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. 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.

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

`point` is specified using the following syntax:

(,x)y,xy

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 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,x2y2

where the arguments are

- (
,*x1*)*y1*

(,*x2*)*y2* The end points of the line segment

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

`box` is specified using the following syntax:

( (,x1) , (y1,x2) ) (y2,x1) , (y1,x2)y2,x1,y1,x2y2

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 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.

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,xnyn

where the arguments are

- (
,*x*)*y* End points 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.

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,xnyn

where the arguments are

- (
,*x*)*y* End points of the line segments comprising the boundary of the polygon

Polygons are output using the first syntax.

Circles are represented by a center point and a radius.

`circle` is specified using the following syntax:

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

where the arguments are

- (
,*x*)*y* Center of the circle

*r*Radius of the circle

Circles are output using the first syntax.