[PyX-devel] Another geometry version

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

Luckily, I couldn't quite stop playing around with this... My first
thought was to rewrite everything, writing custom stuff to integrate
the linear equation solving stuff and my lazy points. I guess that is
still an option, but I decided to do a very simple version instead.

So, here is a version which uses Andr=E9's linear equation stuff
(although I've switched to numarray -- it's what I use; and numarray
1.0 is out now, so... Hooray for that :).

A point is simply a list of variables. By using ordinary list
notation, such as p[0] one gets at these variables (their values are
available through p[0].value and so forth) but by using the syntactic
sugar p.x (or p.y or p.z) one gets (or sets) their values. For general
dimensions beyond the third, use p.get(dim) or p.set(dim, val) (or,
equivalently, p[dim].value and p[dim].value =3D val).

The lsys class is a simple wrapper that handles left and right hand
sides with more than one element (for multidimensional equations).

There is precious little one can do directly with points at the moment
(such as addition/multiplication) but adding that should be easy. I've
added a single transformation as an example:

"""
def rotated(point, a):
    assert len(point) =3D=3D 2 # To keep it simple :)
    return (point[0]*cos(a)-point[1]*sin(a),
            point[1]*cos(a)+point[0]*sin(a))
"""

Note that this works with the *variables*, not their *values*. Thus,
one can use this transform either way in an equation:

"""
from geom import *
from math import pi

a =3D pt()
b =3D pt()
c =3D pt()

eqs =3D lsys()

a.x =3D 0
a.y =3D 10

eqs.eq(a, rotated(b, pi/2))
eqs.eq(c, rotated(a, pi/2))
eqs.solve()

print b.x, b.y
# Prints out 10.0 0.0
print c.x, c.y
# Prints out -10.0 0.0
"""

So, presto, we've got a bidirectional thingy. Note that the angle in
the transform is still a constant, though. As Andr=E9 pointed out, if
the angle is to be a variable, we'd end up getting equations with
sin() and cos(), and that's not exactly pleasant.

So, this code is still sort of hackish, but it's a starting point that
actually works... And that's always good, isn't it? :)

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