Engineering at Alberta Courses » Zero Degree Spline Interpolation

Piecewise Interpolation: Zero Degree Spline Interpolation

0 Degree Spline Interpolation

Given a set of $k$ data points $(x_1,y_1),(x_2,y_2),\cdots, (x_k,y_k)$ , a spline of degree 0 can be defined as:

$y=\begin{cases} y_1,&x\in [x_1, x_2) \\ y_2,&x\in [x_2, x_3) \\ \vdots & \vdots \\ y_{k-1},&x\in [x_{k-1}, x_k) \\ y_k, & x=x_k \end{cases}$

In the previous spline definition, the interpolated value in the interval $[x_{i-1},x_i)$ is equal to the data value $y_{i-1}$ . Alternatively, the interpolated value in the interval $(x_{i-1},x_i]$ can be set equal to the data value $y_i$ . In this case, $y$ can be defined as follows: