3D mesh to particle cloud conversion

Question

I need to convert arbitrary triangulated 3D mesh to cloud of particles that are uniformly spaced. First thought was to try find a way to fill one 3D triangle. And then fill each triangle of mesh, removing duplicated particles on edges, but that's just hard and too much work. I was hoping for some more-math way.

Can anyone point me to an algorithm which can help me do my task correctly... well, at least approximatively?

Thanks

If you would be satisfied with particles that are uniformly distributed (as opposed to uniformly spaced) you could build on triangle sampling algorithms such as http://mathworld.wolfram.com/TrianglePointPicking.html. But it looks from your self-answer that you want uniformly spaced. — brainjam, Mar 20 '11 at 18:26

score 1 · Accepted Answer · answered Mar 16 '11 at 13:35

There are two main options:

Voxelization of mesh. Easy to implement the conversion of mesh to voxels, but it's inaccurate since uniform spacing cannot be achieved: distance between cubes can be x, x*sqrt(2) or x*sqrt(3) depending if neighbor cubes are in same plane and adjacent.
Poisson disk sampling on surface. Hard to implement and lack of research material and code, but mathematically very correct. Some links:

http://research.microsoft.com/apps/pubs/default.aspx?id=135760

http://web.mysites.ntu.edu.sg/cwfu/public/Shared%20Documents/dualtiling/index.html

Benjamin · Answer 2 · 2011-03-14T15:01:04.947

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You could convert the TIN to raster using a GIS package or software such as R, then retrieve one point at the center of each pixel representing the value. (Example in ArcGIS)

EDIT: If the irregular 3D mesh has multiple heights per {x, y} a similar approach would be to sample the mesh using a voxel "grid" and keep one value per voxel. GRASS GIS has the functionality to take the vertices of the TIN (3d mesh) and convert them to voxels, then back to a regular 3d cloud.

edited Mar 14 '11 at 15:01

answered Mar 14 '11 at 14:33

Benjamin

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@J.B.: I'm suggesting that you then convert that "heightmap" back to a regular 3d mesh by extracting the value of each pixel and using it as a z value. – Benjamin Mar 14 '11 at 14:45
But for regular 3D mesh - one pair {x,y} can have multiple z values, thus this is not for complex 3D shapes to 3D point cloud conversion I need. Or am I missing something? – J.B. Mar 14 '11 at 14:51
@J.B.: I might have misinterpreted your question. I was thinking in terms of terrain surface, but it seems you are dealing with some sort of 3D object with multiple heights at the same {x,y}? If so, there might be a similar solution using voxels to sample the mesh and return a point per voxel. – Benjamin Mar 14 '11 at 15:00
Correct, I was thinking of arbitrary 3D mesh (concave, convex, whatever). Voxels you say... that's a nice idea, I'll check it out. – J.B. Mar 14 '11 at 15:04
I have just analyzed the solution. Voxelization will yield errors - particles wont be uniformly spaced. This is because distance between cube centers in the same plane is 'a', and between two diagonal neighbor cubes 'a*sqrt(3)=a*1.73', which yields great local errors (for example imagine voxelizing simple slope). – J.B. Mar 14 '11 at 20:02
Won't all regular 3D meshes do that? In any case, you can always reduce the voxel size to a point where this "error" is acceptable. This is no different then the 2D case. – Benjamin Mar 14 '11 at 20:08
Yeah I was hoping there could be other algos, not grid-based, that would be more correct. But I guess I will have to stick with voxels i.e. uniform grid. – J.B. Mar 14 '11 at 22:14

3D mesh to particle cloud conversion

2 Answers2