# Well-known text

(Redirected from Well-known binary)

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

In total, there are 18 distinct geometric objects that can be represented:

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 `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)))```

The following are some other examples of geometric WKT strings:

```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

## 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.

1. ```PARAM_MT["Mercator_2SP",
```
2. ```    PARAMETER["semi_major",6370997.0],
```
3. ```    PARAMETER["semi_minor",6370997.0],
```
4. ```    PARAMETER["central_meridian",180.0],
```
5. ```    PARAMETER["false_easting",-500000.0],
```
6. ```    PARAMETER["false_northing",-1000000.0],
```
7. ```    PARAMETER["standard parallel 1",60.0]]
```
8. ```PARAM_MT["Affine",
```
9. ```    PARAMETER["num_row",3],
```
10. ```    PARAMETER["num_col",3],
```
11. ```    PARAMETER["elt_0_1",1],
```
12. ```    PARAMETER["elt_0_2",2],
```
13. ```    PARAMETER["elt 1 2",3]]
```

## Atlas/Mapping software that provides support

• Nunaliit participatory atlas creation and data management framework

## Variations

• EWKT and EWKBExtended Well-Known Text/Binary – A PostGIS-specific format that includes the spatial reference system identifier (SRID) and up to 4 ordinate values.[3][4] For example: `SRID=4326;POINT(-44.3 60.1)` to locate a longitude/latitude coordinate using the WGS 84 reference coordinate system.
• AGF TextAutodesk Geometry Format – An extension to OGC's Standard (at the time), to include curved elements; most notably used in MapGuide.[5]