Improve robustness of conservative spherical polygon interpolation for high resolution meshes

[sbrdar]

Fixing #129

• improvement in polygon intersection (more robust Sutherland-Hodgman algorithm)
• print out the worst under-covering and over-covering of target polygons
• output in JSON format
  Remaining issue from Development of efficient conservative spherical polygon interpolation #129
• searching of candidate source polygons to intersect a give target polygon should not be done via std::set and comparison of centroids to determine if two polygons are same. The coefficient ATLAS_COMPAREPOINTXYZ_EPS_FACTOR should be set to 1e4 for high grid res, but 1e8 for low mesh. This has to be removed in the future version.

[FussyDuck]

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[andreapiacentini]

Hi, sorry I did not enter the details of these changes (and honesty I probably wouldn't understand them), but I take the opportunity to share with you what we are dealing with in OASIS and that has already been fixed in ESMF and YAC interpolators (not sure about XIOS). Some finite volumes models (e.g the FESOM2 ocean model https://fesom.de/models/fesom20/) define the control volumes with an enhanced dual mesh also passing by the midpoints of the primal mesh edges (cf the C_i cell in Fig 2. from https://fesom2.readthedocs.io/en/latest/geometry.html).
This leads to non convex cells and ESMF and YAC adapted their Sutherland-Hodgman algorithm so that it can deal with concave cells (at least for one of the two grids).
If you aim at having a generic spherical conservative interpolation, that could be an interesting enhancement for Atlas too.
FESOM2 grids can be found here https://gitlab.awi.de/fesom
If you just need the dual grid for the CORE2 resolution (the one really needed for flux interpolations) I can provide you with the one is causing problems in the "pre-Sutherland-Hodgman" SCRIP library.

[codecov-commenter]

Codecov Report

Patch coverage: 88.85% and project coverage change: +0.66 🎉

Comparison is base (7d4fac6) 77.36% compared to head (dd1503c) 78.02%.

Additional details and impacted files

@@             Coverage Diff             @@
##           develop     #130      +/-   ##
===========================================
+ Coverage    77.36%   78.02%   +0.66%     
===========================================
  Files          810      810              
  Lines        58708    58896     +188     
===========================================
+ Hits         45420    45956     +536     
+ Misses       13288    12940     -348     

Impacted Files	Coverage Δ
...ctured/ConservativeSphericalPolygonInterpolation.h	100.00% <ø> (ø)
...tured/ConservativeSphericalPolygonInterpolation.cc	87.47% <79.76%> (+27.08%)	⬆️
src/atlas/util/ConvexSphericalPolygon.cc	92.14% <89.79%> (+2.88%)	⬆️
src/tests/util/test_convexsphericalpolygon.cc	99.48% <99.31%> (-0.52%)	⬇️
src/atlas/util/ConvexSphericalPolygon.h	100.00% <100.00%> (ø)
...s/interpolation/test_interpolation_conservative.cc	100.00% <100.00%> (ø)

... and 4 files with indirect coverage changes

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[sbrdar]

Hi Andrea. Thanks for your good remarks! We do aim for a generic conservative interpolation, MPI-parallel & 1st/2nd order. Data on mesh can be either in the cell centres or on the vertices of a mesh. We intersect only convex polygons and polygon edges being great arcs, so we have to split non-convex polygon around a vertex into convex quads. This has worked well for us so far. I would be grateful if you can provide us with the one example causing problems in the "pre-Sutherland-Hodgman" SCRIP library. Thanks again!

[andreapiacentini]

if you can provide us with the one example

Done!
At least if you mail has the usual format name.family_name@ecmwf.int
Let me know if you get the message and the file transfer. The grids coordinates are in a scrip like grids file. There were loader around at the time when I tested Atlas interpolations, but at the time we did not talk much of non-convex dual finite volumes grids!
Don't hesitate to get in touch for any questions or brainstorming. I can also put you in touch with the FESOM developers: they certainly know much more than I do about these grids. Sometimes my Italian flavor of written English collides with their German flavor, but it would be easier for you !

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[wdeconinck]

Great work @sbrdar !!!

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