I have data $x$ and $y$ which are noisy evaluations of a function $f:[0,max] to [0,1]$. I know that $f(0) = 0$ and $f(max) = 1.

Is there any way to enforce these boundary conditions when fitting a spline?

Here is a picture, where one sees that the spline fits nicely, but the approximation is bad around 0, where it takes a value around 0.1:

I am aware of bc_type for various splines, but as far as I can tell this only allows one to specify 1st and 2nd derivative, and not fix boundary values.

(Probably this question betrays my ignorance of how splines are fitted, and that what I am asking for is not possible. I just want to make sure I’m not missing something obvious.)