Note
Go to the end to download the full example code.
Uber H3 Spatial Index#
This example demonstrates the Uber H3 hexagonal hierarchical spatial index.
💼 Background#
The relationship between the H3 base icosahedron Platonic solid and its
base resolution mesh consisting of 110 hexagons and 12 pentagons
defines the starting point of this hierarchical sequence of hexagonal meshes.
Note that, a spherical surface cannot be tessellated solely with hexagons;
pentagons are also required.
The 12 vertices of the underlying base icosahedron anchors the center of the 12 pentagon cells, around which the 110 hexagon cells are tessellated to form a fixed base mesh. Note that, all pentagons are located over ocean, which suits the business model of Uber, and incidentally are the locations of most projection distortion.
H3 is a hierarchical geospatial index. Each cell has a unique 64-bit
H3Index that identifies its geospatial location and position in the H3
hierarchy. Every parent hexagonal cell is subdivided into 7 child
hexagonal cells, and every parent pentagon cell is subdivided into 6 child
cells, one of which is a pentagon.
From the coarsest base resolution, consisting of 122 cells, there are a further 15 increasingly higher resolution hierarchical child meshes. The finest resolution mesh consists of 569,707,381,193,162 cells, with each resolution always containing 12 pentagon cells centered over the base icosahedron vertices.
The average area of a base (coarsest) resolution hexagonal polyhedron cell is ~4,357,449 km^2, whereas the average area of the finest resolution hexagonal cell is ~0.895 m^2.
Given a H3Index, it is trivial to calculate the resolution, location
and neighbours of a cell, as well as all its child cells and parent cell.
Note that, the neighbours of a hexagon or a pentagon cell in a tessellated
mesh are equidistant, unlike a mesh consisting of triangular or rectangular
cells.
This example renders the H3 base resolution mesh and the next 3 child
resolutions in the hierarchy, along with the base icosahedron and its
projected edges on the sphere.
Natural Earth coastlines are rendered to clarify geolocation, along with a Natural Earth base layer.
The visibility of each actor, apart from the coastlines, can be toggled interactively via checkbox buttons, allowing the viewer to easily explore the relationship between the geometric objects rendered in the scene.
For further information see https://h3geo.org/.
🦉 Walk-Through#
First, let’s import the package dependencies required by the example.
from __future__ import annotations
from dataclasses import dataclass
from functools import partial
from itertools import combinations
try:
import h3
except ImportError:
emsg = (
"Missing optional dependency 'h3' is required for the "
"`uber_h3.py` example. Use pip or conda to install."
)
raise ImportError(emsg) from None
import numpy as np
from numpy import ma
from numpy.typing import ArrayLike
from pyvista import Actor, PolyData
import geovista
from geovista.geodesic import line
import geovista.theme
As a convenience, we create some type aliases and data containers
to simplify the code and improve readability. Firstly, the H3Asset
container holds the various VTK actors that will be rendered within
the scene.
#: Missing Data Indicator
MDI = -1
#: Type alias
H3AssetLike = str | PolyData
H3Indexes = set[str]
@dataclass(slots=True)
class H3Asset:
"""Data container of Uber H3 assets."""
icosahedron: H3AssetLike
icosahedron_edges: H3AssetLike
resolution_0: H3AssetLike
resolution_1: H3AssetLike
resolution_2: H3AssetLike
resolution_3: H3AssetLike
base_layer: H3AssetLike
The GeoSurface container holds the geometry and topology of the
H3 base icosahedron.
The generate_icosahedron_surface function generates the geometry
and topology of the H3 base icosahedron, which is the foundation
of the entire Uber H3 spatial index.
def generate_icosahedron_surface(resolution: int | None = 0) -> GeoSurface:
"""Find the location and connectivity of all pentagon cells.
For each ``resolution`` there will always be 12 pentagons,
centered at the vertices of the underlying (Platonic solid)
icosahedron.
Parameters
----------
resolution : int
The resolution of the Uber H3 mesh.
Returns
-------
GeoSurface
The lat/lon cell centers of the pentagon cells and the
icosahedron face connectivity.
"""
pairs = [h3.h3_to_geo(cell) for cell in sorted(h3.get_pentagon_indexes(resolution))]
lats, lons = list(zip(*pairs, strict=True))
# An icosahedron contains 20 equilateral triangle faces,
# 12 vertices and 30 edges.
connectivity = [
[0, 1, 2],
[0, 3, 1],
[0, 2, 4],
[0, 4, 5],
[0, 5, 3],
[1, 6, 2],
[1, 3, 7],
[1, 7, 6],
[2, 6, 8],
[2, 8, 4],
[4, 8, 10],
[4, 10, 5],
[5, 10, 9],
[5, 9, 3],
[3, 9, 7],
[11, 6, 7],
[11, 8, 6],
[11, 10, 8],
[11, 9, 10],
[11, 7, 9],
]
return GeoSurface(lons=lons, lats=lats, connectivity=connectivity)
The GeoSurface created by the generate_icosahedron_surface function
is then used to create a pyvista.PolyData mesh containing only the
geodesic edges of the base icosahedron.
