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Re: Re: 3D graphics

  • To: mathgroup at smc.vnet.net
  • Subject: [mg22793] Re: [mg22720] Re: 3D graphics
  • From: Bojan Bistrovic <bojanb at python.physics.odu.edu>
  • Date: Sat, 25 Mar 2000 03:58:31 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

> Hi,
> 
> since your function jump from 0 to 1 you can simply use a
> ContourPlot3D[] with
> contourlevel 1/2
> 
> Needs["ContourPlot3D`"]
> 
> fun[x_?NumericQ, y_?NumericQ, z_?NumericQ] := 
>   If[N[x^2 + y^2 + z^2] < 1., 0., 1.]
> 
> 
> ContourPlot3D[fun[x, y, z],
>   {x, -1.1, 1.1}, {y, -1.1, 1.1}, {z, -1.1, 1.1}, Contours -> {0.5}]
> 
> Regards
>   Jens
> 
> Bernhard Adams wrote:
> > 
> > Hi everybody,
> > 
> > I would like to plot a body in 3D whose volume is defined by a function
> > f[x,y,z] which returns 1 if (x,y,z) is inside the body and 0 if outside.
> > How to plot this?
> > 
> > Thanx, Bernhard Adams
> 
You'll probably wan't to change the default option PlotPoints->{3,5} to get
the better quality of the output. This will naturally increase the time needed
so be careful:

In[10]:= ContourPlot3D[fun[x, y, z],
   {x, -1.1, 1.1}, {y, -1.1, 1.1}, {z, -1.1, 1.1}, Contours -> {0.5}]//Timing

Out[10]= {4.21 Second, - Graphics3D - }

In[11]:= ContourPlot3D[fun[x, y, z],
  {x, -1.1, 1.1}, {y, -1.1, 1.1}, {z, -1.1, 1.1}, Contours -> {0.5},
    PlotPoints->{4,6}]//Timing

Out[11]= {18.48 Second, - Graphics3D - }

This one is alreasy recognisable as sphere, but it's still far from perfect:

In[12]:= ContourPlot3D[fun[x, y, z],
  {x, -1.1, 1.1}, {y, -1.1, 1.1}, {z, -1.1, 1.1}, Contours -> {0.5},
    PlotPoints->{5,7}]//Timing

Out[12]= {56.83 Second, - Graphics3D - }

In[13]:= ContourPlot3D[fun[x, y, z],
  {x, -1.1, 1.1}, {y, -1.1, 1.1}, {z, -1.1, 1.1}, Contours -> {0.5},
    PlotPoints->{6,8}]//Timing

Out[13]= {145.6 Second , - Graphics3D - }

One that looks good is

In[14]:= ContourPlot3D[fun[x, y, z],
  {x, -1.1, 1.1}, {y, -1.1, 1.1}, {z, -1.1, 1.1}, Contours -> {0.5},
    PlotPoints->{7,9}]//Timing

Out[13]= {278.31 Second, , - Graphics3D - }

Bye, Bojan

--
---------------------------------------------------------------------
Bojan Bistrovic,                                      bojanb at jlab.org
Old Dominion University, Norfolk VA & Jefferson Lab, Newport News, VA
---------------------------------------------------------------------



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