def _rhumb3(self, other):
'''(INTERNAL) Rhumb_ helper function.
@param other: The other point (spherical LatLon).
'''
self.others(other)
a1, b1 = self.to2ab()
a2, b2 = other.to2ab()
# if |db| > 180 take shorter rhumb
# line across the anti-meridian
db = wrapPI(b2 - b1)
dp = log(tanPI_2_2(a2) / tanPI_2_2(a1))
return (a2 - a1), db, dp
def _rhumb3(self, other):
'''(INTERNAL) Rhumb_ helper function.
@param other: The other point (spherical LatLon).
'''
self.others(other)
a1 = radians(self.lat)
a2 = radians(other.lat)
# if |db| > 180 take shorter rhumb
# line across the anti-meridian
db = radiansPI(other.lon - self.lon)
ds = log(tanPI_2_2(a2) / tanPI_2_2(a1))
return (a2 - a1), db, ds
def rhumbDestination(self, distance, bearing, radius=R_M, height=None):
'''Return the destination point having travelled along
a rhumb (loxodrome) line from this point the given
distance on the given bearing.
@param distance: Distance travelled (same units as radius).
@param bearing: Bearing from this point (compass degrees).
@keyword radius: Optional, mean earth radius (meter).
@keyword height: Optional height, overriding the default
height (meter or same unit as radius).
@return: The destination point (spherical LatLon).
@example:
>>> p = LatLon(51.127, 1.338)
>>> q = p.rhumbDestination(40300, 116.7) # 50.9642°N, 001.8530°E
@JSname: I{rhumbDestinationPoint}
'''
a1, b1 = self.to2ab()
r = float(distance) / float(radius) # angular distance in radians
t = radians(bearing)
da = r * cos(t)
a2 = a1 + da
# normalize latitude if past pole
if a2 > PI_2:
a2 = PI - a2
elif a2 < -PI_2:
a2 = -PI - a2
dp = log(tanPI_2_2(a2) / tanPI_2_2(a1))
# E-W course becomes ill-conditioned with 0/0
if abs(dp) > EPS:
q = da / dp
else:
q = cos(a1)
if abs(q) > EPS:
b2 = b1 + r * sin(t) / q
else:
b2 = b1
h = self.height if height is None else height
return self.classof(degrees90(a2), degrees180(b2), height=h)
def rhumbMidpointTo(self, other, height=None):
'''Return the (loxodromic) midpoint between this and
an other point.
@param other: The other point (spherical LatLon).
@keyword height: Optional height, overriding the mean height
(meter or same unit as radius).
@return: The midpoint (spherical LatLon).
@raise TypeError: The other point is not spherical.
@example:
>>> p = LatLon(51.127, 1.338)
>>> q = LatLon(50.964, 1.853)
>>> m = p.rhumb_midpointTo(q)
>>> m.toStr() # '51.0455°N, 001.5957°E'
'''
self.others(other)
# see <http://mathforum.org/library/drmath/view/51822.html>
a1, b1 = self.to2ab()
a2, b2 = other.to2ab()
if abs(b2 - b1) > PI:
b1 += PI2 # crossing anti-meridian
a3 = favg(a1, a2)
b3 = favg(b1, b2)
f1 = tanPI_2_2(a1)
if abs(f1) > EPS:
f2 = tanPI_2_2(a2)
f = f2 / f1
if abs(f) > EPS:
f = log(f)
if abs(f) > EPS:
f3 = tanPI_2_2(a3)
b3 = fsum_(b1 * log(f2), -b2 * log(f1),
(b2 - b1) * log(f3)) / f
h = self._havg(other) if height is None else height
return self.classof(degrees90(a3), degrees180(b3), height=h)
def rhumbMidpointTo(self, other):
'''Return the loxodromic midpoint between this and an
other point.
@param other: The other point (spherical LatLon).
@return: The midpoint (spherical LatLon).
@raise TypeError: The other point is not spherical.
@example:
>>> p = LatLon(51.127, 1.338)
>>> q = LatLon(50.964, 1.853)
>>> m = p.rhumb_midpointTo(q)
>>> m.toStr() # '51.0455°N, 001.5957°E'
'''
self.others(other)
# see http://mathforum.org/library/drmath/view/51822.html
a1, b1 = self.to2ab()
a2, b2 = other.to2ab()
if abs(b2 - b1) > PI:
b1 += PI2 # crossing anti-meridian
a3 = (a1 + a2) * 0.5
b3 = (b1 + b2) * 0.5
f1 = tanPI_2_2(a1)
if abs(f1) > EPS:
f2 = tanPI_2_2(a2)
f = f2 / f1
if abs(f) > EPS:
f = log(f)
if abs(f) > EPS:
f3 = tanPI_2_2(a3)
b3 = (b1 * log(f2) - b2 * log(f1) +
(b2 - b1) * log(f3)) / f
return self.topsub(degrees90(a3),
degrees180(b3),
height=self._alter(other))
def _tdef(self, lat):
'''(INTERNAL) Compute t(lat).
'''
return max(0, tanPI_2_2(-lat) / self._pdef(lat))