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301 lines
10 KiB
Python
301 lines
10 KiB
Python
import time
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from math import pi, sin, cos, acos, tan, atan, atan2
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from math import radians, degrees, sqrt
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# WGS84 Parameters
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# a = 6378137.0,
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# f = 0.0033528106647474805,
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# e2 = 0.0066943799901413165,
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# b = 6356752.314245179,
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# Planetary metrics
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equatorial_radius = 6378.137 *1e3
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polar_radius = 6356.7523142 *1e3
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ellipsoid_flattening = 1-(polar_radius/equatorial_radius)
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eccentricity_squared = 2*ellipsoid_flattening-pow(ellipsoid_flattening,2)
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###############################
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mean_earth_radius = (1/3)*(2*equatorial_radius+polar_radius)
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def central_angle(c1, c2):
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lat1 = radians(c1[0]); lon1 = radians(c1[1])
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lat2 = radians(c2[0]); lon2 = radians(c2[1])
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d_lat = abs(lat1-lat2)
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d_lon = abs(lon1-lon2)
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ca = acos(
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sin(lat1) * sin(lat2) +
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cos(lat1) * cos(lat2) * cos(d_lon)
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)
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return ca
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def geocentric_latitude(geodetic_latitude):
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e2 = eccentricity_squared
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lat = radians(geodetic_latitude)
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return degrees(atan((1.0 - e2) * tan(lat)))
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def geodetic_latitude(geocentric_latitude):
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e2 = eccentricity_squared
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lat = radians(geocentric_latitude)
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return degrees(atan( (1/(1.0 - e2)) * tan(lat)))
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def ellipsoid_radius_at(latitude):
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lat = radians(latitude)
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a = equatorial_radius; b = polar_radius;
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a2 = pow(a,2); b2 = pow(b,2)
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r = sqrt(
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( pow(a2*cos(lat), 2) + pow(b2*sin(lat), 2) )
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/
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( pow(a*cos(lat), 2) + pow(b*sin(lat), 2) )
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)
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return r
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def euclidian_point(latitude, longtitude, altitude=0, ellipsoid=True):
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# Convert latitude and longtitude to radians
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# and get ellipsoid or sphere radius
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lat = radians(latitude); lon = radians(longtitude)
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r = ellipsoid_radius_at(latitude) if ellipsoid else mean_earth_radius
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# Calculate euclidian coordinates from longtitude
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# and geocentric latitude.
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gclat = radians(geocentric_latitude(latitude)) if ellipsoid else lat
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x = cos(lon)*cos(gclat)*r
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y = cos(gclat)*sin(lon)*r
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z = sin(gclat)*r
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# Calculate surface normal of ellipsoid at
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# coordinates to add altitude to point
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normal_x = cos(lat)*cos(lon)
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normal_y = cos(lat)*sin(lon)
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normal_z = sin(lat)
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if altitude != 0:
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x += altitude*normal_x
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y += altitude*normal_y
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z += altitude*normal_z
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return (x,y,z, normal_x, normal_y, normal_z)
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def distance(p1, p2):
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dx = p1[0]-p2[0]
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dy = p1[1]-p2[1]
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dz = p1[2]-p2[2]
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return sqrt(dx*dx + dy*dy + dz*dz)
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def euclidian_distance(c1, c2, ellipsoid=True):
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lat1 = c1[0]; lon1 = c1[1]; alt1 = c1[2]
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lat2 = c2[0]; lon2 = c2[1]; alt2 = c2[2]
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if len(c1) >= 2 and len(c2) >= 2:
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if len(c1) == 2: c1 += (0,)
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if len(c2) == 2: c2 += (0,)
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return distance(
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euclidian_point(lat1, lon1, alt1, ellipsoid=ellipsoid),
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euclidian_point(lat2, lon2, alt2, ellipsoid=ellipsoid)
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)
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else:
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return None
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def spherical_distance(c1, c2, altitude=0, r=mean_earth_radius):
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d = (r+altitude)*central_angle(c1, c2)
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return d
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def ellipsoid_distance(c1, c2):
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# TODO: Update this to the method described by Karney in 2013
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# instead of using Vincenty's algorithm.
