When another data point is inserted and the Voronoi diagram reconstructed, the newly created region displaces the area that once belonged to the old regions. Those points whose regions were displaced are considered natural neighbours to the new point. The weight of each natural neighbour is given by the area taken from the total area occupied by the new region. In 3D, we measure polyhedral volumes instead of areas.
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It’s also worth noting that even if alternatives superior to agar were found, scientists are reluctant to abandon established protocols (even when microbiologists do use other jellies, they often still add agar to the mix, for example, to increase the gel strength of the solid media). As agar has been the standard gelling agent in microbiology for around 150 years, an enormous infrastructure of standardized methods, reference values, and quality control procedures has emerged around its specific properties. Switching to a different medium (even a superior one) means results may not be directly comparable to decades of published literature or to other laboratories’ findings.