Re: [PyX-devel] Re: [PyX-user] Some geometry thoughts

[Magnus L. H. <ma...@he...>]

Andre Wobst <wo...@us...>:
>
> Hi,
>=20
[snip]
> Ok, lets do some ASCII art (is it art?):
>=20
> /x'\   /a b\/x\   /e\
> |  | =3D |   || | + | |
> \y'/   \c d/\y/   \f/
>=20
> If you do not define the transformation matrix (i.e. the variables a,
> b, c, and d) and you also keep the point p, i.e. x and y, variable,
> the left hand side contains terms like a*x, which is non-linear.
>=20
> You may, at a later point, find out, that you already know the value
> of x, for example. Than the term becomes linear ...

Ah, right. Indeed. Intuitively it just seems underdetermined if you're
trying to find out the transform *and* the points, even if you know
enough to make it, say, a quadratic problem (or something).

In practical applications I guess you'd always(?) know enough about
the points to get rid of such non-linear terms.

> And I think, that's what needs to be coded.

Right. I have no idea (off the top of my head, at least) how one would
deal with that; just a bit of book-keeping, perhaps? ;)

[snip]
> Or just think what we can code right now after thinking about the
> problem. I think its not that complex.

Sounds good.

> Those non-linear terms might be hidden in some additional
> "non-linear variable" in a code along the lines I've started. Should
> be possible. Just replace a*x by AX and keep on going.

Sounds like a clever move.

> Once a or x becomes available by other means, the "non-linear
> variable" can be resolved and a linear equation is restored.

Yeah -- a bit of book-keeping, still...

> What's also needed are equations for 2d points etc., but those might
> be build on top of the term class as well.

I'm dealing with these email out of order, so I guess this part is
already solved (by your vector equation code).

> So I think, yes, we can really get this working ...

Wohoo! :)

[snip]
> Andr=E9
>=20
> PS: I've also seen your comment about isinstance. Right. Currently I'm
>     using it in this solver code to differenciate in __add__ etc.
>     between the different types. Not yet perfect, right ... ;-)
>     (I've the Python Cookbook and read about isstring, yes.)

Heh. It works, for now; just thought I'd mention it. Perhaps the code
can be made more generic at some later stage (so that I can, for
example, multiply terms by a number-like class without having to
subclass int or the like).

BTW: Unless you're targeting old Pythons (maybe you are?) you don't
have to use types.IntType and the like; just use int (and float and
long). e.g. isinstance(foo, (int, float, long)). (No big point, as
types.IntType is simply int and so forth.)

--=20
Magnus Lie Hetland     "Canned Bread: The greatest thing since sliced
http://hetland.org      bread!" [from a can in Spongebob Squarepants]