Creating a zone system based on Hex Bins

In this example, we show how to create hex bin zones covering an arbitrary area.

We use the Nauru example to create roughly 100 zones covering the whole modeling area as delimited by the entire network

You are obviously welcome to create whatever zone system you would like, as long as you have the geometries for them. In that case, you can just skip the hex bin computation part of this notebook.

We also add centroid connectors to our network to make it a pretty complete example

Imports

from uuid import uuid4
from tempfile import gettempdir
from os.path import join
from math import sqrt
from shapely.geometry import Point
import shapely.wkb
from aequilibrae.utils.create_example import create_example, list_examples

We create an empty project on an arbitrary folder

fldr = join(gettempdir(), uuid4().hex)

# We can print the list of examples that ship with AequilibraE
print(list_examples())

# Let's use the Nauru example project for display
project = create_example(fldr, "nauru")

['coquimbo', 'sioux_falls', 'nauru']

We said we wanted 100 zones

zones = 100

Hex Bins using Spatialite

Spatialite requires a few things to compute hex bins. One of them is the area you want to cover.

network = project.network

# So we use the convenient network method ``convex_hull()`` (it may take some time for very large networks)
geo = network.convex_hull()

The second thing is the side of the hex bin, which we can compute from its area. The approximate area of the desired hex bin is

zone_area = geo.area / zones
# Since the area of the hexagon is **3 * sqrt(3) * side^2 / 2**
# is side is equal to  **sqrt(2 * sqrt(3) * A/9)**
zone_side = sqrt(2 * sqrt(3) * zone_area / 9)

Now we can run an SQL query to compute the hexagonal grid. There are many ways to create hex bins (including with a GUI on QGIS), but we find that using SpatiaLite is a pretty neat solution. For which we will use the entire network bounding box to make sure we cover everything

extent = network.extent()

curr = project.conn.cursor()
b = extent.bounds
curr.execute(
    "select st_asbinary(HexagonalGrid(GeomFromWKB(?), ?, 0, GeomFromWKB(?)))",
    [extent.wkb, zone_side, Point(b[2], b[3]).wkb],
)
grid = curr.fetchone()[0]
grid = shapely.wkb.loads(grid)

Since we used the bounding box, we have WAY more zones than we wanted, so we clean them by only keeping those that intersect the network convex hull.

grid = [p for p in grid.geoms if p.intersects(geo)]

# Let's re-number all nodes with IDs smaller than 300 to something bigger as to free space to our centroids to go from 1
# to N
nodes = network.nodes
for i in range(1, 301):
    nd = nodes.get(i)
    nd.renumber(i + 1300)

Now we can add them to the model And add centroids to them while we are at it

zoning = project.zoning
for i, zone_geo in enumerate(grid):
    zone = zoning.new(i + 1)
    zone.geometry = zone_geo
    zone.save()
    # None means that the centroid will be added in the geometric point of the zone
    # But we could provide a Shapely point as an alternative
    zone.add_centroid(None)

Centroid connectors

for zone_id, zone in zoning.all_zones().items():
    # We will connect for walk, with 1 connector per zone
    zone.connect_mode(mode_id="w", connectors=1)

    # And for cars, for cars with 2 connectors per zone
    # We also specify the link types we accept to connect to (can be used to avoid connection to ramps or freeways)
    zone.connect_mode(mode_id="c", link_types="ytrusP", connectors=2)

    # This takes a few minutes to compute, so we will break after processing the first 10 zones
    if zone_id >= 10:
        break

Let’s add special generator zones We also add a centroid at the airport terminal

nodes = project.network.nodes

# Let's use some silly number for its ID, like 10,000, just so we can easily differentiate it
airport = nodes.new_centroid(10000)
airport.geometry = Point(166.91749582, -0.54472590)
airport.save()

# When connecting a centroid not associated with a zone, we need to tell AequilibraE what is the initial area around
# the centroid that needs to be considered when looking for candidate nodes.
# Distance here is in degrees, so 0.01 is equivalent to roughly 1.1km
airport.connect_mode(airport.geometry.buffer(0.01), mode_id="c", link_types="ytrusP", connectors=1)

project.close()