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

• To: mathgroup at smc.vnet.net
• Subject: [mg96353] Re: Help! About drawing a high-precision 3D graph
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Thu, 12 Feb 2009 06:35:45 -0500 (EST)
• Organization: The Open University, Milton Keynes, UK
• References: <gmu8la\$ggt\$1@smc.vnet.net>

```In article <gmu8la\$ggt\$1 at smc.vnet.net>,
Chris <chris_wen_11 at hotmail.com> 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
*ListPointPlot3D*

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
numbers.

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

In:= FullForm[g]//Short

Out//Short=
Graphics3D[List[List[Hue[0.67`,0.6`,0.6`],Point[List[\[LeftSkeleton]1\[Ri
ghtSkeleton]]]]],\[LeftSkeleton]1\[RightSkeleton]]

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

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

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

Out//Short=
{MachinePrecision,MachinePrecision,<<958>>,MachinePrecision}

In:= \$MachinePrecision

Out= 15.9546

Regards,
--Jean-Marc

```

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