Well-known text representation of geometry

Short description: Computer markup language

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. The current standard definition is in the ISO/IEC 13249-3:2016 standard.

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, then 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.

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

Type	2D	Z	M	ZM
Geometry	0000	1000	2000	3000
Point	0001	1001	2001	3001
LineString	0002	1002	2002	3002
Polygon	0003	1003	2003	3003
MultiPoint	0004	1004	2004	3004
MultiLineString	0005	1005	2005	3005
MultiPolygon	0006	1006	2006	3006
GeometryCollection	0007	1007	2007	3007
CircularString	0008	1008	2008	3008
CompoundCurve	0009	1009	2009	3009
CurvePolygon	0010	1010	2010	3010
MultiCurve	0011	1011	2011	3011
MultiSurface	0012	1012	2012	3012
Curve	0013	1013	2013	3013
Surface	0014	1014	2014	3014
PolyhedralSurface	0015	1015	2015	3015
TIN	0016	1016	2016	3016
Triangle	0017	1017	2017	3017
Circle	0018	1018	2018	3018
GeodesicString	0019	1019	2019	3019
EllipticalCurve	0020	1020	2020	3020
NurbsCurve	0021	1021	2021	3021
Clothoid	0022	1022	2022	3022
SpiralCurve	0023	1023	2023	3023
CompoundSurface	0024	1024	2024	3024
BrepSolid		1025
AffinePlacement	102	1102

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). For example: SRID=4326;POINT(-44.3 60.1) to locate a longitude/latitude coordinate using the WGS 84 reference coordinate system. It also supports circular curves, following elements named (but not fully defined) within the original WKT: CircularString, CompoundCurve, CurvePolygon and CompoundSurface.

AGF Text – Autodesk Geometry Format

An extension to OGC's Standard (at the time), to include curved elements; most notably used in MapGuide.

See also

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

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