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try:
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if c1[:2] == c2[:2]:
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return 0
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if c1[0] == 0.0: c1 = (1e-6, c1[1])
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a = equatorial_radius
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f = ellipsoid_flattening
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b = (1 - f)*a # polar radius
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tolerance = 1e-9 # to stop iteration
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phi1, phi2 = radians(c1[0]), radians(c2[0])
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U1 = atan((1-f)*tan(phi1))
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U2 = atan((1-f)*tan(phi2))
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L1, L2 = radians(c1[1]), radians(c2[1])
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L = L2 - L1
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lambda_old = L + 0
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max_iterations = 10000
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iteration = 0
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timeout = 1.0
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st = time.time()
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while True:
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iteration += 1
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t = (cos(U2)*sin(lambda_old))**2
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t += (cos(U1)*sin(U2) - sin(U1)*cos(U2)*cos(lambda_old))**2
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sin_sigma = t**0.5
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cos_sigma = sin(U1)*sin(U2) + cos(U1)*cos(U2)*cos(lambda_old)
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sigma = atan2(sin_sigma, cos_sigma)
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sin_alpha = cos(U1)*cos(U2)*sin(lambda_old) / sin_sigma
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cos_sq_alpha = 1 - sin_alpha**2
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cos_2sigma_m = cos_sigma - 2*sin(U1)*sin(U2)/cos_sq_alpha
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C = f*cos_sq_alpha*(4 + f*(4-3*cos_sq_alpha))/16
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t = sigma + C*sin_sigma*(cos_2sigma_m + C*cos_sigma*(-1 + 2*cos_2sigma_m**2))
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lambda_new = L + (1 - C)*f*sin_alpha*t
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if abs(lambda_new - lambda_old) <= tolerance:
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break
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else:
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lambda_old = lambda_new
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if iteration%1000 == 0:
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if iteration >= max_iterations:
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return None
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if time.time() > st+timeout:
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return None
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u2 = cos_sq_alpha*((a**2 - b**2)/b**2)
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A = 1 + (u2/16384)*(4096 + u2*(-768+u2*(320 - 175*u2)))
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B = (u2/1024)*(256 + u2*(-128 + u2*(74 - 47*u2)))
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t = cos_2sigma_m + 0.25*B*(cos_sigma*(-1 + 2*cos_2sigma_m**2))
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t -= (B/6)*cos_2sigma_m*(-3 + 4*sin_sigma**2)*(-3 + 4*cos_2sigma_m**2)
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delta_sigma = B * sin_sigma * t
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s = b*A*(sigma - delta_sigma)
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return s
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except Exception as e:
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return None
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def azalt(c1, c2, ellipsoid=True):
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c2rp = rotate_globe(c1, c2, ellipsoid=ellipsoid)
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altitude = None
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azimuth = None
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if (c2rp[2]*c2rp[2]) + (c2rp[1]*c2rp[1]) > 1e-6:
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theta = degrees(atan2(c2rp[2], c2rp[1]))
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azimuth = 270 - theta
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if azimuth < 0: azimuth += 360
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if azimuth > 360: azimuth -= 360
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azimuth = round(azimuth,4)
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c1p = euclidian_point(c1[0], c1[1], c1[2], ellipsoid=ellipsoid)
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c2p = euclidian_point(c2[0], c2[1], c2[2], ellipsoid=ellipsoid)
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nvd = normalised_vector_diff(c2p, c1p)
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if nvd != None:
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cax = nvd[0]; cay = nvd[1]; caz = nvd[2]
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cnx = c1p[3]; cny = c1p[4]; cnz = c1p[5]
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a = acos(cax*cnx + cay*cny + caz*cnz)
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altitude = round(90 - degrees(a),4)
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return (azimuth, altitude,4)
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def normalised_vector_diff(b, a):
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dx = b[0] - a[0]
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dy = b[1] - a[1]
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dz = b[2] - a[2]
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d_squared = dx*dx + dy*dy + dz*dz
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if d_squared == 0:
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return None
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d = sqrt(d_squared)
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return (dx/d, dy/d, dz/d)
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def rotate_globe(c1, c2, ellipsoid=True):
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if len(c1) >= 2 and len(c2) >= 2:
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if len(c1) == 2: c1 += (0,)
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if len(c2) == 2: c2 += (0,)
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c2r = (c2[0], c2[1]-c1[1], c2[2])
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c2rp = euclidian_point(c2r[0], c2r[1], c2r[2], ellipsoid=ellipsoid)
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lat1 = -1*radians(c1[0])
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if ellipsoid:
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lat1 = radians(geocentric_latitude(degrees(lat1)))
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lat1cos = cos(lat1)
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lat1sin = sin(lat1)
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c2x = (c2rp[0] * lat1cos) - (c2rp[2] * lat1sin)
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c2y = c2rp[1]
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c2z = (c2rp[0] * lat1sin) + (c2rp[2] * lat1cos)
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return (c2x, c2y, c2z)
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def orthodromic_distance(c1, c2, ellipsoid=True):
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if ellipsoid:
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return ellipsoid_distance(c1, c2)
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else:
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return spherical_distance(c1, c2)
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def distance_to_horizon(c, ellipsoid=False):
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if ellipsoid:
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raise NotImplementedError("Distance to horizon on the ellipsoid is not yet implemented")
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else:
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# TODO: This is a only barely functional simplification.
