Fix consistency of different lines in solar eclipse maps #3757
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The old version took Earth flattening into account in a not quite precise way. Particularly, the intersection of the shadow border with the Earth's rim was computed assuming them both being circular, apparently with some fixups done afterwards. This patch implements the more direct computation, which, albeit more complicated, gets more precise results.
This is less dependent on the way the limit lines are computed (and they are more complicated as functions of JD than the rise-set lines).
The original implementation ignores that rho != 1 for the flattened Earth. The new one implements the more precise version accounting for this inequality.
Previous version didn't quite match the rise-set curve, crossing it or failing to reach instead of touching. The crossing was likely due to a bad approximation for taking into account Earth flattening, and the failure to reach the final point was due to the fact that a single point in time may generate two points of a single limit curve, while the iteration in the original implementation (and the one in the book) are only capable of generating one. The new implementation goes a very different route: a single equation is derived for all the limit points at a given time, and these points are then found by Newton's method of locating roots. This is not completely robust, so I there may be cases when this fails due to Newton's method's lack of guarantees of convergence. When this happens, we'll see discontinuities in the curves. But from what I tested, these discontinuities, when present (particularly when the lines naturally have multiple branches), are not critical due to refinement being done at their ends.
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Great PR! Please pay attention to the following items before merging: Files matching
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If you are going to merge this, please don't squash. These commits are big enough to be kept separate. |
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Thanks. While the shown cases look indeed much better and seem more correct, note that not all lines meet at expected places, there are sometimes unexpected intersections in the begin/end regions. See the discussions in Meeus, Morsels (1-3?). |
Maximum in the horizon and penumbra limits must join by construction (they follow the same equation, just with different constraints). Same for shadow limits and rise-set limit curve, since they both denote the limits for the shadow, just for different stages of shadowing. Indeed, the rise-set limit intersects the maximum in horizon curve at odd places, which is to be expected since they are quite unrelated geometrically. Anyway, I followed the geometrical logic while implementing this, rather than try to fit the curves, so this nice result is just a side effect of correctness. |
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Here are some examples of oddly-looking intersections that are still correct: 2025-03-29
2024-10-02
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Yes, this is what I meant. I just wanted to start compiling to check that despite lack of time. I also like the good docs! OK, Looks good to me! |
alex-w
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Hello @10110111! Please check the fresh version (development snapshot) of Stellarium: |
alex-w
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Hello @10110111! Please check the latest stable version of Stellarium: |
The original version of the eclipse maps has some ugly artifacts at the locations where the limit lines connect, like rise-set limit vs the penumbra limits, which should touch but not cross, while they instead either cross or don't reach each other (see the screenshots below). This happens because of a few issues with the implementation:
This PR reimplements some of these functions, trying to avoid any dubious approximations and also avoiding the procedures given in the reference book that don't yield satisfactory results.
There are a few caveats, which you can read in the commit messages, but to me the result looks better than it was before.
Screenshots (solar eclipse on 2025-03-29)
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