Interpolation and Smoothing - Maple Help

Interpolated Plotting and Smoothing:

Example Worksheet

The topic of this worksheet is interpolation and smoothing of given 2-dimensional and 3-dimensional data. The organization is by dimension, task, and regularity of the data.

One common task is to generate only a plot of the data, as a curve or surface which passes through or approximates the data points.

Another task is to generate a procedure or piecewise spline expression which approximates the data and which can be queried for a value at any individual point nearby the original data points.

Another choice is whether to produce a curve or surface which passes through the given data points (and so interpolates them) or which simply approximates them (by smoothing). Is the data known to contain noise or measurement error? If the dependent data is expected to contain error or noise then it is reasonable to fit a smoothed surface or curve to the data, where the smoothed fit does not necessarily pass through or match the dependent data at the given data points. On the other hand, if the data is expected to be fully correct then it is reasonable to produce an interpolated curve or surface which passes through all the given data points.

A curve or surface may also be plotted directly from the data, or indirectly by first creating a procedure or (in the 2D case) a piecewise spline, and then subsequently supplying that to the plot or plot3d command. The constructed procedure would accept individual 1D or 2D independent data points and compute a dependent scalar value for that input.

Another relevant distinction for 3D data is whether the independent portion of the data lies on a regular grid in the 2D plane or whether it is comprised of points which are irregularly spaced in both directions.

This worksheet elaborates and compares these approaches for 2D and 3D plotting.

 > restart; with(LinearAlgebra): with(CurveFitting): with(Interpolation): with(plots): with(Statistics): randomize():