Add tolerance to avoid empty CGAL intersections due to roundoff

[jh66637]

Dependent on the element configuration, it might happen that intersections are not found. Therefore, I would like to introduce a parameter to be able to truncate vertices if needed. I still have to write a test and check if the implementation actually resolves this behavior in any case.

@fdrmrc @peterrum

[peterrum]

Question: how does n_truncation_digits differ from tol? Isn't the effect similar?

[jh66637]

tol is used to discard elements with volumes smaller than tol. We could rename to tol_discard if this is more clear.

[peterrum]

tol is used to discard elements with volumes smaller than tol. We could rename to tol_discard if this is more clear.

Renaming would definitely make sense. But I still a bit unsure if it really makes sense to use the number of digits. Do we have other places where we do this like this? I guess in most cases we use absolute or relative tolerances!?

[jh66637]

The problem is that there is no way to hand over a tolerance to CGAL as far as I know. So the input already has to be in a form such that CGAL detects the intersection. If you have any better idea how to achieve this, I am curious. I don't like the solution a lot, but it worked (in a slightly modified way) in all of my use-cases by now.

[jh66637]

I rewrote the routines such that the use can give a tolerance instead of n_digits. Still, the backend uses n_digits to achieve the rounding. I think this is a good compromise, since I can not think about a different way to achieve described behavior.

[jh66637]

During testing the functionality of the PR, I stumbled across a bug #14359. This is, however, not related to this PR. From my point of view, this PR is ready to review and should be safe to merge.

We could however also wait before merging, since for the rest of the implementations I am planning to do, the additional tolerance is just one additional parameter to pass. However, if you could still give me a review, I would be happy :)

[jh66637]

I think this should be merged after #14360

[fdrmrc]

I agree with your choice. Depending on the field, someone could say that if cells are not intersecting up to eps, then no intersection is expected, while in other scenarios (like the one you have), one really wants it to be found.

From a user's perspective, I just think vertex_tolerance should be documented a little more extensively, adding for instance that coordinates are rounded so that intersections are found, maybe with a little sketch. We can do that later, I don't want to be picky and block you with minor stuff

[jh66637]

@mfeder Thanks for the input. I couldn't think about a meaningful sketch, but I extended the documentation :)

[jh66637]

Let's put this on hold while I try https://stackoverflow.com/a/54303150