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Re: Help! About drawing a high-precision 3D graph

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  • Subject: [mg96353] Re: Help! About drawing a high-precision 3D graph
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at>
  • Date: Thu, 12 Feb 2009 06:35:45 -0500 (EST)
  • Organization: The Open University, Milton Keynes, UK
  • References: <gmu8la$ggt$>

In article <gmu8la$ggt$1 at>,
 Chris <chris_wen_11 at> wrote:

> I met a problem with drawing a 3D graph. My data to be used in Mathematica 
> Software is 15 digits, which means an example of those data is 
> 58.1234343253452. These data represent the latitude an d longitude of world. 
> So, I need to precisely paint those coordinate in a 3D space as a tiny point, 
> perhaps the method ListPoint3D to be used.However, it seems that ListPoint3D 
> does not support morn than 6 significant digits. So, can anyone help me ?

First, I assume you are talking about the standard built-in function 

Second, you seems to imply that *ListPointPlot3D* works with single 
floating-point precision numbers. How did you reach this --- erroneous 
--- conclusion? Regarding hardware precision arithmetic, Mathematica 
uses only *double* precision floating-point numbers. 

Since seeing is believing, we check that the points within the plot are 
represented in double-precision floating-point numbers. We create a 
graph, use FullForm to spot where the points are stored (as a list of 
triples within a structure Point[]), and check the precision of these 

In[1]:= g=ListPointPlot3D[Table[Sin[j^2+i],{i,0,3,0.1},{j,0,3,0.1}]]

In[2]:= FullForm[g]//Short


In[3]:= g[[1,1,2]]//Short

Out[3]//Short= Point[{{1.,1.,0.},<<959>>,{31.,31.,-0.536573}}]

In[4]:= Precision/@g[[1,1,2,1]]//Short


In[5]:= $MachinePrecision

Out[5]= 15.9546


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