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]

Geometric objects

WKT can represent the following distinct geometric objects:

• Point, MultiPoint
• LineString, MultiLineString
• Polygon, MultiPolygon, Triangle
• PolyhedralSurface
• TIN (Triangulated irregular network)
• GeometryCollection

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:

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

• Amazon Redshift since November 21, 2019^[7]
• Apache Drill supports full range of geospatial queries since version 1.12 as well as reading ESRI Shape files (SHP).
• Apache Solr enterprise search server since 4.0^[8] through JTS
• Elasticsearch distributed, RESTful search and analytics engine since 6.2^[9]
• Google BigQuery supports BigQuery Geographic Information Systems since April 2019.
• GigaSpaces InsightEdge^[10]
• PostgreSQL with PostGIS Module 2.0
• Kinetica GPU-accelerated geospatial database
• Oracle Spatial 9i, 10g, 11g
• OmniSci since 4.0
• MarkLogic Server since 4.2^[11]
• MemSQL since 4^[12]
• MySQL since 4.1^[13]
• MariaDB, all versions
• Neo4j^[14]
• OrientDB^[15]
• IBM DB2 LUW 9, 10, 11.1 with Spatial Extender; 11.5 with either Spatial Analytics or Spatial Extender^[16]
• IBM DB2 for z/OS 9, 10 with Spatial Support
• IBM Netezza with Netezza Spatial
• IBM Informix 9,10,11 with Spatial datablade module
• Microsoft SQL Server since 2008 R2^[17]
• Snowflake Inc.
• SpatiaLite
• Teradata 6.1, 6.2, 12, 13 (native in 13 through add-in in previous versions)
• Ingres GeoSpatial
• Altibase 5.x
• SQL Anywhere 12
• SAP HANA SP07,SP08
• H2 since 1.3.173 (2013-07-28)^[18]
• Vertica since 7.1.0^[19]
• VoltDB since V6.0^[20]

APIs

• Boost C++ libraries (C++): See Geometry io/wkt headers
• Esri geometry-api-java
• GEOS (C/C++)

• Shapely (Python): See Shapely Documentation and Shapely in PyPI
• GeoPHP (PHP)

• GDAL (C/C++ with bindings to Java, Python, and others)
• GeoRust: rust-wkt (Rust bindings)
• JTS Topology Suite (Java)
• Spatial4j (Java)
• NetTopologySuite (.NET)
• OpenLayers (JavaScript)
• OpenScales (ActionScript)
• parsewkt (Python) is a peg parser from WKT to python dictionaries
• pygeoif (Python) parses wkt with regular expressions
• rgeo (Ruby)
• sf (R)
• Terraformer (JavaScript)
• WellKnownLib (C# .Net) Well-Known Text and Binary Parser

Protocols

• GeoSPARQL
• SensorThings API

See also

• Simple Features
• Geography Markup Language
• Well-known text representation of coordinate reference systems

References

External links

• Simple Feature Access Specification
• ISO Spatial standard (there is a charge for this)
• BNF Notation of WKT
• EBNF Notation of WKT
• Online conversion between geometry objects representations