Plot 3D surface that is not the graph of a function

Question

I have a 3D data set of a surface that is not a function graph. The data is just a bunch of points in 3D, and the only thing I could think of was to try scatter3 in Matlab. Surf will not work since the surface is not a function graph.

Using scatter3 gave a not so ideal result since there is no perspective/shading of any sort.

Any thoughts? It does not have to be Matlab, but that is my go-to source for plotting.

To get an idea of the type of surface I have, consider the four images:

The first is a 3D contour plot, the second is a slice in a plane {z = 1.8} of the contour. My goal is to pick up all the red areas. I have a method to do this for each slice {z = k}. This is the 3rd plot, and I like what I see here a lot.

Iterating this over z give will give a surface, which is the 4th plot, which is a bit noisy (though I have ideas to reduce the noise...). If I plot just the black surface using scatter3 without the contour all I get is a black indistinguishable blob, but for every slice I get a smooth curve, and I have noticed that the curves vary pretty smoothly when I adjust z.

Some fine-tuning will give a much better 4th plot, but still, even if I get the 4th plot to have no noise at all, the result using scatter3 will be a black incomprehensible blob when plotted alone and not on top of the 3D contour. I would like to get a nice picture of the full surface that is not plotted on top of the 3D contour plot

In fact, just to compare and show how bad scatter3 is for surfaces, even if you had exact points on a sphere and used scatter3 the result would be a black blob, and wouldn't even look like a sphere

Can POV-Ray handle this? I've never used it...

Answer 1

just wanted to follow up on this question. A quick nice way to do this in Matlab is the following:

Consider the function d(x, y, z) defined as the minimum distance from (x, y, z) to your data set. Make sure d(x, y, z) is defined on some grid that contains the data set you're trying to plot.

Then use isosurface to plot a (some) countour(s) of d(x, y, z). For me plotting the contour 0.1 of d(x, y ,z) was enough: Matlab will plot a nice looking surface of all points within a distance 0.1 of the data set with good lighting and all.

Answer 2

If you have a triangulation of your points, you could consider using the trisurf function. I have used that before to generate closed surfaces that have no boundary (such as polyhedra and spheres). The downside is that you have to generate a triangulation of your points. This may not be ideal to your needs but it definitely an option.

EDIT: As @High Performance Mark suggests, you could try using delaunay to generate a triangulation in Matlab

Answer 3

In povray, a blob object could be used to display a very dense collection of points, if you make them centers of spheres.
http://www.povray.org/documentation/view/3.6.1/71/ If you want to be able to make slices of "space" and have them colored as per your data, then maybe the object pattern (based on a #declared blob object) might do the trick.

Povray also has a way to work with df3 files, which I've never worked with, but this user appears to have done something similar to your visualization. http://paulbourke.net/miscellaneous/df3/