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: pygal 3.1.0 | Python 3.13.13
Quality: 73/100 | Updated: 2026-05-17
"""
import os
import xml.etree.ElementTree as ET
import cairosvg
import numpy as np
from scipy.spatial import Voronoi
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"
BRAND = "#009E73"
IMPRINT = ("#009E73", "#C475FD", "#4467A3", "#BD8233", "#AE3030", "#2ABCCD", "#954477")
np.random.seed(42)
points = np.random.uniform(0.5, 10.5, size=(25, 2))
vor = Voronoi(points)
WIDTH = 4800
HEIGHT = 2700
margin_left = 400
margin_right = 200
margin_top = 300
margin_bottom = 250
plot_width = WIDTH - margin_left - margin_right
plot_height = HEIGHT - margin_top - margin_bottom
x_min, x_max = 0.5, 10.5
y_min, y_max = 0.5, 10.5
def data_to_svg(x, y):
svg_x = margin_left + (x - x_min) / (x_max - x_min) * plot_width
svg_y = margin_top + (y_max - y) / (y_max - y_min) * plot_height
return svg_x, svg_y
def voronoi_finite_polygons_2d(vor, radius=None):
if vor.points.shape[1] != 2:
raise ValueError("Requires 2D input")
new_regions = []
new_vertices = vor.vertices.tolist()
center = vor.points.mean(axis=0)
if radius is None:
radius = vor.points.ptp().max() * 2
all_ridges = {}
for (p1, p2), (v1, v2) in zip(vor.ridge_points, vor.ridge_vertices, strict=True):
all_ridges.setdefault(p1, []).append((p2, v1, v2))
all_ridges.setdefault(p2, []).append((p1, v1, v2))
for p1, region in enumerate(vor.point_region):
vertices = vor.regions[region]
if all(v >= 0 for v in vertices):
new_regions.append(vertices)
continue
ridges = all_ridges[p1]
new_region = [v for v in vertices if v >= 0]
for p2, v1, v2 in ridges:
if v2 < 0:
v1, v2 = v2, v1
if v1 >= 0:
continue
t = vor.points[p2] - vor.points[p1]
t /= np.linalg.norm(t)
n = np.array([-t[1], t[0]])
midpoint = vor.points[[p1, p2]].mean(axis=0)
direction = np.sign(np.dot(midpoint - center, n)) * n
far_point = vor.vertices[v2] + direction * radius
new_region.append(len(new_vertices))
new_vertices.append(far_point.tolist())
vs = np.asarray([new_vertices[v] for v in new_region])
c = vs.mean(axis=0)
angles = np.arctan2(vs[:, 1] - c[1], vs[:, 0] - c[0])
new_region = np.array(new_region)[np.argsort(angles)].tolist()
new_regions.append(new_region)
return new_regions, np.asarray(new_vertices)
def clip_polygon_to_box(vertices, x_min, x_max, y_min, y_max):
def inside_edge(p, edge):
x, y = p
if edge == "left":
return x >= x_min
if edge == "right":
return x <= x_max
if edge == "bottom":
return y >= y_min
if edge == "top":
return y <= y_max
def intersect(p1, p2, edge):
x1, y1 = p1
x2, y2 = p2
dx = x2 - x1
dy = y2 - y1
if edge == "left":
t = (x_min - x1) / (dx + 1e-12)
elif edge == "right":
t = (x_max - x1) / (dx + 1e-12)
elif edge == "bottom":
t = (y_min - y1) / (dy + 1e-12)
else:
t = (y_max - y1) / (dy + 1e-12)
return (x1 + t * dx, y1 + t * dy)
output = list(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]
prev = input_list[i - 1]
if inside_edge(current, edge):
if not inside_edge(prev, edge):
output.append(intersect(prev, current, edge))
output.append(current)
elif inside_edge(prev, edge):
output.append(intersect(prev, current, edge))
return output
regions, vertices = voronoi_finite_polygons_2d(vor, radius=20)
svg_ns = "http://www.w3.org/2000/svg"
ET.register_namespace("", svg_ns)
svg_root = ET.Element("svg", xmlns=svg_ns, width=str(WIDTH), height=str(HEIGHT), viewBox=f"0 0 {WIDTH} {HEIGHT}")
svg_root.set("style", f"background-color: {PAGE_BG};")
title_elem = ET.SubElement(svg_root, "text")
title_elem.set("x", str(WIDTH / 2))
title_elem.set("y", "150")
title_elem.set("text-anchor", "middle")
title_elem.set("fill", INK)
title_elem.set("font-size", "28")
title_elem.set("font-family", "sans-serif")
title_elem.set("font-weight", "500")
title_elem.text = "voronoi-basic · pygal · anyplot.ai"
x_label = ET.SubElement(svg_root, "text")
x_label.set("x", str(margin_left + plot_width / 2))
x_label.set("y", str(HEIGHT - 80))
x_label.set("text-anchor", "middle")
x_label.set("fill", INK)
x_label.set("font-size", "22")
x_label.set("font-family", "sans-serif")
x_label.text = "X Coordinate (units)"
y_label = ET.SubElement(svg_root, "text")
y_label.set("x", "110")
y_label.set("y", str(margin_top + plot_height / 2))
