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SPARTA.py
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SPARTA.py
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from random import *
from math import *
from CONSTANT import *
from numpy import sqrt, dot, cross
from numpy.linalg import norm
# Contains the logic for vanilla SPARTA
# Find the intersection of three spheres
# P1,P2,P3 are the centers, r1,r2,r3 are the radii
# Implementaton based on Wikipedia Trilateration article.
def trilaterate(P1, P2, P3, r1, r2, r3):
try:
v12 = [P2[i] - P1[i] for i in range(3)]
d = norm(v12)
e_x = v12 / norm(v12)
v13 = [P3[i] - P1[i] for i in range(3)]
i = dot(e_x, v13)
temp3 = v13 - i * e_x
e_y = temp3 / norm(temp3)
e_z = cross(e_x, e_y)
j = dot(e_y, v13)
x = (r1 * r1 - r2 * r2 + d * d) / (2 * d)
y = (r1 * r1 - r3 * r3 - 2 * i * x + i * i + j * j) / (2 * j)
temp4 = r1 * r1 - x * x - y * y
if temp4 < 0:
return False, False
z = sqrt(temp4)
p_12_a = P1 + x * e_x + y * e_y + z * e_z
p_12_b = P1 + x * e_x + y * e_y - z * e_z
return list(p_12_a), list(p_12_b)
except:
return False, False
class IntersectionPoint(object):
def __init__(self, v, parent):
self.v = v
self.parent = parent
self.cover = []
def is_cover(self, Sphere):
if Sphere not in self.cover:
if dist(self.v, Sphere.v) <= Sphere.R or Sphere in self.parent:
return True
return False
def is_remove(self, rD):
if len(self.parent) == 3:
if self.parent[0] in rD or self.parent[1] in rD or self.parent[2] in rD:
return True
if len(self.parent) == 2:
if self.parent[0] in rD or self.parent[1] in rD:
return True
return False
def remove_cover(self, rD):
for r in rD:
if r in self.cover:
self.cover.remove(r)
class Sphere(object):
def __init__(self, T, R, index):
self.T = T
self.v = T.v
self.q = T.q
self.R = R
self.index = index
self.pair = []
def SPARTA(T, Rs):
"""
Contains the logic of SPARTA.
@param T: Target set
@param Rs: sensing radius
@return: Sensor set
"""
n = len(T)
D = [Sphere(T[i], Rs, i) for i in range(n)] # set of Sphere
D.sort(key=lambda x: x.q)
S = [] # set of sensor
intersection_points = []
# calc intersection points
# find triad
triad = []
for i in range(n - 2):
for j in range(i + 1, n - 1):
for k in range(j + 1, n):
p1, p2 = trilaterate(D[i].v, D[j].v, D[k].v, Rs, Rs, Rs)
if p1 and p2:
parent = (D[i], D[j], D[k])
intersection_points.append(IntersectionPoint(p1, parent))
intersection_points.append(IntersectionPoint(p2, parent))
triad += list(parent)
# find pair
for i in range(n - 1):
for j in range(i + 1, n):
if dist(D[i].v, D[j].v) <= 2 * Rs:
parent = (D[i], D[j])
x = (D[i].v[0] + D[j].v[0]) / 2
y = (D[i].v[1] + D[j].v[1]) / 2
z = (D[i].v[2] + D[j].v[2]) / 2
intersection_points.append(IntersectionPoint((x, y, z), parent))
intersection_points.append(IntersectionPoint((x, y, z), parent))
# calc point cover by intersection_points
for point in intersection_points:
for Di in D:
if point.is_cover(Di):
point.cover.append(Di)
# calc number of sensor
while len(D) != 0:
# add Q sensors to Sphere that don't intersect with any other Sphere
if len(intersection_points) == 0:
for Di in D:
for j in range(Di.q):
xi, yi, zi = Di.v
t = uniform(0, 2 * pi)
a = random()
if a > 0.5:
a -= 0.001
x, y, z = cos(t) * a * Rs + xi, sin(t) * a * Rs + yi, zi
sensor = (x, y, z)
tempS = Sensor(sensor, Rs, [Di.T])
S.append(tempS)
Di.T.Sensors.append(S[-1])
D = []
# calc number of Sphere covered and index of that Sphere
else:
# sort set of intersection points in descending order of number of Target covered
intersection_points.sort(reverse=True, key=lambda x: len(x.cover))
# point A
A = intersection_points[0]
x1, y1, z1 = A.v
for i in range(1, len(intersection_points)):
if intersection_points[i].cover == A.cover:
# point B
x2, y2, z2 = intersection_points[i].v
break
# add Q sensors to S
A.cover.sort(key=lambda x: x.q)
minq = A.cover[0].q
for i in range(minq):
# place random
# a = random()
# x = x1 + a*(x2-x1)
# y = y1 + a*(y2-y1)
# place evenly
x = x1 + (i + 1) * (x2 - x1) / (minq + 1)
y = y1 + (i + 1) * (y2 - y1) / (minq + 1)
z = z1 + (i + 1) * (z2 - z1) / (minq + 1)
sensor = (x, y, z)
tempS = Sensor(sensor, Rs, [])
S.append(tempS)
for j in range(len(A.cover)):
A.cover[j].T.Sensors.append(S[-1])
S[-1].Targets.append(A.cover[j].T)
rD = []
for i in range(len(A.cover)):
A.cover[i].q -= minq
if A.cover[i].q <= 0:
rD.append(A.cover[i])
# remove sastified Sphere
i = 0
while i < len(intersection_points):
if intersection_points[i].is_remove(rD):
intersection_points.pop(i)
i -= 1
else:
intersection_points[i].remove_cover(rD)
i += 1
for r in rD:
D.remove(r)
return S