This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# InterpolationOrder

 InterpolationOrder 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 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.
Use different interpolation orders for curves:
Use different interpolation orders for surfaces:
Use different interpolation orders when constructing an InterpolatingFunction:
Use different interpolation orders for curves:
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Use different interpolation orders for surfaces:
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Use different interpolation orders when constructing an InterpolatingFunction:
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 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:
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:
Zero-order interpolation, with Voronoi cells having the constant value:
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