Re: [Algorithms] decompose onto non-orthogonal vectors

[Peter D. <pd...@mm...>]

> 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.

Easy. dot the equation with a and b, correspondingly:

u * (a dot a) + v * (b dot a) = p dot a;
v * (a dot b) + v * (b dot b) = p dot b.

Solve the system.

--
Peter Dimov
Multi Media Ltd.