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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Imagine a vast shopping mall parking lot with thousands of individual parking spots and internal lanes (representing road segments within a cluster). No matter how complex it is inside, there are usually only a few key exits to the main roads. Our goal was to identify these natural "exits" for each map cluster. For instance, the complex road network around Amsterdam Airport Schiphol (see on OpenStreetMap) has many internal roads but limited primary access points.
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