# 8.7. Geometric Types

Geometric data types represent two-dimensional spatial objects. Table 8-16 shows the geometric types available in PostgreSQL. The most fundamental type, the point, forms the basis for all of the other types.

Table 8-16. Geometric Types

NameStorage SizeRepresentationDescription
point16 bytesPoint on the plane(x,y)
line32 bytesInfinite line (not fully implemented)((x1,y1),(x2,y2))
lseg32 bytesFinite line segment((x1,y1),(x2,y2))
box32 bytesRectangular box((x1,y1),(x2,y2))
path16+16n bytesClosed path (similar to polygon)((x1,y1),...)
path16+16n bytesOpen path[(x1,y1),...]
polygon40+16n bytesPolygon (similar to closed path)((x1,y1),...)
circle24 bytesCircle<(x,y),r> (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. They are explained in Section 9.9.

## 8.7.1. Points

Points are the fundamental two-dimensional building block for geometric types. Values of type point are specified using the following syntax:

```( x , y )
x , y```

where x and y are the respective coordinates as floating-point numbers.

## 8.7.2. Line Segments

Line segments (lseg) are represented by pairs of points. Values of type lseg are specified using the following syntax:

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

where (x1,y1) and (x2,y2) are the end points of the line segment.

## 8.7.3. Boxes

Boxes are represented by pairs of points that are opposite corners of the box. Values of type box is specified using the following syntax:

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

where (x1,y1) and (x2,y2) are the opposite corners of the box.

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

## 8.7.4. Paths

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. The functions `popen(p)` and `pclose(p)` are supplied to force a path to be open or closed, and the functions `isopen(p)` and `isclosed(p)` are supplied to test for either type in an expression.

Values of type path are 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 points are the end points of the line segments comprising the path. Square brackets ([]) indicate an open path, while parentheses (()) indicate a closed path.

Paths are output using the first syntax.

## 8.7.5. Polygons

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.

Values of type polygon are specified using the following syntax:

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

where the points are the end points of the line segments comprising the boundary of the polygon.

Polygons are output using the first syntax.

## 8.7.6. Circles

Circles are represented by a center point and a radius. Values of type circle are specified using the following syntax:

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

where (x,y) is the center and r is the radius of the circle.

Circles are output using the first syntax.