Question Type 4: Adding sites to update Voronoi Diagrams Exercises

Given two sites at $P_1=(0,0)$ and $P_2=(4,0)$, the Voronoi diagram is the line $x=2$. Now a third site $P_3=(2,0)$ is added. Determine the equations of the boundaries of the Voronoi cell for the new site $P_3$ and specify the region it occupies.

For sites at $A=(0,0)$, $B=(4,0)$, $C=(4,4)$, and $D=(0,4)$, the Voronoi diagram partitions the square into four regions. Determine the equation of the Voronoi edge between $A$ and $D$ and specify its domain.

Using the same rectangle sites $R_1=(2,0)$, $R_2=(6,0)$, $R_3=(6,4)$, $R_4=(2,4)$, determine the equation and domain of the Voronoi edge between $R_3$ and $R_4$.

Sites $A=(0,0)$, $B=(4,0)$, and $C=(2,4)$ form three regions in their Voronoi diagram. Determine the equation of the edge between $A$ and $C$ and describe its domain.

For the rectangle with sites $R_1=(2,0)$, $R_2=(6,0)$, $R_3=(6,4)$, $R_4=(2,4)$, find the Voronoi cell of $R_1$: give the equations of its edges and their intersection points.

Sites $P_1=(-2,0)$, $P_2=(2,0)$, and $P_3=(0,3)$ define a Voronoi diagram. Find the equation of the Voronoi edge between $P_1$ and $P_3$ and specify its domain.

Given three sites $S_1=(1,1)$, $S_2=(5,1)$, $S_3=(3,5)$, you add a new site $S_4=(4,2)$. Determine the equation and domain of the new Voronoi edge between $S_4$ and $S_2$.

Sites $A=(0,0)$, $B=(6,0)$, $C=(3,4)$ form a triangle. A new site $D=(4,1)$ is added. Determine the equation and endpoints of the Voronoi edge between $D$ and $B$.

Given four sites $A=(0,0)$, $B=(4,1)$, $C=(2,3)$, $D=(-1,2)$, you insert a new site $E=(1,1)$. Determine the equation and domain of the Voronoi edge between $E$ and $C$.

Given four sites $Q_1=(0,0)$, $Q_2=(5,0)$, $Q_3=(6,3)$, and $Q_4=(1,4)$, determine the equation of the Voronoi edge between $Q_1$ and $Q_4$ and specify its endpoints.

Sites $P_1=(0,0)$, $P_2=(4,0)$, $P_3=(5,3)$, $P_4=(2,5)$, and $P_5=(-1,3)$ form a Voronoi diagram. Determine the equation and domain of the Voronoi edge between $P_2$ and $P_3$.

Five sites are $A=(0,0)$, $B=(4,1)$, $C=(2,3)$, $D=(-1,2)$, and $E=(3,-1)$. Determine the Voronoi cell of $C$: give the equations of its bounding edges and their intersection points.