Well-known text representation of geometry

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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]

Contents

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. [3]

Geometry primitives (2D)
TypeExamples
Point SFA Point.svg POINT (30 10)
LineString SFA LineString.svg LINESTRING (30 10, 10 30, 40 40)
Polygon SFA Polygon.svg POLYGON ((30 10, 40 40, 20 40, 10 20, 30 10))
SFA Polygon with hole.svg POLYGON ((35 10, 45 45, 15 40, 10 20, 35 10),
(20 30, 35 35, 30 20, 20 30))
Multipart geometries (2D)
TypeExamples
MultiPoint SFA MultiPoint.svg MULTIPOINT ((10 40), (40 30), (20 20), (30 10))
MULTIPOINT (10 40, 40 30, 20 20, 30 10)
MultiLineString SFA MultiLineString.svg MULTILINESTRING ((10 10, 20 20, 10 40),
(40 40, 30 30, 40 20, 30 10))
MultiPolygon SFA MultiPolygon.svg MULTIPOLYGON (((30 20, 45 40, 10 40, 30 20)),
((15 5, 40 10, 10 20, 5 10, 15 5)))
SFA MultiPolygon with hole.svg 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 SFA GeometryCollection.svg 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:

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

Geometry types, and WKB integer codes (specified below in decimal)
Type2DZMZM
Geometry0100020003000
Point1100120013001
LineString2100220023002
Polygon3100320033003
MultiPoint4100420043004
MultiLineString5100520053005
MultiPolygon6100620063006
GeometryCollection7100720073007
CircularString8100820083008
CompoundCurve9100920093009
CurvePolygon10101020103010
MultiCurve11101120113011
MultiSurface12101220123012
Curve13101320133013
Surface14101420143014
PolyhedralSurface15101520153015
TIN16101620163016
Triangle17101720173017
Circle18101820183018
GeodesicString19101920193019
EllipticalCurve20102020203020
NurbsCurve21102120213021
Clothoid22102220223022
SpiralCurve23102320233023
CompoundSurface24102420243024
BrepSolid1025
AffinePlacement1021102

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:

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. It also supports circular curves, following elements named (but not fully defined) within the original WKT
CircularString, CompoundCurve, CurvePolygon and CompoundSurface. [6]
AGF Text – Autodesk Geometry Format
An extension to OGC's Standard (at the time), to include curved elements; most notably used in MapGuide. [7]

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. ↑ "Postgis/Postgis". GitHub . 6 October 2021.
  5. ↑ "ST_GeomFromEWKT" . Retrieved 2022-11-25.
  6. ↑ "Chapter 4: Using PostGIS: Data Management and Queries". postgis.net. Retrieved 2021-07-30.
  7. ↑ "MapGuide API Reference: AGF Text" . Retrieved 2023-09-14.
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