Well-known text representation of geometry explained

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:

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.[1]

Geometry primitives (2D)
TypeExamples
PointPOINT (30 10)
LineStringLINESTRING (30 10, 10 30, 40 40)
PolygonPOLYGON ((30 10, 40 40, 20 40, 10 20, 30 10))
POLYGON ((35 10, 45 45, 15 40, 10 20, 35 10),<br /> (20 30, 35 35, 30 20, 20 30))
Multipart geometries (2D)
TypeExamples
MultiPointMULTIPOINT ((10 40), (40 30), (20 20), (30 10))
MULTIPOINT (10 40, 40 30, 20 20, 30 10)
MultiLineStringMULTILINESTRING ((10 10, 20 20, 10 40),<br /> (40 40, 30 30, 40 20, 30 10))
MultiPolygonMULTIPOLYGON (((30 20, 45 40, 10 40, 30 20)),<br /> ((15 5, 40 10, 10 20, 5 10, 15 5)))
MULTIPOLYGON (((40 40, 20 45, 45 30, 40 40)),<br /> ((20 35, 10 30, 10 10, 30 5, 45 20, 20 35),<br /> (30 20, 20 15, 20 25, 30 20)))
GeometryCollectionGEOMETRYCOLLECTION (POINT (40 10), <br /> LINESTRING (10 10, 20 20, 10 40), <br /> 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 EMPTYMULTIPOLYGON EMPTYTRIANGLE((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:

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
Geometry0000 1000 2000 3000
Point0001 1001 2001 3001
LineString0002 1002 2002 3002
Polygon0003 1003 2003 3003
MultiPoint0004 1004 2004 3004
MultiLineString0005 1005 2005 3005
MultiPolygon0006 1006 2006 3006
GeometryCollection0007 1007 2007 3007
CircularString0008 1008 2008 3008
CompoundCurve0009 1009 2009 3009
CurvePolygon0010 1010 2010 3010
MultiCurve0011 1011 2011 3011
MultiSurface0012 1012 2012 3012
Curve0013 1013 2013 3013
Surface0014 1014 2014 3014
PolyhedralSurface0015 1015 2015 3015
TIN0016 1016 2016 3016
Triangle0017 1017 2017 3017
Circle0018 1018 2018 3018
GeodesicString0019 1019 2019 3019
EllipticalCurve0020 1020 2020 3020
NurbsCurve0021 1021 2021 3021
Clothoid0022 1022 2022 3022
SpiralCurve0023 1023 2023 3023
CompoundSurface0024 1024 2024 3024
BrepSolid 1025
AffinePlacement102 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: <span style="background:yellow">00</span><span style="background:lightblue">00000001</span><span style="background:lightsalmon">4000000000000000</span><span style="background:lightgreen">4010000000000000</span>, where:

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).[2] [3] 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.[4]
  • AGF Text – Autodesk Geometry Format : An extension to OGC's Standard (at the time), to include curved elements; most notably used in MapGuide.[5]

    • See also

    References

    1. See the OGC Implementation Specification for geographic information – Simple Feature Access, section 6.1.11.1. http://www.opengeospatial.org/standards/sfa
    2. Web site: Postgis/Postgis. GitHub. 6 October 2021.
    3. Web site: ST_GeomFromEWKT. 2022-11-25.
    4. Web site: Chapter 4: Using PostGIS: Data Management and Queries. 2021-07-30. postgis.net.
    5. Web site: MapGuide API Reference: AGF Text . 2023-09-14 .

    External links

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