[SciPy-User] trusting splprep

[elliot]

backstory:
I am working on an optical raytracing program written in python.
Currently, I am reworking the face that uses a spline approximation of
a profile.  Specifically, moving from a second order to third order.
The evaluating of the spline is done in c code that I intend to write,
and so in exploring what exactly the output of splprep means, and how
to construct the curve in question from tck, I discovered that I need
to know how to use splprep better.

question:
How can I be sure that my spline approximation is sufficiently
accurate?  In ray tracing, a slight inaccuracy in the derivative of
the interpolation could have a large effect.  My use of splprep is
awkward, so i am looking for some advice.

for instance, just trying a simple example:

#####
>>>x = range(0,6)
>>>y = [c**3 for c in x]
>>>tck,uout = scipy.interpolate.splprep([x,y],s=.000005,k=3)
>>>t = numpy.linspace(0,1,6)      #evenly spaced parameters, should correspond to x
>>> xy = scipy.interpolate.splev(t,tck)
>>> print xy[0]     #should be same as x

array([ 0.10119217,  2.81103321,  3.959404  ,  3.90686522,
3.85308141,
        4.99999962]

# !! x went backwards as parameter progressed: graph is not a function

>>> inty = [c**3 for c in xy[0]]

#differance between interpolated y's and cubes of interpolated x's
>>> numpy.array(xy[1])-numpy.array(inty)

array([ -6.36532821e-04,   2.50019069e+00,  -1.25009170e+01,
         1.53618385e+01,   4.31465996e+01,   2.89434607e-05])

####

Now, this is pretty large error considering that this is a cubic
spline on a simple cubic function.  This should be pretty accurate, if
not exact, but an order of magnitude off just isn't right.  changing
the smoothness from .00005 to 5 doesn't make a difference.

So, how do I use splprep correctly.  And, does anyone have any
pointers regarding ensuring a certain level of accuracy in the
results, or at least raising an error if the spline is not accurate
enough.

thanks,

Elliot