Implementing natural neighbour interpolation implies the construction of a geometric Voronoi diagram, however this is not strictly the case. Since the Delaunay triangulation is the dual graph of the Voronoi diagram, all the information needed to perform natural neighbour interpolation is already implicit within the triangulation itself. Algorithms to determine natural neighbours from the Delaunay triangulation can be found in several papers within the literature[4][5]. Unfortunately the relative complexity of natural neighbour interpolation means that it is slower than barycentric interpolation by a considerable margin.
We provided Google with concrete examples from their own infrastructure to demonstrate the issue. One of the keys we tested was embedded in the page source of a Google product's public-facing website. By checking the Internet Archive, we confirmed this key had been publicly deployed since at least February 2023, well before the Gemini API existed. There was no client-side logic on the page attempting to access any Gen AI endpoints. It was used solely as a public project identifier, which is standard for Google services.
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