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# Need to calculate the geodesic distance to the horizon
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# instead.
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if len(c) >= 3:
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r = mean_earth_radius
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h = c[2]
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return sqrt(pow((h+r),2) - r*r)
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else:
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return None
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def angle_to_horizon(c, ellipsoid=False):
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if ellipsoid:
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raise NotImplementedError("Angle to horizon on the ellipsoid is not yet implemented")
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else:
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r = mean_earth_radius
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h = c[2]
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return degrees(-acos(r/(r+h)))
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def radio_horizon(c1, c2, ellipsoid=False):
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# dr = 4.12*(√h1 + √h2)
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if ellipsoid:
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raise NotImplementedError("Radio horizon on the ellipsoid is not yet implemented")
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else:
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h1 = c1[2]
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h2 = c2[2]
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ed = euclidian_distance(c1,c2)
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rh1 = 1e3*4.12*(sqrt(h1))
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rh2 = 1e3*4.12*(sqrt(h2))
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rhc = 1e3*4.12*(sqrt(h1) + sqrt(h2))
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return (rh1, rh2, rhc, rhc > ed)
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def tests():
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import RNS
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import numpy as np
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from geographiclib.geodesic import Geodesic
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geod = Geodesic.WGS84
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coords = [
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[(51.2308, 4.38703, 0.0), (47.699437, 9.268651, 0.0)],
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[(51.2308, 4.38703, 0.0), (47.699437, 9.268651, 30.0*1e3)],
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# [(51.230800, 4.38703, 0.0), (51.230801, 4.38703, 0.0)],
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# [(35.3524, 135.0302, 100), (35.3532,135.0305, 500)],
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# [(57.758793, 22.605194, 0.0), (43.048838, -9.241343, 0.0)],
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# [(0.0, 0.0, 0.0), (0.0, 0.0, 0.0)],
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# [(-90.0, 0.0, 0.0), (90.0, 0.0, 0.0)],
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# [(-90.0, 0.0, 0.0), (78.0, 0.0, 0.0)],
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# [(0.0, 0.0, 0.0), (0.5, 179.5, 0.0)],
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# [(0.7, 0.0, 0.0), (0.0, -180.0, 0.0)],
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]
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for cs in coords:
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c1 = cs[0]; c2 = cs[1]
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print("Testing: "+str(c1)+" -> "+str(c2))
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us = time.time()
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ld = c1+c2; g = geod.Inverse(c1[0], c1[1], c2[0], c2[1])
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print("Lib computed in "+str(round((time.time()-us)*1e6, 3))+"us")
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us = time.time()
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eld = orthodromic_distance(c1,c2,ellipsoid=True)
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if eld:
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print("Own computed in "+str(round((time.time()-us)*1e6, 3))+"us")
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else:
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print("Own timed out in "+str(round((time.time()-us)*1e6, 3))+"us")
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ed_own = euclidian_distance(c1,c2,ellipsoid=True)
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sd_own = orthodromic_distance(c1,c2,ellipsoid=False)
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aa = azalt(c1,c2,ellipsoid=True)
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fac = 1
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if eld: print("LibDiff = "+RNS.prettydistance(g['s12']-eld)+f" {fac*g['s12']-fac*eld}")
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print("Spherical = "+RNS.prettydistance(sd_own)+f" {fac*sd_own}")
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# print("EllipLib = "+RNS.prettydistance(g['s12'])+f" {fac*g['s12']}")
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if eld: print("Ellipsoid = "+RNS.prettydistance(eld)+f" {fac*eld}")
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print("Euclidian = "+RNS.prettydistance(ed_own)+f" {fac*ed_own}")
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print("AzAlt = "+f" {aa[0]} / {aa[1]}")
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print("")
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