Polygon boundary errors in diamond grid

[good-kiwi]

There seems to be some error in calculating the boundary polygon at resolution 2 and higher in the diamond grid. (Please see attached image) Red lines are resolution 2, Green lines are resolution 1. Higher resolutions exhibit a similar issue.

When I manually calculate the midpoint of the great circle arc between vertexes of the resolution 1 diamond, I get the following result. Yellow pin is my manually calculated mid point of the edge.

I'm guessing this is an error in the linked DGGS library itself, but I can't seem to find a github repository for that library. I used the contact page at discreteglobalgrids.com to try and alert them to the issue as well, but not sure if the people running the site are the same people maintaining the DDGS library.

[good-kiwi]

As an additional detail to my note above, I'm using Google Earth's engine to draw the great circle arcs between points. I am only supplying the vertices from the resolutions that were published here: http://webpages.sou.edu/~sahrk/dgg/isea.old/gen/isea4d.html

I'm not sure if these files are old and it has since been corrected, but I started digging into this because I noticed some odd cell shapes in the resolution 8 grid that I was working with, so I think this is still an issue.

[good-kiwi]

So after some additional research on my end, this discrepancy is a result of my misunderstanding of how the grid is constructed. The grids are constructed on the Icosahedral Snyder Equal Area (ISEA) projection. This projection splits the globe into 10 equal area diamonds of the '0' resolution. The edge of each diamond is exactly a great circle arc.

While the ISEA4D grid continues to sub divide each of the original diamonds into 4 smaller diamonds, the projection itself subdivides the diamond into 12 right angle triangles that share 3 vertices internal to the diamond. Only the edges of the triangles correspond to great circle arcs, while any points on the interior suffer from some distortion of distance. Since the edges of the children diamonds do not travel along any edge of the triangles, the edges of the children diamonds do not lie on the great circle arc when drawing the inverse projection on the globe.