On Efficient Deployment of Wireless Sensors for Coverage and Connectivity in Constrained 3D Space

. 2017 Oct 10;17(10):2304. doi: 10.3390/s17102304

Algorithm 2 Division Calculation
Input: A continuous area A, m circles

{c_{1}, c_{2}, \dots, c_{m}}

on A.
Output: All divisions within A.

1:
$C i r s = {c_{1}, c_{2}, \dots, c_{m}}, A r c s = \emptyset, D i v s = \emptyset, D i v C m p s = \emptyset$ ;
2:
Calculate all the intersection points on $c_{i} \in C i r s$ and $\bar{A}$ , and record the list of intersection points on $c_{i}$ ;
3:
Add all the arcs in $\bar{A}$ to $A r c s$ if $\bar{A}$ has intersection points;
4:
for all $c_{i} \in C i r s$ do
5:
if $c_{i}$ has no intersection point and is inside A then
6:
Add $c_{i}$ to $D i v C m p s$ and then to $D i v s$ ;
7:
else
8:
Add all arcs on $c_{i}$ and inside A to $A r c s$ ;
9:
for all $a r c_{s r c} \in A r c s - \bar{A}$ do
10:
$a r c_{c u r} = a r c_{s r c}$ ;
11:
repeat
12:
Select $a r c_{n e x t} \in A r c s$ such that $a r c_{n e x t}$ share the endpoint $e n d_{1} (a r c_{c u r})$ and the angle from $a r c_{n e x t}$ to $a r c_{c u r}$ is minimized;
13:
$a r c_{c u r}$ = $a r c_{n e x t}$ ;
14:
until $(a r c_{c u r}$ == $a r c_{s r c})$
15:
if the chain $d_{1}$ of arcs form the profile of multiple circles then
16:
Add $d_{1}$ to $D i v C m p s$ if $d_{1} \notin D i v C m p s$ ;
17:
else
18:
Add $d_{1}$ to $D i v s$ if $d_{1} \notin D i v s$ ;
19:
$a r c_{c u r} = a r c_{s r c}$ ;
20:
repeat
21:
Select $a r c_{n e x t} \in A r c s$ such that $a r c_{n e x t}$ share the endpoint $e n d_{2} (a r c_{c u r})$ and the angle from $a r c_{n e x t}$ to $a r c_{c u r}$ is minimized;
22:
$a r c_{c u r}$ = $a r c_{n e x t}$ ;
23:
until $(a r c_{c u r}$ == $a r c_{s r c})$
24:
if the chain $d_{2}$ of arcs form the profile of multiple circles then
25:
Add $d_{2}$ to $D i v C m p s$ if $d_{2} \notin D i v C m p s$ ;
26:
else
27:
Add $d_{2}$ to $D i v s$ if $d_{2} \notin D i v s$ ;
28:
if there is no intersection point in $\bar{A}$ then
29:
if $D i v s \neq \emptyset$ or A is inside a circle then
30:
Add $\bar{A}$ to $D i v s$ ;
31:
for all $d_{i} \in D i v C m p s$ do
32:
$d_{m i n} = \emptyset$ ;
33:
for all $d_{j} \in D i v s$ do
34:
if $d_{j}$ encloses $d_{i}$ and ( $d_{m i n} = \emptyset$ or d encloses $d_{j}$ ) then
35:
$d_{m i n} = d_{j}$ ;
36:
Incorporate $d_{i}$ into $d_{m i n}$ and update $d_{m i n}$ in $D i v s$ ;
37:
return $D i v s$ .