GEO0001`	The supplied element is not recognized as a valid geometry.
`GEO0002`	The supplied geometry cannot be read by the underlying geometry reader.
`GEO0003`	The supplied element must be a line; other geometries are not accepted.

Examples

import module namespace geo = 'http://expath.org/ns/geo';
declare namespace gml = 'http://www.opengis.net/gml';

geo:is-ring(
  <gml:LineString>
    <gml:coordinates>2,1 3,3 4,4</gml:coordinates>
  </gml:LineString>
)

Checks whether a linestring is a ring.

`geo:point-n`

Signature

geo:point-n(
  $line  as element(*),
  $n     as xs:integer
) as element(*)

Summary Returns the Nth point in the supplied line $line. The input must be a single line geometry (LineString or LinearRing).

Errors

`GEO0001`	The supplied element is not recognized as a valid geometry.
`GEO0002`	The supplied geometry cannot be read by the underlying geometry reader.
`GEO0003`	The supplied element must be a line; other geometries are not accepted.
`GEO0004`	The supplied point index is out of range.
`GEO0005`	The output object cannot be written as an element by the underlying geometry writer.

Examples

import module namespace geo = 'http://expath.org/ns/geo';
declare namespace gml = 'http://www.opengis.net/gml';

let $line :=
  <gml:LineString>
    <gml:coordinates>2,1 3,3 4,4</gml:coordinates>
  </gml:LineString>
return geo:point-n($line, 1)

Returns the first point of a linestring.

`geo:exterior-ring`

Signature

geo:exterior-ring(
  $polygon  as element(*)
) as element(*)

Summary Returns the outer ring of the supplied polygon $polygon as a gml:LineString.

Errors

`GEO0001`	The supplied element is not recognized as a valid geometry.
`GEO0002`	The supplied geometry cannot be read by the underlying geometry reader.
`GEO0003`	The supplied element must be a polygon; other geometries are not accepted.
`GEO0005`	The output object cannot be written as an element by the underlying geometry writer.

Examples

import module namespace geo = 'http://expath.org/ns/geo';
declare namespace gml = 'http://www.opengis.net/gml';

let $polygon :=
  <gml:Polygon>
    <gml:outerBoundaryIs>
      <gml:LinearRing>
        <gml:coordinates>10,10 20,10 30,40 20,40 10,10</gml:coordinates>
      </gml:LinearRing>
    </gml:outerBoundaryIs>
  </gml:Polygon>
return geo:exterior-ring($polygon)

Returns the exterior ring of a polygon.

`geo:num-interior-ring`

Signature

geo:num-interior-ring(
  $polygon  as element(*)
) as xs:integer

Summary Returns the number of interior rings of the supplied polygon $polygon.

Errors

`GEO0001`	The supplied element is not recognized as a valid geometry.
`GEO0002`	The supplied geometry cannot be read by the underlying geometry reader.
`GEO0003`	The supplied element must be a polygon; other geometries are not accepted.

Examples

import module namespace geo = 'http://expath.org/ns/geo';
declare namespace gml = 'http://www.opengis.net/gml';

geo:num-interior-ring(
  <gml:Polygon>
    <gml:outerBoundaryIs>
      <gml:LinearRing>
        <gml:coordinates>1,1 20,1 20,20 30,20 30,30 1,30 1,1</gml:coordinates>
      </gml:LinearRing>
    </gml:outerBoundaryIs>
    <gml:innerBoundaryIs>
      <gml:LinearRing>
        <gml:coordinates>2,2 3,2 3,3 2,3 2,2</gml:coordinates>
      </gml:LinearRing>
    </gml:innerBoundaryIs>
    <gml:innerBoundaryIs>
      <gml:LinearRing>
        <gml:coordinates>10,10 19,10 19,19 10,19 10,10</gml:coordinates>
      </gml:LinearRing>
    </gml:innerBoundaryIs>
  </gml:Polygon>
)

Counts interior rings of a polygon with two holes.

`geo:interior-ring-n`

Signature

geo:interior-ring-n(
  $polygon  as element(*),
  $n        as xs:integer
) as element(*)

Summary Returns the Nth interior ring of the supplied polygon $polygon as a gml:LineString.

Errors

`GEO0001`	The supplied element is not recognized as a valid geometry.
`GEO0002`	The supplied geometry cannot be read by the underlying geometry reader.
`GEO0003`	The supplied element must be a polygon; other geometries are not accepted.
`GEO0004`	The supplied ring index is out of range.
`GEO0005`	The output object cannot be written as an element by the underlying geometry writer.

Examples

import module namespace geo = 'http://expath.org/ns/geo';
declare namespace gml = 'http://www.opengis.net/gml';

let $polygon :=
  <gml:Polygon>
    <gml:outerBoundaryIs>
      <gml:LinearRing>
        <gml:coordinates>1,1 20,1 20,20 30,20 30,30 1,30 1,1</gml:coordinates>
      </gml:LinearRing>
    </gml:outerBoundaryIs>
    <gml:innerBoundaryIs>
      <gml:LinearRing>
        <gml:coordinates>2,2 3,2 3,3 2,3 2,2</gml:coordinates>
      </gml:LinearRing>
    </gml:innerBoundaryIs>
    <gml:innerBoundaryIs>
      <gml:LinearRing>
        <gml:coordinates>10,10 19,10 19,19 10,19 10,10</gml:coordinates>
      </gml:LinearRing>
    </gml:innerBoundaryIs>
  </gml:Polygon>
return geo:interior-ring-n($polygon, 1)

Returns the first interior ring of a polygon.

Errors

Code	Description
`GEO0001`	Unrecognized Geo type.
`GEO0002`	The input GML node cannot be read by GMLreader.
`GEO0003`	Input geometry is not an appropriate geometry for this function.
`GEO0004`	The input index is out of range.
`GEO0005`	The result geometry can not be written by GMLwriter.
`GEO0006`	The input matrix is invalid.

Changelog

Version 13.0

Added: Module re-added with GML 3 support.

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