Re: [Algorithms] decompose onto non-orthogonal vectors

[<ro...@do...>]

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.