hexasphere

A module to create (almost) hexagonal grids of variable size on a sphere, fully implemented in python.

description of the grid

base polyhedron

The grid is built by subdividing a base polyhedron into hexagon tiles. The base polyhedron is an icosahedron, which comprises:

• 20 faces (equilateral triangles)
• 12 vertices
• 30 edges

At the vertices of the icosahedron, instead of an hexagon, a pentagon is constructed.

For a given grid resolution n, each edge of the icosahedron goes through exactly n hexagon centers (not counting the polygons found at the ends). The inside of faces is then filled with tile-centers by following a triangular pattern. This allows to cover the icosahedron. Its surface is then mapped to the sphere using a projection.

Here, n = 7

projection

There are two available projections in projection module:

• GnomonicProj: a simple projection, which produces hexagonal tiles about 60% larger (in area) at the corners of a face than at its center.

• SnyderEAProj: a more complex projection, slower to compute (roughly 3x slower than Gnomonic projection), but which preserves areas. The implementation is based on Brenton R S Recht's blog. See there for more details.

hexagon tile identifier

A tile identifier has the following pattern: ?XXXXX-YYYYY-ZZZZZ

• ? is one of the 20 letters A ... T, each letter corresponding to one face of the icosahedron
• XXXXX, YYYYY, ZZZZZ are the integer coordinates of the tile in the triangular mesh covering face ?. An useful property holds:

XXXXX + YYYYY + ZZZZZ = 2 * (n + 1)

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getting started

1. Install the package with pip

$ pip install hexasphere

2. Import the library in python

from hexasphere import hexgrid, projection

usage

construction of a grid

1. Create a HexGrid object:

my_grid = hexgrid.HexGrid()

2. Instantiate a projection system Projection associated with this grid:

my_projection = projection.MyProjection(my_grid)

3. Provide the projection system to the grid:

my_grid.projection = my_projection

playing with grid resolutions

• Compute closest grid resolution n for any desired hex dimension (in kilometers):

n = my_grid.compute_n_for_radius(0.25)
n = my_grid.compute_n_for_height(0.25)
n = my_grid.compute_n_for_side(0.25)

• Retrieve average hex dimension (in kilometers) for any given resolution n:

my_grid.compute_radius_for_n(n)
my_grid.compute_height_for_n(n)
my_grid.compute_side_for_n(n)

encoding and decoding

• To find the string identifier of the hexagon to which a geographic point (lat, lon) belongs, call:

hex_identifier = my_grid.latlon_to_hex(lat, lon, n, out_str=True)[0]

• To find the (lat, lon) coordinates of the center of an hex, call:

my_grid.hex_to_latlon(hex_identifier, in_str=True)
my_grid.hex_to_latlon(hex_identifier, n, in_str=True) # n is here not required

overlapping grids

grid.latlon_to_hex also supports overlapping grids:

value = 12 # Overlap distance (in km)
my_grid.set_overlap(value)

The method grid.latlon_to_hex returns the list of distinct hexes a point of coordinates (lat, lon) belongs to:

hexes_identifier = my_grid.latlon_to_hex(lat, lon, n, out_str=True)

playing with hexagons

retrieving shape data

One can also deal with an Hexagon object instead of an hexagon string identifier:

hex_object = my_grid.latlon_to_hex(lat, lon, n)[0]
hex_object = hexgrid.Hexagon(my_grid, str_id=hexagon_identifier)

The coordinates of the vertices of the corresponding shape can then be retrieved:

shape_coordinates = hex_object.retrieve_polygon(out_latlon=True)

moving on the grid

To retrieve a neighboring hex:

hex_neighbor = hex_object.compute_neighbor(dP=(0, 1, -1))

To retrieve the list of hexes in the k-ring centered on the hex object:

hexes = hex_object.k_ring(k, out_str=True)