Re: [Matplotlib-users] plotting 3d function

[Benjamin R. <ben...@ou...>]

On Mon, Jan 21, 2013 at 8:06 PM, Pau <vim...@go...> wrote:

> Hi,
>
> I am somehow new to matplotlib and I am trying to plot this function of x
> ,y ,z
>
> F(x,y,z)=
> 38244.74787*Pi*(x^2+y^2+z^2)^.125+1615.975261*Pi*z^2/(x^2+y^2+z^2)^.875-1292.780210*Pi*z^2/((x^2+y^2+z^2)^.875*(1+y^2/x^2))+1292.78*Pi*(x^2+y^2+z^2)^.125/(1+y^2/x^2)
>
> in a similar way as
>
> http://matplotlib.org/mpl_examples/mplot3d/contour3d_demo3.hires.png
>
> The code is
> http://matplotlib.org/mpl_examples/mplot3d/contour3d_demo3.py
>
> But I have no idea where to start...
>
> some help would be appreciated...
>
> thanks
>
>
The reason you are having difficulty coming up with a way to plot this is
because you have 3 input dimensions, and 1 output dimension that you wish
to plot.  If you were to plot this in 3D space, it would have to be done as
F(x,y,z) as a colored "mist" in the domain of (x,y,z).  While a "mist"
can't be done in mplot3d, you could plot out scatter points to emulate
this.  One could also use contourf3d(..., zdir='z', offset=...) to create
slices of the filled contours, similar to this example:

http://matplotlib.org/examples/mplot3d/contourf3d_demo2.html

Now, if the domain of (x,y,z) can be parameterized as a surface (i.e., a
sphere or a cylinder), then you are looking to do an image of F(x,y,z)
plotted on that surface, which is a little bit difficult, but also do-able
using the plot_surface() function.

Cheers!
Ben Root