Rendering these geodesic edges will help clarify to the viewer the position of the underlying icosahedron even when it is obscured by a texture mapped base layer.
def generate_geodesic_edges(surface: GeoSurface) -> PolyData:
"""Create the mesh of icosahedron geodesic edges.
Parameters
----------
surface : GeoSurface
The 12 lat/lon vertices and connectivity of the 20 icosahedron faces.
Returns
-------
PolyData
The mesh of icosahedron geodesic edges.
"""
# Generate the set of 30 unique vertex index pairs defining
# the icosahedron edges.
segments = set()
for vertices in surface.connectivity:
pairs = [tuple(sorted(pair)) for pair in combinations(vertices, 2)]
segments.update(pairs)
# Create the geodesic lines between each edge vertex.
meshes = []
for idx0, idx1 in segments:
lons = [surface.lons[idx0], surface.lons[idx1]]
lats = [surface.lats[idx0], surface.lats[idx1]]
meshes.append(line(lons, lats))
# Combine the geodesic lines into one mesh.
return meshes[0].append_polydata(*meshes[1:])
The to_children function generates all the child cells at the
next (finer) resolution for each parent cell represented in the set
of H3Index strings.
def to_children(h3indexes: H3Indexes) -> H3Indexes:
"""Determine the child cells of the parent cells.
The child hexagon/pentagon cells will be at the next
resolution (finer) of the parent cell resolution (coarser).
Note that, a hexagon parent has 7 children, whereas a pentagon
parent only has 6 children. A pentagon parent will always
contain a pentagon child. A hexagon parent will never contain
a pentagon child.
Parameters
----------
h3indexes : set of str
One or more 64-bit ``H3Index`` strings of parent cells.
Returns
-------
set of str
The children cell indexes.
"""
result = set()
children = [h3.h3_to_children(h3index) for h3index in h3indexes]
result.update(*children)
return result
The to_mesh function converts a set of H3Index strings,
each of which represent a cell from the same resolution in the
Uber H3 spatial hierarchy, into a pyvista.PolyData
mesh surface.
Together, the to_children and to_mesh functions can be used
to generate the mesh surface of any resolution in the Uber H3
spatial hierarchy.
def to_mesh(h3indexes: H3Indexes) -> PolyData:
"""Create a mesh surface for the provided Uber H3 cells.
Parameters
----------
h3indexes : set of str
One or more 64-bit ``H3Index`` strings, specifying each
cell to add to the mesh.
Returns
-------
PolyData
The H3 mesh surface.
"""
nverts, lats, lons = [], [], []
# Get the lat/lon vertices of each H3Index cell polygon.
for h3index in h3indexes:
boundary = h3.h3_to_geo_boundary(h3index, geo_json=False)
boundary_lats, boundary_lons = zip(*boundary, strict=True)
lats.extend(boundary_lats)
lons.extend(boundary_lons)
nverts.append(len(boundary_lats))
# Create an empty cell connectivity for the mesh filled
# with MDI. Note that, each cell may contain a variable
# number of vertices.
shape = (len(nverts), np.max(nverts))
connectivity = np.ones(shape, dtype=int) * MDI
# Now populate the connectivity with the cell indices.
start = 0
for i, step in enumerate(nverts):
connectivity[i, :step] = range(start, start + step)
start += step
# Create the mesh from the H3 geometry and topology.
connectivity = ma.masked_equal(connectivity, MDI)
return geovista.Transform.from_unstructured(lons, lats, connectivity=connectivity)
The add_checkboxes function adds a checkbox button widget to the
plotter for each H3Asset actor, which includes the following:
A Natural Earth texture mapped base layer.
The icosahedron surface.
The icosahedron geodesic edges.
The base resolution mesh (coarsest).
The next 3 child resolution meshes (increasingly finer).
def add_checkboxes(
plotter: geovista.GeoPlotter, colors: H3Asset, actors: H3Asset
) -> None:
"""Render the checkbox for each ``H3Asset``.
A checkbox is created for each actor that allows the
visibility of the actor to be toggled on/off within the
`plotter` scene.
