A Voronoi diagram partitions a plane into regions based on the distance to a set of seed points, where each region contains all points closer to its seed than to any other. This visualization is essential for understanding spatial relationships, proximity analysis, and territorial boundaries. It reveals natural clustering patterns and helps identify areas of influence around data points.
""" anyplot.ai
voronoi-basic: Voronoi Diagram for Spatial Partitioning
Library: plotly 6.7.0 | Python 3.13.13
Quality: 87/100 | Updated: 2026-05-17
"""
import os
import sys
# Remove current directory from path BEFORE importing plotly
cur_dir = os.path.dirname(os.path.abspath(__file__))
sys.path = [p for p in sys.path if os.path.abspath(p) != cur_dir]
import numpy as np
import plotly.graph_objects as go
from scipy.spatial import Voronoi
# Theme tokens
THEME = os.getenv("ANYPLOT_THEME", "light")
PAGE_BG = "#FAF8F1" if THEME == "light" else "#1A1A17"
ELEVATED_BG = "#FFFDF6" if THEME == "light" else "#242420"
INK = "#1A1A17" if THEME == "light" else "#F0EFE8"
INK_SOFT = "#4A4A44" if THEME == "light" else "#B8B7B0"
GRID = "rgba(26,26,23,0.10)" if THEME == "light" else "rgba(240,239,232,0.10)"
# Okabe-Ito palette (position 1 is brand color #009E73)
IMPRINT = ["#009E73", "#C475FD", "#4467A3", "#BD8233", "#AE3030", "#2ABCCD", "#954477"]
# Data - Generate seed points (retail stores) within city bounds
np.random.seed(42)
n_stores = 20
x = np.random.uniform(10, 90, n_stores)
y = np.random.uniform(10, 90, n_stores)
points = np.column_stack([x, y])
# Bounding box for city area
x_min, x_max = 0, 100
y_min, y_max = 0, 100
# Add far-away boundary points to ensure finite regions within bounding box
boundary_offset = 200
boundary_points = np.array(
[
[x_min - boundary_offset, y_min - boundary_offset],
[x_max + boundary_offset, y_min - boundary_offset],
[x_min - boundary_offset, y_max + boundary_offset],
[x_max + boundary_offset, y_max + boundary_offset],
[(x_min + x_max) / 2, y_min - boundary_offset],
[(x_min + x_max) / 2, y_max + boundary_offset],
[x_min - boundary_offset, (y_min + y_max) / 2],
[x_max + boundary_offset, (y_min + y_max) / 2],
]
)
all_points = np.vstack([points, boundary_points])
# Compute Voronoi diagram
vor = Voronoi(all_points)
# Extended color palette (cycle through Okabe-Ito + supplementary colors)
extended_colors = IMPRINT + [
"#FF9AA2",
"#FFB7B2",
"#E0BBE4",
"#957DAD",
"#D291BC",
"#C9B1FF",
"#A1C4FD",
"#B5EAD7",
"#C7CEEA",
"#FFDAC1",
"#E2F0CB",
]
# Create figure
fig = go.Figure()
# Draw Voronoi cells (service areas for retail stores)
for idx in range(n_stores):
region_idx = vor.point_region[idx]
region = vor.regions[region_idx]
if not region or -1 in region:
continue
vertices = [list(vor.vertices[v]) for v in region]
# Clip polygon to bounding box using Sutherland-Hodgman algorithm
polygon = vertices
for edge, bounds in [("left", x_min), ("right", x_max), ("bottom", y_min), ("top", y_max)]:
if len(polygon) == 0:
break
clipped = []
for i in range(len(polygon)):
curr = polygon[i]
next_v = polygon[(i + 1) % len(polygon)]
# Check if points are inside edge
if edge == "left":
curr_in, next_in = curr[0] >= bounds, next_v[0] >= bounds
elif edge == "right":
curr_in, next_in = curr[0] <= bounds, next_v[0] <= bounds
elif edge == "bottom":
curr_in, next_in = curr[1] >= bounds, next_v[1] >= bounds
else: # top
curr_in, next_in = curr[1] <= bounds, next_v[1] <= bounds
# Compute intersection if needed
if curr_in != next_in:
dx, dy = next_v[0] - curr[0], next_v[1] - curr[1]
if edge in ("left", "right"):
t = (bounds - curr[0]) / dx if dx != 0 else 0
intersect = [bounds, curr[1] + t * dy]
else:
t = (bounds - curr[1]) / dy if dy != 0 else 0
intersect = [curr[0] + t * dx, bounds]
if curr_in:
clipped.append(curr)
if not next_in:
clipped.append(intersect)
elif next_in:
clipped.append(intersect)
polygon = clipped
if len(polygon) >= 3:
polygon_x = [p[0] for p in polygon] + [polygon[0][0]]
polygon_y = [p[1] for p in polygon] + [polygon[0][1]]
fig.add_trace(
go.Scatter(
x=polygon_x,
y=polygon_y,
fill="toself",
fillcolor=extended_colors[idx % len(extended_colors)],
opacity=0.6,
line={"color": INK_SOFT, "width": 2},
mode="lines",
hoverinfo="skip",
showlegend=False,
)
)
# Draw seed points (store locations) on top
fig.add_trace(
go.Scatter(
x=x,
y=y,
mode="markers",
marker={"size": 18, "color": IMPRINT[0], "line": {"color": ELEVATED_BG, "width": 3}, "symbol": "circle"},
name="Store Location",
hovertemplate="Store %{pointNumber}<br>Latitude: %{y:.1f}<br>Longitude: %{x:.1f}<extra></extra>",
)
)
# Update layout with theme-adaptive colors
fig.update_layout(
title={
"text": "voronoi-basic · plotly · pyplots.ai",
"font": {"size": 28, "color": INK},
"x": 0.5,
"xanchor": "center",
},
xaxis={
"title": {"text": "Longitude (°)", "font": {"size": 22, "color": INK}},
"tickfont": {"size": 18, "color": INK_SOFT},
"range": [-5, 105],
"showgrid": True,
"gridwidth": 1,
"gridcolor": GRID,
"zeroline": False,
"linecolor": INK_SOFT,
},
yaxis={
"title": {"text": "Latitude (°)", "font": {"size": 22, "color": INK}},
"tickfont": {"size": 18, "color": INK_SOFT},
"range": [-5, 105],
"showgrid": True,
"gridwidth": 1,
"gridcolor": GRID,
"zeroline": False,
"scaleanchor": "x",
"scaleratio": 1,
"linecolor": INK_SOFT,
},
paper_bgcolor=PAGE_BG,
plot_bgcolor=PAGE_BG,
font={"color": INK},
showlegend=True,
legend={
"font": {"size": 16, "color": INK_SOFT},
"x": 0.02,
"y": 0.98,
"bgcolor": ELEVATED_BG,
"bordercolor": INK_SOFT,
"borderwidth": 1,
},
margin={"l": 80, "r": 40, "t": 100, "b": 80},
)
# Save as PNG and HTML (square format for Voronoi diagram)
fig.write_image(f"plot-{THEME}.png", width=1200, height=1200, scale=3)
fig.write_html(f"plot-{THEME}.html", include_plotlyjs="cdn")
Part of Voronoi Diagram for Spatial Partitioning on anyplot.ai.