Enclosed Tessellation for enclosures with cul-de-sac

[yu-ta-sato]

Thank you so much for developing this wonderful package!

I am planning to apply momepy for a research project and identified a potential issue regarding momepy.enclosed_tessellation.
When an enclosure contains cul-de-sacs, the voronoi_frame from libpysal does not consider these barriers to generate the tessellaiton cells. I tried to tweak parameters or give buffers to streets, but it seems the boundaries are made beyond the cul-de-sac. Ideally, the tessellation could consider the barriers even inside of the enclosures.

If you have already tackled with this issue, it would be highly helpful.

1. General information

momepy.__version__ == "0.9.1"

2. Sample data for replication

import momepy
import geopandas as gpd
from shapely.geometry import LineString, Polygon

# ------------------------
# 1) Define Bounding Box & Main Vertical Street (all coordinates * 10)
# ------------------------
bottom_edge = LineString([(0, 0), (80, 0)])
right_edge  = LineString([(80, 0), (80, 120)])
top_edge    = LineString([(80, 120), (0, 120)])
left_edge   = LineString([(0, 120), (0, 0)])

# Main vertical street from x=40, y=0 to y=110
main_vertical = LineString([(40, 0), (40, 110)])

# ------------------------
# 2) Define Three Cul-de-Sacs (All 30 Units Long)
# ------------------------
cul_left_bottom = LineString([(10, 30), (40, 30)])
cul_left_top    = LineString([(10, 90), (40, 90)])
cul_right_middle = LineString([(40, 60), (70, 60)])

streets_data = {
    'name': [
        'Bottom Edge', 'Right Edge', 'Top Edge', 'Left Edge',
        'Main Vertical',
        'Left Cul-de-Sac (Bottom)',
        'Left Cul-de-Sac (Top)',
        'Right Cul-de-Sac (Middle)'
    ],
    'geometry': [
        bottom_edge, right_edge, top_edge, left_edge,
        main_vertical,
        cul_left_bottom, cul_left_top, cul_right_middle
    ]
}
cds_streets_gdf = gpd.GeoDataFrame(streets_data, crs="EPSG:3857")

# ------------------------
# 3) Define Buildings (all coordinates * 10)
# ------------------------
bld_left_bot_top = Polygon([
    (15, 32), (35, 32),
    (35, 38), (15, 38)
])
bld_left_bot_bottom = Polygon([
    (15, 22), (35, 22),
    (35, 28), (15, 28)
])

bld_left_top_top = Polygon([
    (15, 92), (35, 92),
    (35, 98), (15, 98)
])
bld_left_top_bottom = Polygon([
    (15, 82), (35, 82),
    (35, 88), (15, 88)
])

bld_right_mid_top = Polygon([
    (45, 62), (65, 62),
    (65, 68), (45, 68)
])
bld_right_mid_bottom = Polygon([
    (45, 52), (65, 52),
    (65, 58), (45, 58)
])

building_polygons = [
    bld_left_bot_top, 
    bld_left_bot_bottom,
    bld_left_top_top,
    bld_left_top_bottom,
    bld_right_mid_top,
    bld_right_mid_bottom
]
building_data = {
    'building_id': list(range(1, len(building_polygons) + 1)),
    'geometry': building_polygons
}
cds_buildings_gdf = gpd.GeoDataFrame(building_data, crs="EPSG:3857")

import matplotlib.pyplot as plt

# Create a figure and axis
fig, ax = plt.subplots(figsize=(5, 5))

# Plot streets in blue
cds_streets_gdf.plot(ax=ax, color='blue', linewidth=2)

# Plot buildings in red with some transparency
cds_buildings_gdf.plot(ax=ax, color='red')

# Add title
plt.title('Cul-de-Sac Streets and Buildings')

# Show the plot
plt.show()

3. Sample code for generating enclosed tessellation

# Create enclosures and enclosed tessellation
cds_enclosures = momepy.enclosures(cds_streets_gdf)
cds_enclosed_tess = momepy.enclosed_tessellation(cds_buildings_gdf, cds_enclosures)

# plot the enclosed tessellation
fig, ax = plt.subplots(figsize=(5, 5))

# Plot streets in blue
cds_streets_gdf.plot(ax=ax, color='blue', alpha=1, linewidth=2)

# Plot buildings in red with some transparency
cds_buildings_gdf.plot(ax=ax, color='red', alpha=1)

# Plot enclosed tessellation in green
cds_enclosed_tess.plot(ax=ax, color='red', alpha=0.5, edgecolor='black', linestyle='--')

# Add title
plt.title('Cul-de-Sac Streets, Buildings, and Enclosed Tessellation')

# Show the plot
plt.show()

[martinfleis]

We are aware, this is an inherent limitation of the algorithm. Yet, there are no plans on changing the behaviour as it would be very complicated to do so.

[yu-ta-sato]

Thanks for the reply! I tried many ways but not worked to capture the non-Euclidean distance in the topology, so switched my mind to approximate the tessellation numerically by meshes, inspired by this paper using Cellular Automata. It worked, but is different from the original Enclosed Tessellation. I belong to GDSL with supervision of Dani, so let me reach out to you later for this proposal.

[martinfleis]

Ah, yeah, I can imagine this algorithm works. So you'd apply this within each enclosure and vectorize geometries? It probably won't be the fastest thing even but happy to give it a go.

[yu-ta-sato]

That is right, it is merely a numeric approximation and not computationally efficient. I'll anyway look for alternative solution for this issue but am happy to raise a PR once done!