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.
In recent years, LLMs have shown significant improvements in their overall performance. When they first became mainstream a couple of years before, they were already impressive with their seemingly human-like conversation abilities, but their reasoning always lacked. They were able to describe any sorting algorithm in the style of your favorite author; on the other hand, they weren't able to consistently perform addition. However, they improved significantly, and it's more and more difficult to find examples where they fail to reason. This created the belief that with enough scaling, LLMs will be able to learn general reasoning.
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