We will use the following data:

```
x = 1:5:50;
y = randi([-10 10],1,10);
```

Hereby `x`

and `y`

are the coordinates of the data points and `z`

are the points we need information about.

```
z = 0:0.25:50;
```

One way to find the y-values of z is piecewise linear interpolation.

```
z_y = interp1(x,y,z,'linear');
```

Hereby one calculates the line between two adjacent points and gets `z_y`

by assuming that the point would be an element of those lines.

`interp1`

provides other options too like nearest interpolation,

```
z_y = interp1(x,y,z, 'nearest');
```

next interpolation,

```
z_y = interp1(x,y,z, 'next');
```

previous interpolation,

```
z_y = interp1(x,y,z, 'previous');
```

Shape-preserving piecewise cubic interpolation,

```
z_y = interp1(x,y,z, 'pchip');
```

cubic convolution, z_y = interp1(x,y,z, 'v5cubic');

and spline interpolation

```
z_y = interp1(x,y,z, 'spline');
```

Hereby are nearst, next and previous interpolation piecewise constant interpolations.