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 argument||type target||returns|
|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|
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 <>.
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
|operator||operator 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)
Another binary relationship is crossing. pgSphere supports only crossing of lines. The correlative operator is named #.
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).
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)
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).
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).
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)
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.