Is it possible for firedrake to compute the global orientation of a surface mesh automatically? #4789
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I have this question because in theory, the orientability/orientation of a surface is determined by itself. |
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Happy New Year! In principle one could do this, as you say up to an arbitrary sign change for the two available orientations. It would involve some work to write the code that propagates the orientation over the surface (one would have to start from the orientation of one cell and spread this over the whole mesh). This would have to happen in parallel so it would take some effort and thought. I would be very happy to consider a PR along those lines, but it's unlikely to be something that the core team finds time to do. |
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Happy New Year! Sure. But I would like to share my preliminary ideas here (Maybe you have already know). I believe there can be a parallel approach. For example, start the process from several initial cells, each oriented randomly, and spread their orientations simultaneously. When two oriented spreading regions meet each other on their common border, random one of them flips orientation, and they join into a larger region. Go on and on ... until the whole mesh is oriented (or it turns out to be non-orientable). Finally, check if the orientation is the expected one of the user. I am not an expert of finite element, my major demand is in differential geometry. From my point of view, the feature of automatic orientation is quite useful. The point is that there are many finite element softwares. To me, the most attractive feature of Firedrake/FEniCS is the support for computation on manifolds, which seems not supported well by traditional finite element softwares (I might be wrong). The category of manifolds is far broader than that of Euclidean spaces, although their applications in other scientific and engineering fields have not been explored much yet. |
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Yes, I agree that's how you'd do it. Indeed, Firedrake already contains a closely related algorithm for setting facet orientations on quadrilateral meshes. It's described here: https://doi.org/10.1137/15M1021325 |
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Thanks for letting me know this :) |
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Happy New Year!
In principle one could do this, as you say up to an arbitrary sign change for the two available orientations. It would involve some work to write the code that propagates the orientation over the surface (one would have to start from the orientation of one cell and spread this over the whole mesh). This would have to happen in parallel so it would take some effort and thought. I would be very happy to consider a PR along those lines, but it's unlikely to be something that the core team finds time to do.