Re: [Algorithms] decompose onto non-orthogonal vectors

[Pierre T. <p.t...@wa...>]

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

- Add a point c to form a triangle abc.
- Now you can use the standard raytracing code which computes (u,v) =
ray-triangle impact (texture) coordinates, then check if  0<u<1, 0<v<1 and
0<u+v<1 to keep or discard the impact.

The underlying method is the same as the one already suggested (expressing p
in the abc basis). But in the raytracing field you'll find less formal and
more pragmatic/optimized-to-death answers/code.

/*
Pierre Terdiman       *   Home: p.t...@wa...
Software engineer    *   Zappy's Lair:  www.codercorner.com
*/

----- Original Message -----
From: Discoe, Ben <ben...@in...>
To: <gda...@li...>
Sent: Saturday, July 15, 2000 4:08 AM
Subject: [Algorithms] decompose onto non-orthogonal vectors


>
> 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:
>
>
> 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/
>
>
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