Ist
\(P_0 = (x_{P_0}, y_{P_0})\), \(P_1 = (x_{P_1}, y_{P_1})\), \(P_2 = (x_{P_2}, y_{P_2})\)
und
\(P(t) = \begin{cases}p_0(t)&x_{P_0} < x < x_{P_1}\\ p_1(t)&x_{P_1} < x < x_{P_2}\text{,}\end{cases}\)
dann lautet das Gleichungssystem zur Bestimmung des Splines
\(\begin{aligned} p_0''(x_{P_0}) &= 0\\ p_0(x_{P_0}) &= y_{P_0}\\ p_0(x_{P_1}) &= y_{P_1}\\ p_0'(x_{P_1})&= p_1'(x_{P_1})\\ p_0''(x_{P_1})&= p_1''(x_{P_1})\\ p_1(x_{P_1}) &= y_{P_1}\\ p_1(x_{P_2}) &= y_{P_2}\\ p_1''(x_{P_2}) &=0\text{.} \end{aligned}\)
