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Added az/alt calculator to geodesy functions, fixed error in euclidian distance calculation
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Mark Qvist
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815f85adeb
commit
628c93e1f1
@ -2,12 +2,19 @@ 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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# Default planetary metrics
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equatorial_radius = 6378.137 *1e3
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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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@ -52,7 +59,7 @@ def euclidian_point(latitude, longtitude, altitude=0, ellipsoid=True):
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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(lat)*cos(lon)*r
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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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@ -67,21 +74,23 @@ def euclidian_point(latitude, longtitude, altitude=0, ellipsoid=True):
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y += altitude*normal_y
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z += altitude*normal_z
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return (x,y,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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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(c1[0], c1[1], c1[2], ellipsoid=ellipsoid),
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euclidian_point(c2[0], c2[1], c2[2], ellipsoid=ellipsoid)
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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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@ -94,6 +103,9 @@ 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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@ -151,40 +163,104 @@ def ellipsoid_distance(c1, c2):
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except Exception as e:
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return None
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def orthodromic_distance(c1, c2, spherical=False):
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if spherical:
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return spherical_distance(c1, c2)
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else:
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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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print(str(c2rp))
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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 = 90.0 - 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 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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# [(57.758793, 22.605194), (43.048838, -9.241343)],
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# [(0.0, 0.0), (0.0, 0.0)],
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# [(-90.0, 0.0), (90.0, 0.0)],
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# [(-90.0, 0.0), (78.0, 0.0)],
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# [(0.0, 0.0), (0.5, 179.5)],
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# [(0.7, 0.0), (0.0, -180.0)],
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# [(51.2308, 4.38703, 0.0), (47.699437, 9.268651, 0.0)],
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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(*ld)
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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,spherical=False)
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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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# print("Euclidian = "+RNS.prettydistance(euclidian_distance(c1,c2)))
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# print("Spherical = "+RNS.prettydistance(orthodromic_distance(c1,c2)))
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# if eld: print("Ellipsoid = "+RNS.prettydistance(eld))
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# print("EllipLib = "+RNS.prettydistance(g['s12']))
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# if eld: print("Diff = "+RNS.prettydistance(g['s12']-eld))
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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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