Question Type 2: Finding the area of a closed region within a Voronoi Diagram Exercises

Seven sites are at $(1,1)$, $(5,2)$, $(3,6)$, $(0,4)$, $(-1,1)$, $(3,0)$ and the central site at $(2,2)$. Compute the area of the Voronoi cell around $(2,2)$.

Six sites lie at $(2,1)$, $(5,1)$, $(4,4)$, $(1,3)$, $(0,1)$ and the center site at $(2,2)$. Determine the area of the Voronoi cell surrounding the point $(2,2)$.

A Voronoi diagram is defined by seven sites in the Cartesian plane. Six of these sites are located at the corners and midpoints of the longer edges of a rectangle: $(0,0)$, $(3,0)$, $(6,0)$, $(0,4)$, $(3,4)$, and $(6,4)$. The seventh site is located at the center of the rectangle, $(3,2)$.

Calculate the area of the Voronoi cell for the site at $(3,2)$.

Six points lie at the vertices of a regular hexagon of circumradius $3$ centered at the origin. Find the area of the Voronoi cell of the center.

Eight sites are located at $(2, 2)$, $(-2, 2)$, $(-2, -2)$, $(2, -2)$, $(3, 0)$, $(0, 3)$, $(-3, 0)$, and $(0, -3)$. A ninth site is located at the origin $(0, 0)$.

Find the area of the Voronoi cell for the site at the origin.

Twelve points lie equally spaced on a circle of radius $6$ centred at the origin. Find the area of the Voronoi cell of the origin.

Eight points lie on a circle of radius $4$ equally spaced around the origin. Compute the area of the Voronoi cell of the origin.

Ten points lie on a circle of radius $5$ equally spaced around the origin. Find the area of the Voronoi cell of the origin.

Given the five points at $(0,0)$, $(1,1)$, $(-1,1)$, $(-1,-1)$ and $(1,-1)$, find the area of the Voronoi cell corresponding to the point $(0,0)$.

Five sites are located in a plane. Four of the sites are at $A(0,0)$, $B(6,0)$, $C(3,5)$, and $D(0,5)$. The fifth site, $P$, is located at $(2,2)$. Determine the area of the Voronoi cell containing the site $P$.

Five sites are at $(1,0)$, $(4,0)$, $(4,3)$, $(1,3)$ and the center site at $(2.5,1.5)$. Find the area of the Voronoi cell around $(2.5,1.5)$.