Monitoring Moving Queries inside a Safe Region

Algorithm 2

Monitoring moving range query algorithm.

(1)   /*𝑞: query point, 𝑣: the velocity of 𝑞 and 𝑒: the Euclidean distance threshold */

(2)   Call Extended Safe Region algorithm to find safe-object list

(3)   From the safe-object list, find the closest border (Ced𝑥) of 𝑝𝑥 to 𝑞

(4)   Find the start and end angle of Ced𝑥 and add them to the table of start and end angle

(5)   TCed=Ced𝑥

(6)   for all   𝑝𝑖 in the safe-object list  do

(7)    if   TCed intersects with the border of 𝑝𝑖   then

(8)     𝑝𝑖 should share an angle with TCed

(9)     add ed𝑖 and its angles to start and end angle table

(10)    TCed=ed𝑖

(11)   else

(12)    Ignore this 𝑝𝑖

(13)   end if

(14)   Exit for, if the table completed 360° degree

(15)  end for

(16)  Monitoring 𝑞 inside safe region

(17)  for all   ed𝑖 in the start and end angle table  do

(18)   if   MINDIST𝑞,ed𝑖<𝑒   then

(19)    the curve is convex

(20)    ×(𝑎)𝑐=arcsinMINDIST𝑞,𝑝𝑖sin𝑒

(21)   else

(22)    the curve is concave

(23)    ×(𝑎)𝑐=180−arcsinMINDIST𝑞,𝑝3sin𝑒

(24)   end if

(25)   𝑏=180−𝑎−𝑐

(26)   (𝑏)𝐷1=𝑒×sinsin(𝑎)

(27)  end for

(28)  if   𝑞 changes it direction at anytime before crosses any ed𝑖 in the start and end angle table

    then

(29)   go to (17) and use the new position of 𝑞

(30)  end if