Parameters
----------
plotter : GeoPlotter
The plotter to render the checkboxes.
colors : H3Asset
The color of each checkbox asset.
actors : H3Asset
The VTK actors to be toggled by each checkbox.
"""
color_off = "white"
size, pad = 30, 3
x, y = 10, 10
offset = size * 0.2
def callback(actor: Actor, flag: bool) -> None:
actor.SetVisibility(flag)
for i, slot in enumerate(sorted(H3Asset.__slots__)):
plotter.add_checkbox_button_widget(
partial(callback, getattr(actors, slot)),
value=True,
color_on=getattr(colors, slot),
color_off=color_off,
size=size,
position=(x, y + i * (size + pad)),
)
title = " ".join([word.capitalize() for word in slot.split("_")])
x_offset = x + size + offset
y_offset = y + i * (size + pad) + offset
plotter.add_text(
title,
position=(x_offset, y_offset),
font_size=8,
shadow=True,
color=getattr(colors, slot),
)
Note
The checkboxes will not be rendered when viewing the documentation on
ReadtheDocs, as the appropriate VTK widget is not supported in this
headless environment.
Finally, we create the GeoPlotter and add the
base icosahedron surface and geodesic edges,
a Natural Earth base layer and coastlines.
We also use the h3.get_res0_indexes() function to bootstrap the
Uber H3 hierarchy by generating the H3Index strings for all
the cells participating in the base (coarsest) resolution .
The to_mesh function is then used to convert the H3Index strings
into a pyvista.PolyData mesh surface, which is then added to
the plotter. The to_children function is then used to generate the
H3Index strings for the next 3 child resolutions, which are then
converted into mesh surfaces and also added to the plotter.
def main() -> None:
"""Plot the Uber H3 spatial index.
Notes
-----
.. versionadded:: 0.5.0
"""
color = H3Asset(
icosahedron="grey",
icosahedron_edges="darkgrey",
resolution_0="black",
resolution_1="orange",
resolution_2="lightblue",
resolution_3="lightgrey",
base_layer="blue",
)
indexes_resolution_0 = h3.get_res0_indexes()
mesh_resolution_0 = to_mesh(indexes_resolution_0)
indexes_resolution_1 = to_children(indexes_resolution_0)
mesh_resolution_1 = to_mesh(indexes_resolution_1)
indexes_resolution_2 = to_children(indexes_resolution_1)
mesh_resolution_2 = to_mesh(indexes_resolution_2)
indexes_resolution_3 = to_children(indexes_resolution_2)
mesh_resolution_3 = to_mesh(indexes_resolution_3)
# Create the icosahedron surface.
surface = generate_icosahedron_surface()
icosahedron = geovista.Transform.from_unstructured(
surface.lons, surface.lats, connectivity=surface.connectivity
)
plotter = geovista.GeoPlotter()
style = "wireframe"
actor_base_layer = plotter.add_base_layer(
texture=geovista.natural_earth_hypsometric(), zlevel=0
)
actor_resolution_0 = plotter.add_mesh(
mesh_resolution_0,
style=style,
line_width=4,
color=color.resolution_0,
zlevel=60,
lighting=False,
)
actor_icosahedron_edges = plotter.add_mesh(
generate_geodesic_edges(surface),
line_width=4,
color=color.icosahedron_edges,
zlevel=60,
lighting=False,
)
actor_resolution_1 = plotter.add_mesh(
mesh_resolution_1,
style=style,
line_width=3,
color=color.resolution_1,
zlevel=10,
lighting=False,
)
actor_resolution_2 = plotter.add_mesh(
mesh_resolution_2,
style=style,
line_width=2,
color=color.resolution_2,
zlevel=5,
lighting=False,
)
actor_resolution_3 = plotter.add_mesh(
mesh_resolution_3,
style=style,
line_width=1,
color=color.resolution_3,
zlevel=1,
lighting=False,
)
actor_icosahedron = plotter.add_mesh(
icosahedron, show_edges=True, color=color.icosahedron
)
actor = H3Asset(
icosahedron=actor_icosahedron,
icosahedron_edges=actor_icosahedron_edges,
resolution_0=actor_resolution_0,
resolution_1=actor_resolution_1,
resolution_2=actor_resolution_2,
resolution_3=actor_resolution_3,
base_layer=actor_base_layer,
)
add_checkboxes(plotter, color, actor)
plotter.add_text(
"Uber H3: Hexagonal Hierarchical Spatial Index",
position="upper_left",
font_size=10,
shadow=True,
)
plotter.add_coastlines()
plotter.camera.zoom(1.5)
plotter.show()
if __name__ == "__main__":
main()
