.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "generated/gallery/spatial_index/uber_h3.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` to download the full example code. .. rst-class:: sphx-glr-example-title .. _sphx_glr_generated_gallery_spatial_index_uber_h3.py: Uber H3 Spatial Index --------------------- This example demonstrates the Uber ``H3`` hexagonal hierarchical spatial index. 💼 Background ^^^^^^^^^^^^^ A spatial index is a structured collection of shapes that allows you to approximately describe any region by simply taking a subset of shapes from that index. The ``H3`` library, developed by Uber as an open source project, uses hexagons to divide up the earth into cells. ``H3`` is hierarchical, meaning that there are multiple resolutions of hexagonal meshes dividing the earth. Depending on the resolution, these hexagonal cells range from **~1m^2** to **~4,000,000km^2**. The coarsest mesh in ``H3``, the **base resolution mesh**, consists of **110 hexagons** and **12 pentagons**, this is the starting point in a hierarchical sequence of hexagonal meshes. Its structure is built on top of a **base icosahedron**, the relationship between the **base icosahedron** and the **base resolution mesh** informs the structure of the meshes of the further meshes in the sequence. Note that, a spherical surface cannot be tessellated solely with hexagons; pentagons are also required. The **12 vertices** of the underlying **base icosahedron** anchor the center of the **12 pentagon cells**, around which the **110 hexagon cells** are tessellated to form a fixed base mesh. Note that the center of all pentagons are located over ocean, which suits the business model of Uber. Incidentally, these 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**, precisely 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/. .. tags:: Coastlines, Globe, Texture, Unstructured ---- .. GENERATED FROM PYTHON SOURCE LINES 80-84 🦉 Walk-Through ^^^^^^^^^^^^^^^ First, let's ``import`` the package dependencies required by the example. .. GENERATED FROM PYTHON SOURCE LINES 84-108 .. code-block:: Python 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 .. GENERATED FROM PYTHON SOURCE LINES 109-113 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. .. GENERATED FROM PYTHON SOURCE LINES 113-135 .. code-block:: Python #: 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 .. GENERATED FROM PYTHON SOURCE LINES 136-138 The ``GeoSurface`` container holds the **geometry** and **topology** of the ``H3`` **base icosahedron**. .. GENERATED FROM PYTHON SOURCE LINES 138-149 .. code-block:: Python @dataclass class GeoSurface: """Geometry and topology of a geo-located surface.""" lons: ArrayLike lats: ArrayLike connectivity: ArrayLike .. GENERATED FROM PYTHON SOURCE LINES 150-153 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. .. GENERATED FROM PYTHON SOURCE LINES 153-205 .. code-block:: Python 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.cell_to_latlng(cell) for cell in sorted(h3.get_pentagons(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) .. GENERATED FROM PYTHON SOURCE LINES 206-213 The ``GeoSurface`` created by the ``generate_icosahedron_surface`` function is then used to create a :class:`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. .. GENERATED FROM PYTHON SOURCE LINES 213-247 .. code-block:: Python 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:]) .. GENERATED FROM PYTHON SOURCE LINES 248-251 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. .. GENERATED FROM PYTHON SOURCE LINES 251-282 .. code-block:: Python 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.cell_to_children(h3index) for h3index in h3indexes] result.update(*children) return result .. GENERATED FROM PYTHON SOURCE LINES 283-291 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 :class:`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. .. GENERATED FROM PYTHON SOURCE LINES 291-336 .. code-block:: Python 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.cell_to_boundary(h3index) 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) .. GENERATED FROM PYTHON SOURCE LINES 337-345 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). .. GENERATED FROM PYTHON SOURCE LINES 345-396 .. code-block:: Python 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), ) .. GENERATED FROM PYTHON SOURCE LINES 397-403 .. only:: on_rtd .. 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. .. GENERATED FROM PYTHON SOURCE LINES 405-418 Finally, we create the :class:`~geovista.geoplotter.GeoPlotter` and add the **base icosahedron** surface and geodesic edges, a Natural Earth base layer and coastlines. We also use the :func:`h3.get_res0_cells` 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 :class:`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. .. GENERATED FROM PYTHON SOURCE LINES 418-525 .. code-block:: Python 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_cells() 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() .. tab-set:: .. tab-item:: Static Scene .. image-sg:: /generated/gallery/spatial_index/images/sphx_glr_uber_h3_001.png :alt: uber h3 :srcset: /generated/gallery/spatial_index/images/sphx_glr_uber_h3_001.png :class: sphx-glr-single-img .. tab-item:: Interactive Scene .. offlineviewer:: /home/docs/checkouts/readthedocs.org/user_builds/geovista/checkouts/v0.5.3/docs/src/generated/gallery/spatial_index/images/sphx_glr_uber_h3_001.vtksz .. _sphx_glr_download_generated_gallery_spatial_index_uber_h3.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: uber_h3.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: uber_h3.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: uber_h3.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_