Add the new site, construct the perpendicular bisectors between it and the relevant existing sites, and keep the bisector segments that separate points closest to the new site from points closest to the old sites. Then trim any old edges that lie inside the new site’s cell.
This is part of SL 3.6: Voronoi diagrams in IB Mathematics: Applications and Interpretation. A Voronoi cell contains every point that is closer to its own site than to any other site.
| Step | What to do |
|---|---|
| 1 | Plot and label the new site, usually inside or near an existing cell. |
| 2 | Join the new site temporarily to each nearby existing site. |
| 3 | Construct the perpendicular bisector of each temporary joining segment. |
| 4 | Keep the half-plane containing the new site. The intersection of these half-planes forms the new Voronoi cell. |
| 5 | Erase or trim old Voronoi edges that now lie inside the new cell. Leave unaffected cells unchanged. |
For example, suppose the new site is and an existing site is . Their midpoint is , and is horizontal, so its perpendicular bisector is the vertical line . The region is closer to than to , so that is the side retained when forming the new cell.
