Construct an approximate function that interpolates the data:

Apply the function to find interpolated values:

Plot the interpolation function:

Compare with the original data:

Find the interpolated value immediately:

Interpolate between points at arbitrary values:

Create data with Table:

Form the interpolation:

Plot the interpolated function:

Create a list of multidimensional data:

Create an approximate interpolating function:

Plot the interpolating function:

Form an interpolation from data given as a TimeSeries:

Plot the interpolated function:

Create data that includes derivatives at each point:

Construct an interpolation:

Plot the interpolation:

Create 2D data that includes a gradient vector at each point:

Compare with data that does not include gradients:

Also include tensors of second derivatives:

Create a vector-valued InterpolatingFunction of one variable from unstructured vector-valued data:

The value is a vector:

Plot will show both components:

Unstructured data can be used in the one-variable case.

Create a vector-valued InterpolatingFunction of two variables from structured vector-valued data:

The value is a vector:

Plot3D will show all three components:

A single component may be plotted using Part:

Derivatives may also be included for Hermite interpolation:

Interpolate random data:

Find a continuous interpolation of the GCD function:

Interpolate through a set of points with a spline:

Create a spline interpolation:

Visualize the interpolation and the set of points:

The interpolating function always goes through the data points:

Find the integral of an interpolating function:

Plot the interpolating function and its integral:

Extrapolation is attempted to go beyond the original data:

With the default choice of order, at least 4 points are needed in each dimension:

With a lower order, fewer points are needed:

The interpolation function will always be continuous, but may not be differentiable: