<p>I have a point cloud that I would like to convert to a surface, in the form of a wireframe lattice structure.</p>

<p>This means, from a sequence of 3D points <em>(x,y,z)</em>, obtaining three 2D matrices <em>X,Y,Z</em> of the same size. In this way the points should be topologically related with a neighborhood of 4 (North, South, East, West). Such an organization of the points might, then, be plotted with functions such as <em>matplotlib</em>'s <a href="http://matplotlib.org/mpl_toolkits/mplot3d/tutorial.html#wireframe-plots" rel="nofollow"><code>Axes3D.plot_wireframe</code></a> or <a href="http://matplotlib.org/mpl_toolkits/mplot3d/tutorial.html#mpl_toolkits.mplot3d.Axes3D.plot_surface" rel="nofollow"><code>Axes3D.plot_surface</code></a></p>

<p>From what I understood, the relationship of a point with the neighboring points is characterized by having minimal distance. I think that this is a combinatorial optimization problem, and NP-hard.</p>

<p>Now the question: are there algorithms that, given a list of 3D points, return the three aforementioned matrices X,Y,Z ?</p>

<p>Thank you very much. I also hope this is the correct stack exchange forum for this kind of question.</p>

CC BY-SA 3.0
2014-08-04T10:29:32.747Z
Hmm, I am not sure I understood your question... you mean optimization constraints?
fstab
CC BY-SA 3.0
2014-08-04T15:02:31.130Z
Can you explain/more precisely define a "wireframe lattice structure"?
usul
CC BY-SA 3.0
2014-08-04T15:15:53.227Z
What I mean with 'wireframe lattice structure' is just a grid, folded into a specific shape, for example, as representing the surface of an object. The nodes of this grid may well be the original points, with neighbourhood information attached.
fstab
CC BY-SA 3.0
2014-08-05T04:06:46.423Z
there is some theoretical/ algorithmic/ research angle here but this sounds more like an applied/ standardized raytracing type question to me where surfaces are "triangulated" for visualization purposes, and various well-known algorithms are built into GPU cards etc. the closest related se for it might be [gamedev.se]
vzn
<ds.algorithms><cg.comp-geom>
Is there an algorithm that, given a point cloud, infers an optimal wireframe (surface) structure?
fstab
# Is there an algorithm that, given a point cloud, infers an optimal wireframe (surface) structure?

(Asked by: username_0 on 2014-08-03)

I have a point cloud that I would like to convert to a surface, in the form of a wireframe lattice structure.

This means, from a sequence of 3D points *(x,y,z)*, obtaining three 2D matrices *X,Y,Z* of the same size. In this way the points should be topologically related with a neighborhood of 4 (North, South, East, West). Such an organization of the points might, then, be plotted with functions such as *matplotlib*'s [`Axes3D.plot_wireframe`](http://matplotlib.org/mpl_toolkits/mplot3d/tutorial.html#wireframe-plots) or [`Axes3D.plot_surface`](http://matplotlib.org/mpl_toolkits/mplot3d/tutorial.html#mpl_toolkits.mplot3d.Axes3D.plot_surface)

From what I understood, the relationship of a point with the neighboring points is characterized by having minimal distance. I think that this is a combinatorial optimization problem, and NP-hard.

Now the question: are there algorithms that, given a list of 3D points, return the three aforementioned matrices X,Y,Z ?

Thank you very much. I also hope this is the correct stack exchange forum for this kind of question.

**Tags:** ds.algorithms, cg.comp-geom

> **Comments:**
> **username_0**: Hmm, I am not sure I understood your question... you mean optimization constraints?  
> **username_1**: Can you explain/more precisely define a "wireframe lattice structure"?  
> **username_0**: What I mean with 'wireframe lattice structure' is just a grid, folded into a specific shape, for example, as representing the surface of an object. The nodes of this grid may well be the original points, with neighbourhood information attached.  
> **username_2**: there is some theoretical/ algorithmic/ research angle here but this sounds more like an applied/ standardized raytracing type question to me where surfaces are "triangulated" for visualization purposes, and various well-known algorithms are built into GPU cards etc. the closest related se for it might be [gamedev.se]  

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