The Interpolation package contains functions for interpolation.

It includes methods that support interpolation of irregularly spaced data and a method for kriging interpolation using variograms.

Each command in the Interpolation package can be accessed by using either the long form or the short form of the command name in the calling sequence.

The long form, Interpolation:-command, is always available. The short form can be used after loading the package.

The CurveFitting package also supports various interpolation methods. This section compares the interpolation functionality in both packages. There are many concrete examples on the Interpolation and Smoothing example help page.

The interpolation methods available in the Interpolation package all work as follows. First, the user calls one of the commands in the package, submitting the input points and the values at these points. This returns an object encapsulating all the data and options submitted. This object can then be used like a normal mathematical function, e.g. for plotting, integration, or just to evaluate at a given point. This feature makes this package a little easier to use than similar functionality in the CurveFitting package.

Additionally, the Interpolation package supports some methods of interpolation not supported by the CurveFitting package - in particular, the CurveFitting package only supports interpolation with more than one independent dimension if the input points form a grid; this is not needed for Radial Basis Function Interpolation, Inverse Distance Weighted Interpolation, Kriging Interpolation, Natural Neighbor Interpolation, or Linear Triangular Interpolation available in the Interpolation package.

On the other hand, the CurveFitting package supports some functionality not supported by the Interpolation package:

The Lowess command applies smoothing to the given data points; it performs approximation rather than interpolation. There is some similar functionality in the CurveFitting[LeastSquares] command, in various commands in the Statistics package, and in the TimeSeriesAnalysis package.

The BSpline and BSplineCurve commands define arbitrary curves in the plane, rather than functional relationship with an input and output.

The PolynomialInterpolation, RationalInterpolation, Spline, and Thiele commands allow for symbolic expressions as the results.

Consequently, use of the Interpolation package is recommended whenever you want to do interpolation and get floating-point answers, or if you want to do interpolation with more than one independent dimension.

The Interpolation package was introduced in Maple 2018.

For more information on Maple 2018 changes, see Updates in Maple 2018.