# RCAIDE/Library/Methods/Geodesics/Geodesics.py
#
#
# Adapted: Oct 2024, A. Molloy
#
# This is a built-in adaptation of the Geopy distance claculation capabilities. It primarily serves to calcualte distances
# lat/long coordinate points. Minor adjustments have been made to better fit within the RCAIDE frameowkr (for instance, results
# only returned in kilometers).
#
# Distinct classes that are included in one palce here include the original Constants, Distance, Geodesic,
# GeodesicCapability, Geodesic_Calculate, and Math classes.
# ----------------------------------------------------------------------------------------------------------------------
# IMPORT
# ----------------------------------------------------------------------------------------------------------------------
import math
import sys
"""Evaluate the thrust produced by the energy network.
Assumptions:
WGS-84 Ellipsoid model
Source:
Karney, C. F., (2022) Geopy Python Code [source code]. https://geographiclib.sourceforge.io/
Args:
Returns:
"""
# geodesic.py
#
# This is a rather literal translation of the GeographicLib::Geodesic class to
# python. See the documentation for the C++ class for more information at
#
# https://geographiclib.sourceforge.io/html/annotated.html
#
# The algorithms are derived in
#
# Charles F. F. Karney,
# Algorithms for geodesics, J. Geodesy 87, 43-55 (2013),
# https://doi.org/10.1007/s00190-012-0578-z
# Addenda: https://geographiclib.sourceforge.io/geod-addenda.html
#
# Copyright (c) Charles Karney (2011-2022) <charles@karney.com> and licensed
# under the MIT/X11 License. For more information, see
# https://geographiclib.sourceforge.io/
######################################################################
[docs]
class Math:
"""
Additional math routines for GeographicLib.
"""
[docs]
@staticmethod
def sq(x):
"""Square a number"""
return x * x
[docs]
@staticmethod
def cbrt(x):
"""Real cube root of a number"""
return math.copysign(math.pow(abs(x), 1/3.0), x)
[docs]
@staticmethod
def norm(x, y):
"""Private: Normalize a two-vector."""
r = (math.sqrt(Math.sq(x) + Math.sq(y))
# hypot is inaccurate for 3.[89]. Problem reported by agdhruv
# https://github.com/geopy/geopy/issues/466 ; see
# https://bugs.python.org/issue43088
# Visual Studio 2015 32-bit has a similar problem.
if (3, 8) <= sys.version_info < (3, 10)
else math.hypot(x, y))
return x/r, y/r
[docs]
@staticmethod
def sum(u, v):
"""Error free transformation of a sum."""
# Error free transformation of a sum. Note that t can be the same as one
# of the first two arguments.
s = u + v
up = s - v
vpp = s - up
up -= u
vpp -= v
t = s if s == 0 else 0.0 - (up + vpp)
# u + v = s + t
# = round(u + v) + t
return s, t
[docs]
@staticmethod
def polyval(N, p, s, x):
"""Evaluate a polynomial."""
y = float(0 if N < 0 else p[s]) # make sure the returned value is a float
while N > 0:
N -= 1; s += 1
y = y * x + p[s]
return y
[docs]
@staticmethod
def AngRound(x):
"""Private: Round an angle so that small values underflow to zero."""
# The makes the smallest gap in x = 1/16 - nextafter(1/16, 0) = 1/2^57
# for reals = 0.7 pm on the earth if x is an angle in degrees. (This
# is about 1000 times more resolution than we get with angles around 90
# degrees.) We use this to avoid having to deal with near singular
# cases when x is non-zero but tiny (e.g., 1.0e-200).
z = 1/16.0
y = abs(x)
# The compiler mustn't "simplify" z - (z - y) to y
if y < z: y = z - (z - y)
return math.copysign(y, x)
[docs]
@staticmethod
def remainder(x, y):
"""remainder of x/y in the range [-y/2, y/2]."""
return math.remainder(x, y) if math.isfinite(x) else math.nan
[docs]
@staticmethod
def AngNormalize(x):
"""reduce angle to [-180,180]"""
y = Math.remainder(x, 360)
return math.copysign(180.0, x) if abs(y) == 180 else y
[docs]
@staticmethod
def LatFix(x):
"""replace angles outside [-90,90] by NaN"""
return math.nan if abs(x) > 90 else x
[docs]
@staticmethod
def AngDiff(x, y):
"""compute y - x and reduce to [-180,180] accurately"""
d, t = Math.sum(Math.remainder(-x, 360), Math.remainder(y, 360))
d, t = Math.sum(Math.remainder(d, 360), t)
if d == 0 or abs(d) == 180:
d = math.copysign(d, y - x if t == 0 else -t)
return d, t
[docs]
@staticmethod
def sincosd(x):
"""Compute sine and cosine of x in degrees."""
r = math.fmod(x, 360) if math.isfinite(x) else math.nan
q = 0 if math.isnan(r) else int(round(r / 90))
r -= 90 * q; r = math.radians(r)
s = math.sin(r); c = math.cos(r)
q = q % 4
if q == 1: s, c = c, -s
elif q == 2: s, c = -s, -c
elif q == 3: s, c = -c, s
c = c + 0.0
if s == 0: s = math.copysign(s, x)
return s, c
[docs]
@staticmethod
def sincosde(x, t):
"""Compute sine and cosine of (x + t) in degrees with x in [-180, 180]"""
q = int(round(x / 90)) if math.isfinite(x) else 0
r = x - 90 * q; r = math.radians(Math.AngRound(r + t))
s = math.sin(r); c = math.cos(r)
q = q % 4
if q == 1: s, c = c, -s
elif q == 2: s, c = -s, -c
elif q == 3: s, c = -c, s
c = c + 0.0
if s == 0: s = math.copysign(s, x)
return s, c
[docs]
class GeodesicCapability:
"""
Capability constants shared between Geodesic and GeodesicLine.
