Originally Posted by

**lvleph** Based on your data there is a partition of the interval $\displaystyle [x_0=0,x_2=2]$ into subintervals $\displaystyle [x_0=0,x_1=1]$ and $\displaystyle [x_1=1,x_2=2]$. The corresponding y-values are $\displaystyle y_0 = 0, y_1 = 1, y_2 = 2$.

EDIT: Splines are defined on intervals. In your case there will be a spline function $\displaystyle S_0(x)$ defined on the interval $\displaystyle [0,1]$ and another spline function $\displaystyle S_1(x)$ defined on the interval $\displaystyle [1,2]$.