Re: [Matplotlib-users] Level surface of a function of 3 variables

[Jason G. <jas...@cr...>]

On 9/17/10 9:08 PM, Fernando Perez wrote:
> Hi Luke,
>
> On Fri, Sep 17, 2010 at 5:49 PM, Dale Lukas Peterson
> <haz...@gm...>  wrote:
>>
>>   I'm not sure I understand how I would make use of my function then.
>>   My function needs to be evaluated over a 3-d mesh (x, y, and z) , and then the
>>   level surfaces (not contour lines) calculated.  I guess I could treat
>>   z as a parameter, then plot the zero level contour lines of my function for
>>   a discrete number of z values, but then I would need to adjust the
>>   height that each countour line is plotted at when I do the 3-d plot.
>>   This still would only give bunch of vertically stacked contour
>>   lines, rather than a nice smooth 3-d surface.
>>
>>   If I'm misunderstanding what you meant, perhaps you could point me
>>   to an example of something that makes a level surface of a function
>>   of 3 (not 2) variables?
>
> You're looking for an isosurface; as far as I know matplotlib does not
> have isosurface modules, only 2-d contours embedded in 3d (such as
> those illustrated in
> http://matplotlib.sourceforge.net/examples/mplot3d/contourf3d_demo.html).
>
> VTK does have powerful isosurface capabilities, nicely exposed by mayavi:
>
> http://code.enthought.com/projects/mayavi/docs/development/html/mayavi/auto/mlab_helper_functions.html#contour3d


Sage will also do this sort of thing, though it's not as powerful as 
VTK/Mayavi in this functionality:

http://www.sagemath.org/doc/reference/sage/plot/plot3d/implicit_plot3d.html

Here are lots of sheets on sagenb.org that use implicit_plot3d somewhere:

http://sagenb.org/pub/?typ=pub&search=implicit_plot3d


Thanks,

Jason