RevisionDojo

Question 1

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

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Question 2

Given four sites $Q_1(0,0)$ , $Q_2(5,0)$ , $Q_3(6,3)$ , and $Q_4(1,4)$ , find the equation of the perpendicular bisector between $Q_1$ and $Q_4$ . Hence, determine the coordinates of the Voronoi vertex formed by $Q_1$ , $Q_2$ , and $Q_4$ .

[7]

Question 3

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

[5]

Question 4

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 $S_2$ .

[7]

Question 5

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.

[5]

Question 6

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.

[6]

Question 7

The following question is based on the application of Voronoi diagrams in a coordinate plane.

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 the domain of the Voronoi edge between $P_2$ and $P_3$ .

[7]

Question 8

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.

[7]

Question 9

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.

[6]

Question 10

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

[4]

Question 11

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.

[6]

Question 12

The sites $A(0,0)$ , $B(6,0)$ , and $C(3,4)$ form a triangle. A new site $D(4,1)$ is added within this triangle to form a new Voronoi diagram.

Determine the equation and the coordinates of the endpoints of the Voronoi edge between sites $D$ and $B$ .

[6]

Question Type 4: Adding sites to update Voronoi Diagrams Exercises