Re: [Matplotlib-users] plot arbitrary 3D surface

[Peter K. <pke...@gm...>]

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 
> <jer...@un... <mailto:jer...@un...>> 
> 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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