 # Level surface of a function of 3 variables

I have a function of three variables and am interested in plotting the zero level surface:

f(x,y,z) = 0

Is there a simple way to plot this level surface in 3-D without having to resort to meshing up x and y, and solving for the z that satisfies the equation? I can do this, but it gets messy because there are anywhere from 0 to 2 solutions to the equation for each point in the x-y plane.

The mplot3d examples all seem to calculate the z-data simply from simple functions of x and y.

Thanks,

~Luke

I think you can make it with pyplot.contourf() and the argument V

http://matplotlib.sourceforge.net/api/pyplot_api.html#matplotlib.pyplot.contour

"contour(Z,V)
contour(X,Y,Z,V)

draw contour lines at the values specified in sequence V"

···

On Wed, Sep 15, 2010 at 9:02 PM, Luke <hazelnusse@...287...> wrote:

I have a function of three variables and am interested in plotting the zero
level surface:
f(x,y,z) = 0
Is there a simple way to plot this level surface in 3-D without having to
resort to meshing up x and y, and solving for the z that satisfies the
equation? I can do this, but it gets messy because there are anywhere from
0 to 2 solutions to the equation for each point in the x-y plane.
The mplot3d examples all seem to calculate the z-data simply from simple
functions of x and y.
Thanks,
~Luke
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David,
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?

Thanks,
~Luke

···

On Thu, Sep 16, 2010 at 05:28:47AM +0200, Daπid wrote:

I think you can make it with pyplot.contourf() and the argument V

http://matplotlib.sourceforge.net/api/pyplot_api.html#matplotlib.pyplot.contour

"contour(Z,V)
contour(X,Y,Z,V)

draw contour lines at the values specified in sequence V"

On Wed, Sep 15, 2010 at 9:02 PM, Luke <hazelnusse@...287...> wrote:
> I have a function of three variables and am interested in plotting the zero
> level surface:
> f(x,y,z) = 0
> Is there a simple way to plot this level surface in 3-D without having to
> resort to meshing up x and y, and solving for the z that satisfies the
> equation? I can do this, but it gets messy because there are anywhere from
> 0 to 2 solutions to the equation for each point in the x-y plane.
> The mplot3d examples all seem to calculate the z-data simply from simple
> functions of x and y.
> Thanks,
> ~Luke
> ------------------------------------------------------------------------------
> Start uncovering the many advantages of virtual appliances
> and start using them to simplify application deployment and
> accelerate your shift to cloud computing.
> http://p.sf.net/sfu/novell-sfdev2dev
> _______________________________________________
> Matplotlib-users mailing list
> Matplotlib-users@lists.sourceforge.net
> https://lists.sourceforge.net/lists/listinfo/matplotlib-users
>
>

Hi Luke,

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

If the mlab helper isn't sufficient for you, you can create directly
VTK isosurfaces, the heart example is a good point to start learning:

http://code.enthought.com/projects/mayavi/docs/development/html/mayavi/example_heart.html

Regards,

f

···

On Fri, Sep 17, 2010 at 5:49 PM, Dale Lukas Peterson <hazelnusse@...287...> wrote:

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

···

On 9/17/10 9:08 PM, Fernando Perez wrote:

Hi Luke,

On Fri, Sep 17, 2010 at 5:49 PM, Dale Lukas Peterson > <hazelnusse@...287...> 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