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vincenty.py
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#!/usr/bin/env python3
# WGS 84
#a = 6378137 # meters
#f = 1 / 298.257223563
#b = 6356752.314245 # meters; b = (1 - f)a
#f: flattening of the ellipsoid
#a: radius of the ellipsoid, meteres
#phi1: latitude of the start point, decimal degrees
#lembda1: longitude of the start point, decimal degrees
#alpha12: bearing, decimal degrees
#s: Distance to endpoint, meters
import sys
from math import atan
from math import atan2
from math import cos
from math import radians
from math import degrees
from math import sin, asin
from math import sqrt
from math import tan
from math import pow
a=6378137.0 # radius at equator in meters (WGS-84)
f=1/298.257223563 # flattening of the ellipsoid (WGS-84)
b=(1-f)*a
def haversine(lat1, lon1, lat2, lon2):
# convert decimal degrees to radians
lon1, lat1, lon2, lat2 = map(radians, [lon1, lat1, lon2, lat2])
# haversine formula
dlon = lon2 - lon1
dlat = lat2 - lat1
c = 2 * asin(sqrt(sin(dlat/2)**2 + cos(lat1) * cos(lat2) * sin(dlon/2)**2))
return c * a
def get_heading(coord1, coord2):
lat1 = radians(coord1[0])
lon1 = radians(coord1[1])
lat2 = radians(coord2[0])
lon2 = radians(coord2[1])
bearing_plot_X = cos(lat2) * sin(lon2 - lon1)
bearing_plot_Y = cos(lat1) * sin(lat2) - sin(lat1) * cos(lat2) * cos(lon1 - lon2)
heading = degrees(atan2(bearing_plot_X,bearing_plot_Y))
if heading <0: heading += 360
return heading
def inverse(coord1,coord2,maxIter=200,tol=10**-12):
global a
global f
global b
phi_1,L_1,=coord1
phi_2,L_2,=coord2
u_1=atan((1-f)*tan(radians(phi_1)))
u_2=atan((1-f)*tan(radians(phi_2)))
L=radians(L_2-L_1)
Lambda=L # set initial value of lambda to L
sin_u1=sin(u_1)
cos_u1=cos(u_1)
sin_u2=sin(u_2)
cos_u2=cos(u_2)
try:
iters=0
for i in range(0,maxIter):
iters+=1
cos_lambda=cos(Lambda)
sin_lambda=sin(Lambda)
sin_sigma=sqrt((cos_u2*sin(Lambda))**2+(cos_u1*sin_u2-sin_u1*cos_u2*cos_lambda)**2)
cos_sigma=sin_u1*sin_u2+cos_u1*cos_u2*cos_lambda
sigma=atan2(sin_sigma,cos_sigma)
sin_alpha=(cos_u1*cos_u2*sin_lambda)/sin_sigma
cos_sq_alpha=1-sin_alpha**2
cos2_sigma_m=cos_sigma-((2*sin_u1*sin_u2)/cos_sq_alpha)
C=(f/16)*cos_sq_alpha*(4+f*(4-3*cos_sq_alpha))
Lambda_prev=Lambda
Lambda=L+(1-C)*f*sin_alpha*(sigma+C*sin_sigma*(cos2_sigma_m+C*cos_sigma*(-1+2*cos2_sigma_m**2)))
# successful convergence
diff=abs(Lambda_prev-Lambda)
if diff<=tol:
break
u_sq=cos_sq_alpha*((a**2-b**2)/b**2)
A=1+(u_sq/16384)*(4096+u_sq*(-768+u_sq*(320-175*u_sq)))
B=(u_sq/1024)*(256+u_sq*(-128+u_sq*(74-47*u_sq)))
delta_sig=B*sin_sigma*(cos2_sigma_m+0.25*B*(cos_sigma*(-1+2*cos2_sigma_m**2)-(1/6)*B*cos2_sigma_m*(-3+4*sin_sigma**2)*(-3+4*cos2_sigma_m**2)))
alpha12 = get_heading(coord1, coord2)
m=(b*A*(sigma-delta_sig))#/1000 # output distance in m
return (m,alpha12)
except ZeroDivisionError:
return (0,0)
