PostgreSQL
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# Geometric Types

Geometric types represent two-dimensional spatial objects. The most fundamental type, the point, forms the basis for all of the other types.

Table 3-18. Postgres Geometric Types

Geometric Type | Storage | Representation | Description
--- | --- | --- | ---
point | 16 bytes | (x,y) | Point in space
line | 32 bytes | ((x1,y1),(x2,y2)) | Infinite line
lseg | 32 bytes | ((x1,y1),(x2,y2)) | Finite line segment
box | 32 bytes | ((x1,y1),(x2,y2)) | Rectangular box
path | 4+32n bytes | ((x1,y1),...) | Closed path (similar to polygon)
path | 4+32n bytes | [(x1,y1),...] | Open path
polygon | 4+32n bytes | ((x1,y1),...) | Polygon (similar to closed path)
circle | 24 bytes | <(x,y),r> | Circle (center and radius)

A rich set of functions and operators is available to perform various geometric operations such as scaling, translation, rotation, and determining intersections.

## Point

Points are the fundamental two-dimensional building block for geometric types.

point is specified using the following syntax:

    ( x , y )
      x , y

where the arguments are

`x`

  The x-axis coordinate as a floating point number.

`y`

  The y-axis coordinate as a floating point number.

## Line Segment

Line segments (lseg) are represented by pairs of points.

lseg is specified using the following syntax:

    ( ( x1 , y1 ) , ( x2 , y2 ) )
      ( x1 , y1 ) , ( x2 , y2 )
        x1 , y1   ,   x2 , y2

where the arguments are

(`x1`,`y1`), (`x2`,`y2`)

  The endpoints of the line segment.

## Box

Boxes are represented by pairs of points which are opposite corners of the box.

box is specified using the following syntax:

    ( ( x1 , y1 ) , ( x2 , y2 ) )
      ( x1 , y1 ) , ( x2 , y2 )
        x1 , y1   ,   x2 , y2

where the arguments are

(`x1`,`y1`), (`x2`,`y2`)

  Opposite corners of the box.

Boxes are output using the first syntax. The corners are reordered on input to store the lower left corner first and the upper right corner last. Other corners of the box can be entered, but the lower left and upper right corners are determined from the input and stored.

## Path

Paths are represented by connected sets of points. Paths can be "open", where the first and last points in the set are not connected, and "closed", where the first and last point are connected. Functions `popen(p)` and `pclose(p)` are supplied to force a path to be open or closed, and functions `isopen(p)` and `isclosed(p)` are supplied to test for either type in a query.

path is specified using the following syntax:

    ( ( x1 , y1 ) , ... , ( xn , yn ) )
    [ ( x1 , y1 ) , ... , ( xn , yn ) ]
      ( x1 , y1 ) , ... , ( xn , yn )
      ( x1 , y1   , ... ,   xn , yn )
        x1 , y1   , ... ,   xn , yn

where the arguments are

(`x`,`y`)

  Endpoints of the line segments comprising the path. A leading square bracket ("[") indicates an open path, while a leading parenthesis ("(") indicates a closed path.

Paths are output using the first syntax. Note that Postgres versions prior to v6.1 used a format for paths which had a single leading parenthesis, a "closed" flag, an integer count of the number of points, then the list of points followed by a closing parenthesis. The built-in function `upgradepath` is supplied to convert paths dumped and reloaded from pre-v6.1 databases.

## Polygon

Polygons are represented by sets of points. Polygons should probably be considered equivalent to closed paths, but are stored differently and have their own set of support routines.

polygon is specified using the following syntax:

    ( ( x1 , y1 ) , ... , ( xn , yn ) )
      ( x1 , y1 ) , ... , ( xn , yn )
      ( x1 , y1   , ... ,   xn , yn )
        x1 , y1   , ... ,   xn , yn

where the arguments are

(`x`,`y`)

  Endpoints of the line segments comprising the boundary of the polygon.

Polygons are output using the first syntax. Note that Postgres versions prior to v6.1 used a format for polygons which had a single leading parenthesis, the list of x-axis coordinates, the list of y-axis coordinates, followed by a closing parenthesis. The built-in function `upgradepoly` is supplied to convert polygons dumped and reloaded from pre-v6.1 databases.

## Circle

Circles are represented by a center point and a radius.

circle is specified using the following syntax:

    < ( x , y ) , r >
    ( ( x , y ) , r )
      ( x , y ) , r
        x , y   , r

where the arguments are

(`x`,`y`)

  Center of the circle.

`r`

  Radius of the circle.

Circles are output using the first syntax.

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