Stefan Schenk wrote:
Hi Mico,
Am Freitag 22 August 2008 20:36 schrieb Mico Filós:
[...]
Describing this in words is painful. I hope you see what I mean.
I think i now understand the pain;-) You want to achieve something like the
following?
#------------------------------------------------------------------------------
from pyx import *
g = graph.graphxy(width=8)
f = g.plot(graph.data.function("y(x)=sin(x)/x", min=-10, max=10))
g.doplot(f)
# The point that defines the tangent
l = 0.51*f.path.arclen()
x0, y0 = f.path.at(l)
tangent = f.path.tangent(l, length=4)
g.stroke(tangent)
# Path that is perpendicular to tangent
projector = tangent.transformed(trafo.rotate(90, x0, y0))
# Some other arbitrary point
l2 = 0.7*f.path.arclen()
x1, y1 = f.path.at(l2)
# Find the intersection of a line from x1, y1 perpendicular to tangent with
# tangent
a, b = projector.transformed(trafo.translate(x1-x0,
y1-y0)).intersect(tangent)
u, v = tangent.at(b[0])
g.stroke(path.line(x1, y1, u, v))
g.writeEPSfile("project_function_to_tangent")
#------------------------------------------------------------------------------
However there is still the problem that the points (x0, y0) and (x1, y1)
are determined by some length of the path.
Does anyone know a way in pyx to translate some graph-coordinate x into a
path-length?
If not, you probably have to do tangent by hand and (x1, y1) will be
something like
x1, y1 = g.pos(x, y(x))
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There is a genuine problem here that would be useful to solve, in the
context of
involutes and evolutes, of constucting a curve as an envelope, and similar
tasks.
It is a task that should almost certainly be solved for parametric paths
rather than
graphs of functions, although they would be a special case.
Another special case, that of applying unequal axis-scaling, possibly
not even linear,
as here, is possible I suppose, but is quite likely to be silly. If you
distort
your geometry in this way, you should surely distort your
ruler/tape-measure and
protractor to match.
The idea of starting with such a pathological example as
("y(x)=sin(x)/x", min=-10, max=10)
is either tongue-in-cheek, or a troll.
----------------------------------------------------
So let us start with the simpler (but not insubstantial)
task:
Same problem, but restricted to paths that consist of a
single, non-self-intersecting cubic Bezier.
Can this be solved analytically, and if not
what is the most stable, accurate, and/or
quickest numerical method that Python can provide ?
I can't imagine that recursive chopping in half, followed
by Pythagoras' theorem on all the bits is likely to be it.
Cheers,
Ken.
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