Spherical cap plot recipe

[asinghvi17]

using GLMakie
import GeometryOps as GO
import GeometryOps.UnitSpherical
import LinearAlgebra, Rotations, GeometryBasics

function Makie.convert_arguments(::Type{Makie.Mesh}, cap::UnitSpherical.SphericalCap)
    N = 40
    rmin = 0.1
    rect = GeometryBasics.Tesselation(Rect2d(0, 0, 2pi, cap.radius), (N, ceil(Int, cap.radius / rmin)))
    faces = GeometryBasics.decompose(Makie.GLTriangleFace, rect)
    points = GeometryBasics.coordinates(rect)
    # Remove the first N points and set the first point to (0,0)
    # such that the first point is the center of the cap.
    points = points[N:end]
    points[1] = Point2d(0)
    faces = map(faces) do f
        Makie.GLTriangleFace(
            f[1] <= N ? Makie.GLIndex(1) : f[1] - N + 1,
            f[2] <= N ? Makie.GLIndex(1) : f[2] - N + 1,
            f[3] <= N ? Makie.GLIndex(1) : f[3] - N + 1,
        )
    end
    # Convert back to unit-spherical space.
    three_d_points = map(points) do (theta, phi)
        if phi == 0
            offset_point = cap.point
        else
            offset_point = LinearAlgebra.normalize(cap.point + LinearAlgebra.normalize(Point3d(cos(phi), sin(phi), 0.0)))
        end
        LinearAlgebra.normalize(Point3d(cap.point + phi * Rotations.AngleAxis(theta, cap.point...) * offset_point))
    end
    # Convert back to geographic space.
    # This is so that `zlevel` works right.
    return (GeometryBasics.normal_mesh(UnitSpherical.GeographicFromUnitSphere().(three_d_points) .|> Point2d, faces),)
    # return (GeometryBasics.normal_mesh(three_d_points, faces),)
end
Makie.convert_arguments(::Type{Makie.Poly}, cap::UnitSpherical.SphericalCap) = Makie.convert_arguments(Makie.Mesh, cap)

cap = UnitSpherical.SphericalCap((90, 0), 0.3)
f, a, p = meshimage(-180..180, -90..90, GeoMakie.earth(); uv_transform = :rotr90, axis = (; type = GlobeAxis, camera_longlat = (90, 0)))
poly!(a, cap; alpha = 0.7, zlevel = 100_000)
f