RE: [Algorithms] decompose onto non-orthogonal vectors

[Tom F. <to...@mu...>]

True - I did take a few short-cuts when describing the solution. :-)

Tom Forsyth - Muckyfoot bloke.
Whizzing and pasting and pooting through the day.

> -----Original Message-----
> From: ro...@do... [mailto:ro...@do...]
> Sent: 15 July 2000 18:22
> To: gda...@li...
> Subject: Re: [Algorithms] decompose onto non-orthogonal vectors
> 
> 
> I  wrote:
> 
> >Tom Forsyth  wrote:
> >
> >>Throw one of the dimensions away (any one) - then you have only two
> >>equations. NOW can you solve it? :-)
> >>
> >>The third dimension will just give the same answer if p 
> lies in the plane of
> >>a and b. If it isn't, then it's not a well-formed question, 
> and you'll need
> >>another axis (c) to define a suitable basis. 
> >
> >Not true.  p can very well lie in the plane of a and b without that
> >plane being a coordinate plane.  In that case, the problem is well
> >formed and your solution will give the wrong answer.
> 
>  Ooops, you are indeed correct.   But your solution does not detect
> the ill-formed case.  And moreover, you do have to be careful about
> which dimension to throw away.  If the thing does lie in one of the
> coordinate planes then you can't throw away that dimension.  And you
> can also use some intellegence about which coordiate plane to throw
> away to minimize the errors.
> 
> 
> 
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