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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

Description

• 

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).

• 

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.

Examples

First, some data is constructed and noise is then added to the z-component.

withStatistics:

X:=SampleUniform50,50,175:

Y:=SampleUniform50,50,175:

Zerror:=SampleNormal0,100,175:

Z:=Array1..175,i→sinYi20Xi62+Yi72+Zerrori:

XYZ:=MatrixX,Y,Z,datatype=float8%T

XYZ:= 175 x 3 MatrixData Type: float8Storage: rectangularOrder: Fortran_order

(1)

The view from above shows the irregular spacing of the x-y components of the data.

ScatterPlot3DXYZ,axes=box,orientation=20,0,0

A fitting order of 0 produces a form of weighted moving average.

ScatterPlot3DXYZ,lowess,fitorder=0,rule=0,grid=25,25,axes=box,orientation=20,70,0

Linear or quadratic fitting, with a fitting order of 1 or 2 respectively, produce smoother plots.

ScatterPlot3DXYZ,lowess,fitorder=1,rule=2,grid=25,25,axes=box,orientation=20,70,0

ScatterPlot3DXYZ,lowess,fitorder=1,rule=2,showpoints=false,grid=25,25,axes=box,orientation=20,70,0

ScatterPlot3DXYZ,lowess,fitorder=2,rule=3,grid=25,25,axes=box,orientation=20,70,0

See Also

CurveFitting, Statistics, Statistics[ScatterPlot], Statistics[Visualization], plots[surfdata], examples,Interpolation_and_Smoothing, Statistics[Lowess]


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