If Voronoi diagrams are about dividing space into territories, Delaunay triangulation is about connecting it. Discover the elegant, powerful relationship that turns a scatter of points into the most natural network imaginable. Introduction In a previous exploration, we delved into the world of Voronoi diagrams—the beautiful geometric patterns that arise from a simple rule of proximity. We imagined a city full of coffee shops and saw how Voronoi diagrams perfectly partition the city into zones, where every location in a zone is closest to its designated coffee shop. It’s a geometry of separation, of defining territories. But what if we asked the opposite question? Instead of dividing the city, what if we wanted to connect those coffee shops to form the most natural and efficient network of paths? What if we wanted to create a mesh of triangles linking them together, but not just any random set of triangles the best possible set? It turns out that the answer to this question is ...
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