import time
import RNS
from math import pi, sin, cos, acos, asin, tan, atan, atan2
from math import radians, degrees, sqrt
# WGS84 Parameters
# a = 6378137.0,
# f = 0.0033528106647474805,
# e2 = 0.0066943799901413165,
# b = 6356752.314245179,
# Planetary metrics
equatorial_radius = 6378.137 *1e3
polar_radius = 6356.7523142 *1e3
ellipsoid_flattening = 1-(polar_radius/equatorial_radius)
eccentricity_squared = 2*ellipsoid_flattening-pow(ellipsoid_flattening,2)
###############################
mean_earth_radius = (1/3)*(2*equatorial_radius+polar_radius)
def geocentric_latitude(geodetic_latitude):
e2 = eccentricity_squared
lat = radians(geodetic_latitude)
return degrees(atan((1.0 - e2) * tan(lat)))
def geodetic_latitude(geocentric_latitude):
e2 = eccentricity_squared
lat = radians(geocentric_latitude)
return degrees(atan( (1/(1.0 - e2)) * tan(lat)))
def ellipsoid_radius_at(latitude):
lat = radians(latitude)
a = equatorial_radius; b = polar_radius;
a2 = pow(a,2); b2 = pow(b,2)
r = sqrt(
( pow(a2*cos(lat), 2) + pow(b2*sin(lat), 2) )
/
( pow(a*cos(lat), 2) + pow(b*sin(lat), 2) )
)
return r
def euclidian_point(latitude, longtitude, altitude=0, ellipsoid=True):
# Convert latitude and longtitude to radians
# and get ellipsoid or sphere radius
lat = radians(latitude); lon = radians(longtitude)
r = ellipsoid_radius_at(latitude) if ellipsoid else mean_earth_radius
# Calculate euclidian coordinates from longtitude
# and geocentric latitude.
gclat = radians(geocentric_latitude(latitude)) if ellipsoid else lat
x = cos(lon)*cos(gclat)*r
y = cos(gclat)*sin(lon)*r
z = sin(gclat)*r
# Calculate surface normal of ellipsoid at
# coordinates to add altitude to point
normal_x = cos(lat)*cos(lon)
normal_y = cos(lat)*sin(lon)
normal_z = sin(lat)
if altitude != 0:
x += altitude*normal_x
y += altitude*normal_y
z += altitude*normal_z
return (x,y,z, normal_x, normal_y, normal_z)
def distance(p1, p2):
dx = p1[0]-p2[0]
dy = p1[1]-p2[1]
dz = p1[2]-p2[2]
return sqrt(dx*dx + dy*dy + dz*dz)
def euclidian_distance(c1, c2, ellipsoid=True):
lat1 = c1[0]; lon1 = c1[1]; alt1 = c1[2]
lat2 = c2[0]; lon2 = c2[1]; alt2 = c2[2]
if len(c1) >= 2 and len(c2) >= 2:
if len(c1) == 2: c1 += (0,)
if len(c2) == 2: c2 += (0,)
return distance(
euclidian_point(lat1, lon1, alt1, ellipsoid=ellipsoid),
euclidian_point(lat2, lon2, alt2, ellipsoid=ellipsoid)
)
else:
return None
def central_angle(c1, c2):
lat1 = radians(c1[0]); lon1 = radians(c1[1])
lat2 = radians(c2[0]); lon2 = radians(c2[1])
d_lat = abs(lat1-lat2)
d_lon = abs(lon1-lon2)
ca = acos(
sin(lat1) * sin(lat2) +
cos(lat1) * cos(lat2) * cos(d_lon)
)
return ca
def arc_length(central_angle, r=mean_earth_radius):
return r*central_angle;
def spherical_distance(c1, c2, altitude=0, r=mean_earth_radius):
d = (r+altitude)*central_angle(c1, c2)
return d
def ellipsoid_distance(c1, c2):