"""
CAP_NONE = 0
CAP_C1 = 1 << 0
CAP_C1p = 1 << 1
CAP_C2 = 1 << 2
CAP_C3 = 1 << 3
CAP_C4 = 1 << 4
CAP_ALL = 0x1F
CAP_MASK = CAP_ALL
OUT_ALL = 0x7F80
OUT_MASK = 0xFF80 # Includes LONG_UNROLL
EMPTY = 0
LATITUDE = 1 << 7 | CAP_NONE
LONGITUDE = 1 << 8 | CAP_C3
AZIMUTH = 1 << 9 | CAP_NONE
DISTANCE = 1 << 10 | CAP_C1
STANDARD = LATITUDE | LONGITUDE | AZIMUTH | DISTANCE
DISTANCE_IN = 1 << 11 | CAP_C1 | CAP_C1p
REDUCEDLENGTH = 1 << 12 | CAP_C1 | CAP_C2
GEODESICSCALE = 1 << 13 | CAP_C1 | CAP_C2
AREA = 1 << 14 | CAP_C4
LONG_UNROLL = 1 << 15
ALL = OUT_ALL | CAP_ALL # Does not include LONG_UNROLL
[docs]
class Constants:
"""
Constants describing the WGS84 ellipsoid
"""
WGS84_a = 6378137.0 # meters
"""the equatorial radius in meters of the WGS84 ellipsoid in meters"""
WGS84_f = 1/298.257223563
"""the flattening of the WGS84 ellipsoid, 1/298.257223563"""
[docs]
class Geodesic:
"""Solve geodesic problems"""
GEOGRAPHICLIB_GEODESIC_ORDER = 6
nA1_ = GEOGRAPHICLIB_GEODESIC_ORDER
nC1_ = GEOGRAPHICLIB_GEODESIC_ORDER
nC1p_ = GEOGRAPHICLIB_GEODESIC_ORDER
nA2_ = GEOGRAPHICLIB_GEODESIC_ORDER
nC2_ = GEOGRAPHICLIB_GEODESIC_ORDER
nA3_ = GEOGRAPHICLIB_GEODESIC_ORDER
nA3x_ = nA3_
nC3_ = GEOGRAPHICLIB_GEODESIC_ORDER
nC3x_ = (nC3_ * (nC3_ - 1)) // 2
nC4_ = GEOGRAPHICLIB_GEODESIC_ORDER
nC4x_ = (nC4_ * (nC4_ + 1)) // 2
maxit1_ = 20
maxit2_ = maxit1_ + sys.float_info.mant_dig + 10
tiny_ = math.sqrt(sys.float_info.min)
tol0_ = sys.float_info.epsilon
tol1_ = 200 * tol0_
tol2_ = math.sqrt(tol0_)
tolb_ = tol0_ * tol2_
xthresh_ = 1000 * tol2_
CAP_NONE = GeodesicCapability.CAP_NONE
CAP_C1 = GeodesicCapability.CAP_C1
CAP_C1p = GeodesicCapability.CAP_C1p
CAP_C2 = GeodesicCapability.CAP_C2
CAP_C3 = GeodesicCapability.CAP_C3
CAP_C4 = GeodesicCapability.CAP_C4
CAP_ALL = GeodesicCapability.CAP_ALL
CAP_MASK = GeodesicCapability.CAP_MASK
OUT_ALL = GeodesicCapability.OUT_ALL
OUT_MASK = GeodesicCapability.OUT_MASK
@staticmethod
def _SinCosSeries(sinp, sinx, cosx, c):
"""Private: Evaluate a trig series using Clenshaw summation."""
# Evaluate
# y = sinp ? sum(c[i] * sin( 2*i * x), i, 1, n) :
# sum(c[i] * cos((2*i+1) * x), i, 0, n-1)
# using Clenshaw summation. N.B. c[0] is unused for sin series
# Approx operation count = (n + 5) mult and (2 * n + 2) add
k = len(c) # Point to one beyond last element
n = k - sinp
ar = 2 * (cosx - sinx) * (cosx + sinx) # 2 * cos(2 * x)
y1 = 0 # accumulators for sum
if n & 1:
k -= 1; y0 = c[k]
else:
y0 = 0
# Now n is even
n = n // 2
while n: # while n--:
n -= 1
# Unroll loop x 2, so accumulators return to their original role
k -= 1; y1 = ar * y0 - y1 + c[k]
k -= 1; y0 = ar * y1 - y0 + c[k]
return ( 2 * sinx * cosx * y0 if sinp # sin(2 * x) * y0
else cosx * (y0 - y1) ) # cos(x) * (y0 - y1)
@staticmethod
def _A1m1f(eps):
"""Private: return A1-1."""
coeff = [
1, 4, 64, 0, 256,
]
m = Geodesic.nA1_//2
t = Math.polyval(m, coeff, 0, Math.sq(eps)) / coeff[m + 1]
return (t + eps) / (1 - eps)
@staticmethod
def _C1f(eps, c):
"""Private: return C1."""
coeff = [
-1, 6, -16, 32,
-9, 64, -128, 2048,
9, -16, 768,
3, -5, 512,
-7, 1280,
-7, 2048,
]
eps2 = Math.sq(eps)
d = eps
o = 0
for l in range(1, Geodesic.nC1_ + 1): # l is index of C1p[l]
m = (Geodesic.nC1_ - l) // 2 # order of polynomial in eps^2
c[l] = d * Math.polyval(m, coeff, o, eps2) / coeff[o + m + 1]
o += m + 2
d *= eps
@staticmethod
def _A2m1f(eps):
"""Private: return A2-1"""
coeff = [
-11, -28, -192, 0, 256,
]
m = Geodesic.nA2_//2
t = Math.polyval(m, coeff, 0, Math.sq(eps)) / coeff[m + 1]
return (t - eps) / (1 + eps)
@staticmethod
def _C2f(eps, c):
"""Private: return C2"""
coeff = [
1, 2, 16, 32,
35, 64, 384, 2048,
15, 80, 768,
7, 35, 512,
63, 1280,
77, 2048,
]
eps2 = Math.sq(eps)
d = eps
o = 0
for l in range(1, Geodesic.nC2_ + 1): # l is index of C2[l]
m = (Geodesic.nC2_ - l) // 2 # order of polynomial in eps^2
c[l] = d * Math.polyval(m, coeff, o, eps2) / coeff[o + m + 1]
o += m + 2
d *= eps
[docs]
def __init__(self, a, f):
"""Construct a Geodesic object
:param a: the equatorial radius of the ellipsoid in meters
:param f: the flattening of the ellipsoid
An exception is thrown if *a* or the polar semi-axis *b* = *a* (1 -
*f*) is not a finite positive quantity.
"""
self.a = float(a)
"""The equatorial radius in meters (readonly)"""
self.f = float(f)
"""The flattening (readonly)"""
self._f1 = 1 - self.f
self._e2 = self.f * (2 - self.f)
self._ep2 = self._e2 / Math.sq(self._f1) # e2 / (1 - e2)
self._n = self.f / ( 2 - self.f)
