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: letsplot 4.9.0 | Python 3.13.13
Quality: 90/100 | Updated: 2026-05-17
"""
import os
import numpy as np
import pandas as pd
from lets_plot import (
LetsPlot,
aes,
coord_fixed,
element_blank,
element_line,
element_rect,
element_text,
geom_point,
geom_polygon,
ggplot,
ggsave,
ggsize,
labs,
scale_fill_manual,
theme,
theme_minimal,
)
from scipy.spatial import Voronoi
LetsPlot.setup_html()
# Theme tokens
THEME = os.getenv("ANYPLOT_THEME", "light")
PAGE_BG = "#FAF8F1" if THEME == "light" else "#1A1A17"
INK = "#1A1A17" if THEME == "light" else "#F0EFE8"
INK_SOFT = "#4A4A44" if THEME == "light" else "#B8B7B0"
# Data - Generate seed points for spatial partitioning
np.random.seed(42)
n_points = 20
# Generate clustered seed points representing facility locations
x = np.concatenate([np.random.normal(25, 8, n_points // 2), np.random.normal(75, 8, n_points // 2)])
y = np.concatenate([np.random.normal(40, 10, n_points // 2), np.random.normal(60, 10, n_points // 2)])
# Define bounding box for clipping
x_min, x_max = 0, 100
y_min, y_max = 0, 100
# Add boundary points to ensure all regions are clipped
boundary_margin = 200
boundary_points = np.array(
[
[x_min - boundary_margin, y_min - boundary_margin],
[x_min - boundary_margin, y_max + boundary_margin],
[x_max + boundary_margin, y_min - boundary_margin],
[x_max + boundary_margin, y_max + boundary_margin],
]
)
# Combine seed points with boundary points
all_points = np.column_stack([x, y])
points_with_boundary = np.vstack([all_points, boundary_points])
# Compute Voronoi tessellation
vor = Voronoi(points_with_boundary)
# Build polygon data for each Voronoi region using Sutherland-Hodgman clipping
polygon_data = []
for idx, region_idx in enumerate(vor.point_region[: len(all_points)]):
region = vor.regions[region_idx]
if not region or -1 in region:
continue
# Get vertices for this region
vertices = [list(vor.vertices[i]) for i in region]
# Sutherland-Hodgman polygon clipping to bounding box
output = vertices
for edge in ["left", "right", "bottom", "top"]:
if len(output) == 0:
break
input_list = output
output = []
for i in range(len(input_list)):
current = input_list[i]
previous = input_list[i - 1]
# Check if point is inside this edge
if edge == "left":
curr_inside = current[0] >= x_min
prev_inside = previous[0] >= x_min
elif edge == "right":
curr_inside = current[0] <= x_max
prev_inside = previous[0] <= x_max
elif edge == "bottom":
curr_inside = current[1] >= y_min
prev_inside = previous[1] >= y_min
else: # top
curr_inside = current[1] <= y_max
prev_inside = previous[1] <= y_max
# Compute intersection if crossing edge
if curr_inside != prev_inside:
x1, y1 = previous
x2, y2 = current
if edge == "left":
t = (x_min - x1) / (x2 - x1) if x2 != x1 else 0
ix, iy = x_min, y1 + t * (y2 - y1)
elif edge == "right":
t = (x_max - x1) / (x2 - x1) if x2 != x1 else 0
ix, iy = x_max, y1 + t * (y2 - y1)
elif edge == "bottom":
t = (y_min - y1) / (y2 - y1) if y2 != y1 else 0
ix, iy = x1 + t * (x2 - x1), y_min
else: # top
t = (y_max - y1) / (y2 - y1) if y2 != y1 else 0
ix, iy = x1 + t * (x2 - x1), y_max
output.append([ix, iy])
if curr_inside:
output.append(current)
# Add clipped polygon vertices to data
if len(output) >= 3:
for vx, vy in output:
polygon_data.append({"x": vx, "y": vy, "region": f"Region {idx + 1}"})
df_polygons = pd.DataFrame(polygon_data)
# Create seed points dataframe
df_seeds = pd.DataFrame({"x": x, "y": y, "label": [f"P{i + 1}" for i in range(len(x))]})
# Color palette for regions - diverse and visually distinct
colors = [
"#009E73",
"#C475FD",
"#4467A3",
"#BD8233",
"#AE3030",
"#2ABCCD",
"#954477",
"#1B9E77",
"#D95F02",
"#7570B3",
"#E7298A",
"#66A61E",
"#E6AB02",
"#A6761D",
"#666666",
"#1B9E77",
"#D95F02",
"#7570B3",
"#E7298A",
"#66A61E",
]
# Build plot with Voronoi cells and seed points
plot = (
ggplot()
+ geom_polygon(data=df_polygons, mapping=aes(x="x", y="y", fill="region"), color=INK_SOFT, size=1.5, alpha=0.7)
+ geom_point(data=df_seeds, mapping=aes(x="x", y="y"), color=INK, size=8)
+ geom_point(data=df_seeds, mapping=aes(x="x", y="y"), color=PAGE_BG, size=4)
+ scale_fill_manual(values=colors)
+ coord_fixed(xlim=[x_min, x_max], ylim=[y_min, y_max])
+ labs(x="X Coordinate", y="Y Coordinate", title="voronoi-basic · letsplot · anyplot.ai")
+ theme_minimal()
+ theme(
plot_background=element_rect(fill=PAGE_BG, color=PAGE_BG),
panel_background=element_rect(fill=PAGE_BG),
panel_grid_major=element_blank(),
panel_grid_minor=element_blank(),
plot_title=element_text(size=24, color=INK),
axis_title=element_text(size=20, color=INK),
axis_text=element_text(size=16, color=INK_SOFT),
axis_line=element_line(color=INK_SOFT),
legend_position="none",
)
+ ggsize(1600, 900)
)
# Save outputs with theme suffix
ggsave(plot, f"plot-{THEME}.png", path=".", scale=3)
ggsave(plot, f"plot-{THEME}.html", path=".")
Part of Voronoi Diagram for Spatial Partitioning on anyplot.ai.