y_label.set("text-anchor", "middle")
y_label.set("fill", INK)
y_label.set("font-size", "22")
y_label.set("font-family", "sans-serif")
y_label.set("transform", f"rotate(-90, 110, {margin_top + plot_height / 2})")
y_label.text = "Y Coordinate (units)"
plot_bg = ET.SubElement(svg_root, "rect")
plot_bg.set("x", str(margin_left))
plot_bg.set("y", str(margin_top))
plot_bg.set("width", str(plot_width))
plot_bg.set("height", str(plot_height))
plot_bg.set("fill", PAGE_BG)
plot_bg.set("stroke", INK_SOFT)
plot_bg.set("stroke-width", "2")
defs = ET.SubElement(svg_root, "defs")
clip_path = ET.SubElement(defs, "clipPath", id="plot-area")
clip_rect = ET.SubElement(clip_path, "rect")
clip_rect.set("x", str(margin_left))
clip_rect.set("y", str(margin_top))
clip_rect.set("width", str(plot_width))
clip_rect.set("height", str(plot_height))
grid_g = ET.SubElement(svg_root, "g")
grid_g.set("class", "grid")
grid_color = "rgba(26,26,23,0.10)" if THEME == "light" else "rgba(240,239,232,0.10)"
for x_val in np.arange(1, 11, 1):
sx, _ = data_to_svg(x_val, 0)
_, sy_top = data_to_svg(0, y_max)
_, sy_bot = data_to_svg(0, y_min)
line = ET.SubElement(grid_g, "line")
line.set("x1", f"{sx:.1f}")
line.set("y1", f"{sy_top:.1f}")
line.set("x2", f"{sx:.1f}")
line.set("y2", f"{sy_bot:.1f}")
line.set("stroke", INK_SOFT)
line.set("stroke-width", "1")
line.set("opacity", "0.15")
for y_val in np.arange(1, 11, 1):
_, sy = data_to_svg(0, y_val)
sx_left, _ = data_to_svg(x_min, 0)
sx_right, _ = data_to_svg(x_max, 0)
line = ET.SubElement(grid_g, "line")
line.set("x1", f"{sx_left:.1f}")
line.set("y1", f"{sy:.1f}")
line.set("x2", f"{sx_right:.1f}")
line.set("y2", f"{sy:.1f}")
line.set("stroke", INK_SOFT)
line.set("stroke-width", "1")
line.set("opacity", "0.15")
for x_val in range(1, 11, 2):
sx, _ = data_to_svg(x_val, 0)
tick_label = ET.SubElement(svg_root, "text")
tick_label.set("x", f"{sx:.1f}")
tick_label.set("y", str(margin_top + plot_height + 60))
tick_label.set("text-anchor", "middle")
tick_label.set("fill", INK_SOFT)
tick_label.set("font-size", "18")
tick_label.set("font-family", "sans-serif")
tick_label.text = str(x_val)
for y_val in range(1, 11, 2):
_, sy = data_to_svg(0, y_val)
tick_label = ET.SubElement(svg_root, "text")
tick_label.set("x", str(margin_left - 40))
tick_label.set("y", f"{sy + 8:.1f}")
tick_label.set("text-anchor", "end")
tick_label.set("fill", INK_SOFT)
tick_label.set("font-size", "18")
tick_label.set("font-family", "sans-serif")
tick_label.text = str(y_val)
cells_g = ET.SubElement(svg_root, "g")
cells_g.set("class", "voronoi-cells")
cells_g.set("clip-path", "url(#plot-area)")
for i, region in enumerate(regions):
if not region or len(region) < 3:
continue
poly_verts = [vertices[v] for v in region]
clipped = clip_polygon_to_box(poly_verts, x_min, x_max, y_min, y_max)
if len(clipped) < 3:
continue
svg_points = [data_to_svg(x, y) for x, y in clipped]
points_str = " ".join([f"{x:.1f},{y:.1f}" for x, y in svg_points])
polygon = ET.SubElement(cells_g, "polygon")
polygon.set("points", points_str)
color = IMPRINT[i % len(IMPRINT)]
polygon.set("fill", color)
polygon.set("fill-opacity", "0.6")
polygon.set("stroke", INK_SOFT)
polygon.set("stroke-width", "2")
title = ET.SubElement(polygon, "title")
title.text = f"Region {i + 1}: ({vor.points[i][0]:.2f}, {vor.points[i][1]:.2f})"
points_g = ET.SubElement(svg_root, "g")
points_g.set("class", "seed-points")
for i, (px, py) in enumerate(vor.points):
sx, sy = data_to_svg(px, py)
outer = ET.SubElement(points_g, "circle")
outer.set("cx", f"{sx:.1f}")
outer.set("cy", f"{sy:.1f}")
outer.set("r", "16")
outer.set("fill", PAGE_BG)
outer.set("stroke", INK_SOFT)
outer.set("stroke-width", "2")
inner = ET.SubElement(points_g, "circle")
inner.set("cx", f"{sx:.1f}")
inner.set("cy", f"{sy:.1f}")
inner.set("r", "12")
color = IMPRINT[i % len(IMPRINT)]
inner.set("fill", color)
title = ET.SubElement(inner, "title")
title.text = f"Point {i + 1}: ({px:.2f}, {py:.2f})"
svg_output = ET.tostring(svg_root, encoding="unicode")
with open(f"plot-{THEME}.html", "w") as f:
f.write(svg_output)
cairosvg.svg2png(bytestring=svg_output.encode("utf-8"), write_to=f"plot-{THEME}.png")
Part of Voronoi Diagram for Spatial Partitioning on anyplot.ai.