How to map rectangular lat/lon region on non-rectangular projection with GeoMakie?

I’m trying to map a rectangular lat/lon polygon on a non-rectangular map projection using GeoMakie,

When I use four corner points to define the region, GeoMakie draws straight lines between them. The example below shows what I am getting. I would like the polygon to follow the curvature of the meridians instead.

using Makie, CairoMakie
using GeoMakie
using Makie, CairoMakie
using GeoMakie

fig = Figure()
ax = GeoAxis(fig[1, 1], title="poly = [(60, -30),  (180, -30),  (180, 30),  (60, 30)]")
poly = [(60, -30), (180, -30), (180, 30), (60, 30)]
poly!(ax, poly, color=:red)
fig

The default projection for GeoMakie is Equal Earth as I understand it, and the source default is Plate Caree, so I thought this would work. The corner points are obviously projected properly on the map.

What am I missing? Is there some way to accomplish what I want?

The thing is just that Makie currently doesn’t subsample data when it encounters nonlinear projections. So the vertices of the poly are correct but the lines between them are straight in screen space. If you made a polygon with more points between the corners, it would look better. I’m not sure yet what a good general solution to this could be without making it slow for larger datasets

From the standpoint of Makie this makes sense.

For GeoMakie, I was thinking the dest keyword would set to plot a geodetic polygon. It would be nice to have plotting in GeoMake obey something like a transform keyword in cartopy. But maybe that’s not optimal or simple.

Might look at the GeoMakie code to see how it draws the graticules on non-rectangular projections, which curve as expected. That seems essentially the same problem.