Well-known text

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Well-known text (WKT) is a text markup language for representing vector geometry objects on a map, spatial reference systems of spatial objects and transformations between spatial reference systems. A binary equivalent, known as well-known binary (WKB), is used to transfer and store the same information on databases, such as PostGIS, Microsoft SQL Server and DB2. The formats were originally defined by the Open Geospatial Consortium (OGC) and described in their Simple Feature Access and Coordinate Transformation Service specifications. The current standard definition is in the ISO/IEC 13249-3:2011 standard, "Information technology -- Database languages -- SQL multimedia and application packages -- Part 3: Spatial" (SQL/MM).

Geometric objects

WKT can represent 18 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 which 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.

It's useful to note that 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 counter clockwise 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.[1]

Geometry primitives (2D)
Type Examples
Point File:SFA Point.svg POINT (30 10)
LineString File:SFA LineString.svg LINESTRING (30 10, 10 30, 40 40)
Polygon File:SFA Polygon.svg POLYGON ((30 10, 40 40, 20 40, 10 20, 30 10))
File: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)
Type Examples
MultiPoint File:SFA MultiPoint.svg MULTIPOINT ((10 40), (40 30), (20 20), (30 10))
MULTIPOINT (10 40, 40 30, 20 20, 30 10)
MultiLineString File:SFA MultiLineString.svg MULTILINESTRING ((10 10, 20 20, 10 40),
(40 40, 30 30, 40 20, 30 10))
MultiPolygon File:SFA MultiPolygon.svg MULTIPOLYGON (((30 20, 45 40, 10 40, 30 20)),
((15 5, 40 10, 10 20, 5 10, 15 5)))
File: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)))

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
CIRCULARSTRING(1 5, 6 2, 7 3)
COMPOUNDCURVE(CIRCULARSTRING(0 0,1 1,1 0),(1 0,0 1))
CURVEPOLYGON(CIRCULARSTRING(-2 0,-1 -1,0 0,1 -1,2 0,0 2,-2 0),(-1 0,0 0.5,1 0,0 1,-1 0))
MULTICURVE((5 5,3 5,3 3,0 3),CIRCULARSTRING(0 0,2 1,2 2))
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 (
    ((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 second part is an 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

Each data type has a unique data structure, such as the number of points or linear rings, followed by coordinates in double-precision floating-point format (double).

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

Coordinate reference system

WKT can describe coordinate reference systems. The standard, "Well-known text representation of coordinate reference systems" was adopted by the Open Geospatial Consortium in 2015.[2] For example:

CS[Cartesian,3],
AXIS["(X)",geocentricX],
AXIS["(Y)",geocentricY],
AXIS["(Z)",geocentricZ],
LENGTHUNIT[“metre”,1.0]

Transformations

A WKT format is defined to describe the transformation methods and parameters used to convert coordinates between two different spatial reference systems.

Below are two examples of WKT transformation descriptions.

PARAM_MT["Mercator_2SP", 
    PARAMETER["semi_major",6370997.0], 
    PARAMETER["semi_minor",6370997.0], 
    PARAMETER["central_meridian",180.0], 
    PARAMETER["false_easting",-500000.0], 
    PARAMETER["false_northing",-1000000.0], 
    PARAMETER["standard parallel 1",60.0]]
PARAM_MT["Affine",
    PARAMETER["num_row",3],
    PARAMETER["num_col",3],
    PARAMETER["elt_0_1",1],
    PARAMETER["elt_0_2",2],
    PARAMETER["elt 1 2",3]]

RDBMS Engines that provide support

APIs that provide support

Protocols that provide support

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.[7][8] 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.[9]

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. ↑ Lua error in package.lua at line 80: module 'strict' not found.
  3. ↑ Solr GEO support
  4. ↑ https://docs.marklogic.com/guide/search-dev/geospatial
  5. ↑ Well-Known Text (WKT) Format, MySQL documentation
  6. ↑ H2 create spatial index documentation
  7. ↑ https://github.com/postgis/postgis/blob/2.1.0/doc/ZMSgeoms.txt
  8. ↑ http://postgis.org/docs/ST_GeomFromEWKT.html
  9. ↑ http://www.osgeo.org/files/mapguide/docs/2.0/da/dc0/group___agf_text.htm

External links

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