self._b = self.a * self._f1
# authalic radius squared
self._c2 = (Math.sq(self.a) + Math.sq(self._b) *
(1 if self._e2 == 0 else
(math.atanh(math.sqrt(self._e2)) if self._e2 > 0 else
math.atan(math.sqrt(-self._e2))) /
math.sqrt(abs(self._e2))))/2
# The sig12 threshold for "really short". Using the auxiliary sphere
# solution with dnm computed at (bet1 + bet2) / 2, the relative error in
# the azimuth consistency check is sig12^2 * abs(f) * min(1, 1-f/2) / 2.
# (Error measured for 1/100 < b/a < 100 and abs(f) >= 1/1000. For a given
# f and sig12, the max error occurs for lines near the pole. If the old
# rule for computing dnm = (dn1 + dn2)/2 is used, then the error increases
# by a factor of 2.) Setting this equal to epsilon gives sig12 = etol2.
# Here 0.1 is a safety factor (error decreased by 100) and max(0.001,
# abs(f)) stops etol2 getting too large in the nearly spherical case.
self._etol2 = 0.1 * Geodesic.tol2_ / math.sqrt( max(0.001, abs(self.f)) *
min(1.0, 1-self.f/2) / 2 )
if not(math.isfinite(self.a) and self.a > 0):
raise ValueError("Equatorial radius is not positive")
if not(math.isfinite(self._b) and self._b > 0):
raise ValueError("Polar semi-axis is not positive")
self._A3x = list(range(Geodesic.nA3x_))
self._C3x = list(range(Geodesic.nC3x_))
self._C4x = list(range(Geodesic.nC4x_))
self._A3coeff()
self._C3coeff()
self._C4coeff()
def _A3coeff(self):
"""Private: return coefficients for A3"""
coeff = [
-3, 128,
-2, -3, 64,
-1, -3, -1, 16,
3, -1, -2, 8,
1, -1, 2,
1, 1,
]
o = 0; k = 0
for j in range(Geodesic.nA3_ - 1, -1, -1): # coeff of eps^j
m = min(Geodesic.nA3_ - j - 1, j) # order of polynomial in n
self._A3x[k] = Math.polyval(m, coeff, o, self._n) / coeff[o + m + 1]
k += 1
o += m + 2
def _C3coeff(self):
"""Private: return coefficients for C3"""
coeff = [
3, 128,
2, 5, 128,
-1, 3, 3, 64,
-1, 0, 1, 8,
-1, 1, 4,
5, 256,
1, 3, 128,
-3, -2, 3, 64,
1, -3, 2, 32,
7, 512,
-10, 9, 384,
5, -9, 5, 192,
7, 512,
-14, 7, 512,
21, 2560,
]
o = 0; k = 0
for l in range(1, Geodesic.nC3_): # l is index of C3[l]
for j in range(Geodesic.nC3_ - 1, l - 1, -1): # coeff of eps^j
m = min(Geodesic.nC3_ - j - 1, j) # order of polynomial in n
self._C3x[k] = Math.polyval(m, coeff, o, self._n) / coeff[o + m + 1]
k += 1
o += m + 2
def _C4coeff(self):
"""Private: return coefficients for C4"""
coeff = [
97, 15015,
1088, 156, 45045,
-224, -4784, 1573, 45045,
-10656, 14144, -4576, -858, 45045,
64, 624, -4576, 6864, -3003, 15015,
100, 208, 572, 3432, -12012, 30030, 45045,
1, 9009,
-2944, 468, 135135,
5792, 1040, -1287, 135135,
5952, -11648, 9152, -2574, 135135,
-64, -624, 4576, -6864, 3003, 135135,
8, 10725,
1856, -936, 225225,
-8448, 4992, -1144, 225225,
-1440, 4160, -4576, 1716, 225225,
-136, 63063,
1024, -208, 105105,
3584, -3328, 1144, 315315,
-128, 135135,
-2560, 832, 405405,
128, 99099,
]
o = 0; k = 0
for l in range(Geodesic.nC4_): # l is index of C4[l]
for j in range(Geodesic.nC4_ - 1, l - 1, -1): # coeff of eps^j
m = Geodesic.nC4_ - j - 1 # order of polynomial in n
self._C4x[k] = Math.polyval(m, coeff, o, self._n) / coeff[o + m + 1]
k += 1
o += m + 2
def _A3f(self, eps):
"""Private: return A3"""
# Evaluate A3
return Math.polyval(Geodesic.nA3_ - 1, self._A3x, 0, eps)
def _C3f(self, eps, c):
"""Private: return C3"""
# Evaluate C3
# Elements c[1] thru c[nC3_ - 1] are set
mult = 1
o = 0
for l in range(1, Geodesic.nC3_): # l is index of C3[l]
m = Geodesic.nC3_ - l - 1 # order of polynomial in eps
mult *= eps
c[l] = mult * Math.polyval(m, self._C3x, o, eps)
o += m + 1
# return s12b, m12b, m0, M12, M21
def _Lengths(self, eps, sig12,
ssig1, csig1, dn1, ssig2, csig2, dn2, cbet1, cbet2, outmask,
# Scratch areas of the right size
C1a, C2a):
"""Private: return a bunch of lengths"""
# Return s12b, m12b, m0, M12, M21, where
# m12b = (reduced length)/_b; s12b = distance/_b,
# m0 = coefficient of secular term in expression for reduced length.
outmask &= Geodesic.OUT_MASK
# outmask & DISTANCE: set s12b
# outmask & REDUCEDLENGTH: set m12b & m0
# outmask & GEODESICSCALE: set M12 & M21
s12b = m12b = m0 = M12 = M21 = math.nan
if outmask & (Geodesic.DISTANCE | Geodesic.REDUCEDLENGTH |
Geodesic.GEODESICSCALE):
A1 = Geodesic._A1m1f(eps)
Geodesic._C1f(eps, C1a)
if outmask & (Geodesic.REDUCEDLENGTH | Geodesic.GEODESICSCALE):
A2 = Geodesic._A2m1f(eps)
Geodesic._C2f(eps, C2a)
m0x = A1 - A2
A2 = 1 + A2
A1 = 1 + A1
if outmask & Geodesic.DISTANCE:
B1 = (Geodesic._SinCosSeries(True, ssig2, csig2, C1a) -
Geodesic._SinCosSeries(True, ssig1, csig1, C1a))
# Missing a factor of _b
s12b = A1 * (sig12 + B1)
if outmask & (Geodesic.REDUCEDLENGTH | Geodesic.GEODESICSCALE):
B2 = (Geodesic._SinCosSeries(True, ssig2, csig2, C2a) -
Geodesic._SinCosSeries(True, ssig1, csig1, C2a))
J12 = m0x * sig12 + (A1 * B1 - A2 * B2)
elif outmask & (Geodesic.REDUCEDLENGTH | Geodesic.GEODESICSCALE):
# Assume here that nC1_ >= nC2_
for l in range(1, Geodesic.nC2_):
C2a[l] = A1 * C1a[l] - A2 * C2a[l]
J12 = m0x * sig12 + (Geodesic._SinCosSeries(True, ssig2, csig2, C2a) -
Geodesic._SinCosSeries(True, ssig1, csig1, C2a))
if outmask & Geodesic.REDUCEDLENGTH:
m0 = m0x
# Missing a factor of _b.
# Add parens around (csig1 * ssig2) and (ssig1 * csig2) to ensure
# accurate cancellation in the case of coincident points.
m12b = (dn2 * (csig1 * ssig2) - dn1 * (ssig1 * csig2) -
csig1 * csig2 * J12)
if outmask & Geodesic.GEODESICSCALE:
csig12 = csig1 * csig2 + ssig1 * ssig2
t = self._ep2 * (cbet1 - cbet2) * (cbet1 + cbet2) / (dn1 + dn2)
M12 = csig12 + (t * ssig2 - csig2 * J12) * ssig1 / dn1
M21 = csig12 - (t * ssig1 - csig1 * J12) * ssig2 / dn2
return s12b, m12b, m0, M12, M21
# return sig12, salp1, calp1, salp2, calp2, dnm
def _InverseStart(self, sbet1, cbet1, dn1, sbet2, cbet2, dn2,
lam12, slam12, clam12,
# Scratch areas of the right size
C1a, C2a):
"""Private: Find a starting value for Newton's method."""
