Question Type 1: Finding the closest site for a given point in a Voronoi Diagram Exercises

Given sites $S_1=(0,0)$ and $S_2=(3,0)$, determine which site is closest to point $P=(1,2)$.

Given sites $S_1=(0,0)$, $S_2=(4,0)$ and $S_3=(0,4)$, find the site closest to point $P=(2,1)$.

Sites lie at $S_1=(0,0)$, $S_2=(3,0)$ and $S_3=(8,0)$ inside the rectangle $0\le x\le10$, $0\le y\le5$. Find the area of the Voronoi cell for $S_2$ within the rectangle.

Given sites $S_1=(0,1)$, $S_2=(2,5)$ and $S_3=(4,2)$, determine which site is nearest to $P=(1,3)$.

Sites are $A=(2,3)$, $B=(5,1)$ and $C=(6,4)$. Which site is closest to $P=(4,3)$?

Consider the rectangle $0\le x\le6$, $0\le y\le4$ with two sites $S_1=(0,0)$ and $S_2=(6,0)$. Find the area of the Voronoi cell of $S_1$ within this rectangle.

Sites are at $(0,0)$, $(5,0)$, $(0,5)$ and $(5,5)$. Identify the nearest site to point $P=(3,2)$.

In the square $0\le x,y\le6$, two sites are at $S_1=(2,3)$ and $S_2=(4,3)$. Compute the area of the Voronoi cell for $S_1$.

On the square $0\le x,y\le4$, five sites are at the midpoints of the sides and the center: $(2,2)$, $(4,2)$, $(2,4)$, $(0,2)$, $(2,0)$. Find the area of the Voronoi cell of the center site $(2,2)$.

Within the triangle with vertices $(0,0)$, $(6,0)$ and $(0,6)$, three sites are placed at these vertices. Find the area of the Voronoi region for the site at $(0,0)$, restricted to the triangle.

Five sites are $A=(1,2)$, $B=(3,5)$, $C=(6,1)$, $D=(4,4)$ and $E=(2,6)$. Which site is closest to $P=(3,3)$?

In the square $0\le x,y\le4$, five sites are at the four corners $(0,0)$, $(4,0)$, $(4,4)$, $(0,4)$ and the center $(2,2)$. Determine the area of the Voronoi region for the center site.