From: Wayne Piekarski
Subject: Re: Solution to a vector problem
To: rusin@math.niu.edu (Dave Rusin)
Date: Tue, 22 Nov 1994 15:06:00 +1523847 (CST)
> >I have an equation p = o + Xu + Yv where p, o, u, and v are all three
> >dimensional vectors, and X and Y are numerical values. I want to be able
> >to solve for X and Y. I cannot see any normal way to do this, so I
>
> If I understand you right, you're trying to find real numbers X and Y
> such that the linear combination Xu+Yv of vectors comes out to the
> vector p-o, right? First off, this may not be possible. You need to
Yes, basically a virtual screen is defined in 3D with the origin at 'o'
and the u and v vectors defining up and right.
> verify that p-o lies in the plane spanned by u and v. One way to
> do this is to take the cross product of the vectors u and v, then
> take the dot product of that with p-o. If you don't get zero, quit -- no
> X's and Y's can be found. If you do get zero proceed as follows. Take
> a vector w perpendicular to u but not to v -- (u x v) x u will do --
> and then take dot products with both sides of the equation. The Xu will
> drop out and you can solve for Y = (w . (p-o)) / (w. v). Similarly,
> you solve for X.
>
> Is that what you wanted?
Thanks for that. It is exactly what I wanted. I'll try it out and see what
happens....
thanks,
Wayne
_
| \ /\ / |_) | waynep@cleese.apana.org.au |
| \/ \/ ayne | iekarski | Adelaide - South Australia |