# Return a starting point for Newton's method in salp1 and calp1 (function
# value is -1). If Newton's method doesn't need to be used, return also
# salp2 and calp2 and function value is sig12.
sig12 = -1; salp2 = calp2 = dnm = math.nan # Return values
# bet12 = bet2 - bet1 in [0, pi); bet12a = bet2 + bet1 in (-pi, 0]
sbet12 = sbet2 * cbet1 - cbet2 * sbet1
cbet12 = cbet2 * cbet1 + sbet2 * sbet1
# Volatile declaration needed to fix inverse cases
# 88.202499451857 0 -88.202499451857 179.981022032992859592
# 89.262080389218 0 -89.262080389218 179.992207982775375662
# 89.333123580033 0 -89.333123580032997687 179.99295812360148422
# which otherwise fail with g++ 4.4.4 x86 -O3
sbet12a = sbet2 * cbet1
sbet12a += cbet2 * sbet1
shortline = cbet12 >= 0 and sbet12 < 0.5 and cbet2 * lam12 < 0.5
if shortline:
sbetm2 = Math.sq(sbet1 + sbet2)
# sin((bet1+bet2)/2)^2
# = (sbet1 + sbet2)^2 / ((sbet1 + sbet2)^2 + (cbet1 + cbet2)^2)
sbetm2 /= sbetm2 + Math.sq(cbet1 + cbet2)
dnm = math.sqrt(1 + self._ep2 * sbetm2)
omg12 = lam12 / (self._f1 * dnm)
somg12 = math.sin(omg12); comg12 = math.cos(omg12)
else:
somg12 = slam12; comg12 = clam12
salp1 = cbet2 * somg12
calp1 = (
sbet12 + cbet2 * sbet1 * Math.sq(somg12) / (1 + comg12) if comg12 >= 0
else sbet12a - cbet2 * sbet1 * Math.sq(somg12) / (1 - comg12))
ssig12 = math.hypot(salp1, calp1)
csig12 = sbet1 * sbet2 + cbet1 * cbet2 * comg12
if shortline and ssig12 < self._etol2:
# really short lines
salp2 = cbet1 * somg12
calp2 = sbet12 - cbet1 * sbet2 * (Math.sq(somg12) / (1 + comg12)
if comg12 >= 0 else 1 - comg12)
salp2, calp2 = Math.norm(salp2, calp2)
# Set return value
sig12 = math.atan2(ssig12, csig12)
elif (abs(self._n) >= 0.1 or # Skip astroid calc if too eccentric
csig12 >= 0 or
ssig12 >= 6 * abs(self._n) * math.pi * Math.sq(cbet1)):
# Nothing to do, zeroth order spherical approximation is OK
pass
else:
# Scale lam12 and bet2 to x, y coordinate system where antipodal point
# is at origin and singular point is at y = 0, x = -1.
# real y, lamscale, betscale
lam12x = math.atan2(-slam12, -clam12)
if self.f >= 0: # In fact f == 0 does not get here
# x = dlong, y = dlat
k2 = Math.sq(sbet1) * self._ep2
eps = k2 / (2 * (1 + math.sqrt(1 + k2)) + k2)
lamscale = self.f * cbet1 * self._A3f(eps) * math.pi
betscale = lamscale * cbet1
x = lam12x / lamscale
y = sbet12a / betscale
else: # _f < 0
# x = dlat, y = dlong
cbet12a = cbet2 * cbet1 - sbet2 * sbet1
bet12a = math.atan2(sbet12a, cbet12a)
# real m12b, m0, dummy
# In the case of lon12 = 180, this repeats a calculation made in
# Inverse.
dummy, m12b, m0, dummy, dummy = self._Lengths(
self._n, math.pi + bet12a, sbet1, -cbet1, dn1, sbet2, cbet2, dn2,
cbet1, cbet2, Geodesic.REDUCEDLENGTH, C1a, C2a)
x = -1 + m12b / (cbet1 * cbet2 * m0 * math.pi)
betscale = (sbet12a / x if x < -0.01
else -self.f * Math.sq(cbet1) * math.pi)
lamscale = betscale / cbet1
y = lam12x / lamscale
if y > -Geodesic.tol1_ and x > -1 - Geodesic.xthresh_:
# strip near cut
if self.f >= 0:
salp1 = min(1.0, -x); calp1 = - math.sqrt(1 - Math.sq(salp1))
else:
calp1 = max((0.0 if x > -Geodesic.tol1_ else -1.0), x)
salp1 = math.sqrt(1 - Math.sq(calp1))
else:
# Estimate alp1, by solving the astroid problem.
#
# Could estimate alpha1 = theta + pi/2, directly, i.e.,
# calp1 = y/k; salp1 = -x/(1+k); for _f >= 0
# calp1 = x/(1+k); salp1 = -y/k; for _f < 0 (need to check)
#
# However, it's better to estimate omg12 from astroid and use
# spherical formula to compute alp1. This reduces the mean number of
# Newton iterations for astroid cases from 2.24 (min 0, max 6) to 2.12
# (min 0 max 5). The changes in the number of iterations are as
# follows:
#
# change percent
# 1 5
# 0 78
# -1 16
# -2 0.6
# -3 0.04
# -4 0.002
#
# The histogram of iterations is (m = number of iterations estimating
# alp1 directly, n = number of iterations estimating via omg12, total
# number of trials = 148605):
#
# iter m n
# 0 148 186
# 1 13046 13845
# 2 93315 102225
# 3 36189 32341
# 4 5396 7
# 5 455 1
# 6 56 0
#
# Because omg12 is near pi, estimate work with omg12a = pi - omg12
k = Geodesic._Astroid(x, y)
omg12a = lamscale * ( -x * k/(1 + k) if self.f >= 0
else -y * (1 + k)/k )
somg12 = math.sin(omg12a); comg12 = -math.cos(omg12a)
# Update spherical estimate of alp1 using omg12 instead of lam12
salp1 = cbet2 * somg12
calp1 = sbet12a - cbet2 * sbet1 * Math.sq(somg12) / (1 - comg12)
# Sanity check on starting guess. Backwards check allows NaN through.
if not (salp1 <= 0):
salp1, calp1 = Math.norm(salp1, calp1)
else:
salp1 = 1; calp1 = 0
return sig12, salp1, calp1, salp2, calp2, dnm
# return lam12, salp2, calp2, sig12, ssig1, csig1, ssig2, csig2, eps,
# domg12, dlam12
def _Lambda12(self, sbet1, cbet1, dn1, sbet2, cbet2, dn2, salp1, calp1,
slam120, clam120, diffp,
# Scratch areas of the right size
C1a, C2a, C3a):
"""Private: Solve hybrid problem"""
if sbet1 == 0 and calp1 == 0:
# Break degeneracy of equatorial line. This case has already been
# handled.
calp1 = -Geodesic.tiny_
# sin(alp1) * cos(bet1) = sin(alp0)
salp0 = salp1 * cbet1
calp0 = math.hypot(calp1, salp1 * sbet1) # calp0 > 0
# real somg1, comg1, somg2, comg2, lam12
# tan(bet1) = tan(sig1) * cos(alp1)
# tan(omg1) = sin(alp0) * tan(sig1) = tan(omg1)=tan(alp1)*sin(bet1)
ssig1 = sbet1; somg1 = salp0 * sbet1
csig1 = comg1 = calp1 * cbet1
ssig1, csig1 = Math.norm(ssig1, csig1)
