[Algorithms] decompose onto non-orthogonal vectors

[Discoe, B. <ben...@in...>]

I thought it would be a simple problem, but all usual sources failed to
answer, so perhaps it will be obvious to someone on this list.

Given a point p and two unit vectors a and b like this:

      b
     /
   v/----p
   /    /
  /    /
 /    /
---------a
    u

how to you get scalars (u,v) such that u*a + v*b = p?
Ie. decompose p onto a and b.

I promise i consulted an academic, a linear algebra textbook and the WWW
(all failed) before resorting the list :)

Thanks,
Ben
http://vterrain.org/