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

Sites lie at $S_1(0,0)$, $S_2(3,0)$ and $S_3(8,0)$ inside the rectangle $0 ≤ x ≤ 10$, $0 ≤ y ≤ 5$. 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 $P(1, 3)$.

On the square defined by $0 \le x \le 4$ and $0 \le y \le 4$, five sites are located at the center and the midpoints of the sides: $(2, 2)$, $(4, 2)$, $(2, 4)$, $(0, 2)$, and $(2, 0)$.

Find the area of the Voronoi cell for the center site $(2, 2)$.

In the square region defined by $0 \le x \le 6$ and $0 \le y \le 6$, two sites are located at $S_1 = (2, 3)$ and $S_2 = (4, 3)$.

Calculate the area of the Voronoi cell for $S_1$.

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

The coordinates of three sites are $A(2, 3)$, $B(5, 1)$, and $C(6, 4)$. Determine which site is closest to the point $P(4, 3)$.

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.

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

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 $0 \le x, y \le 4$, five sites are located 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.

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

Consider the rectangle $0 \le x \le 6$, $0 \le y \le 4$ 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.