# Math.norm(somg1, comg1); -- don't need to normalize!
# Enforce symmetries in the case abs(bet2) = -bet1. Need to be careful
# about this case, since this can yield singularities in the Newton
# iteration.
# sin(alp2) * cos(bet2) = sin(alp0)
salp2 = salp0 / cbet2 if cbet2 != cbet1 else salp1
# calp2 = sqrt(1 - sq(salp2))
# = sqrt(sq(calp0) - sq(sbet2)) / cbet2
# and subst for calp0 and rearrange to give (choose positive sqrt
# to give alp2 in [0, pi/2]).
calp2 = (math.sqrt(Math.sq(calp1 * cbet1) +
((cbet2 - cbet1) * (cbet1 + cbet2) if cbet1 < -sbet1
else (sbet1 - sbet2) * (sbet1 + sbet2))) / cbet2
if cbet2 != cbet1 or abs(sbet2) != -sbet1 else abs(calp1))
# tan(bet2) = tan(sig2) * cos(alp2)
# tan(omg2) = sin(alp0) * tan(sig2).
ssig2 = sbet2; somg2 = salp0 * sbet2
csig2 = comg2 = calp2 * cbet2
ssig2, csig2 = Math.norm(ssig2, csig2)
# Math.norm(somg2, comg2); -- don't need to normalize!
# sig12 = sig2 - sig1, limit to [0, pi]
sig12 = math.atan2(max(0.0, csig1 * ssig2 - ssig1 * csig2) + 0.0,
csig1 * csig2 + ssig1 * ssig2)
# omg12 = omg2 - omg1, limit to [0, pi]
somg12 = max(0.0, comg1 * somg2 - somg1 * comg2) + 0.0
comg12 = comg1 * comg2 + somg1 * somg2
# eta = omg12 - lam120
eta = math.atan2(somg12 * clam120 - comg12 * slam120,
comg12 * clam120 + somg12 * slam120)
# real B312
k2 = Math.sq(calp0) * self._ep2
eps = k2 / (2 * (1 + math.sqrt(1 + k2)) + k2)
self._C3f(eps, C3a)
B312 = (Geodesic._SinCosSeries(True, ssig2, csig2, C3a) -
Geodesic._SinCosSeries(True, ssig1, csig1, C3a))
domg12 = -self.f * self._A3f(eps) * salp0 * (sig12 + B312)
lam12 = eta + domg12
if diffp:
if calp2 == 0:
dlam12 = - 2 * self._f1 * dn1 / sbet1
else:
dummy, dlam12, dummy, dummy, dummy = self._Lengths(
eps, sig12, ssig1, csig1, dn1, ssig2, csig2, dn2, cbet1, cbet2,
Geodesic.REDUCEDLENGTH, C1a, C2a)
dlam12 *= self._f1 / (calp2 * cbet2)
else:
dlam12 = math.nan
return (lam12, salp2, calp2, sig12, ssig1, csig1, ssig2, csig2, eps,
domg12, dlam12)
# return a12, s12, salp1, calp1, salp2, calp2, m12, M12, M21, S12
def _GenInverse(self, lat1, lon1, lat2, lon2, outmask):
"""Private: General version of the inverse problem"""
a12 = s12 = m12 = M12 = M21 = S12 = math.nan # return vals
outmask &= Geodesic.OUT_MASK
# Compute longitude difference (AngDiff does this carefully). Result is
# in [-180, 180] but -180 is only for west-going geodesics. 180 is for
# east-going and meridional geodesics.
lon12, lon12s = Math.AngDiff(lon1, lon2)
# Make longitude difference positive.
lonsign = math.copysign(1, lon12)
lon12 = lonsign * lon12; lon12s = lonsign * lon12s
lam12 = math.radians(lon12)
# Calculate sincos of lon12 + error (this applies AngRound internally).
slam12, clam12 = Math.sincosde(lon12, lon12s)
lon12s = (180 - lon12) - lon12s # the supplementary longitude difference
# If really close to the equator, treat as on equator.
lat1 = Math.AngRound(Math.LatFix(lat1))
lat2 = Math.AngRound(Math.LatFix(lat2))
# Swap points so that point with higher (abs) latitude is point 1
# If one latitude is a nan, then it becomes lat1.
swapp = -1 if abs(lat1) < abs(lat2) or math.isnan(lat2) else 1
if swapp < 0:
lonsign *= -1
lat2, lat1 = lat1, lat2
# Make lat1 <= 0
latsign = math.copysign(1, -lat1)
lat1 *= latsign
lat2 *= latsign
# Now we have
#
# 0 <= lon12 <= 180
# -90 <= lat1 <= 0
# lat1 <= lat2 <= -lat1
#
# longsign, swapp, latsign register the transformation to bring the
# coordinates to this canonical form. In all cases, 1 means no change was
# made. We make these transformations so that there are few cases to
# check, e.g., on verifying quadrants in atan2. In addition, this
# enforces some symmetries in the results returned.
# real phi, sbet1, cbet1, sbet2, cbet2, s12x, m12x
sbet1, cbet1 = Math.sincosd(lat1); sbet1 *= self._f1
# Ensure cbet1 = +epsilon at poles
sbet1, cbet1 = Math.norm(sbet1, cbet1); cbet1 = max(Geodesic.tiny_, cbet1)
sbet2, cbet2 = Math.sincosd(lat2); sbet2 *= self._f1
# Ensure cbet2 = +epsilon at poles
sbet2, cbet2 = Math.norm(sbet2, cbet2); cbet2 = max(Geodesic.tiny_, cbet2)
# If cbet1 < -sbet1, then cbet2 - cbet1 is a sensitive measure of the
# |bet1| - |bet2|. Alternatively (cbet1 >= -sbet1), abs(sbet2) + sbet1 is
# a better measure. This logic is used in assigning calp2 in Lambda12.
# Sometimes these quantities vanish and in that case we force bet2 = +/-
# bet1 exactly. An example where is is necessary is the inverse problem
# 48.522876735459 0 -48.52287673545898293 179.599720456223079643
# which failed with Visual Studio 10 (Release and Debug)
if cbet1 < -sbet1:
if cbet2 == cbet1:
sbet2 = math.copysign(sbet1, sbet2)
else:
if abs(sbet2) == -sbet1:
cbet2 = cbet1
dn1 = math.sqrt(1 + self._ep2 * Math.sq(sbet1))
dn2 = math.sqrt(1 + self._ep2 * Math.sq(sbet2))
# real a12, sig12, calp1, salp1, calp2, salp2
# index zero elements of these arrays are unused
C1a = list(range(Geodesic.nC1_ + 1))
C2a = list(range(Geodesic.nC2_ + 1))
C3a = list(range(Geodesic.nC3_))
meridian = lat1 == -90 or slam12 == 0
if meridian:
# Endpoints are on a single full meridian, so the geodesic might lie on
# a meridian.
calp1 = clam12; salp1 = slam12 # Head to the target longitude
calp2 = 1.0; salp2 = 0.0 # At the target we're heading north
# tan(bet) = tan(sig) * cos(alp)
ssig1 = sbet1; csig1 = calp1 * cbet1
ssig2 = sbet2; csig2 = calp2 * cbet2
# sig12 = sig2 - sig1
sig12 = math.atan2(max(0.0, csig1 * ssig2 - ssig1 * csig2) + 0.0,
csig1 * csig2 + ssig1 * ssig2)
s12x, m12x, dummy, M12, M21 = self._Lengths(
self._n, sig12, ssig1, csig1, dn1, ssig2, csig2, dn2, cbet1, cbet2,
outmask | Geodesic.DISTANCE | Geodesic.REDUCEDLENGTH, C1a, C2a)
