FunctionInterpolation over an open interval

2018-02-18 20:16:47

I'm trying to obtain an arc-length parametrization of a spline curve as per To do so, I need to calculate partial derivatives of such curve and then perform a FunctionInterpolation. The spline curve is continuous over its whole domain, but not differentiable at its knots (left-side derivatives are different from the right-side ones). Therefore, I'd need to create several FunctionInterpolations, each defined on an open interval between two consecutive knots.

Is that possible? And if so, how? If not, how can I overcome this limitation?

Here is the actual data I'm working on: