HEALPix (maybe even others) connectivities and split visualizations have issues around the pole

[erogluorhan]

Version

v2025.04.0

How did you install UXarray?

Conda

What happened?

Using UXarray to visualize some coarse resolution HEALPix grids, I notice some issues as follows:

1. Face edges do not seem like great circle arc in ours but the do in the easy.gems visualizations.

UXarray

easy.gems

3. There should be some issues around the Poles, which might be due to connectivity generation and/or periodic elements handling (Western faces being split but the Eastern ones, no splitting seems needed from easy.gems), but there does not seem to be issues with the actual corner nodes and face centers:

What did you expect to happen?

Already clarified above I believe

Can you provide a MCVE to repoduce the bug?

# Let us open a pretty coarse HEALPix grid because we will visualize it later
uxgrid = ux.Grid.from_healpix(zoom=0, pixels_only=False)

uxgrid.plot(
    periodic_elements="split",         
    projection=ccrs.Mollweide(),
    width=800,
    title="HEALPix, zoom=0")

# Other plotting code in the figures above can also be inspected here

[philipc2]

This appears to be due to how we represent the boundaries. We connect the corners of the boundaries and treat it as a GCA, which differs from how the true boundaries are computed.

The issue here seems to be more with our visualization. Using a Geodetic source projection produces a more representative example.

[erogluorhan]

Geodetic visulaizations seem to be working for the time being. Regarding the HEALPIx edge geometry definition in UXarray's representation, we can revisit them in the future if need be.