# Add the check for sig12 since zero length geodesics might yield m12 <
# 0. Test case was
#
# echo 20.001 0 20.001 0 | GeodSolve -i
#
# In fact, we will have sig12 > pi/2 for meridional geodesic which is
# not a shortest path.
if sig12 < 1 or m12x >= 0:
if (sig12 < 3 * Geodesic.tiny_ or
# Prevent negative s12 or m12 for short lines
(sig12 < Geodesic.tol0_ and (s12x < 0 or m12x < 0))):
sig12 = m12x = s12x = 0.0
m12x *= self._b
s12x *= self._b
a12 = math.degrees(sig12)
else:
# m12 < 0, i.e., prolate and too close to anti-podal
meridian = False
# end if meridian:
# somg12 == 2 marks that it needs to be calculated
somg12 = 2.0; comg12 = 0.0; omg12 = 0.0
if (not meridian and
sbet1 == 0 and # and sbet2 == 0
# Mimic the way Lambda12 works with calp1 = 0
(self.f <= 0 or lon12s >= self.f * 180)):
# Geodesic runs along equator
calp1 = calp2 = 0.0; salp1 = salp2 = 1.0
s12x = self.a * lam12
sig12 = omg12 = lam12 / self._f1
m12x = self._b * math.sin(sig12)
if outmask & Geodesic.GEODESICSCALE:
M12 = M21 = math.cos(sig12)
a12 = lon12 / self._f1
elif not meridian:
# Now point1 and point2 belong within a hemisphere bounded by a
# meridian and geodesic is neither meridional or equatorial.
# Figure a starting point for Newton's method
sig12, salp1, calp1, salp2, calp2, dnm = self._InverseStart(
sbet1, cbet1, dn1, sbet2, cbet2, dn2, lam12, slam12, clam12, C1a, C2a)
if sig12 >= 0:
# Short lines (InverseStart sets salp2, calp2, dnm)
s12x = sig12 * self._b * dnm
m12x = (Math.sq(dnm) * self._b * math.sin(sig12 / dnm))
if outmask & Geodesic.GEODESICSCALE:
M12 = M21 = math.cos(sig12 / dnm)
a12 = math.degrees(sig12)
omg12 = lam12 / (self._f1 * dnm)
else:
# Newton's method. This is a straightforward solution of f(alp1) =
# lambda12(alp1) - lam12 = 0 with one wrinkle. f(alp) has exactly one
# root in the interval (0, pi) and its derivative is positive at the
# root. Thus f(alp) is positive for alp > alp1 and negative for alp <
# alp1. During the course of the iteration, a range (alp1a, alp1b) is
# maintained which brackets the root and with each evaluation of f(alp)
# the range is shrunk if possible. Newton's method is restarted
# whenever the derivative of f is negative (because the new value of
# alp1 is then further from the solution) or if the new estimate of
# alp1 lies outside (0,pi); in this case, the new starting guess is
# taken to be (alp1a + alp1b) / 2.
# real ssig1, csig1, ssig2, csig2, eps
numit = 0
tripn = tripb = False
# Bracketing range
salp1a = Geodesic.tiny_; calp1a = 1.0
salp1b = Geodesic.tiny_; calp1b = -1.0
while numit < Geodesic.maxit2_:
# the WGS84 test set: mean = 1.47, sd = 1.25, max = 16
# WGS84 and random input: mean = 2.85, sd = 0.60
(v, salp2, calp2, sig12, ssig1, csig1, ssig2, csig2,
eps, domg12, dv) = self._Lambda12(
sbet1, cbet1, dn1, sbet2, cbet2, dn2,
salp1, calp1, slam12, clam12, numit < Geodesic.maxit1_,
C1a, C2a, C3a)
# Reversed test to allow escape with NaNs
if tripb or not (abs(v) >= (8 if tripn else 1) * Geodesic.tol0_):
break
# Update bracketing values
if v > 0 and (numit > Geodesic.maxit1_ or
calp1/salp1 > calp1b/salp1b):
salp1b = salp1; calp1b = calp1
elif v < 0 and (numit > Geodesic.maxit1_ or
calp1/salp1 < calp1a/salp1a):
salp1a = salp1; calp1a = calp1
numit += 1
if numit < Geodesic.maxit1_ and dv > 0:
dalp1 = -v/dv
sdalp1 = math.sin(dalp1); cdalp1 = math.cos(dalp1)
nsalp1 = salp1 * cdalp1 + calp1 * sdalp1
if nsalp1 > 0 and abs(dalp1) < math.pi:
calp1 = calp1 * cdalp1 - salp1 * sdalp1
salp1 = nsalp1
salp1, calp1 = Math.norm(salp1, calp1)
# In some regimes we don't get quadratic convergence because
# slope -> 0. So use convergence conditions based on epsilon
# instead of sqrt(epsilon).
tripn = abs(v) <= 16 * Geodesic.tol0_
continue
# Either dv was not positive or updated value was outside
# legal range. Use the midpoint of the bracket as the next
# estimate. This mechanism is not needed for the WGS84
# ellipsoid, but it does catch problems with more eccentric
# ellipsoids. Its efficacy is such for
# the WGS84 test set with the starting guess set to alp1 = 90deg:
# the WGS84 test set: mean = 5.21, sd = 3.93, max = 24
# WGS84 and random input: mean = 4.74, sd = 0.99
salp1 = (salp1a + salp1b)/2
calp1 = (calp1a + calp1b)/2
salp1, calp1 = Math.norm(salp1, calp1)
tripn = False
tripb = (abs(salp1a - salp1) + (calp1a - calp1) < Geodesic.tolb_ or
abs(salp1 - salp1b) + (calp1 - calp1b) < Geodesic.tolb_)
lengthmask = (outmask |
(Geodesic.DISTANCE
if (outmask & (Geodesic.REDUCEDLENGTH |
Geodesic.GEODESICSCALE))
else Geodesic.EMPTY))
s12x, m12x, dummy, M12, M21 = self._Lengths(
eps, sig12, ssig1, csig1, dn1, ssig2, csig2, dn2, cbet1, cbet2,
lengthmask, C1a, C2a)
m12x *= self._b
s12x *= self._b
a12 = math.degrees(sig12)
if outmask & Geodesic.AREA:
# omg12 = lam12 - domg12
sdomg12 = math.sin(domg12); cdomg12 = math.cos(domg12)
somg12 = slam12 * cdomg12 - clam12 * sdomg12
comg12 = clam12 * cdomg12 + slam12 * sdomg12
# end elif not meridian
if outmask & Geodesic.DISTANCE:
s12 = 0.0 + s12x # Convert -0 to 0
if outmask & Geodesic.REDUCEDLENGTH:
m12 = 0.0 + m12x # Convert -0 to 0
if outmask & Geodesic.AREA:
# From Lambda12: sin(alp1) * cos(bet1) = sin(alp0)
salp0 = salp1 * cbet1
calp0 = math.hypot(calp1, salp1 * sbet1) # calp0 > 0
# real alp12
if calp0 != 0 and salp0 != 0:
# From Lambda12: tan(bet) = tan(sig) * cos(alp)
ssig1 = sbet1; csig1 = calp1 * cbet1
ssig2 = sbet2; csig2 = calp2 * cbet2
k2 = Math.sq(calp0) * self._ep2
eps = k2 / (2 * (1 + math.sqrt(1 + k2)) + k2)
