Hi Jerzy and Ben,
Thanks for you answers!
I must say that although Ben is right in principle, Jerzy's answer is
exactly what I was looking for. Even if matplotlib can't do it by
itself, there appears to be other libraries that do the heavy lifting
and return a set of triangles which can then be placed in a
Polygon3DCollection and plotted.
It's always good to know what something is called. Searching for '3D
contours' was leading nowhere, but plugging in '*polygonization of the
implicit surface' *returned a multitude of descriptions of the problem
and libraries. It turns out I had been trying to implement the marching
cubes algorithm myself for the better part of the last week. Oops!
Thanks again to the both of you!!
-Peter
On 11/1/14, 8:34 PM, Benjamin Root wrote:
Jerzy,
Actually, my response is still completely valid. You can only plot
surfaces that can be represented parametrically in two dimensions.
Find me a single plotting library that can do differently without
having to get to this final step. For matplotlib, it is up to the user
to get the data to that point. As you stated, he is seeking
polygonization of an *implicit* surface. Matplotlib has no means of
understanding this. And this is unlikely to happen anytime soon given
the inherent 2D limitations of Matplotlib.
I am sorry if the answer is unsatisfactory to you, but it is the
correct one to give.
Ben Root
On Sat, Nov 1, 2014 at 2:49 PM, Jerzy Karczmarczuk
<[email protected] <mailto:[email protected]>>
wrote:
Le 01/11/2014 19:21, Benjamin Root answers the query of Peter
Kerpedjiev, who wants to plot (with Matplotlib) the surface of an
implicit surface (at least it was his presented example).
Your comment "of course, plotting a sphere can be done in
spherical coordinates" is actually the right thought process.
Spherical coordinates is how you parametrize your spherical
surface. Pick a coordinate system that is relevant to your
problem at hand and use it.
Sorry Ben, but this is not an answer. P.K. clearly states that his
case is more complicated, and no parametrization is likely.
Anyway, the spherical exercise as it is presented uses the 3D
constraint, it is not parametric.
The general solution is the *polygonization of the implicit
surface*, which is a well established technology (although
non-trivial). For example the /marching cubes / marching
simplices/ algorithms and their variants.
These are techniques for the polygonization of a mesh.
If P.K. has an analytic formula for his distributions, and is able
to compute gradients, etc., there are some more efficient
techniques, but in general it is the case for solving the equation
F(x,y,z)=0 for {x,y,z} ; here Matplotlib doesn't offer (yet) any
tools if I am not mistaken.
Jerzy Karczmarczuk
Caen, France.
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