We’ve looked at how we can geometrically find the linear combination using barycentric coordinates, but it is not the only way to do so. Natural neighbour interpolation works by observing what happens when an input point is inserted into a set of points represented by a Voronoi diagram. The Voronoi diagram is simply a partition of space into polygonal regions for each data point, such that any point inside a given region is proximal to its corresponding data point.
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Quadtrees aren't limited to point data. They can also partition regions of continuous data, like the pixels of an image.