Why the Poisson reconstruction of the Hopf torus is so ugly?

[stla]

Hello,

Here is a beautiful Hopf torus:

It has 20000 points. When I run the Poisson reconstruction on it (with poisson_surface_reconstruction_delaunay, default parameters), I get this monster:

I tried to change the parameters but I always got such an output.

[afabri]

Can you please provide the point set.

[stla]

Hello @afabri

Here it is.

[afabri]

The point cloud is very sparse

[afabri]

The normal computation will already have a hard time to produce something reasonable.

[stla]

Ah ok. Will try to construct this point set in another way.

[sloriot]

Actually, if you are computing the point set yourself, maybe you can create the normal at the same time? I don't know what is your setting. Also let me point out this package in case you want to mesh an implicit function.

[stla]

Wow, I have this points cloud now. The Poisson reconstruction is still ugly but the Advanded front surface recontruction is perfect.

[stla]

@sloriot Even with the "true normals", the Poisson reconstruction is ugly.

[stla]

Actually, if you are computing the point set yourself, maybe you can create the normal at the same time? I don't know what is your setting. Also let me point out this package in case you want to mesh an implicit function.

Thanks, very interesting. The solid Möbius strip is an implicit surface. I have a ton of other ones.

[stla]

I tried the "uniform remesh" feature of VCG. The points cloud look nice, highly less sparse:

However, when I run the Poisson reconstruction on these points, two lobes look nice while the third one is monstruous:

That is strange, since the point set is rather symmetric.

[stla]

Ah, there's an option multisample and the Poisson torus looks perfect:

[stla]

I've tried the pca normals.

• For the toroidal helix, the result is highly better than the result with the jet normals.
• I tried both types of CGAL normals (jet and pca) on the uniformly remeshed Hopf torus, and that is very strange : the torus loses a lobe, there are only two lobes left instead of three:

(I'm talking about the Poisson reconstruction)

[stla]

Here are the data if you want to take a look.

uniformMesh.txt

[stla]

FYI, it works well with reconstruct_surface of the PyVista library. I don't know what is the algorithm used.