Re: [PyX-user] merging paths and graphs

[Ken S. <ke...@la...>]

  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.