Here is one way to define a RectilinearGrid with Spherical coordinates:
using Meshes
using CoordRefSystems
import GLMakie as Mke
r = Float32[1.677044, 1.8385518, 2.0156136, 2.2097273, 2.4225352, 2.6558375, 2.911608, 3.1920104, 3.499417, 3.8364286, 4.205896, 4.6109447, 5.055002, 5.5418243, 6.0755296, 6.660634, 7.3020864, 8.005314]
θ = Float32[0.049087387, 0.14726216, 0.24543692, 0.3436117]
ϕ = Float32[0.19634955, 0.5890486, 0.9817477, 1.3744467, 1.7671459, 2.1598449, 2.552544, 2.9452431, 3.3379421, 3.7306414, 4.12334, 4.5160394, 4.9087386, 5.3014374, 5.6941366, 6.086836]
g = RectilinearGrid{𝔼,typeof(Spherical(0,0,0))}(r, θ, ϕ)
viz(g)
The type parameters in the constructor are a bit low-level, but I think they match what you have in mind. The first type parameter 𝔼 refers to the manifold where the geometries live. In this case this is the Euclidean manifold. The second type parameter is the coordinate reference system type, which I am producing with a typeof(Spherical(0,0,0)) call.
You can also define the periodicity of each coordinate. Below you can find an alternative code that considers one of the angular coordinates to be periodic. First, it creates a GridTopology with the number of elements in the grid and the periodicity information, and then it feeds the topology as the second argument of the RectilinearGrid:
# grid topology with given number of elements per dimension
# the last coordinate is periodic so we set (false, false, true)
t = GridTopology((length(r)-1, length(θ)-1, length(ϕ)-1), (false, false, true))
g = RectilinearGrid{𝔼,typeof(Spherical(0,0,0))}((r, θ, ϕ), t)
viz(g)
Notice how the cone is now full-filled compared with the previous one.
