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 Plot Irregularly Spaced 3-D Data as a Surface

Real-world data doesn't always live on a structured grid—data can often be unstructured and non-uniform. For example,

 • experimental data (e.g. pressure vs enthalpy vs temperature)
 • weather data (e.g. longitude vs latitude vs temperature)
 • GIS (e.g. a LIDAR point cloud)
 • or finite element analysis on an irregular mesh

A common factor is a dependent variable arbitrarily placed upon an independent variable plane.

With Maple, you can generate surface plots from irregularly spaced 3-D points.

 • The Interpolation package contains tools for the interpolation of irregularly spaced data using several methods (e.g. Kriging and inverse distance weighting). The package generates what is essentially a normal mathematical function that can be analyzed or plotted.
 • surfdata will generate a surface constructed from triangles passing precisely through each data point.
 • ScatterPlot3D with the option lowess will generate a surface using lowess smoothing. The surface will not pass precisely through each data point; however, various options can be used to control the type of surface generated.

 Generate Irregularly Spaced Points

 > $N≔75:$

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 > $M≔⟨⟨X|Y|Z⟩⟩$
 >

 Kriging Interpolation

 >
 ${f}{≔}\left(\begin{array}{c}{Kriging intⅇrpolation obȷⅇct with 75 samplⅇ points}\\ {Variogram: Sphⅇrical\left(.00224838890116667,.0596838206033333,2.112716683\right)}\end{array}\right)$ (1)

This function can be interogated just like any normal mathematical function. Note that the function passes precisely through each data point.

 > $f\left(M\left[1,1\right],M\left[1,2\right]\right)$
 ${0.0305112187500000617}$ (2)

The function can also be plotted. Note that the function passes p

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 Delaunay Triangulation

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 Lowess Surface Fitting

Lowess surfaces smooth the data and do not pass precisely through each data point

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