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Well-known text representation of geometry

Computer markup language From Wikipedia, the free encyclopedia

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

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

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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]

More information Type, Examples ...
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))
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More information Type, Examples ...
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)))
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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

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

The first byte indicates the byte order for the data:

  • 0x00 : big endian
  • 0x01 : little endian

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

More information Type, 2D ...
Geometry types, and WKB integer codes (specified below in decimal)
Type2DZMZM
Geometry 0100020003000
Point 1100120013001
LineString 2100220023002
Polygon 3100320033003
MultiPoint 4100420043004
MultiLineString 5100520053005
MultiPolygon 6100620063006
GeometryCollection 7100720073007
CircularString 8100820083008
CompoundCurve 9100920093009
CurvePolygon 10101020103010
MultiCurve 11101120113011
MultiSurface 12101220123012
Curve 13101320133013
Surface 14101420143014
PolyhedralSurface 15101520153015
TIN 16101620163016
Triangle 17101720173017
Circle 18101820183018
GeodesicString 19101920193019
EllipticalCurve 20102020203020
NurbsCurve 21102120213021
Clothoid 22102220223022
SpiralCurve 23102320233023
CompoundSurface 24102420243024
BrepSolid 1025
AffinePlacement 1021102
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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. 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

External links

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