# Converting a BSplinecurve to function

I am having two set of data. This is d000 and d001. The set d001 is a subset of d000. I am fitting the d000 data by using the BSpline of the d001 data according to the following commands:

Table[Graphics[{Green, PointSize[Large], Point[d000], Red,
Point[d001], Black, BSplineCurve[d001]}, AspectRatio -> 1,
Axes -> True]]
SP = BSplineFunction[d001, SplineKnots -> "Unclamped"]
dsp[t_] = 2*0.33*10^(-9)*10^(12)*D[SP[t], t]


My problem is that the SP is defined with respect to the parameter t of the curve (that does the fitting), not with respect to a variable x, that defines the domain of the data d000. Does anyone know how I can convert the SP to a function of x?

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Please provide a minimal but complete working example, including the data (or workable subset), explanation of code where needed (e.g., what is dsp[t_]...) etc. Otherwise, much less likely to get responses. – ciao Mar 7 '14 at 8:42
Strongly related: "Arbitrary precision spline interpolation." – Alexey Popkov Mar 7 '14 at 8:42
@AlexeyPopkov: Nice link, had not seen it before. Belisarius and his usual top quality answer. – ciao Mar 7 '14 at 8:46
@rasher Unfortunately the answer by belisarius does not answer the question as I mention in the comment. It does not contain new information as compared to excellent Ｊ. Ｍ. 's answer he cite. – Alexey Popkov Mar 7 '14 at 9:14