def direct(phi1, lembda1, alpha12, s): #lat, lon, bearing, distance
global a
global f
global b
piD4 = atan( 1.0 )
two_pi = piD4 * 8.0
phi1 = phi1 * piD4 / 45.0
lembda1 = lembda1 * piD4 / 45.0
alpha12 = alpha12 * piD4 / 45.0
if ( alpha12 < 0.0 ) :
alpha12 = alpha12 + two_pi
if ( alpha12 > two_pi ) :
alpha12 = alpha12 - two_pi
TanU1 = (1-f) * tan(phi1)
U1 = atan( TanU1 )
sigma1 = atan2( TanU1, cos(alpha12) )
Sinalpha = cos(U1) * sin(alpha12)
cosalpha_sq = 1.0 - Sinalpha * Sinalpha
u2 = cosalpha_sq * (a * a - b * b ) / (b * b)
A = 1.0 + (u2 / 16384) * (4096 + u2 * (-768 + u2 * \
(320 - 175 * u2) ) )
B = (u2 / 1024) * (256 + u2 * (-128 + u2 * (74 - 47 * u2) ) )
# Starting with the approx
sigma = (s / (b * A))
last_sigma = 2.0 * sigma + 2.0 # something impossible
# Iterate the following 3 eqs unitl no sig change in sigma
# two_sigma_m , delta_sigma
while ( abs( (last_sigma - sigma) / sigma) > 1.0e-9 ):
two_sigma_m = 2 * sigma1 + sigma
delta_sigma = B * sin(sigma) * ( cos(two_sigma_m) \
+ (B/4) * (cos(sigma) * \
(-1 + 2 * pow( cos(two_sigma_m), 2 ) - \
(B/6) * cos(two_sigma_m) * \
(-3 + 4 * pow(sin(sigma), 2 )) * \
(-3 + 4 * pow( cos (two_sigma_m), 2 )))))
last_sigma = sigma
sigma = (s / (b * A)) + delta_sigma
phi2 = atan2 ( (sin(U1) * cos(sigma) +\
cos(U1) * sin(sigma) * cos(alpha12) ), \
((1-f) * sqrt( pow(Sinalpha, 2) + \
pow(sin(U1) * sin(sigma) - cos(U1) * \
cos(sigma) * cos(alpha12), 2))))
lembda = atan2( (sin(sigma) * sin(alpha12 )),\
(cos(U1) * cos(sigma) - \
sin(U1) * sin(sigma) * cos(alpha12)))
C = (f/16) * cosalpha_sq * (4 + f * (4 - 3 * cosalpha_sq ))
omega = lembda - (1-C) * f * Sinalpha * \
(sigma + C * sin(sigma) * (cos(two_sigma_m) + \
C * cos(sigma) * (-1 + 2 *\
pow(cos(two_sigma_m), 2) )))
lembda2 = lembda1 + omega
alpha21 = atan2 ( Sinalpha, (-sin(U1) * \
sin(sigma) +
cos(U1) * cos(sigma) * cos(alpha12)))
alpha21 = alpha21 + two_pi / 2.0
if ( alpha21 < 0.0 ) :
alpha21 = alpha21 + two_pi
if ( alpha21 > two_pi ) :
alpha21 = alpha21 - two_pi
phi2 = phi2 * 45.0 / piD4
lembda2 = lembda2 * 45.0 / piD4
alpha21 = alpha21 * 45.0 / piD4
return (phi2, lembda2)#, alpha21
if __name__ == '__main__':
help = """Usage:
vincenty.py [option] [value1] [value2] [value3] [value4]
Get distance between two points in meters:
vincenty.py inverse lat1 lon1 lat2 lon2
Get coordinate at a given distance and heading:
vincenty.py direct lat1 lon1 heading distance
Get the heading between two coordinates:
vincenty.py heading lat1 lon1 lat2 lon2"""
try:
op1 = float(sys.argv[2])
op2 = float(sys.argv[3])
op3 = float(sys.argv[4])
op4 = float(sys.argv[5])
if sys.argv[1] == "inverse":
output = inverse((op1, op2),(op3, op4))[0]
elif sys.argv[1] == "direct":
output = str(direct(op1, op2, op3, op4))[1:-1]
elif sys.argv[1] == "heading":
output = get_heading((op1, op2),(op3, op4))
else:
output = help
print(output)
except:
print(help)