# Multiplier = a^2 * e^2 * cos(alpha0) * sin(alpha0).
A4 = Math.sq(self.a) * calp0 * salp0 * self._e2
ssig1, csig1 = Math.norm(ssig1, csig1)
ssig2, csig2 = Math.norm(ssig2, csig2)
C4a = list(range(Geodesic.nC4_))
self._C4f(eps, C4a)
B41 = Geodesic._SinCosSeries(False, ssig1, csig1, C4a)
B42 = Geodesic._SinCosSeries(False, ssig2, csig2, C4a)
S12 = A4 * (B42 - B41)
else:
# Avoid problems with indeterminate sig1, sig2 on equator
S12 = 0.0
if not meridian and somg12 == 2.0:
somg12 = math.sin(omg12); comg12 = math.cos(omg12)
if (not meridian and
# omg12 < 3/4 * pi
comg12 > -0.7071 and # Long difference not too big
sbet2 - sbet1 < 1.75): # Lat difference not too big
# Use tan(Gamma/2) = tan(omg12/2)
# * (tan(bet1/2)+tan(bet2/2))/(1+tan(bet1/2)*tan(bet2/2))
# with tan(x/2) = sin(x)/(1+cos(x))
domg12 = 1 + comg12; dbet1 = 1 + cbet1; dbet2 = 1 + cbet2
alp12 = 2 * math.atan2( somg12 * ( sbet1 * dbet2 + sbet2 * dbet1 ),
domg12 * ( sbet1 * sbet2 + dbet1 * dbet2 ) )
else:
# alp12 = alp2 - alp1, used in atan2 so no need to normalize
salp12 = salp2 * calp1 - calp2 * salp1
calp12 = calp2 * calp1 + salp2 * salp1
# The right thing appears to happen if alp1 = +/-180 and alp2 = 0, viz
# salp12 = -0 and alp12 = -180. However this depends on the sign
# being attached to 0 correctly. The following ensures the correct
# behavior.
if salp12 == 0 and calp12 < 0:
salp12 = Geodesic.tiny_ * calp1
calp12 = -1.0
alp12 = math.atan2(salp12, calp12)
S12 += self._c2 * alp12
S12 *= swapp * lonsign * latsign
# Convert -0 to 0
S12 += 0.0
# Convert calp, salp to azimuth accounting for lonsign, swapp, latsign.
if swapp < 0:
salp2, salp1 = salp1, salp2
calp2, calp1 = calp1, calp2
if outmask & Geodesic.GEODESICSCALE:
M21, M12 = M12, M21
salp1 *= swapp * lonsign; calp1 *= swapp * latsign
salp2 *= swapp * lonsign; calp2 *= swapp * latsign
return a12, s12, salp1, calp1, salp2, calp2, m12, M12, M21, S12
[docs]
def Inverse(self, lat1, lon1, lat2, lon2,
outmask = GeodesicCapability.STANDARD):
"""Solve the inverse geodesic problem
:param lat1: latitude of the first point in degrees
:param lon1: longitude of the first point in degrees
:param lat2: latitude of the second point in degrees
:param lon2: longitude of the second point in degrees
:param outmask: the :ref:`output mask <outmask>`
:return: a :ref:`dict`
Compute geodesic between (*lat1*, *lon1*) and (*lat2*, *lon2*).
The default value of *outmask* is STANDARD, i.e., the *lat1*,
*lon1*, *azi1*, *lat2*, *lon2*, *azi2*, *s12*, *a12* entries are
returned.
"""
a12, s12, salp1,calp1, salp2,calp2, m12, M12, M21, S12 = self._GenInverse(
lat1, lon1, lat2, lon2, outmask)
outmask &= Geodesic.OUT_MASK
if outmask & Geodesic.LONG_UNROLL:
lon12, e = Math.AngDiff(lon1, lon2)
lon2 = (lon1 + lon12) + e
else:
lon2 = Math.AngNormalize(lon2)
result = {'lat1': Math.LatFix(lat1),
'lon1': lon1 if outmask & Geodesic.LONG_UNROLL else
Math.AngNormalize(lon1),
'lat2': Math.LatFix(lat2),
'lon2': lon2}
result['a12'] = a12
if outmask & Geodesic.DISTANCE: result['s12'] = s12
if outmask & Geodesic.AZIMUTH:
result['azi1'] = Math.atan2d(salp1, calp1)
result['azi2'] = Math.atan2d(salp2, calp2)
if outmask & Geodesic.REDUCEDLENGTH: result['m12'] = m12
if outmask & Geodesic.GEODESICSCALE:
result['M12'] = M12; result['M21'] = M21
if outmask & Geodesic.AREA: result['S12'] = S12
return result
# return a12, lat2, lon2, azi2, s12, m12, M12, M21, S12
def _GenDirect(self, lat1, lon1, azi1, arcmode, s12_a12, outmask):
"""Private: General version of direct problem"""
from geographiclib.geodesicline import GeodesicLine
# Automatically supply DISTANCE_IN if necessary
if not arcmode: outmask |= Geodesic.DISTANCE_IN
line = GeodesicLine(self, lat1, lon1, azi1, outmask)
return line._GenPosition(arcmode, s12_a12, outmask)
EMPTY = GeodesicCapability.EMPTY
"""No capabilities, no output."""
LATITUDE = GeodesicCapability.LATITUDE
"""Calculate latitude *lat2*."""
LONGITUDE = GeodesicCapability.LONGITUDE
"""Calculate longitude *lon2*."""
AZIMUTH = GeodesicCapability.AZIMUTH
"""Calculate azimuths *azi1* and *azi2*."""
DISTANCE = GeodesicCapability.DISTANCE
"""Calculate distance *s12*."""
STANDARD = GeodesicCapability.STANDARD
"""All of the above."""
DISTANCE_IN = GeodesicCapability.DISTANCE_IN
"""Allow distance *s12* to be used as input in the direct geodesic
problem."""
REDUCEDLENGTH = GeodesicCapability.REDUCEDLENGTH
"""Calculate reduced length *m12*."""
GEODESICSCALE = GeodesicCapability.GEODESICSCALE
"""Calculate geodesic scales *M12* and *M21*."""
AREA = GeodesicCapability.AREA
"""Calculate area *S12*."""
ALL = GeodesicCapability.ALL
"""All of the above."""
LONG_UNROLL = GeodesicCapability.LONG_UNROLL
"""Unroll longitudes, rather than reducing them to the range
[-180d,180d].
"""
Geodesic.WGS84 = Geodesic(Constants.WGS84_a, Constants.WGS84_f)
"""Instantiation for the WGS84 ellipsoid"""
[docs]
class Distance:
""" Modified to remve unit conversions to stay with RCAIDE conventions - Oct. 2024
Base class for other distance algorithms. Represents a distance.
Can be used for units conversion::
>>> from geopy.distance import Distance
>>> Distance(miles=10).km
16.09344
Distance instances have all *distance* properties from :mod:`geopy.units`,
e.g.: ``km``, ``m``, ``meters``, ``miles`` and so on.
Distance instances are immutable.
