Uniformly Distributed Points

[19kdc3]

Hi Marco,

I'm wondering if you have any suggestions to uniformly distribute a set number of points throughout a mesh. The mesh will be either 2D or 3D, and in the case of 3D, points should also be distributed throughout the body (i.e. not only the surface). These points are later used to probe the original mesh.

Currently I've tried decimating the original mesh setting "n" to the number of points/probes I want, but I run into 2 issues:

1. The result doesn't always have "n" number of points
2. The result points aren't uniformly distributed

Thanks for your help!

[marcomusy]

Hi @kman750 what about this:

from vedo import *

msh = Polygon(nsides=5)

pts = utils.pack_spheres(msh, radius=0.1)

# optionally add some noise:
jitter = np.random.randn(len(pts),3)/1000
jitter[:,2] = 0
pts += jitter

pts = Points(pts)
pts.cut_with_line(msh.points()) # needs an ordered set of points

show(msh, pts, axes=1)

I would not use decimate.
Also you can extend easily this to 3D (you can use cut_with_mesh() or some_mesh.inside_points(my_points) to test the points).

[marcomusy]

You cannot have both things, I'm not aware of any algorithm that can give you the exact nr of points, unless, as I said you first make an estimate based on the area/volume and then refine it by trying different values of radius.

[19kdc3]

Thank you very much for your help and suggestions Marco! I really appreciate it.

[marcomusy]

You're welcome!

[RyanConway91]

Perhaps an iterative solution? Generate grids of different spacings and then query the number of points in the grid and repeat until have the desired number of points? Not sure what solver you would use to run the optimization though.

[marcomusy]

I think any non-gradient based optimizer would work - there are 2 examples here:
https://github.com/marcomusy/vedo/blob/master/examples/other/iminuit1.py (must choose "simplex")
https://github.com/marcomusy/vedo/blob/master/examples/other/nevergrad_opt.py

..or simple trial and error :)