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.
EXAMPLES
Basic Examples 
Scope 