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Given two sites at P1=(0,0)P_1=(0,0)P1=(0,0) and P2=(4,0)P_2=(4,0)P2=(4,0), the Voronoi diagram is the line x=2x=2x=2. Now a third site P3=(2,0)P_3=(2,0)P3=(2,0) is added. Determine the equations of the boundaries of the Voronoi cell for the new site P3P_3P3 and specify the region it occupies.
For sites at A=(0,0)A=(0,0)A=(0,0), B=(4,0)B=(4,0)B=(4,0), C=(4,4)C=(4,4)C=(4,4), and D=(0,4)D=(0,4)D=(0,4), the Voronoi diagram partitions the square into four regions. Determine the equation of the Voronoi edge between AAA and DDD and specify its domain.
Using the same rectangle sites R1=(2,0)R_1=(2,0)R1=(2,0), R2=(6,0)R_2=(6,0)R2=(6,0), R3=(6,4)R_3=(6,4)R3=(6,4), R4=(2,4)R_4=(2,4)R4=(2,4), determine the equation and domain of the Voronoi edge between R3R_3R3 and R4R_4R4.
Sites A=(0,0)A=(0,0)A=(0,0), B=(4,0)B=(4,0)B=(4,0), and C=(2,4)C=(2,4)C=(2,4) form three regions in their Voronoi diagram. Determine the equation of the edge between AAA and CCC and describe its domain.
For the rectangle with sites R1=(2,0)R_1=(2,0)R1=(2,0), R2=(6,0)R_2=(6,0)R2=(6,0), R3=(6,4)R_3=(6,4)R3=(6,4), R4=(2,4)R_4=(2,4)R4=(2,4), find the Voronoi cell of R1R_1R1: give the equations of its edges and their intersection points.
Sites P1=(−2,0)P_1=(-2,0)P1=(−2,0), P2=(2,0)P_2=(2,0)P2=(2,0), and P3=(0,3)P_3=(0,3)P3=(0,3) define a Voronoi diagram. Find the equation of the Voronoi edge between P1P_1P1 and P3P_3P3 and specify its domain.
Given three sites S1=(1,1)S_1=(1,1)S1=(1,1), S2=(5,1)S_2=(5,1)S2=(5,1), S3=(3,5)S_3=(3,5)S3=(3,5), you add a new site S4=(4,2)S_4=(4,2)S4=(4,2). Determine the equation and domain of the new Voronoi edge between S4S_4S4 and S2S_2S2.
Sites A=(0,0)A=(0,0)A=(0,0), B=(6,0)B=(6,0)B=(6,0), C=(3,4)C=(3,4)C=(3,4) form a triangle. A new site D=(4,1)D=(4,1)D=(4,1) is added. Determine the equation and endpoints of the Voronoi edge between DDD and BBB.
Given four sites A=(0,0)A=(0,0)A=(0,0), B=(4,1)B=(4,1)B=(4,1), C=(2,3)C=(2,3)C=(2,3), D=(−1,2)D=(-1,2)D=(−1,2), you insert a new site E=(1,1)E=(1,1)E=(1,1). Determine the equation and domain of the Voronoi edge between EEE and CCC.
Given four sites Q1=(0,0)Q_1=(0,0)Q1=(0,0), Q2=(5,0)Q_2=(5,0)Q2=(5,0), Q3=(6,3)Q_3=(6,3)Q3=(6,3), and Q4=(1,4)Q_4=(1,4)Q4=(1,4), determine the equation of the Voronoi edge between Q1Q_1Q1 and Q4Q_4Q4 and specify its endpoints.
Sites P1=(0,0)P_1=(0,0)P1=(0,0), P2=(4,0)P_2=(4,0)P2=(4,0), P3=(5,3)P_3=(5,3)P3=(5,3), P4=(2,5)P_4=(2,5)P4=(2,5), and P5=(−1,3)P_5=(-1,3)P5=(−1,3) form a Voronoi diagram. Determine the equation and domain of the Voronoi edge between P2P_2P2 and P3P_3P3.
Five sites are A=(0,0)A=(0,0)A=(0,0), B=(4,1)B=(4,1)B=(4,1), C=(2,3)C=(2,3)C=(2,3), D=(−1,2)D=(-1,2)D=(−1,2), and E=(3,−1)E=(3,-1)E=(3,−1). Determine the Voronoi cell of CCC: give the equations of its bounding edges and their intersection points.
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Question Type 3: Constructing Voronoi Diagrams for a given number of points
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Question Type 5: Determining equations of edges with specific domains