They support comparison::
>>> from geopy.distance import Distance
>>> Distance(kilometers=2) == Distance(meters=2000)
True
>>> Distance(kilometers=2) > Distance(miles=1)
True
String representation::
>>> from geopy.distance import Distance
>>> repr(Distance(kilometers=2))
'Distance(2.0)'
>>> str(Distance(kilometers=2))
'2.0 km'
>>> repr(Distance(miles=2))
'Distance(3.218688)'
>>> str(Distance(miles=2))
'3.218688 km'
Arithmetics::
>>> from geopy.distance import Distance
>>> -Distance(miles=2)
Distance(-3.218688)
>>> Distance(miles=2) + Distance(kilometers=1)
Distance(4.218688)
>>> Distance(miles=2) - Distance(kilometers=1)
Distance(2.218688)
>>> Distance(kilometers=6) * 5
Distance(30.0)
>>> Distance(kilometers=6) / 5
Distance(1.2)
"""
[docs]
def __init__(self, *args, **kwargs):
"""
There are 3 ways to create a distance:
- From kilometers::
>>> from geopy.distance import Distance
>>> Distance(1.42)
Distance(1.42)
- From points (for non-abstract distances only),
calculated as a sum of distances between all points::
>>> from geopy.distance import geodesic
>>> geodesic((40, 160), (40.1, 160.1))
Distance(14.003702498106215)
>>> geodesic((40, 160), (40.1, 160.1), (40.2, 160.2))
Distance(27.999954644813478)
"""
kilometers = kwargs.pop('kilometers', 0)
if len(args) == 1:
# if we only get one argument we assume
# it's a known distance instead of
# calculating it first
kilometers += args[0]
elif len(args) > 1:
kilometers = self.measure(args[0], args[1])
#elif len(args) > 1:
# for a, b in #util.pairwise(args):
#kilometers += self.measure(a, b)
#kilometers += units.kilometers(**kwargs)
self.__kilometers = kilometers
def __add__(self, other):
if isinstance(other, Distance):
return self.__class__(self.kilometers + other.kilometers)
else:
raise TypeError("Distance instance must be added with Distance instance.")
def __neg__(self):
return self.__class__(-self.kilometers)
def __sub__(self, other):
return self + -other
def __mul__(self, other):
if isinstance(other, Distance):
raise TypeError("Distance instance must be multiplicated with numbers.")
else:
return self.__class__(self.kilometers * other)
def __rmul__(self, other):
if isinstance(other, Distance):
raise TypeError("Distance instance must be multiplicated with numbers.")
else:
return self.__class__(other * self.kilometers)
def __truediv__(self, other):
if isinstance(other, Distance):
return self.kilometers / other.kilometers
else:
return self.__class__(self.kilometers / other)
def __floordiv__(self, other):
if isinstance(other, Distance):
return self.kilometers // other.kilometers
else:
return self.__class__(self.kilometers // other)
def __abs__(self):
return self.__class__(abs(self.kilometers))
def __bool__(self):
return bool(self.kilometers)
[docs]
def measure(self, a, b):
# Intentionally not documented, because this method is not supposed
# to be used directly.
raise NotImplementedError("Distance is an abstract class")
[docs]
def destination(self, point, bearing, distance=None):
"""
Calculate destination point using a starting point, bearing
and a distance. This method works for non-abstract distances only.
Example: a point 10 miles east from ``(34, 148)``::
>>> import geopy.distance
>>> geopy.distance.distance(miles=10).destination((34, 148), bearing=90)
Point(33.99987666492774, 148.17419994321995, 0.0)
:param point: Starting point.
:type point: :class:`geopy.point.Point`, list or tuple of ``(latitude,
longitude)``, or string as ``"%(latitude)s, %(longitude)s"``.
:param float bearing: Bearing in degrees: 0 -- North, 90 -- East,
180 -- South, 270 or -90 -- West.
:param distance: Distance, can be used to override
this instance::
>>> from geopy.distance import distance, Distance
>>> distance(miles=10).destination((34, 148), bearing=90, \distance=Distance(100))
Point(33.995238229104764, 149.08238904409637, 0.0)
:type distance: :class:`.Distance`
:rtype: :class:`geopy.point.Point`
"""
raise NotImplementedError("Distance is an abstract class")
def __repr__(self): # pragma: no cover
return 'Distance(%s)' % self.kilometers
def __str__(self): # pragma: no cover
return '%s km' % self.__kilometers
def __cmp__(self, other): # py2 only
if isinstance(other, Distance):
return cmp(self.kilometers, other.kilometers)
else:
return cmp(self.kilometers, other)
def __hash__(self):
return hash(self.kilometers)
def __eq__(self, other):
return self.__cmp__(other) == 0
def __ne__(self, other):
return self.__cmp__(other) != 0
def __gt__(self, other):
return self.__cmp__(other) > 0
def __lt__(self, other):
return self.__cmp__(other) < 0
def __ge__(self, other):
return self.__cmp__(other) >= 0
def __le__(self, other):
return self.__cmp__(other) <= 0
@property
def kilometers(self):
return self.__kilometers
@property
def km(self):
return self.kilometers
[docs]
class Geodesic_Calculate(Distance):
"""
Calculate the geodesic distance between points.
Set which ellipsoidal model of the earth to use by specifying an
``ellipsoid`` keyword argument. The default is 'WGS-84', which is the
most globally accurate model. If ``ellipsoid`` is a string, it is
looked up in the `ELLIPSOIDS` dictionary to obtain the major and minor
semiaxes and the flattening. Otherwise, it should be a tuple with those
values. See the comments above the `ELLIPSOIDS` dictionary for
more information.
Example::
>>> from geopy.distance import geodesic
>>> newport_ri = (41.49008, -71.312796)
>>> cleveland_oh = (41.499498, -81.695391)
>>> print(geodesic(newport_ri, cleveland_oh).miles)
538.390445368
"""
[docs]
def __init__(self, *args, **kwargs):
self.ellipsoid_key = None
self.ELLIPSOID = None
self.geod = None
self.set_ellipsoid(kwargs.pop('ellipsoid', 'WGS-84'))
major, minor, f = self.ELLIPSOID
super().__init__(*args, **kwargs)
[docs]
def set_ellipsoid(self, ellipsoid):
if isinstance(ellipsoid, str):
try:
self.ELLIPSOID = (6378.137, 6356.7523142, 1 / 298.257223563) # Assigns WGS-84 Ellipsoid parameters
self.ellipsoid_key = ellipsoid
except KeyError:
raise Exception(
"Invalid ellipsoid. See geopy.distance.ELLIPSOIDS"
)
else:
self.ELLIPSOID = ellipsoid
self.ellipsoid_key = None
[docs]
def measure(self, a, b):
#a, b = Point(a), Point(b)
#_ensure_same_altitude(a, b)
lat1, lon1 = a[0], a[1]
lat2, lon2 = b[0], b[1]
if not (isinstance(self.geod, Geodesic) and
self.geod.a == self.ELLIPSOID[0] and
self.geod.f == self.ELLIPSOID[2]):
self.geod = Geodesic(self.ELLIPSOID[0], self.ELLIPSOID[2])
s12 = self.geod.Inverse(lat1, lon1, lat2, lon2,
Geodesic.DISTANCE)['s12']
return s12
GeodesicDistance = Geodesic_Calculate
# Set the default distance formula
distance = GeodesicDistance
