Re: [PyX-devel] Another geometry version

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

Andre Wobst <wo...@us...>:
>
[snip]
> Well, I have to look at MetaPost at some point.

If you mean a the language/user level -- indeed. Very relevant to PyX.
But I guess, perhaps, you mean at the implementation/code level?
Well... I guess it's still relevant (although I'm not sure I'd dare
venture into that without a good lantern and a trusty sword by my
side... Or something :])

> Don't we really want to create a transformation by setting 3 2d
> input and output points?

That's the canonical problem, I guess.

> This is a linear problem.  How is it in MetaPost?

There's an example on page 32 of the User Manual; the transform T
(called T' in the manual) is not yet defined:

  (0, 1) transformed T =3D (3, 4)
  (1, 1) transformed T =3D (7, 1)
  (1, 0) transformed T =3D (4, -3)

The solugion to this gives the transform factors

  txx =3D 4
  txy =3D -3 [called tyx in the manual]
  tyx =3D 3
  tyy =3D 4
  tx =3D 0
  ty =3D 0

But the problem needn't be this straightforward; these equations must
be fully integrated with the general equation stuff, of course. For
example, on the same page in the manual, the following equations are
used to specify that a given (as yet unknown) transform is
shape-preserving:

  txx =3D tyy; tyx =3D -txy

This automatically only allows rotation, shifting and uniform scaling.
This is used in a very neat example on page 33 of the manual (figure
28).

> Is it allowed to define write P =3D t*p where the points P and p are
> not defined as well as t is not defined? What does MetaPost with
> such an equation? Does it store it for later evaluation

I don't really know; for each non-linear term you have to know (*or*
be able to figure out through some other linear equation system) one
of the two factors before you can start solving things, of course. But
how you deal with this in general (i.e. how you know when to solve a
certain subset of the equations but not the rest of the equations) I
don't know.

> (for example until p and P becomes known)? And what about having
> several transformations: P =3D t2*t1*p?

I would think that would be allowed (as long as you supplied more
equations in addition) but I'm not sure.

> And what about restricting a transformation to a rotation, for
> example?

That can certainly be done (see the example above).

> I should take a look at MetaPost/MetaFont at some point.

Sounds like a good move, indeed :)

I guess one of the few reasons I haven't dropped MetaPost is that PyX
doesn't quite implement all of its functionality (such as this) yet.
:]

(Also, it's nice to be able to use the output from MetaPost directly
in pdflatex without a hickup; if PyX could restrict itself to the same
subset of EPS, possibly with a switch, such as mps=3DTrue or something,
that would be very nice :})

> Andr=E9

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