{{{
trans}}}

The {{{trans}}} function translates coordinates from one coordinate system to another. See on-line help for details.

This can be confusing because "from one coordinate system to another" is difficult if you only have a choice between the current UCS (1) and World UCS (0). Plan of approach in Lisp:
 * Save current UCS.
 * Make WCS active.
 * Get all the points you need.
 * As an option: You can now even create another UCS based on these points.
 * Use trans to be able to use points in the active UCS, for example a function such as angle.
 * When everything is done: Activate the saved UCS.


If we convert those steps into code, the following sample fragments can help:

Save current UCS:
{{{
(if (not current-ucs-tmp)
   (setq current-ucs-tmp (list (getvar "ucsorg") (trans (list 1 0 0) 1 0) (trans (list 0 1 0) 1 0)))
)}}}

WCS:
{{{
(command "._ucs" "_w")}}}

Collect points:
{{{
(setq
   pt-a (getpoint (tra "\nSpecify apex point: "))
   pt-1 (getpoint (tra "\nSpecify end point 1: "))
   pt-2 (getpoint (tra "\nSpecify end point 2: "))
)}}}

Create a new UCS:
{{{
(command "._ucs" "_3p" "_non" pt-a "_non" pt-1 "_non" pt-2)}}}

Do something with the points, below shows how points behave and how they can be manipulated.
{{{
(princ (strcat "\nAngle from apex to point 2 in WCS is: " (rtos (angle pt-a pt-2)) "."))
(princ (strcat "\nAngle from apex to point 2 in plane trough points with point 1 on x-axis is: " (rtos (angle (trans pt-a 0 1) (trans pt-2 0 1))) "."))}}}

Back to where we started:
{{{
(if current-ucs-tmp ; restore ucs
   (progn
      (command "._ucs" "_3p" (trans (nth 0 current-ucs-tmp) 0 1) (trans (nth 1 current-ucs-tmp) 0 1) (trans (nth 2 current-ucs-tmp) 0 1))
      (setq current-ucs-tmp nil)
   )
)}}}