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MathGroup Archive 1997

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Re: Is there a better way to do a 3D List Plot?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg7385] Re: Is there a better way to do a 3D List Plot?
  • From: tburton at cts.com (Tom Burton)
  • Date: Fri, 30 May 1997 01:19:34 -0400 (EDT)
  • Organization: Brahea Consulting
  • Sender: owner-wri-mathgroup at wolfram.com

On 27 May 1997 10:29:40 -0400, in comp.soft-sys.math.mathematica you wrote:

>I have a list of data that I would like to plot
>that looks like:
>
>ResistMap3D1 =
>   {{-1260,0,5060},{-840,0,5048},{-420,0,5032},{0,0,5046},{420,0,5041},{840,0,
>      5046},{1260,0,5052},{0,-1260,5047},{0,-840,5023},{0,-420,5037},{0,420,
>      5037},{0,840,5031},{0,1260,5056},{-840,840,5057},{840,840,5061},{
>      840,-840,5048},{-840,-840,5047},{-420,420,5037},{420,420,5033},{
>      420,-420,5034},{-420,-420,5036}};
>
>It's format it {x,y,z}.
>
>The only way I know of to plot this is:
>
>Resistpp = 
>  Show[Graphics3D[Point[{-1260,0,5060}]],Graphics3D[Point[{-840,0,5048}]],
>    Graphics3D[Point[{-420,0,5032}]],Graphics3D[Point[{0,0,5046}]],
>    Graphics3D[Point[{420,0,5041}]],Graphics3D[Point[{840,0,5046}]],
>    Graphics3D[Point[{1260,0,5052}]],Graphics3D[Point[{-420,420,5037}]],
>    Graphics3D[Point[{420,420,5033}]],Graphics3D[Point[{420,-420,5034}]],
>    Graphics3D[Point[{-420,-420,5036}]],Graphics3D[Point[{-840,840,5057}]],
>    Graphics3D[Point[{840,840,5061}]],Graphics3D[Point[{840,-840,5048}]],
>    Graphics3D[Point[{-840,-840,5047}]],Graphics3D[Point[{0,-1260,5047}]],
>    Graphics3D[Point[{0,-840,5023}]],Graphics3D[Point[{0,-420,5037}]],
>    Graphics3D[Point[{0,420,5037}]],Graphics3D[Point[{0,840,5031}]],
>    Graphics3D[Point[{0,1260,5056}]],AspectRatio->1,ViewPoint -> {0,1,0}];
>
>Is there a better way?  And I can't get the point size to be big enough
>to see.  Is there a way to increase the size?
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>
>
Yes, you can instruct Graphics3D directly to make bigger points, but there are much better ways!  First, a 3D scatterplot will accept a change in point size. The following expression makes pretty big points.


Needs["Graphics`Graphics3D`"]

ScatterPlot3D[ResistMap3D1,PlotStyle->PointSize[.02],BoxRatios->{1,1,1/3}]

You can also make a surface. It's just a bit of work because the points are not arranged in a 2D array. First, form triangles connecting the points in the x-y plane:

Needs["DiscreteMath`ComputationalGeometry`"]

trival=DelaunayTriangulation[ResistMap3D1/.{x_,y_,z_}->{x,y}]

This algorithm is apparently not robust. This pattern of points leads to a failure, and the resulting surface is not complete.  So off the top of my head, I decided to jiggle the points a bit in the x-y plane:

trival=DelaunayTriangulation[
    ResistMap3D1/.{x_,y_,z_}->{x+10Random[]-5,y+10Random[]-5}]
These points generate more complaints but a better triangulation. Then plot the surface.

TriangularSurfacePlot[ResistMap3D1,trival,BoxRatios->{1,1,1}]


Tom Burton


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