# SL AI – Constructing Voronoi Diagrams

##### Constructing a Voronoi Diagram with two sites

Construct a Voronoi diagram for the sites A(3,5) and B(11,9).

##### Constructing a Voronoi Diagram with three sites

Construct a Voronoi diagram for the sites A(3,5), B(11,9) and C(7,13)

Find the equation of the perpendicular bisector of A and C (the equation is shown below the graph).

Draw this on the diagram.

We do not need the part of the perpendicular to the right of point P, so we will erase it.

Now note we also do not need the perpendicular bisector of AB above the point P, so we erase that too.

Perpendicular bisector of A and C has equation: *y*=(23/2)-(1/2)*x*

##### Adding a site to an existing Voronoi diagram

Consider the Voronoi diagram shown below with 5 sites.

Add a site, F(12,-1) to the diagram.

How many perpendicular bisectors will need to be drawn?

The diagram has created a new vertex, labelled below at P.

This point is equidistant from B, D, and F and it indicates that a perpendicular bisector should be constructed between D and F.

Note we already bisectors between B and D and B and F.

This is done below, and then part of the BD bisector is erased (I have just crossed it out – too difficult to do on Geogebra!).

Finally erasing the part to the right that we do not require.

Perpendicular bisector equation *y*=*x*+2

##### Creating a Voronoi Diagram in GeoGebra

## Constructing Voronoi Diagrams

Pdf worksheet with answers on constructing Voronoi diagrams.