Generate a Tripolar Grid

This Examples shows how to generate and visualize a Tripolar grid using the OrthogonalSphericalShellGrids and CairoMakie packages. The script is structured into several key sections, each performing a specific task in the process of creating and displaying the grid.

The script begins by importing the required Julia packages. OrthogonalSphericalShellGrids is used for generating the Tripolar grid, a type of grid used in geophysical and oceanographic modeling due to its ability to handle polar singularities effectively. CairoMakie is used for visualization purposes, allowing the creation of figures and plots to display the grid.

using OrthogonalSphericalShellGrids
using OrthogonalSphericalShellGrids: Face, Center
using OrthogonalSphericalShellGrids: get_cartesian_nodes_and_vertices
using CairoMakie

Grid generation

The grid is generated with a call to OrthogonalSphericalShellGrids.TripolarGrid, specifying the grid size and the latitude of the "north" singularities. In this case, the grid has a resolution of 2 degrees (180x90 grid points) and north singularities at 35 degrees latitude. This setup creates a grid that covers the globe with a specific focus on handling the complexities near the poles.

grid = OrthogonalSphericalShellGrids.TripolarGrid(size = (180, 90, 1), north_poles_latitude = 35)

180×90×1 OrthogonalSphericalShellGrid{Float64, Oceananigans.Grids.Periodic, Oceananigans.Grids.RightConnected, Oceananigans.Grids.Bounded} on Oceananigans.Architectures.CPU with 4×4×4 halo and with precomputed metrics
├── centered at (λ, φ) = (0.0, -3.0052)
├── longitude: Oceananigans.Grids.Periodic  extent 361.246 degrees variably spaced with min(Δλ)=0.0262293, max(Δλ)=2.3423
├── latitude:  Oceananigans.Grids.Periodic  extent 171.889 degrees variably spaced with min(Δφ)=0.0240568, max(Δφ)=1.91011
└── z:         Bounded  z ∈ [0.0, 1.0]                             regularly spaced with Δz=1.0

Retriveing the nodes

The lines retrieve Cartesian coordinates for two types of grid nodes: Face-Face nodes and Center-Centernodes. This is done using thegetcartesiannodesandvertices` function, which converts the grid's spherical coordinates into Cartesian coordinates for easier manipulation and visualization. The coordinates are stored in variables xF, yF, zF for Face-Face nodes, and xC, yC, zC for Center-Center nodes.

cartesian_nodes, _ = get_cartesian_nodes_and_vertices(grid, Face(), Face(), Center())
xF, yF, zF = cartesian_nodes

cartesian_nodes, _ = get_cartesian_nodes_and_vertices(grid, Center(), Center(), Center())
xC, yC, zC = cartesian_nodes

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Visualization

Finally, we can visualize the grid using two types of visual elements: surfaces and wireframes. Surfaces are plotted slightly smaller (0.9999 scale) than the wireframes to create a layered effect, enhancing the visual distinction between the grid's structure and its outline. The Face-Face nodes are visualized with blue surfaces and black wireframes, while the Center-Center nodes are visualized with blue surfaces and wireframes.

fig = Figure()
ax  = LScene(fig[1, 1]; show_axis = false)

surface!(ax, xF.*0.9999, yF.*0.9999, zF.*0.9999, color = :blue)
wireframe!(ax, xF, yF, zF, color = :black)

surface!(ax, xC.*0.9999, yC.*0.9999, zC.*0.9999, color = :blue)
wireframe!(ax, xC, yC, zC, color = :blue)

save("tripolar_grid_nodes.png", fig)

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