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: plotnine 0.15.4 | Python 3.13.13
Quality: 92/100 | Updated: 2026-05-17
"""
import os
import numpy as np
import pandas as pd
from plotnine import (
aes,
coord_fixed,
element_blank,
element_line,
element_rect,
element_text,
geom_point,
geom_polygon,
ggplot,
labs,
scale_fill_manual,
theme,
)
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"
# Seed for reproducibility
np.random.seed(42)
# Generate seed points (20 points for clear visualization)
n_points = 20
x_points = np.random.uniform(1, 9, n_points)
y_points = np.random.uniform(1, 9, n_points)
points = np.column_stack([x_points, y_points])
# Define bounding box for clipping
x_min, x_max = 0, 10
y_min, y_max = 0, 10
# Add mirror points outside bounds to ensure all cells are bounded
margin = 20
mirror_points = []
for px, py in points:
mirror_points.append([2 * x_min - margin - px, py])
mirror_points.append([2 * x_max + margin - px, py])
mirror_points.append([px, 2 * y_min - margin - py])
mirror_points.append([px, 2 * y_max + margin - py])
all_points = np.vstack([points, mirror_points])
# Compute Voronoi diagram with mirrored points
vor = Voronoi(all_points)
# Build polygon dataframe for Voronoi cells
polygon_data = []
for point_idx in range(n_points):
region_idx = vor.point_region[point_idx]
region = vor.regions[region_idx]
if not region or -1 in region:
continue
vertices = [tuple(vor.vertices[v]) for v in region]
# Sutherland-Hodgman polygon clipping algorithm (inline)
polygon = list(vertices)
# Clip left edge
clipped = []
for i in range(len(polygon)):
curr = polygon[i]
prev = polygon[i - 1]
curr_in = curr[0] >= x_min
prev_in = prev[0] >= x_min
if curr_in:
if not prev_in:
x1, y1 = prev
x2, y2 = curr
t = (x_min - x1) / (x2 - x1) if x2 != x1 else 0
clipped.append((x_min, y1 + t * (y2 - y1)))
clipped.append(curr)
elif prev_in:
x1, y1 = prev
x2, y2 = curr
t = (x_min - x1) / (x2 - x1) if x2 != x1 else 0
clipped.append((x_min, y1 + t * (y2 - y1)))
polygon = clipped
# Clip right edge
clipped = []
for i in range(len(polygon)):
curr = polygon[i]
prev = polygon[i - 1]
curr_in = curr[0] <= x_max
prev_in = prev[0] <= x_max
if curr_in:
if not prev_in:
x1, y1 = prev
x2, y2 = curr
t = (x_max - x1) / (x2 - x1) if x2 != x1 else 0
clipped.append((x_max, y1 + t * (y2 - y1)))
clipped.append(curr)
elif prev_in:
x1, y1 = prev
x2, y2 = curr
t = (x_max - x1) / (x2 - x1) if x2 != x1 else 0
clipped.append((x_max, y1 + t * (y2 - y1)))
polygon = clipped
# Clip bottom edge
clipped = []
for i in range(len(polygon)):
curr = polygon[i]
prev = polygon[i - 1]
curr_in = curr[1] >= y_min
prev_in = prev[1] >= y_min
if curr_in:
if not prev_in:
x1, y1 = prev
x2, y2 = curr
t = (y_min - y1) / (y2 - y1) if y2 != y1 else 0
clipped.append((x1 + t * (x2 - x1), y_min))
clipped.append(curr)
elif prev_in:
x1, y1 = prev
x2, y2 = curr
t = (y_min - y1) / (y2 - y1) if y2 != y1 else 0
clipped.append((x1 + t * (x2 - x1), y_min))
polygon = clipped
# Clip top edge
clipped = []
for i in range(len(polygon)):
curr = polygon[i]
prev = polygon[i - 1]
curr_in = curr[1] <= y_max
prev_in = prev[1] <= y_max
if curr_in:
if not prev_in:
x1, y1 = prev
x2, y2 = curr
t = (y_max - y1) / (y2 - y1) if y2 != y1 else 0
clipped.append((x1 + t * (x2 - x1), y_max))
clipped.append(curr)
elif prev_in:
x1, y1 = prev
x2, y2 = curr
t = (y_max - y1) / (y2 - y1) if y2 != y1 else 0
clipped.append((x1 + t * (x2 - x1), y_max))
polygon = clipped
if len(polygon) < 3:
continue
for order, (vx, vy) in enumerate(polygon):
polygon_data.append({"cell_id": str(point_idx), "x": vx, "y": vy, "order": order})
df_polygons = pd.DataFrame(polygon_data)
# Create dataframe for seed points
df_points = pd.DataFrame({"x": x_points, "y": y_points})
# Cell colors - diverse palette starting with Okabe-Ito positions
colors_20 = [
"#009E73",
"#C475FD",
"#4467A3",
"#BD8233",
"#AE3030",
"#2ABCCD",
"#954477",
"#306998",
"#8DD3C7",
"#BEBADA",
"#FB8072",
"#80B1D3",
"#FDB462",
"#B3DE69",
"#FCCDE5",
"#BC80BD",
"#CCEBC5",
"#FFED6F",
"#A6CEE3",
"#B2DF8A",
]
# Create the Voronoi diagram plot
plot = (
ggplot()
+ geom_polygon(df_polygons, aes(x="x", y="y", group="cell_id", fill="cell_id"), color=INK_SOFT, size=1.0, alpha=0.7)
+ geom_point(df_points, aes(x="x", y="y"), color="#009E73", fill="#009E73", size=6, stroke=1.5, shape="o")
+ scale_fill_manual(values=colors_20)
+ coord_fixed(ratio=1.0, xlim=(x_min, x_max), ylim=(y_min, y_max))
+ labs(title="voronoi-basic · plotnine · anyplot.ai", x="X Coordinate", y="Y Coordinate")
+ theme(
figure_size=(12, 12),
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(),
panel_border=element_rect(color=INK_SOFT, fill=None, size=0.5),
axis_line=element_line(color=INK_SOFT, size=0.5),
plot_title=element_text(size=24, color=INK, weight="bold", margin={"b": 20}),
axis_title=element_text(size=20, color=INK),
axis_text=element_text(size=16, color=INK_SOFT),
legend_position="none",
)
)
# Save the plot
plot.save(f"plot-{THEME}.png", dpi=300, verbose=False)
Part of Voronoi Diagram for Spatial Partitioning on anyplot.ai.