Added az/alt calculator to geodesy functions, fixed error in euclidian distance calculation

This commit is contained in:
Mark Qvist 2023-10-25 01:35:46 +02:00
parent 815f85adeb
commit 628c93e1f1
1 changed files with 103 additions and 27 deletions

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@ -2,12 +2,19 @@ import time
from math import pi, sin, cos, acos, tan, atan, atan2
from math import radians, degrees, sqrt
# WGS84 Parameters
# a = 6378137.0,
# f = 0.0033528106647474805,
# e2 = 0.0066943799901413165,
# b = 6356752.314245179,
# Default planetary metrics
equatorial_radius = 6378.137 *1e3
# 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 central_angle(c1, c2):
@ -52,7 +59,7 @@ def euclidian_point(latitude, longtitude, altitude=0, ellipsoid=True):
# Calculate euclidian coordinates from longtitude
# and geocentric latitude.
gclat = radians(geocentric_latitude(latitude)) if ellipsoid else lat
x = cos(lat)*cos(lon)*r
x = cos(lon)*cos(gclat)*r
y = cos(gclat)*sin(lon)*r
z = sin(gclat)*r
@ -67,21 +74,23 @@ def euclidian_point(latitude, longtitude, altitude=0, ellipsoid=True):
y += altitude*normal_y
z += altitude*normal_z
return (x,y,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)
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(c1[0], c1[1], c1[2], ellipsoid=ellipsoid),
euclidian_point(c2[0], c2[1], c2[2], ellipsoid=ellipsoid)
euclidian_point(lat1, lon1, alt1, ellipsoid=ellipsoid),
euclidian_point(lat2, lon2, alt2, ellipsoid=ellipsoid)
)
else:
return None
@ -94,6 +103,9 @@ 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
@ -151,40 +163,104 @@ def ellipsoid_distance(c1, c2):
except Exception as e:
return None
def orthodromic_distance(c1, c2, spherical=False):
if spherical:
return spherical_distance(c1, c2)
else:
def azalt(c1, c2, ellipsoid=True):
c2rp = rotate_globe(c1, c2, ellipsoid=ellipsoid)
print(str(c2rp))
altitude = None
azimuth = None
if (c2rp[2]*c2rp[2]) + (c2rp[1]*c2rp[1]) > 1e-6:
theta = degrees(atan2(c2rp[2], c2rp[1]))
azimuth = 90.0 - 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 tests():
# import RNS
# import numpy as np
# from geographiclib.geodesic import Geodesic
# geod = Geodesic.WGS84
# coords = [
# [(57.758793, 22.605194), (43.048838, -9.241343)],
# [(0.0, 0.0), (0.0, 0.0)],
# [(-90.0, 0.0), (90.0, 0.0)],
# [(-90.0, 0.0), (78.0, 0.0)],
# [(0.0, 0.0), (0.5, 179.5)],
# [(0.7, 0.0), (0.0, -180.0)],
# [(51.2308, 4.38703, 0.0), (47.699437, 9.268651, 0.0)],
# [(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(*ld)
# 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,spherical=False)
# 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")
# print("Euclidian = "+RNS.prettydistance(euclidian_distance(c1,c2)))
# print("Spherical = "+RNS.prettydistance(orthodromic_distance(c1,c2)))
# if eld: print("Ellipsoid = "+RNS.prettydistance(eld))
# print("EllipLib = "+RNS.prettydistance(g['s12']))
# if eld: print("Diff = "+RNS.prettydistance(g['s12']-eld))
# 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("")