Voronoi regions assign each location to its nearest site.
WHAT HAPPENS IF…Move the third site toward the first. What happens to their boundary?
Interactive exploration
Loading the mathematical model…
Connect the picture to the ideaVi={x:∥x−pi∥≤∥x−pj∥∀j}
For two sites, equality of squared distances reduces to a line: their perpendicular bisector. A cell is the intersection of the corresponding nearest-side half-planes. This display classifies small grid-cell centers, so boundaries and areas are pixel approximations.
A detail that matters
The sampled cell area is not an exact polygon-area calculation.