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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If the A* calculation for a shortcut (in Step 3) finds it's now impassable, or if its actual detailed cost is significantly different (e.g., 20%) from the pre-calculated shortcut value: