- 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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