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: bokeh 3.9.0 | Python 3.13.13
Quality: 90/100 | Updated: 2026-05-17
"""
import os
import time
from pathlib import Path
import numpy as np
from bokeh.io import output_file, save
from bokeh.models import ColumnDataSource
from bokeh.plotting import figure
from scipy.spatial import Voronoi
from selenium import webdriver
from selenium.webdriver.chrome.options import Options
# 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"
BRAND = "#009E73" # Okabe-Ito position 1
# Okabe-Ito palette for Voronoi cells
IMPRINT = ["#009E73", "#C475FD", "#4467A3", "#BD8233", "#AE3030", "#2ABCCD", "#954477"]
# Data - seed points for Voronoi diagram
np.random.seed(42)
n_points = 20
x = np.random.uniform(1, 9, n_points)
y = np.random.uniform(1, 9, n_points)
points = np.column_stack([x, y])
# Bounding box for clipping
x_min, x_max = 0, 10
y_min, y_max = 0, 10
# Add mirrored points outside boundaries to handle infinite regions properly
mirrored = []
for px, py in points:
mirrored.append([2 * x_min - px, py])
mirrored.append([2 * x_max - px, py])
mirrored.append([px, 2 * y_min - py])
mirrored.append([px, 2 * y_max - py])
all_points = np.vstack([points, mirrored])
# Compute Voronoi diagram
vor = Voronoi(all_points)
# Create figure
p = figure(
width=4800,
height=2700,
title="voronoi-basic · bokeh · anyplot.ai",
x_axis_label="X Coordinate",
y_axis_label="Y Coordinate",
x_range=(x_min, x_max),
y_range=(y_min, y_max),
)
# Draw Voronoi regions for original points only
for idx in range(n_points):
region_idx = vor.point_region[idx]
region = vor.regions[region_idx]
if not region or -1 in region:
continue
vertices = [vor.vertices[i] for i in region]
# Clip polygon to bounding box using Sutherland-Hodgman algorithm
polygon = list(vertices)
for edge in ["left", "right", "bottom", "top"]:
if not polygon:
break
clipped = []
for i in range(len(polygon)):
curr = polygon[i]
next_v = polygon[(i + 1) % len(polygon)]
curr_in = (
(curr[0] >= x_min if edge == "left" else True)
and (curr[0] <= x_max if edge == "right" else True)
and (curr[1] >= y_min if edge == "bottom" else True)
and (curr[1] <= y_max if edge == "top" else True)
)
next_in = (
(next_v[0] >= x_min if edge == "left" else True)
and (next_v[0] <= x_max if edge == "right" else True)
and (next_v[1] >= y_min if edge == "bottom" else True)
and (next_v[1] <= y_max if edge == "top" else True)
)
if curr_in:
clipped.append(curr)
if not next_in:
x1, y1 = curr
x2, y2 = next_v
dx, dy = x2 - x1, y2 - y1
if edge == "left":
t = (x_min - x1) / dx if dx != 0 else 0
clipped.append([x_min, y1 + t * dy])
elif edge == "right":
t = (x_max - x1) / dx if dx != 0 else 0
clipped.append([x_max, y1 + t * dy])
elif edge == "bottom":
t = (y_min - y1) / dy if dy != 0 else 0
clipped.append([x1 + t * dx, y_min])
elif edge == "top":
t = (y_max - y1) / dy if dy != 0 else 0
clipped.append([x1 + t * dx, y_max])
elif next_in:
x1, y1 = curr
x2, y2 = next_v
dx, dy = x2 - x1, y2 - y1
if edge == "left":
t = (x_min - x1) / dx if dx != 0 else 0
clipped.append([x_min, y1 + t * dy])
elif edge == "right":
t = (x_max - x1) / dx if dx != 0 else 0
clipped.append([x_max, y1 + t * dy])
elif edge == "bottom":
t = (y_min - y1) / dy if dy != 0 else 0
clipped.append([x1 + t * dx, y_min])
elif edge == "top":
t = (y_max - y1) / dy if dy != 0 else 0
clipped.append([x1 + t * dx, y_max])
polygon = clipped
if len(polygon) >= 3:
xs = [v[0] for v in polygon]
ys = [v[1] for v in polygon]
cell_color = IMPRINT[idx % len(IMPRINT)]
p.patch(xs, ys, fill_color=cell_color, fill_alpha=0.5, line_color=INK_SOFT, line_width=2.5)
# Draw seed points prominently
source = ColumnDataSource(data={"x": x, "y": y})
p.scatter("x", "y", source=source, size=22, color=BRAND, line_color=PAGE_BG, line_width=4, alpha=0.95)
# Styling
p.background_fill_color = PAGE_BG
p.border_fill_color = PAGE_BG
p.outline_line_color = INK_SOFT
p.title.text_font_size = "28pt"
p.title.text_color = INK
p.xaxis.axis_label_text_font_size = "22pt"
p.yaxis.axis_label_text_font_size = "22pt"
p.xaxis.axis_label_text_color = INK
p.yaxis.axis_label_text_color = INK
p.xaxis.major_label_text_font_size = "18pt"
p.yaxis.major_label_text_font_size = "18pt"
p.xaxis.major_label_text_color = INK_SOFT
p.yaxis.major_label_text_color = INK_SOFT
p.xaxis.axis_line_color = INK_SOFT
p.yaxis.axis_line_color = INK_SOFT
p.xaxis.major_tick_line_color = INK_SOFT
p.yaxis.major_tick_line_color = INK_SOFT
p.xgrid.grid_line_color = INK_SOFT
p.ygrid.grid_line_color = INK_SOFT
p.xgrid.grid_line_alpha = 0.10
p.ygrid.grid_line_alpha = 0.10
# Save
output_file(f"plot-{THEME}.html")
save(p)
# Screenshot with headless Chrome
W, H = 4800, 2700
opts = Options()
for arg in (
"--headless=new",
"--no-sandbox",
"--disable-dev-shm-usage",
"--disable-gpu",
f"--window-size={W},{H}",
"--hide-scrollbars",
):
opts.add_argument(arg)
driver = webdriver.Chrome(options=opts)
driver.set_window_size(W, H)
driver.get(f"file://{Path(f'plot-{THEME}.html').resolve()}")
time.sleep(3)
driver.save_screenshot(f"plot-{THEME}.png")
driver.quit()
Part of Voronoi Diagram for Spatial Partitioning on anyplot.ai.