-Figure~\ref{twosensors} demonstrates the way of locating the left and right points of a segment for a sensor node $u$ covered by a sensor node $v$. This figure assumes that the neighbor sensor node $v$ is located on the west of a sensor $u$. It is assumed that the two sensor nodes $v$ and $u$ are located in the positions $(v_x,v_y)$ and $(u_x,u_y)$, respectively. The distance between $v$ and $u$ is computed by $Dist(u,v) = \sqrt{\vert u_x - v_x \vert^2 + \vert u_y - v_y \vert^2}$. The angle $\alpha$ is computed through the formula $\alpha = arccos \left(\dfrac{Dist(u,v)}{2R_s} \right)$. So, the arch of sensor $u$ falling in the angle $[\pi - \alpha,\pi + \alpha]$, is said to be perimeter-covered by sensor node $v$.
-
-The left and right points of each segment are placed on the line segment $[0,2\pi]$. Figure~\ref{pcmfig} illustrates the segments for the 9 neighbors of sensor $0$. The points reported on the line segment $[0,2\pi]$ separates it in intervals as shown in figure~\ref{expcm}. For example, for each neighboring sensor of sensor 0, place the points $\alpha^ 1_L$, $\alpha^ 1_R$, $\alpha^ 2_L$, $\alpha^ 2_R$, $\alpha^ 3_L$, $\alpha^ 3_R$, $\alpha^ 4_L$, $\alpha^ 4_R$, $\alpha^ 5_L$, $\alpha^ 5_R$, $\alpha^ 6_L$, $\alpha^ 6_R$, $\alpha^ 7_L$, $\alpha^ 7_R$, $\alpha^ 8_L$, $\alpha^ 8_R$, $\alpha^ 9_L$, and $\alpha^ 9_R$; on the line segment $[0,2\pi]$, and then sort all these points in an ascending order into a list. Traverse the line segment $[0,2\pi]$ by visiting each point in the sorted list from left to right and determine the coverage level of each interval of the sensor 0 (see figure \ref{expcm}). For each interval, we sum up the number of parts of segments, and we deduce a level of coverage for each interval. For instance, the interval delimited by the points $5L$ and $6L$ contains three parts of segments. That means that this part of the perimeter of the sensor $0$ may be covered by three sensors, sensor $0$ itself and sensors $2$ and $5$. The level of coverage of this interval may reach $3$ if all previously mentioned sensors are active. Let say that sensors $0$, $2$ and $5$ are involved in the coverage of this interval. Table~\ref{my-label} summarizes the level of coverage for each interval and the sensors involved in for sensor node 0 in figure~\ref{pcmfig}.
+Figure~\ref{pcm2sensors}(b) describes the geometric information used to find the
+locations of the left and right points of an arc on the perimeter of a sensor
+node~$u$ covered by a sensor node~$v$. Node~$s$ is supposed to be located on the
+west side of sensor~$u$, with the following respective coordinates in the
+sensing area~: $(v_x,v_y)$ and $(u_x,u_y)$. From the previous coordinates we can
+compute the euclidean distance between nodes~$u$ and $v$: $Dist(u,v)=\sqrt{\vert
+ u_x - v_x \vert^2 + \vert u_y-v_y \vert^2}$, while the angle~$\alpha$ is
+obtained through the formula $\alpha = arccos \left(\dfrac{Dist(u,v)}{2R_s}
+\right)$. So, the arc on the perimeter of node~$u$ defined by the angular
+interval $[\pi - \alpha,\pi + \alpha]$ is said to be perimeter-covered by sensor
+node $v$.
+
+Every couple of intersection points is placed on the angular interval $[0,2\pi]$
+in a counterclockwise manner, leading to a partitioning of the interval.
+Figure~\ref{pcm2sensors}(a) illustrates the arcs for the nine neighbors of
+sensor $0$ and figure~\ref{expcm} gives the position of the corresponding arcs
+in the interval $[0,2\pi]$. More precisely, we can see that the points are
+ordered according to the measures of the angles defined by their respective
+positions. The intersection points are then visited one after another, starting
+from first intersection point after point~zero, and the maximum level of
+coverage is determined for each interval defined by two successive points. The
+maximum level of coverage is equal to the number of overlapping arcs. For
+example, between~$5L$ and~$6L$ the maximum level of coverage is equal to $3$
+(the value is highlighted in yellow at the bottom of figure~\ref{expcm}), which
+means that at most 2~neighbors can cover the perimeter in addition to node $0$.
+Table~\ref{my-label} summarizes for each coverage interval the maximum level of
+coverage and the sensor nodes covering the perimeter. The example discussed
+above is thus given by the sixth line of the table.
+
+%The points reported on the line segment $[0,2\pi]$ separates it in intervals as shown in figure~\ref{expcm}. For example, for each neighboring sensor of sensor 0, place the points $\alpha^ 1_L$, $\alpha^ 1_R$, $\alpha^ 2_L$, $\alpha^ 2_R$, $\alpha^ 3_L$, $\alpha^ 3_R$, $\alpha^ 4_L$, $\alpha^ 4_R$, $\alpha^ 5_L$, $\alpha^ 5_R$, $\alpha^ 6_L$, $\alpha^ 6_R$, $\alpha^ 7_L$, $\alpha^ 7_R$, $\alpha^ 8_L$, $\alpha^ 8_R$, $\alpha^ 9_L$, and $\alpha^ 9_R$; on the line segment $[0,2\pi]$, and then sort all these points in an ascending order into a list. Traverse the line segment $[0,2\pi]$ by visiting each point in the sorted list from left to right and determine the coverage level of each interval of the sensor 0 (see figure \ref{expcm}). For each interval, we sum up the number of parts of segments, and we deduce a level of coverage for each interval. For instance, the interval delimited by the points $5L$ and $6L$ contains three parts of segments. That means that this part of the perimeter of the sensor $0$ may be covered by three sensors, sensor $0$ itself and sensors $2$ and $5$. The level of coverage of this interval may reach $3$ if all previously mentioned sensors are active. Let say that sensors $0$, $2$ and $5$ are involved in the coverage of this interval. Table~\ref{my-label} summarizes the level of coverage for each interval and the sensors involved in for sensor node 0 in figure~\ref{pcm2sensors}(a).
