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FunctionInterpolation over an open interval
I'm trying to obtain an arc-length parametrization of a spline curve as per https://mathematica.stackexchange.com/a/8456/6986. 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: