Well-known text representation of geometry

Well-known text (WKT) is a text markup language for representing vector geometry objects. A binary equivalent, known as well-known binary (WKB), is used to transfer and store the same information in a more compact form convenient for computer processing but that is not human-readable. The formats were originally defined by the Open Geospatial Consortium (OGC) and described in their Simple Feature Access.[1] The current standard definition is in the ISO/IEC 13249-3:2016 standard.[2]

"Well-known text" redirects here. For representation of coordinate reference systems, see Well-known text representation of coordinate reference systems.

Geometric objects

WKT can represent the following distinct geometric objects:

Coordinates for geometries may be 2D (x, y), 3D (x, y, z), 4D (x, y, z, m) with an m value that is part of a linear referencing system or 2D with an m value (x, y, m). Three-dimensional geometries are designated by a "Z" after the geometry type and geometries with a linear referencing system have an "M" after the geometry type. Empty geometries that contain no coordinates can be specified by using the symbol EMPTY after the type name.

WKT geometries are used throughout OGC specifications and are present in applications that implement these specifications. For example, PostGIS contains functions that can convert geometries to and from a WKT representation, making them human readable.

The OGC standard definition requires a polygon to be topologically closed. It also states that if the exterior linear ring of a polygon is defined in a counterclockwise direction it will be seen from the "top". Any interior linear rings should be defined in opposite fashion compared to the exterior ring, in this case, clockwise.[3]

Geometry primitives (2D)
Type Examples
Point POINT (30 10)
LineString LINESTRING (30 10, 10 30, 40 40)
Polygon POLYGON ((30 10, 40 40, 20 40, 10 20, 30 10))
POLYGON ((35 10, 45 45, 15 40, 10 20, 35 10),
(20 30, 35 35, 30 20, 20 30))
Multipart geometries (2D)
Type Examples
MultiPoint MULTIPOINT ((10 40), (40 30), (20 20), (30 10))
MULTIPOINT (10 40, 40 30, 20 20, 30 10)
MultiLineString MULTILINESTRING ((10 10, 20 20, 10 40),
(40 40, 30 30, 40 20, 30 10))
MultiPolygon MULTIPOLYGON (((30 20, 45 40, 10 40, 30 20)),
((15 5, 40 10, 10 20, 5 10, 15 5)))
MULTIPOLYGON (((40 40, 20 45, 45 30, 40 40)),
((20 35, 10 30, 10 10, 30 5, 45 20, 20 35),
(30 20, 20 15, 20 25, 30 20)))
GeometryCollection GEOMETRYCOLLECTION (POINT (40 10),
LINESTRING (10 10, 20 20, 10 40),
POLYGON ((40 40, 20 45, 45 30, 40 40)))

The following are some other examples of geometric WKT strings: (Note: Each item below is an individual geometry.)

GEOMETRYCOLLECTION(POINT(4 6),LINESTRING(4 6,7 10))
POINT ZM (1 1 5 60)
POINT M (1 1 80)
POINT EMPTY
MULTIPOLYGON EMPTY
TRIANGLE((0 0 0,0 1 0,1 1 0,0 0 0))
TIN (((0 0 0, 0 0 1, 0 1 0, 0 0 0)), ((0 0 0, 0 1 0, 1 1 0, 0 0 0)))
POLYHEDRALSURFACE Z ( PATCHES
    ((0 0 0, 0 1 0, 1 1 0, 1 0 0, 0 0 0)),
    ((0 0 0, 0 1 0, 0 1 1, 0 0 1, 0 0 0)),
    ((0 0 0, 1 0 0, 1 0 1, 0 0 1, 0 0 0)),
    ((1 1 1, 1 0 1, 0 0 1, 0 1 1, 1 1 1)),
    ((1 1 1, 1 0 1, 1 0 0, 1 1 0, 1 1 1)),
    ((1 1 1, 1 1 0, 0 1 0, 0 1 1, 1 1 1))
  )

Well-known binary

Well-known binary (WKB) representations are typically shown in hexadecimal strings.

