Error, no disk topology

[nantille]

Hello,

I'm trying to use the mac binaries to do the mapping on a mesh I generated. I get the following error: Error! Input does not have a disk topology, it's euler char is 0

There is a typo in "it's", it should read "its". Apart from that I don't understand the error message and what to do about it. Could you clarify?

Thank you,
Nicolas

[MichaelRabinovich]

Your mesh is not a disc topology mesh. I would guess that you probably have a hole somewhere in your mesh, and you might need to patch it up with some tool such as meshlab.

The Euler characteristic of a polyhedra (your mesh) is a topological invariant which is defined as #V-#E+#F. For our use, we wanted to make sure your mesh is of disc topology. If it is, then it has an euler char of 1. If it doesn't than it's not, and it is not a valid mesh for parametrization with SLIM.

[nantille]

I had an error previously with another mesh that wasn't watertight and the app told me so.

I tested with another watertight mesh (which means there are no holes) and that's where the euler char 0 popped. I checked in meshlab it has 0 non manifold vertex, 0 non manifold edge.

Are we supposed to give only quadrilaterals or are triangles accepted?

[MichaelRabinovich]

Only triangles, but the mesh must be a disc topology mesh, and your mesh is not. It is a well known result in math, and you will get quite some recognition for producing a counter example and finding an error in the proof, though there are quite a few though.. (those are derived for V-E+F=2 but you can 'place a hole' and deduce the case for disc topology).

Please send me the mesh to michael.rabinovich.27@gmail.com and hopefully I could see whats wrong with it.

Thanks,
Michael

[MichaelRabinovich]

Also, are you sure your mesh is not of another topology? A clean watertight mesh with cylinder or torus topology will have a 0 euler char and would not work with our algorithm. Our algorithm does not cut a mesh.

[nantille]

Ok only triangles is a bit of a drawback in my case but I triangulated the output and now the errors vary between "Error! Input is not an edge manifold" and "Error! Input has multiple connected components". I sent you an example manifold mesh.

I do not necessarily have a clean topology for all models. But my case of neuron cells meshing, a lot of tubular structures are involved. Is this what you meant with cylinder topology?

[MichaelRabinovich]

Dear Antille,

I would like to help you use our algorithm, so I'll try to see if I can clean the mesh.
As it is a research paper and not a full-fledged system, we do not take care of 'cleaning meshes' or cutting them in the code, and we assume a clean input. Cleaning or cutting a mesh is a work described in other papers, and available in certain tools. My experience with cleaning damaged meshes was pretty bad actually, as there are a lot of things that can go wrong.

I've checked the mesh, and it does seems like it has multiple components. Multiple components imply that it has some triangles that are not connected to others. In general if you have a mesh that contains multiple separate shapes (like a mesh of 2 separate people), the best way to parameterize those is to parameterize each one separately. This is something that we don't handle ourself and we assume that the model is of a certain type (I'll further detail on it later on). You can easily remove those components and keep only the largest one with meshlab under Filters->Cleaning and Repairing -> Remove Isolated Components with respect wrt to face number (I would choose a large number of faces, close to the actual number of faces you have to make sure all components are gone, in your case I've used 100,000).

The problem is, even after removing them the mesh is "damaged". Damaged can mean a lot of things. For instance your mesh had faces that are extremely small with 'zero area', this means that the triangles are actually 3 vertices on a line (so real zero area) or numerically close to it. This is also something that can be cleaned with meshlab. But even after that the euler char is still wrong, this implies that the topology of the mesh is not a disc. An example of a disc topology shape looks like this 2d shape:

You can think about a general disc topology mesh embedded in 3d as any shape you can create while stretching this disc, but not tearing or gluing it. So a head of a person with a hole in the head is something that you can flatten to 2d, but if you fill up the hole in the neck than it has a sphere topology and you cannot flatten it. If it has holes its of different topology as well, but holes are not the only thing that matters in a topology as a closed sphere has a different topology than a disc, and in order to flatten it you first need to cut a hole in it.

Parameterizing a non disc topology mesh first requires cutting it, which we also don't handle in our example code (or discuss in the paper). Cutting a hole in your previously mentioned meshes might actually be sufficient to make them disc topology. For example a closed cylinder cannot be flattened, and you first need to cut it. A single cut in a cylinder will make it a disc topology mesh and you get something that you can flatten.

The current mesh you have sent me seemed to have multiple components, zero area faces, and also wrong topology. I've applied some repairing filters but it is still not clean. I'll try more stuff tomorrow.

[MichaelRabinovich]

This circle picture is way bigger than I wanted it to be. Not sure how to fix that here in github.