As per my Understanding:

Voronoi diagram: A Voronoi diagram is a simple concept, and it's based on the minimal distance needed to reach a landmark. If you need to go to a metro station, the most natural algorithm is going to the nearest one.


Voronoi Diagram: On a plane, for a set of sites (points in that 2D space with similar properties) the Voronoi diagram partitions the space based on the minimal distance to each site.

General Python Implementation:

This implementation takes in a list of points, each point being a tuple and returns a dictionary consisting of all the points at a given site.

from PIL import Image
import random
import math
def generate_voronoi_diagram(width, height, num_cells):
    image = Image.new("RGB", (width, height))
    putpixel = image.putpixel
    imgx, imgy = image.size
    nx = []
    ny = []
    nr = []
    ng = []
    nb = []
    for i in range(num_cells):
    for y in range(imgy):
        for x in range(imgx):
            dmin = math.hypot(imgx-1, imgy-1)
            j = -1
            for i in range(num_cells):
                d = math.hypot(nx[i]-x, ny[i]-y)
                if d < dmin:
                    dmin = d
                    j = i
            putpixel((x, y), (nr[j], ng[j], nb[j]))
    image.save("VoronoiDiagram.png", "PNG")
generate_voronoi_diagram(500, 500, 25)

More Voronoi Diagram Implementations


Imagine a city, where a fire is declared. Emergency services need to send a fire truck to this place. If there are N fire stations, what fire truck should be sent?

enter image description here

The nearest fire truck is in the light green Voronoi Area, the same area as the fire. No other truck can reach any light green point faster than this truck.

My questions are

How to implement the Voronoi diagram for geolocations like places or lat, longs. As in the above cases.

Are there any approaches/techniques that we can consider for similar cases?

Can anyone be kind enough to walk me through it?