is an option for Interpolation, as well as ListLinePlot, ListPlot3D, ListContourPlot, and related functions, that specifies what order of interpolation to use.


  • InterpolationOrder->n specifies that polynomials of degree n should be fitted between data points.
  • For multidimensional data, the polynomials are taken to be of degree n in each variable.
  • InterpolationOrder->None specifies that data points in plots should be joined without interpolation.
  • InterpolationOrder->0 yields a collection of flat regions, with steps at each data point.
  • InterpolationOrder->1 joins data points with straight lines in 2D, and with piecewise polygonal surface elements in 3D.
  • Higher interpolation orders generally lead to increasingly smooth curves or surfaces.
  • In functions such as NDSolve, InterpolationOrder->All specifies that the interpolation order should be chosen to be the same as the order of the underlying solution method.
  • InterpolationOrder can also be used in functions like Manipulate, to specify the smoothness of animations between control points such as bookmarks.


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Basic Examples  (3)

Use different interpolation orders for curves:

Use different interpolation orders for surfaces:

Use different interpolation orders when constructing an InterpolatingFunction:

Scope  (4)

Use piecewise quintic interpolation to approximate the sine function:

Show the approximation error:

Show the smoothing effect of higher interpolation order in plotting:

Show the smoothing effect of higher interpolation order for GCD data:

Get a solution that uses interpolation of the same order as the method from NDSolve:

This is more time consuming than the default interpolation order used:

It is much better in between steps:

Possible Issues  (1)

Very high-order interpolation can lead to large errors:

Interpolate with order 20:

Piecewise interpolation with lower order makes a much better approximation:

Show the approximation error for different interpolation orders:

Neat Examples  (1)

Zero-order interpolation, with Voronoi cells having the constant value:

Introduced in 1996
Updated in 2007