With many DGGSs to choose from, it is valuable to have quantitative ways to compare them.
Perhaps the most important attribute is area variation, where systems close to
equal area are preferred. While area distortion is well-studied, this talk covers
another critical attribute: cell shape distortion---or aspect ratio, anisotropy, or "squish".

The effect can often be very obvious visually. For example, depending on
where they are on the globe, H3 has hexagons which are noticeably wider in one direction.
Shape distortion has real computational effects. Gradients, flows, neighbor distances, and
convolution kernels are all affected when cells are squished.

We present a formulation of a spherical aspect ratio metric based on finding
the tightest enclosing ellipsoid of a set of points on the surface of a sphere.
This problem is related to the well-studied Minimum Volume Enclosing Ellipsoid,
but generalized to the surface of the sphere. Once we've identified the
tightest ellipsoid enclosing the vertices of a spherical polygon or DGGS cell,
we define the aspect ratio as the ratio of the major and minor semi-axes.

We provide open-source software to efficiently compute the spherical aspect
ratio, and show a broad study of spherical AR distributions across DGGS systems
like H3, S2, A5, ISEA7H, IVEA7H, and rHEALPix, along with heatmaps of how AR
varies over the globe in each system. We also compare and contrast it with
complementary metrics like the isoperimetric quotient (IPQ).

We'll end with a discussion of ways to generalize this spherical metric
to ellipsoids like WGS84.

Note: The Python library is currently hosted at https://github.com/ajfriend/skar_py,
but the name will change before the talk due to name conflicts on the
Python Package Index.