Does the spline between two points depend on other points that are *outside* the interval between these two points?

Question

Let's consider

taken from

https://fr.wikipedia.org/wiki/Spline#/media/Fichier:Exemple_de_spline_de_degr%C3%A9_3.png

Let's call the red points as : point 1, point 2, point 3, point 4.

I'm wondering if the spline part (the blue smooth line) between the point 1 and 2 would depend on the points number 3 and 4.

Said differently, does the spline between two points depend on other points that are outside the interval between these two points ?

Answer 1

For sure the spline in one interval depends on the previous and next interval for cubic splines. See this wikipedia article on the algorithm to compute cubic splines.