pgSphere 1.1.5
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# 6. Functions

The functions described below are implemented without having an operator. If you are missing some functions, see Section 5 and use the operators.

## 6.1. 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.

Example 39. Area of a spherical circle as a multiple of π

    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)

## 6.2. spoint functions

### 6.2.1. Longitude and latitude

The functions

``long`(spoint p);`

``lat`(spoint p);`

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

Example 40. 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)

### 6.2.2. 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`.

Example 41. 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);`

Example 42. Get the Cartesian values of a spherical point

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

## 6.3. strans functions

### 6.3.1. Converting to ZXZ

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

Example 43. 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' );

### 6.3.2. Angles and axes

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

Table 4. 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.

Example 44. 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)

## 6.4. 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 `@@` (Section 5.7).

Example 45. Radius of a spherical circle in degrees

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

## 6.5. sellipse functions

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

Table 5. 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 `@@` (Section 5.7) instead of using the function `center(sellipse)`.

Example 46. 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)

## 6.6. sline functions

### 6.6.1. 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);`

Example 47. Get the beginning of a line

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

### 6.6.2. 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.

Example 48. 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)

## 6.7. spath functions

### 6.7.1. Count of points

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

``npoints`(spath path);`

Example 49. Count of spath's points

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

### 6.7.2. 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.

Example 50. Get the “center” of a one segment spath

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

## 6.8. spoly functions

### 6.8.1. Count of edges

Similar to an spath (Section 6.7.1), you can get the count of edges of a spherical polygon using the function:

``npoints`(spoly polygon);`

Example 51. Count of edges of a spherical polygon

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

## 6.9. 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.

Example 52. The southwest edge of a box

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

## 6.10. smoc functions

``smoc_info`(smoc);`

Returns information about the internal representation of the smoc.

Example 53. 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.

Example 54. Computing the overall coverage of a catalog

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

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