Statistics[ScatterPlot3D]  generate 3D scatter plots

Calling Sequence


ScatterPlot3D(XYZ, options, plotoptions)


Parameters


XYZ



Array or Matrix of numeric data, of size mx3

options



(optional) equation(s) of the form option=value where option is one of lowess, bandwidth, fitorder, rule, strictorder, or showpoints; specify options for generating the scatter plot

plotoptions



options to be passed to the plots[display] command





Options



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.


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.


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.

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fitorder=identical(0,1,2)


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


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


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.


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.



Description


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

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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 zcoordinate of a data point.

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

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



Compatibility


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



Examples


First, some data is constructed and noise is then added to the zcomponent.
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 (1) 
The view from above shows the irregular spacing of the xy components of the data.
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A fitting order of 0 produces a form of weighted moving average.
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Linear or quadratic fitting, with a fitting order of 1 or 2 respectively, produce smoother plots.
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