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Plot Irregularly Spaced 3-D Data as a Surface

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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)

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weather data (e.g. longitude vs latitude vs temperature)

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GIS (e.g. a LIDAR point cloud)

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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.

 

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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.

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surfdata will generate a surface constructed from triangles passing precisely through each data point.

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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

 

N75:

 

XLinearAlgebra:-RandomVectorN,generator=2..2.: YLinearAlgebra:-RandomVectorN,generator=2..2.:ZVectorN,iXiexpXi2Yi2+rand1030:

MX|Y|Z

_rtable18446746690600333310

(1)

p1plots:-pointplot3dM,style=patchnogrid,color=black,symbol=solidsphere,symbolsize=20, style=point

Kriging Interpolation

 

f  Interpolation:-KrigingX|Y,Z

fKrⅈgⅈng ⅈntⅇrpolatⅈon obȷⅇct wⅈth 75 samplⅇ poⅈntsVarⅈogram: Sphⅇrⅈcal(.00224838890116667,.0596838206033333,2.112716683)

(2)

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

fM1,1,M1,2

0.0305112187500000617

(3)

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

p2plot3df, 2 .. 2, 2 .. 2, transparency=0.5:plots:-displayp1,p2

Delaunay Triangulation

 p3plots:-surfdataM,style=patchnogrid,color=ColorTools:-ColorRGB,150255,79255,121255: plots:-displayp1,p3

Lowess Surface Fitting

 

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

p4Statistics:-ScatterPlot3DM, lowess, fitorder=2, rule=3, grid=25,25, style=surface,color=ColorTools:-ColorRGB,150255,79255,121255:plots:-displayp1,p4