Re: [Algorithms] decompose onto non-orthogonal vectors

[Jonathan B. <jo...@bo...>]

"Discoe, Ben" wrote:
> 
> 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.

This is one of those "fundamental linear algebra things"
that Ron and I were just talking about.

Your original coordinates of 'p' are in the coordinate
system that we are used to, that is, two basis vectors
that are orthonormal.  We will call this space R.

You want the coordinates of 'p' in a system in which
the vectors are unit, but not orthogonal.  We will call
this space S.

Just build a transformation matrix from R to S, and
call that matrix T.  Then p' = Tp and you are done.

For instructions on how to make a matrix that goes from
one space to another, given the basis vectors of each 
space, consult any one of a trillion graphics books.

   -J.


> I promise i consulted an academic

What kind of academic was that?