BSplineCurve Interpolation

Can I get interpolated values from this B-spline, (shown in red)?

points = {{-2, 2}, {2, 2}, {6, 6}, {10, 7}, {14, 11},
{18, 2}, {22, 1}, {26, 2}, {30, 1}, {34, 1}};

fn1 = Interpolation[points, Method -> "Spline"];
fn2 = Interpolation[points];

Show[ListPlot[points],
Graphics[{Red, BSplineCurve[points]}],
Plot[fn1[x], {x, -2, 36}],
Plot[fn2[x], {x, -2, 36}],
AxesOrigin -> {-2, 0}]


-
The red one is not interpolation - it passes only through the ends, not all points. So you need values of points along B Spline? – Vitaliy Kaurov Dec 7 '12 at 0:51
@Vitaliy - It would do to extract the points of the B-spline and interpolate them, but the B-spline is a graphics primitive, and I can't get the data out of it. – Chris Degnen Dec 7 '12 at 0:53

BSplineCurve is based on BSplineFunction. But BSplineFunction is analytic expression - so you do not need to interpolate it - you can use it as a (parametric) function:
g = BSplineFunction[points];

bspts=Table[g[t], {t, 0, 1, .1}]