What's my vector, Victor? (08 Aug 2007)

In graphics and CAD software, users occasionally have to enter 2D or 3D coordinates. One such application is CoCreate's OneSpace Modeling on which I work day to day to help me fill my fridge.

To make coordinate entry as simple as possible, the implementation of Lisp which is embedded in the product understands the following vector syntax:

  (line :two_points 100,100 0,0)

Common Lisp connoisseurs will notice that this is decidedly non-standard behavior. Those commas aren't supposed to be there; instead, commas serve their purpose in list quoting, particularly in macro definitions. (For a refresher, check out The Common Lisp Cookbook - Macros and Backquote.) And in any other implementation of Lisp, this code would indeed result in an error message such as "comma is illegal outside of backquote".

OneSpace Modeling's embedded Lisp, however, will notice a pair of literal numbers and assume that what the user really meant to specify is a structure of type gpnt2d, which holds x and y slots for the coordinates. And so what is really evaluated is more like this:

  (line :two_points (oli:make-gpnt2d :x 100 :y 100) (oli:make-gpnt2d :x 0 :y 0))

oli is the Lisp package which exports the gpnt2d structure as well as its accessor and constructor functions.

This explicit syntax is actually required whenever you need to specify coordinates using non-literals, such as when the actual coordinates are the results of mathematical calculations. For instance, vector syntax is not recognized in the following:

  (line :two_points (+ 50 50),100 0,0)

Now you'll get the expected error message reporting that "a comma has appeared out of a backquote". To make this work, you'd have to say:

  (line :two_points (oli:make-gpnt2d :x (+ 50 50) :y 100) 0,0)

But despite this limitation, the vector syntax extension was tremendously important for us: Coordinates can be entered in all kinds of places in the user interface where casual users would never suspect that what they are entering is actually thrown into funny engines which the propellerheads at CoCreate call "the Lisp reader" and "the Lisp evaluator".