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Re: How to convert a flat scan of a 3D object, into a 3D picture in cylindrical coordinates?

• To: mathgroup at smc.vnet.net
• Subject: [mg47675] Re: [mg47643] How to convert a flat scan of a 3D object, into a 3D picture in cylindrical coordinates?
• From: Christopher Purcell <christopherpurcell at mac.com>
• Date: Wed, 21 Apr 2004 05:23:17 -0400 (EDT)
• References: <200404200718.DAA27795@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

You can copy your Abe3D.txt file into mathematica, put quotes around it 
to make it a string, and name it 'data'.
Then the following makes a nice live president.

data="pasteyourdatahere";

junk = StringToStream[data];
  morejunk = Partition[ReadList[junk, Number], 73];
lincoln = ListInterpolation[morejunk, {{0., 1.}, {0., 1.}}];
<< RealTime3d`
ParametricPlot3D[{lincoln[u, v]Cos[90 Degree + 2 Pi v], lincoln[u, 
v]Sin[90 Degree + 2 Pi v], -50 u},
{u, 0., 1.}, {v, 0., 1.}, PlotPoints -> {50, 100}, ViewPoint -> {1, -2, 
0},PlotRange -> All];

I'm not sure about the vertical scale factor (here set to 50), he looks 
a little squished.

christopherpurcell at mac.com


On Apr 20, 2004, at 4:18 AM, Gilmar Rodr?guez Pierluissi wrote:

> Please; double-click the following internet links:
>
> http://www.tilmarlily.netfirms.com/download/Abe3D.txt
> http://www.tilmarlily.netfirms.com/download/Abe3D.xls
>
> to download:
>
> (1.) the text file: "Abe3D.txt" and,
> (2.) an Excel spreadsheet: "Abe3D.xls".
>
> The file "Abe3D.txt" is data obtained by scanning the surface of a
> bust of Abraham Lincoln.  This file contains a 95 X 73 array of
> values.  Each line of longitude was smoothened using a cubic spline,
> and the whole array can be used to draw a (rough) 3D picture of the
> bust.
> You can view this picture by opening the spreadsheet Abe3D.xls,
> and opening the Excel chart in it.  Notice that the image of "Abe"
> (for short)
> is flat; i.e. similar to a Mercator map of the World.  My question is:
> How can I build a 3D picture of Abe, using cylindrical coordinates,
> so that the new picture looks like the real bust of Abe, and a person
> can rotate the picture of the bust in 3D?
> Thank you for your help!
>

• References:
  • How to convert a flat scan of a 3D object, into a 3D picture in cylindrical coordinates?
    • From: gilmar.rodriguez@nwfwmd.state.fl.us (Gilmar Rodr?guez Pierluissi)