5. Operators

5.1. Casting

pgSphere provides some casting operators. So, you can transform an object to another data type. A cast is done using a CAST(x AS typename), x::typename or typename(x) construct.

Table 2. Castings

casting argumenttype targetreturns
spoint scircle circle with center position spoint and radius 0.0
spoint sellipse an ellipse at position spoint and radius 0.0
spoint sline a line with length 0.0 at position spoint
scircle sellipse the scircle as sellipse
sline strans the Euler transformation of sline
sellipse scircle the bounding circle of sellipse
sellipse strans the Euler transformation of sellipse

Example 23. Cast a spherical point as a circle


sql> SELECT CAST ( spoint '(10d,20d)' AS scircle );
      scircle
--------------------
 <(10d , 20d) , 0d>
(1 row)
              

5.2. Equality

All data types of pgSphere have equality operators. The equality operator is as in SQL =. Furthermore, there are two valid negators to indicate that two objects are not equal: != and <>.

Example 24. Equality of two spherical points


sql> SELECT spoint '(10d,20d)' = spoint '(370d,20d)' ;
 test
------
 t
(1 row)
              

5.3. Contain and overlap

On sphere, an equality relationship is rarely used. There are frequently questions like Is object a contained by object b? or Does object a overlap object b? pgSphere supports such queries using binary operators returning true or false:

Table 3. Contain and overlap operators

operatoroperator returns true, if
@ the left object is contained by right object
˜ the left object contains right object
!@ the left object is not contained by right object
the left object does not contain right object
&& the objects overlap each other
!&& the objects do not overlap each other

An overlap or contain operator does not exist for all combinations of data types. For instance, scircle @ spoint is useless because a spherical point can never contain a spherical circle.

Example 25. Is the left circle contained by the right circle?


sql> SELECT scircle '<(0d,20d),2d>' @ scircle '<(355d,20d),10d>' AS test ;
test
------
 t
(1 row)
              

Example 26. Are the circles overlapping?


sql> SELECT scircle '<(0d,20d),2d>' && scircle '<(199d,-10d),10d>' AS test ;
 test
------
 f
(1 row)
              

5.4. Crossing of lines

Another binary relationship is crossing. pgSphere supports only crossing of lines. The correlative operator is named #.

Example 27. Are the lines crossed?


sql> SELECT sline '(0d,0d,0d),10d' # sline '(90d,5d,5d,XYZ),10d' AS test ;
 test
------
 t
(1 row)
              

5.5. Distance

The binary distance operator <-> is a non-boolean operator returning the distance between two objects in radians. Currently, pgSphere supports only distances between points, circles, and between point and circle. If the objects are overlapping, the distance operator returns zero (0.0).

Example 28. Distance between two circles


sql> SELECT 180 * ( scircle '<(0d,20d),2d>' <-> scircle '<(0d,40d),2d>' )
        / pi() AS dist ;
 dist
------
 16
(1 row)
              

5.6. Length and circumference

The length/circumference operator @-@ is a non-boolean unary operator returning the cirumference or length of an object. In the current implementation, pgSphere supports only circumferences of circles, polygons, and boxes. It supports lengths of lines and paths too. Instead of using the operator, you can use the functions circum(object) or length(object).

Example 29. Circumference of a circle


sql> SELECT 180 * ( @-@ scircle '<(0d,20d),30d>' )/ pi() AS circ ;
 circ
------
 180
(1 row)
              

Example 30. Length of a line


sql> SELECT 180 * ( @-@ sline '(0d,0d,0d),30d' )/ pi() AS length ;
 length
--------
 30
(1 row)
              

5.7. Center

The center operator @@ is a non-boolean unary operator returning the center of an object. In the current implementation of pgSphere, only centers of circles and ellipses are supported. Instead of using the operator, you can use the function center(object).

Example 31. Center of a circle


sql> SELECT @@ scircle '<(0d,20d),30d>';
              

5.8. Change the direction

The unary operator - changes the direction of sline or spath objects. You can use it with a Euler transformation object in the figurative sense, too (Section 5.10).

Example 32. Swap begin and end of a sline


sql> SELECT - sline (spoint '(0d,0d)', spoint '(10d,0d)');
              

5.9. Turn the path of a line

The unary operator ! turns the path of sline objects, but preserves begin and end of the spherical line. The length of returned line will be 360 minus the line length of operator's argument.

The operator ! returns NULL, if the length of sline argument is 0, because the path of returned sline is undefined.

Example 33. Return length and Check if north pole on slines


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

sql> SELECT length ( sline ( spoint '(0d,0d)', spoint '(0d,10d)' ) ) *
        180.0 / pi() AS length;
 length 
--------
     10
(1 row)

sql> SELECT spoint '(0d,90d)' @
        sline ( spoint '(0d,0d)', spoint '(0d,10d)' ) AS test;
 test 
------
 f
(1 row)

sql> SELECT length ( ! sline ( spoint '(0d,0d)', spoint '(0d,10d)' ) ) *
        180.0 / pi() AS length;
 length 
--------
    350
(1 row)

sql> SELECT spoint '(0d,90d)' @
        ! sline ( spoint '(0d,0d)', spoint '(0d,10d)' ) AS test;
 test 
------
 t
(1 row)
              

5.10. Transformation

As in a plane, translations and rotations are needed to do object or coordinate transformations. With pgSphere, it is done using Euler transformations (strans). On a sphere, there aren't real translations. All movements on a sphere are rotations around axes.

The general syntax for a transformation is always:

object operator euler

where operators are + for a usual transformation, - for an inverse transformation. You can transform any object having a pgSphere data type, except the data type sbox.

Example 34. Transformation of a point

Rotate a spherical point counterclockwise, first 90 around the x-axis, second 90 around the z-axis, and last 40.5 around the x-axis.


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

sql> SELECT spoint '(30d,0d)' + strans '90d, 90d, 40.5d, XZX AS spoint';
   spoint
---------------
 (90d , 70.5d)
(1 row)
              

You can use the + and - operator as unary operators for transformations, too. +strans just returns the transformation itself, -strans returns the inverse transformation.

Example 35. An inverse transformation


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

sql> SELECT - strans '20d, 50d, 80d, XYZ' AS inverted;
      inverted
-----------------------
 280d, 310d, 340d, ZYX
(1 row)