The weighted Voronoi diagram (Laguerre/Power diagram) partitions the plane using power distance d²(p,cᵢ)−rᵢ² — the dual tessellation of a circle packing.
The Laguerre diagram is dual to an additively weighted Delaunay triangulation. Lloyd's algorithm iterates: move each center to the centroid of its Laguerre cell → converges to a centroidal diagram. Used in foam modeling, grain growth, retinal cone mosaics, and optimal quantization (Bennett 1948, Gersho 1979).