Hi,
I'm trying to plot an outline of an arbitrary 3D shape using matplotlib's plot_surface, and I wanted to ask if any one has any ideas as to how to do it. Here's the beginnings of a simple example:
# create a grid
resolution = 10
xs = np.linspace(-1,1,resolution)
ys = np.linspace(-1,1,resolution)
zs = np.linspace(-1,1,resolution)
X,Y,Z = np.meshgrid(xs, ys, zs)
#Then we can calculate the square of the distance of each point to the center:
W = X**2 + Y**2 + Z**2
# Let's see which points are within a certain radius:
C = W < 1.
# this can be used to create a point-cloud
x = X[C]
y = Y[C]
z = Z[C]
From this I tried a lot options, the best being to do some XOR operations on the array C to get a list of points which are on the surface of the sphere. My question is, can anybody see a reasonable way to plot this surface using mplot3D?
Of course plotting a sphere can be done using spherical coordinates, but that defeats the purpose of this example 
This is just a simplification as the application is actually to draw 3D contours (i.e. shapes, rather than iso-lines) of a three-parameter probability distribution.
Thanks in advance,
-Peter
Generally speaking, a plottable 3D surface can be represented parametrically in 2D (hence why it is a surface). Your point cloud can not be represented parametrically in 2 dimensions, hence why you are having difficulty figuring out how to plot it as a surface. I used to have similar problems with 3D plotting (both here and in Matlab) before I came to this realization.
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.
I hope this helps!
Ben Root
···
On Sat, Nov 1, 2014 at 2:07 PM, Peter Kerpedjiev <pkerpedjiev@…287…> wrote:
Hi,
I’m trying to plot an outline of an arbitrary 3D shape using
matplotlib’s plot_surface, and I wanted to ask if any one has any ideas
as to how to do it. Here’s the beginnings of a simple example:
create a grid
resolution = 10
xs = np.linspace(-1,1,resolution)
ys = np.linspace(-1,1,resolution)
zs = np.linspace(-1,1,resolution)
X,Y,Z = np.meshgrid(xs, ys, zs)
#Then we can calculate the square of the distance of each point to the
center:
W = X2 + Y2 + Z**2
Let’s see which points are within a certain radius:
C = W < 1.
this can be used to create a point-cloud
x = X[C]
y = Y[C]
z = Z[C]
From this I tried a lot options, the best being to do some XOR
operations on the array C to get a list of points which are on the
surface of the sphere. My question is, can anybody see a reasonable way
to plot this surface using mplot3D?
Of course plotting a sphere can be done using spherical coordinates, but
that defeats the purpose of this example 
This is just a
simplification as the application is actually to draw 3D contours (i.e.
shapes, rather than iso-lines) of a three-parameter probability
distribution.
Thanks in advance,
-Peter
Matplotlib-users mailing list
Matplotlib-users@lists.sourceforge.net
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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 , which is a well established technology (although
non-trivial). For example the 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.
···
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.
** polygonization of the implicit
surface*** marching cubes / marching
simplices*
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 <jerzy.karczmarczuk@…3937…> 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.
Matplotlib-users mailing list
Matplotlib-users@lists.sourceforge.net
https://lists.sourceforge.net/lists/listinfo/matplotlib-users
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 <jerzy.karczmarczuk@…3937…>
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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Jerzy,
I really do not wish to get into an argument with you. This seems to happen every time you come onto this mailing list. If “winning” this argument is so important to you, then you may have it. I will not continue to split hairs with you.
Thank you for mentioning the concept of implicit surfaces and marching cubes. I am glad that is helpful to the original poster.
Cheers!
Ben Root
···
On Sat, Nov 1, 2014 at 4:38 PM, Jerzy Karczmarczuk <jerzy.karczmarczuk@…3937…> wrote:
Le 01/11/2014 20:34, Benjamin Root a
écrit :
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.
1. I did not claim that you said something invalid, only that it
seemed weakly appropriate for Peter Karpedjiev.
2. Unfortunately NOW you say something inexact. Of course you can
plot implicit surfaces without 2D parametrization. All the
ray-tracing technology is adapted to that.
POV-Ray, etc., if you want some names. Some terrain renderers, such
as Terragen use it as well. YafaRay was once embeddable in Blender.
I am sorry if the answer is unsatisfactory to you, but it
is the correct one to give.
3. But "my satisfaction" is not the issue. I tried to direct Peter
in some usable direction, according to my experience.
Since the implementation of marching cubes, and other similar
techniques is awkward, not very efficient in Python (I tried it), I
suggest very strongly that Peter direct himself -at least
temporarily - to the RT methods.
If he wishes, I might help him in private. Writing a Ray Tracer in
Python/numpy is not so difficult (I gave it as student projects a
few times), and of course everything functional may be programmed in
POV-Ray.
Best regards.
Jerzy K.
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