# TODO: Update this to the method described by Karney in 2013
# instead of using Vincenty's algorithm.
try:
if c1[:2] == c2[:2]:
return 0
if c1[0] == 0.0: c1 = (1e-6, c1[1])
a = equatorial_radius
f = ellipsoid_flattening
b = (1 - f)*a # polar radius
tolerance = 1e-9 # to stop iteration
phi1, phi2 = radians(c1[0]), radians(c2[0])
U1 = atan((1-f)*tan(phi1))
U2 = atan((1-f)*tan(phi2))
L1, L2 = radians(c1[1]), radians(c2[1])
L = L2 - L1
lambda_old = L + 0
max_iterations = 10000
iteration = 0
timeout = 1.0
st = time.time()
while True:
iteration += 1
t = (cos(U2)*sin(lambda_old))**2
t += (cos(U1)*sin(U2) - sin(U1)*cos(U2)*cos(lambda_old))**2
sin_sigma = t**0.5
cos_sigma = sin(U1)*sin(U2) + cos(U1)*cos(U2)*cos(lambda_old)
sigma = atan2(sin_sigma, cos_sigma)
sin_alpha = cos(U1)*cos(U2)*sin(lambda_old) / sin_sigma
cos_sq_alpha = 1 - sin_alpha**2
cos_2sigma_m = cos_sigma - 2*sin(U1)*sin(U2)/cos_sq_alpha
C = f*cos_sq_alpha*(4 + f*(4-3*cos_sq_alpha))/16
t = sigma + C*sin_sigma*(cos_2sigma_m + C*cos_sigma*(-1 + 2*cos_2sigma_m**2))
lambda_new = L + (1 - C)*f*sin_alpha*t
if abs(lambda_new - lambda_old) <= tolerance:
break
else:
lambda_old = lambda_new
if iteration%1000 == 0:
if iteration >= max_iterations:
return None
if time.time() > st+timeout:
return None
u2 = cos_sq_alpha*((a**2 - b**2)/b**2)
A = 1 + (u2/16384)*(4096 + u2*(-768+u2*(320 - 175*u2)))
B = (u2/1024)*(256 + u2*(-128 + u2*(74 - 47*u2)))
t = cos_2sigma_m + 0.25*B*(cos_sigma*(-1 + 2*cos_2sigma_m**2))
t -= (B/6)*cos_2sigma_m*(-3 + 4*sin_sigma**2)*(-3 + 4*cos_2sigma_m**2)
delta_sigma = B * sin_sigma * t
s = b*A*(sigma - delta_sigma)
return s
except Exception as e:
return None
def azalt(c1, c2, ellipsoid=True):
c2rp = rotate_globe(c1, c2, ellipsoid=ellipsoid)
altitude = None
azimuth = None
if (c2rp[2]*c2rp[2]) + (c2rp[1]*c2rp[1]) > 1e-6:
theta = degrees(atan2(c2rp[2], c2rp[1]))
azimuth = 90 - theta
if azimuth < 0: azimuth += 360
if azimuth > 360: azimuth -= 360
azimuth = round(azimuth,4)
c1p = euclidian_point(c1[0], c1[1], c1[2], ellipsoid=ellipsoid)
c2p = euclidian_point(c2[0], c2[1], c2[2], ellipsoid=ellipsoid)
nvd = normalised_vector_diff(c2p, c1p)
if nvd != None:
cax = nvd[0]; cay = nvd[1]; caz = nvd[2]
cnx = c1p[3]; cny = c1p[4]; cnz = c1p[5]
a = acos(cax*cnx + cay*cny + caz*cnz)
altitude = round(90 - degrees(a),4)
return (azimuth, altitude,4)
def normalised_vector_diff(b, a):
dx = b[0] - a[0]
dy = b[1] - a[1]
dz = b[2] - a[2]
d_squared = dx*dx + dy*dy + dz*dz
if d_squared == 0:
return None
d = sqrt(d_squared)
return (dx/d, dy/d, dz/d)
def rotate_globe(c1, c2, ellipsoid=True):
if len(c1) >= 2 and len(c2) >= 2:
if len(c1) == 2: c1 += (0,)
if len(c2) == 2: c2 += (0,)
c2r = (c2[0], c2[1]-c1[1], c2[2])
c2rp = euclidian_point(c2r[0], c2r[1], c2r[2], ellipsoid=ellipsoid)
lat1 = -1*radians(c1[0])
if ellipsoid:
lat1 = radians(geocentric_latitude(degrees(lat1)))
lat1cos = cos(lat1)
lat1sin = sin(lat1)
c2x = (c2rp[0] * lat1cos) - (c2rp[2] * lat1sin)
c2y = c2rp[1]
c2z = (c2rp[0] * lat1sin) + (c2rp[2] * lat1cos)
return (c2x, c2y, c2z)
def orthodromic_distance(c1, c2, ellipsoid=True):
if ellipsoid:
return ellipsoid_distance(c1, c2)
else:
return spherical_distance(c1, c2)
def distance_to_horizon(c, ellipsoid=False):
if ellipsoid:
raise NotImplementedError("Distance to horizon on the ellipsoid is not yet implemented")
else:
# TODO: This is a only barely functional simplification.
# Need to calculate the geodesic distance to the horizon
# instead.
if len(c) >= 3:
r = mean_earth_radius
h = c[2]
return sqrt(pow((h+r),2) - r*r)
else:
return None
def angle_to_horizon(c, ellipsoid=False):
if ellipsoid:
raise NotImplementedError("Angle to horizon on the ellipsoid is not yet implemented")
else:
r = mean_earth_radius
h = c[2]
if h < 0: h = 0
return degrees(-acos(r/(r+h)))
def euclidian_horizon_distance(h):
r = mean_earth_radius
b = r
c = r+h
a = c**2 - b**2
return sqrt(a)
def euclidian_horizon_arc(h):
r = mean_earth_radius
d = euclidian_horizon_distance(h)
a = d; b = r; c = r+h
arc = acos( (b**2+c**2-a**2) / (2*b*c) )
return arc
def radio_horizon(h, rh=0, ellipsoid=False):
if ellipsoid:
raise NotImplementedError("Radio horizon on the ellipsoid is not yet implemented")
else:
geocentric_angle_to_horizon = euclidian_horizon_arc(h)
geodesic_distance = arc_length(geocentric_angle_to_horizon, r=mean_earth_radius)
return geodesic_distance
def shared_radio_horizon(c1, c2,):
lat1 = c1[0]; lon1 = c1[1]; h1 = c1[2]
lat2 = c2[0]; lon2 = c2[1]; h2 = c2[2]
geodesic_distance = orthodromic_distance((lat1, lon1, 0.0), (lat2, lon2, 0.0) , ellipsoid=False)
antenna_distance = euclidian_distance(c1,c2,ellipsoid=False)
rh1 = radio_horizon(h1)
rh2 = radio_horizon(h2)
rhc = rh1+rh2
return {
"horizon1":rh1, "horizon2":rh2, "shared":rhc,
"within":rhc > geodesic_distance,
"geodesic_distance": geodesic_distance,
"antenna_distance": antenna_distance
}
# def tests():
# import RNS
# import numpy as np
# from geographiclib.geodesic import Geodesic
# geod = Geodesic.WGS84
# coords = [
# [(51.2308, 4.38703, 0.0), (47.699437, 9.268651, 0.0)],
# [(51.2308, 4.38703, 0.0), (47.699437, 9.268651, 30.0*1e3)],
# [(0.0, 0.0, 0.0), (0.0, 1.0/60/60, 30.0)],
# # [(51.230800, 4.38703, 0.0), (51.230801, 4.38703, 0.0)],
# # [(35.3524, 135.0302, 100), (35.3532,135.0305, 500)],
# # [(57.758793, 22.605194, 0.0), (43.048838, -9.241343, 0.0)],
# # [(0.0, 0.0, 0.0), (0.0, 0.0, 0.0)],
# # [(-90.0, 0.0, 0.0), (90.0, 0.0, 0.0)],
# # [(-90.0, 0.0, 0.0), (78.0, 0.0, 0.0)],
# # [(0.0, 0.0, 0.0), (0.5, 179.5, 0.0)],
# # [(0.7, 0.0, 0.0), (0.0, -180.0, 0.0)],
# ]
# for cs in coords:
# c1 = cs[0]; c2 = cs[1]
# print("Testing: "+str(c1)+" -> "+str(c2))
# us = time.time()
# ld = c1+c2; g = geod.Inverse(c1[0], c1[1], c2[0], c2[1])
# print("Lib computed in "+str(round((time.time()-us)*1e6, 3))+"us")
# us = time.time()
# eld = orthodromic_distance(c1,c2,ellipsoid=True)
# if eld:
# print("Own computed in "+str(round((time.time()-us)*1e6, 3))+"us")
# else:
# print("Own timed out in "+str(round((time.time()-us)*1e6, 3))+"us")
# ed_own = euclidian_distance(c1,c2,ellipsoid=True)
# sd_own = orthodromic_distance(c1,c2,ellipsoid=False)
# aa = azalt(c1,c2,ellipsoid=True)
# fac = 1
# if eld: print("LibDiff = "+RNS.prettydistance(g['s12']-eld)+f" {fac*g['s12']-fac*eld}")
# print("Spherical = "+RNS.prettydistance(sd_own)+f" {fac*sd_own}")
# # print("EllipLib = "+RNS.prettydistance(g['s12'])+f" {fac*g['s12']}")
# if eld: print("Ellipsoid = "+RNS.prettydistance(eld)+f" {fac*eld}")
# print("Euclidian = "+RNS.prettydistance(ed_own)+f" {fac*ed_own}")
# print("AzAlt = "+f" {aa[0]} / {aa[1]}")
# print("")