def __init__(self, a, f):
"""
Construct a Geodesic object for ellipsoid with major radius a and
flattening f.
"""
self._a = float(a)
self._f = float(f) if f <= 1 else 1.0 / f
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"
self._etol2 = 0.01 * Geodesic.tol2_ / max(0.1, math.sqrt(abs(
self._e2)))
if not (Math.isfinite(self._a) and self._a > 0):
raise ValueError("Major radius is not positive")
if not (Math.isfinite(self._b) and self._b > 0):
raise ValueError("Minor radius is not positive")
self._A3x = range(Geodesic.nA3x_)
self._C3x = range(Geodesic.nC3x_)
self._C4x = range(Geodesic.nC4x_)
self.A3coeff()
self.C3coeff()
self.C4coeff()
def __init__(self, a, f):
"""
Construct a Geodesic object for ellipsoid with major radius a and
flattening f.
"""
self._a = float(a)
self._f = float(f) if f <= 1 else 1.0/f
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"
self._etol2 = 0.01 * Geodesic.tol2_ / max(0.1, math.sqrt(abs(self._e2)))
if not(Math.isfinite(self._a) and self._a > 0):
raise ValueError("Major radius is not positive")
if not(Math.isfinite(self._b) and self._b > 0):
raise ValueError("Minor radius is not positive")
self._A3x = range(Geodesic.nA3x_)
self._C3x = range(Geodesic.nC3x_)
self._C4x = range(Geodesic.nC4x_)
self.A3coeff()
self.C3coeff()
self.C4coeff()
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 __init__(self, a, f):
"""
Construct a Geodesic object for ellipsoid with major radius a and
flattening f.
"""
self._a = float(a)
self._f = float(f) if f <= 1 else 1.0 / f
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("Major radius is not positive")
if not (Math.isfinite(self._b) and self._b > 0):
raise ValueError("Minor radius 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 __init__(self, a, f):
"""Construct a Geodesic object for ellipsoid with major radius a and
flattening f.
"""
self._a = float(a)
self._f = float(f) if f <= 1 else 1.0/f
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("Major radius is not positive")
if not(Math.isfinite(self._b) and self._b > 0):
raise ValueError("Minor radius 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()