# InterpolationOrder

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

# Details

• 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.
• specifies that data points in plots should be joined without interpolation.
• yields a collection of flat regions, with steps at each data point.
• 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, 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.

# Examples

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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:

Wolfram Research (1996), InterpolationOrder, Wolfram Language function, https://reference.wolfram.com/language/ref/InterpolationOrder.html (updated 2008).

#### Text

Wolfram Research (1996), InterpolationOrder, Wolfram Language function, https://reference.wolfram.com/language/ref/InterpolationOrder.html (updated 2008).

#### CMS

Wolfram Language. 1996. "InterpolationOrder." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2008. https://reference.wolfram.com/language/ref/InterpolationOrder.html.

#### APA

Wolfram Language. (1996). InterpolationOrder. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/InterpolationOrder.html

#### BibTeX

@misc{reference.wolfram_2024_interpolationorder, author="Wolfram Research", title="{InterpolationOrder}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/InterpolationOrder.html}", note=[Accessed: 13-August-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_interpolationorder, organization={Wolfram Research}, title={InterpolationOrder}, year={2008}, url={https://reference.wolfram.com/language/ref/InterpolationOrder.html}, note=[Accessed: 13-August-2024 ]}