New cubed sphere 2 grid

[mo-jonasganderton]

Description

Initial implementation of a new cubed sphere grid.

@odlomax and @wdeconinck can both have a look over to recommend any changes - I expect this will have changed once everything else has also been implemented.

Using this implementation generates the following lonlat points - n=12, red=tile0, purple=tile5, darkest point of each colour is tij=0, lightest point is tij=143. This matches the sequence of the points in the LFRic cubed sphere.

Impact

Once everything else is also implemented, this makes the cubed sphere more maintainable.

Checklist

• I have performed a self-review of my own code
• I have made corresponding changes to the documentation
• I have run the unit tests before creating the PR

[FussyDuck]

All committers have signed the CLA.

[odlomax]

Looks good to see a much simpler CS grid! I've added some changes. It's mostly style related. I'm sure @wdeconinck can make some more comments/suggestions.

After this, we should probably plumb the grid into the grid builder.

@wdeconinck, what do you think?

[odlomax]

I think the intent is clearer if we define:

using PointAlphaBeta = Point2;

PointAlphaBeta CubedSphere2::ij_to_curvilinear_coord(idx_t i, idx_t j) {
  const auto get_coord = [&](idx_t idx){
    return M_PI / 2 * (-0.5 + (0.5 + idx) / N());
  };
  return {get_coord(i), get_coord(j)};
}

PointXY CubedSphere2::curvilinear_to_tangent_coord(const PointAlphaBeta& curvi_coord) {
  return {std::tan(curvi_coord[0]), std::tan(curvi_coord[1])};
}

PointXYZ CubedSphere2::tangent_to_xyz_coord(const PointXY& tan_coord) {
  /// Perform coordinate rotations...
}