Spline (mathematics) - Examples

Examples

A simple example of a quadratic spline (a spline of degree 2) is


S(t) = \begin{cases}
(t+1)^2-1 & -2 \le t < 0\\
1-(t-1)^2 & 0 \le t \le 2
\end{cases}

for which .

A simple example of a cubic spline is

as


S(t) = \begin{cases}
t^3 & t \ge 0\\
-t^3 & t < 0
\end{cases}

and

An example of using a cubic spline to create a bell shaped curve is the Irwin-Hall polynomials:


f_X(x)= \begin{cases}
\frac{1}{4}(x+2)^3 & -2\le x \le -1\\
\frac{1}{4}\left(3|x|^3 - 6x^2 +4 \right)& -1\le x \le 1\\
\frac{1}{4}(2-x)^3 & 1\le x \le 2
\end{cases}

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