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

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

Andre Wobst <wo...@us...>:
>
> Hi,
>=20
> I'm moving my posting to pyx-devel ... I think its a much better place
> to post the following code. (Magnus, you're listing here, don't you? I
> think I remember your name from when I looked at the subscriber list
> quite some time ago.)

Sure. I didn't quite remember myself, which is why I used pyx-user...
But, yes, I'm on pyx-devel as well.

> On 27.07.04, Andre Wobst wrote:
> > Beside that my main concern is, whether its enough to stick on this
> > strict assignments. This is quite a limitation. We can't compete to
> > MetaPost by that (but we want, don't we?). I'm not sure whether its
> > possible to cook it all down to an Equality-function:
> >=20
> >     Equal(b, a + Point(10, 0))
>=20
> I just couldn't resist: A linear equation solver can be easily build
> like this.

I know -- I've thought about this myself in the past, and I've even
found code that does this sort of thing. I don't remember exactly
where, but it had a variable class and did all the linear equations
behind the scenes.

Also, numarray (and Numeric) has support for the equation solving
part; I guess they could be optional mechanisms for speed, if this is
indeed the way to go.

> Find some code enclosed. You may consider to go along that line
> (just in case you want to spend some time on this issue).

I might. This is sort of an issue that crops up every now and then for
me (i.e. every time I want to create a figure, basically ;)

> I think, a 2d-point can be build on top of this already by combining
> two variables.

Certainly. It would also be neat to be able to use parametrized curves
in the same system, as in MetaPost; but I guess it's not quite that
critical, as you already have support for finding intersections
in PyX.

> The same for higher dimension points. I'm not totally sure whether a
> transformation can be easily integrated in that concept.

Well, if we use a general matrix-based version, it's all good.
(Haven't looked at your code -- it might work just as well.) That is,
an affine transform are basically just added terms to the linear
equations. And it would be *very* useful to allow them... E.g. "this
point rotated around that point by 60 degrees equals this point
rotated around that point by 30 degrees" and the like.

> My grasp tells me, that a transformation contains another set of
> variables (6 for a 2d->2d affine transformation). When multiplying
> with a (lazy) point (two variables) the system becomes non-linear.
> I'm kind of confused at the moment ... ;-)

Hm. No, I don't think so... If you say that one point, transformed by
an affine transform, equals another point, all you have is a linear
set of two equations in two variables -- no?

Not sure what you mean by "multiplying with a [...] point" here,
though. I may be missing something :]

Anyway, writing a system like this based on linear equations is a bit
more work than a one-way function-based one. I'll have a look but I
can't promise anything.

> Andr=E9

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