Voronoi Diagrams Explained: The Geometry Behind Robotics, Computer Vision, and Spatial Intelligence

Voronoi diagrams divide space into regions based on proximity — every point belongs to its nearest "site," creating a map where boundaries form exactly halfway between neighboring points. First formalized in the 1800s and used as early as 1854 to trace a cholera outbreak, these diagrams now power robot navigation, computer vision, urban planning, and game design. Efficient algorithms like Fortune's sweep line run 1,200 times faster than brute-force methods.