# Functions

The functions described below are implemented without having an operator. If you are missing some functions, see operators and use the operators.

## Area function

The `area` function returns the area of a spherical object in square radians. Supported data types are: `scircle`, `spolygon` (if the polygon is convex), `sbox`, and `smoc`.

### Area of a spherical circle as a multiple of &pgr;

    sql> SELECT area( scircle '<(0d,90d),60d>' ) / pi() AS area;
     area
    ------
     1
    (1 row)
    sql> SELECT area(smoc '0/1-3');
           area
    -------------------
     3.141592653589793
    (1 row)

## `spoint` functions

### Longitude and latitude

The functions

                    long
                      spoint p

                    lat
                      spoint p

returns the longitude or latitude value of a spherical position `p` in radians.

#### Get the longitude and latitude of a spherical point in degrees

    sql> SELECT long ( spoint '(10d,20d)' ) * 180.0 / pi() AS longitude;
     longitude
    ------------
     10
    (1 row)

    sql> SELECT lat ( spoint '(10d,20d)' ) * 180.0 / pi() AS latitude;
     latitude
    ----------
     20
    (1 row)

### Cartesian coordinates

The functions

                    x
                      spoint p

                    y
                      spoint p

                    z
                      spoint p

return the Cartesian `x`, `y` or `z` value of a spherical position `p`. The returned values are always between `-1.0` and `+1.0`.

#### Get the Cartesian `z`-value of a spherical point

    sql> SELECT z ( spoint '(10d,-90d)' ) AS z;
     z
    ----
     -1
    (1 row)

You can get a `float8` array of Cartesian values using the function

                    xyz
                      spoint p

#### Get the Cartesian values of a spherical point

    sql> SELECT xyz ( spoint '(0d,0d)' ) AS cart;
      cart
    ---------
     {1,0,0}
    (1 row)

## `strans` functions

### Converting to ZXZ

Using the function `strans_zxz(strans),` you can convert an Euler transformation to `ZXZ` axes transformation.

#### Change the transformation axes to `ZXZ`

Convert the transformation `strans '20d, -270d, 70.5d, XZY'` to a `ZXZ` transformation.

    sql> SELECT strans_zxz ( strans '20d, -270d, 70.5d, XZY' );

### Angles and axes

It is possible to get the components of an Euler transformation.

### Getting Euler transformation attributes

function | description
`phi` | first angle of a transformation
`theta` | second angle of a transformation
`psi` | third angle of a transformation
`axes` | transformation axes as a three letter code

The angles will always returned as a `float8` value in radians. The axes are returned as a three letter code.

#### Get the second axis and its rotation angle

    sql> SELECT theta( strans '20d,30d,40d,XZY' ) * 180 / pi() AS theta;
     theta
    -------
     30
    (1 row)
    sql> SELECT substring ( axes ( strans '20d,30d,40d,XZY' ) from 2 for 1 ) AS axis;
     axis
    ------
      Z
    (1 row)

## scircle functions

You can get the radius of a spherical circle in radians using the `radius` function. The center of the circle is available with the operator `@@` (op.center).

### Radius of a spherical circle in degrees

    sql> SELECT 180.0 * radius( scircle '<(0d,90d),60d>' ) / pi() AS radius;
     radius
    --------
         60
    (1 row)

## `sellipse` functions

pgSphere provides 4 functions to get the parameters of a spherical ellipse:

## Getting spherical ellipse attributes

function | description
`lrad` | the major radius of the ellipse
`srad` | the minor radius of the ellipse
`center` | the center of the ellipse
`inc` | the inclination of the ellipse

To get the ellipse center, you can use the operator `@@` (op.center) instead of using the function `center(sellipse)`.

### Get the minor radius of an ellipse

    sql> SELECT srad ( sellipse '< { 10d, 5d }, ( 20d, 0d ), 90d >' )
            * 180.0/ pi() AS srad ;
     srad
    ------
      5
    (1 row)

## `sline` functions

### Begin and end

To get the beginning and the end of a line, pgSphere provides two functions:

                      sl_beg
                        sline line

                      sl_end
                        sline line

#### Get the beginning of a line

    sql> SELECT sl_beg( sline '(10d, 90d, 270d, ZXZ ), 20d';

### Create a meridian

You can create a meridian as a line using the function

                        meridian
                          float8 lng

The function returns a line starting at a latitude of -90° and ending at a latitude of 90°. The line goes along the given longitude `lng` in radians.

#### A meridian for longitude 20°

    sql> SELECT set_sphere_output('DEG');
     set_sphere_output
    -------------------
     SET DEG
    (1 row)

    sql> SELECT meridian (20.0 *pi() / 180.0 );
                 sline
    -------------------------------
     ( 270d, 90d, 20d, ZXZ ), 180d
    (1 row)

## `spath` functions

### Count of points

You can get the count of points of a spherical path using the function:

                    npoints
                      spath path

#### Count of spath's points

    sql> SELECT npoints ( spath '{(0,0),(1,0)}' );
     npoints
    ---------
           2
     (1 row)

### Positions at a path

pgSphere provides two functions to get points at a path.

                    spoint
                      spath path
                      int4 i

                    spoint
                      spath  path
                      float8 f

The first function returns the `i`-th point of a path. If `i` is less than 1 or larger than the count of `spath` points, the function returns `NULL`. The second function does nearly the same, but does linear interpolation between edge positions.

#### Get the “center” of a one segment `spath`

    sql> SELECT spoint ( spath '{(0d,0d),(30d,0d)}', 1.5 );
      spoint
    ------------
     (15d , 0d)
    (1 row)

## `spoly` functions

### Count of edges

Similar to an `spath` (funcs.spath.npts), you can get the count of edges of a spherical polygon using the function:

                    npoints
                      spoly polygon

#### Count of edges of a spherical polygon

    sql> SELECT npoints ( spoly '{(0,0),(1,0),(1,1)}' );
     npoints
    ---------
           3
     (1 row)

## `sbox` functions

The functions

                  sw
                    sbox box

                  ne
                    sbox box

                  se
                    sbox box

                  nw
                    sbox box

return the corresponding southwest, northeast, southeast, or northwest edge. The returned value will be a spherical point.

### The southwest edge of a box

    sql> SELECT sw ( sbox '( (0d,0d), (90d,0d) )' ) ;

## `smoc` functions

                  smoc_info
                    smoc

Returns information about the internal representation of the smoc.

### A circle

    sql> SELECT smoc_info('0/4 1/0 2 12-13 34-35 45 47 2/4 6 12 14 56-57 60-61 88 90-91 116-117 119 130-131 134-135 177 179 185 187');
                                                               smoc_info
    --------------------------------------------------------------------------------------------------------------------------------
     version: 0, order: 2, depth: 1, first: 0, last: 3458764513820540928, area: 1261007895663738880, tree_begin: 48, data_begin: 72

                  smoc_degrade
                    order int
                    smoc

Adjusts the order of an smoc to be more or less precise.

When order is smaller than smoc's maximal order, the MOC resolution is degraded to the new order, and its maximal order is set to that order. When order is larger than the smoc's maximal order, smoc's shape is not modified, but its maximal order is raised to order.

                  sum
                    smoc

                  intersection
                    smoc

`smoc` union and intersection are available as aggregate functions that compute the aggretated coverage over a given column.

### Computing the overall coverage of a catalog

    SELECT sum(coverage) FROM ivoa;
        sum
    -----------
     0/0-11 6/