Re: [Algorithms] decompose onto non-orthogonal vectors

[Jim O. <j.o...@in...>]

> > I prefer this answer to mine from a theory standpoint, because it
> > expresses all of the gotchas that I had to list explicitly... code wise,
I
> > wouldn't want to actually make a matrix to solve it (i'm sure you
wouldn't
> > either).
>
> There was once a time when I would have thought this.  But once you get
> ...
> this kind of code in a bug-free manner.

I totally agree. I used to have all sorts of math functions, grabbed from
this tutorial here and that book there and the end result was that I didn't
even understand what was going on inside my own mathematics library - which
makes it *really* hard to find a bug.

Nowadays, I write down which matrices and matrix multiplications I need to
get the job done and then implement it using 'dumb' matrix multiplications.
Once I am sure it works, I feed the matrices and multiplications to this
little tool I have written, which filters out any unnecessary steps in the
multiplications (i.e. B.x.x = A.x.x * I.x.x + A.x.y * I.x.y would simply
become B.x.x = A.x.x as I.x.x = 1 and I.x.y = 0, where I is identity and A
and B are any given matrix).

Works like a charm :-)

Jim Offerman

Innovade
- designing the designer