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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