I didn't fully read all the math yet, but Ithink some of them could be\bm{B} or\vec{B} to differentiate the vectors from the x/y components.

@QuLogic when you get tired of working with the Mac stuff, this is rebased and the math should now render fully (making it marginally easier to review), and I incorporated all of your recommendations.

Since this Pull Request has not been updated in 60 days, it has been marked "inactive." This does not mean that it will be closed, though it may be moved to a "Draft" state. This helps maintainers prioritize their reviewing efforts. You can pick the PR back up anytime - please ping us if you need a review or guidance to move the PR forward! If you do not plan on continuing the work, please let us know so that we can either find someone to take the PR over, or close it.

This was a lot of good work that seems useful to get in. I just rebased this PR and replaced the manual combinatorial function withmath.comb now that we are beyond 3.7 support.

@timhoffm, I share some of your concern, but overall feels like this is an improvement worth adding. If someone wants more complex geometry handling they should likely move over to Shapely and GEOS. But this has the work put into it and I could see people not wanting to have to convert a Matplotlib Path over to Shapely and go back and forth if they can avoid it.

For the equal area markers: I think that is one of the most requested scatter marker "features", so I think people definitely would want it.

@timhoffm, I share some of your concern, but overall feels like this is an improvement worth adding. If someone wants more complex geometry handling they should likely move over to Shapely and GEOS. But this has the work put into it and I could see people not wanting to have to convert a Matplotlib Path over to Shapely and go back and forth if they can avoid it.

We have to be careful what we offer. If we provide a public functionality it should "just work" and we need to document it's scope and limitations. This is more work than just writing it for internal usage.

For example, the currentcontains() implementation depends on the visibility#23875. I assume this has been implemented for event handling, but is very surprising if a user usescontains as an abstract concept. While this could be labelled a design issue, having it public surfaces the problem to the user.

Similarly, marker paths are typically defined in the vicinity of the origin, sowe would not have to care for the possible numeric issue with far-away paths. Also, the precision requirements for reasonable equal-area markers are low. A few percent deviation are tolerable for our use case, but it may not in user applications.
Note also that we could decide to go other routes for equal-area markers. At least for the builtins, we could pre-calculate size-to-area ratios (if need be even through counting covered pixels for a large rendered marker), which would get us 90% the way for equal-area markers without any geometry code.

Generally, geometric calculations are not trivial. I'm quite afraid we provide half-baked solutions, that do not satisfy user needs and will result in follow-up requests to improve on that functionality, which is not our core business.

This is more work than just writing it for internal usage.

The ROSES 2024 grant haspath transformations as an area of focus.

@greglucas if this issue is part of the work that will help w/ that, could you create a roadmap issue of what should be implemented in Matplotlib to facilitate that work?

@greglucas if this issue is part of the work that will help w/ that, could you create a roadmap issue of what should be implemented in Matplotlib to facilitate that work?

No this isn't related to that. The PR after this (path_length) would be more related, but not directly as that work is all done within Cartopy.

I don't personally have a direct benefit from this at this point in time, so I will just leave the rebased version here in case someone else wants to advocate for it again in the future or use it as a reference, I don't feel strongly enough to advocate for this right now.