The ScatterPlot3D command generates 3D a scatter plot for the specified 2D data together with a surface approximated using lowess smoothing (LOcally Weighted Scatterplot Smoothing).

The first parameter, XYZ, is the data sample - given as a Matrix or Array with three columns and as many rows as there are distinct data points. Each row represents the x-, y-, and z-coordinate of a data point.

The collection of x- and y-components of all the data points need not collectively form a regular grid in the x-y plane. The data points may be irregularly spaced when projected onto the x-y plane.

As this is a smoothing technique, the resulting surface will not necessarily pass exactly through all the the 3D data points.

The options argument can contain one or more of the options shown below. All unrecognized options will be passed to the plots[display] command. See plot[options] for details.

lowess=truefalse

Designates whether lowess smoothing should be applied to the scatter plot. The smoothing behavior is modified by the options bandwidth, fitorder, rule, and strictorder; see these options for more details. The default value is false.

bandwidth=realcons

This option is used to control the bandwidth of the lowess smoothing algorithm, when lowess fitting is enabled. The value of this option specifies the ratio of the size of the rectangular fitting window to the entire range of the independent data. The default value is . At the value of  all data points in the sample will be used to compute each plotted grid value, which is quite expensive and not really in the spirit of lowess smoothing. As this value is decreased, fewer data points will be found within the window and used for each individual local fit, and this will decrease the duration of the whole computation. As this value is increased, more points farther away will influence the output value for each local fit, and this will also increase the duration of the whole computation.

fitorder=identical(0,1,2)

The degree of the bivariate polynomial used in lowess smoothing, when lowess fitting is enabled. The default value is .

rule=identical(1,2,3)

Designates the rule by which the nearby points falling in the window specified by bandwidth are weighted. The default value is  , which denotes the tri-cubed rule. A value of 0 for this option means that all points found in the window will have the same weight.

strictorder=truefalse

Designates whether the order of the fitting curve may not be reduced in the case that the number of points found in the window is less than what would be necessary for the supplied fitorder option. The default value is false, which allows reduction of the order at any individual computed point.

showpoints=truefalse

Designates whether the pointplot component will be included in the output. If false then only the surface will be included. The default value is true.

The Statistics[ScatterPlot3D] command was introduced in Maple 16.

For more information on Maple 16 changes, see Updates in Maple 16.