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.
Examplesopen allclose all
Basic Examples (3)
Use different interpolation orders for curves:
Use different interpolation orders for surfaces:
Use different interpolation orders when constructing an InterpolatingFunction:
Use piecewise quintic interpolation to approximate the sine function:
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:
Possible Issues (1)
Wolfram Research (1996), InterpolationOrder, Wolfram Language function, https://reference.wolfram.com/language/ref/InterpolationOrder.html (updated 2008).
Wolfram Language. 1996. "InterpolationOrder." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2008. https://reference.wolfram.com/language/ref/InterpolationOrder.html.
Wolfram Language. (1996). InterpolationOrder. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/InterpolationOrder.html