The first byte indicates the byte order for the data:

  • 00 : big endian
  • 01 : little endian

The next 4 bytes are a 32-bit unsigned integer for the geometry type, as described below:

Geometry types, and WKB integer codes
Type2DZMZM
Geometry 0000100020003000
Point 0001100120013001
LineString 0002100220023002
Polygon 0003100320033003
MultiPoint 0004100420043004
MultiLineString 0005100520053005
MultiPolygon 0006100620063006
GeometryCollection 0007100720073007
CircularString 0008100820083008
CompoundCurve 0009100920093009
CurvePolygon 0010101020103010
MultiCurve 0011101120113011
MultiSurface 0012101220123012
Curve 0013101320133013
Surface 0014101420143014
PolyhedralSurface 0015101520153015
TIN 0016101620163016
Triangle 0017101720173017
Circle 0018101820183018
GeodesicString 0019101920193019
EllipticalCurve 0020102020203020
NurbsCurve 0021102120213021
Clothoid 0022102220223022
SpiralCurve 0023102320233023
CompoundSurface 0024102420243024
BrepSolid 1025
AffinePlacement 1021102

Each data type has a unique data structure, such as the number of points or linear rings, followed by coordinates in 64-bit double numbers.

For example, the geometry POINT(2.0 4.0) is represented as: 000000000140000000000000004010000000000000, where:

  • 1-byte integer 00 or 0: big endian
  • 4-byte integer 00000001 or 1: POINT (2D)
  • 8-byte float 4000000000000000 or 2.0: x-coordinate
  • 8-byte float 4010000000000000 or 4.0: y-coordinate

Format variations
EWKT and EWKB – Extended Well-Known Text/Binary
A PostGIS-specific format that includes the spatial reference system identifier (SRID) and up to 4 ordinate values (XYZM).[4][5] For example: SRID=4326;POINT(-44.3 60.1) to locate a longitude/latitude coordinate using the WGS 84 reference coordinate system.
AGF Text – Autodesk Geometry Format
An extension to OGC's Standard (at the time), to include curved elements; most notably used in MapGuide.[6]

Software support

Database engines

APIs

Protocols

See also

References
  1. Herring, John R., ed. (2011-05-28), OpenGIS® Implementation Standard for Geographic information – Simple feature access – Part 1: Common architecture, Open Geospatial Consortium, retrieved 2019-01-28
  2. Information technology – Database languages – SQL multimedia and application packages – Part 3: Spatial (5th ed.), ISO, 2016-01-15, retrieved 2019-01-28
  3. See the OGC Implementation Specification for geographic information – Simple Feature Access, section 6.1.11.1. http://www.opengeospatial.org/standards/sfa
  4. https://github.com/postgis/postgis/blob/2.1.0/doc/ZMSgeoms.txt
  5. http://postgis.org/docs/ST_GeomFromEWKT.html
  6. http://e-logistic-plans.gdfsuez.com/mapguide/help/webapi/da/dc0/group___agf_text.htm
  7. Amazon Redshift announces support for spatial data
  8. Solr GEO support
  9. Well-Known Text (WKT) Input Type in Elasticsearch documentation
  10. "Geospatial Queries". docs.gigaspaces.com. Retrieved 2020-06-02.
  11. https://docs.marklogic.com/guide/search-dev/geospatial
  12. http://docs.memsql.com/docs/geospatial-guide
  13. Well-Known Text (WKT) Format, MySQL documentation
  14. https://neo4j-contrib.github.io/spatial/
  15. https://orientdb.com/docs/3.1.x/indexing/Spatial-Index.html
  16. https://docs.microsoft.com/en-us/previous-versions/sql/sql-server-2008-r2/bb933970(v=sql.105)
  17. H2 create spatial index documentation
  18. "HP Vertica 7.1.x Release Notes". my.vertica.com. Retrieved 2018-03-21.
  19. https://www.voltdb.com/company/press-releases/voltdb-adds-geospatial-query-support-industrys-innovative-fast-data-platform/
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