def antipode(self, height=None):
'''Return the antipode, the point diametrically opposite
to this point.
@keyword height: Optional height of the antipode, height
of this point otherwise (C{meter}).
@return: The antipodal point (C{LatLon}).
'''
a, b = antipode(self.lat, self.lon)
h = self.height if height is None else height
return self.classof(a, b, height=h)
def intersection(start1,
end1,
start2,
end2,
height=None,
wrap=False,
LatLon=LatLon):
'''Compute the intersection point of two paths both defined
by two points or a start point and bearing from North.
@param start1: Start point of the first path (L{LatLon}).
@param end1: End point ofthe first path (L{LatLon}) or
the initial bearing at the first start point
(compass C{degrees360}).
@param start2: Start point of the second path (L{LatLon}).
@param end2: End point of the second path (L{LatLon}) or
the initial bearing at the second start point
(compass C{degrees360}).
@keyword height: Optional height for the intersection point,
overriding the mean height (C{meter}).
@keyword wrap: Wrap and unroll longitudes (C{bool}).
@keyword LatLon: Optional (sub-)class for the intersection point
(L{LatLon}) or C{None}.
@return: The intersection point (I{LatLon}) or 3-tuple
(C{degrees90}, C{degrees180}, height) if I{LatLon}
is C{None}. An alternate intersection point might
be the L{antipode} to the returned result.
@raise TypeError: Start or end point(s) not L{LatLon}.
@raise ValueError: Intersection is ambiguous or infinite or
the paths are parallel, coincident or null.
@example:
>>> p = LatLon(51.8853, 0.2545)
>>> s = LatLon(49.0034, 2.5735)
>>> i = intersection(p, 108.547, s, 32.435) # '50.9078°N, 004.5084°E'
'''
_Trll.others(start1, name='start1')
_Trll.others(start2, name='start2')
a1, b1 = start1.to2ab()
a2, b2 = start2.to2ab()
db, b2 = unrollPI(b1, b2, wrap=wrap)
r12 = haversine_(a2, a1, db)
if abs(r12) < EPS: # [nearly] coincident points
a, b = map1(degrees, favg(a1, a2), favg(b1, b2))
# see <http://www.EdWilliams.org/avform.htm#Intersection>
elif isscalar(end1) and isscalar(end2): # both bearings
ca1, ca2, cr12 = map1(cos, a1, a2, r12)
sa1, sa2, sr12 = map1(sin, a1, a2, r12)
x1, x2 = (sr12 * ca1), (sr12 * ca2)
if abs(x1) < EPS or abs(x2) < EPS:
raise ValueError('intersection %s: %r vs %r' % ('parallel',
(start1, end1),
(start2, end2)))
# handle domain error for equivalent longitudes,
# see also functions asin_safe and acos_safe at
# <http://www.EdWilliams.org/avform.htm#Math>
t1, t2 = map1(acos1, (sa2 - sa1 * cr12) / x1, (sa1 - sa2 * cr12) / x2)
if sin(db) > 0:
t12, t21 = t1, PI2 - t2
else:
t12, t21 = PI2 - t1, t2
t13, t23 = map1(radiansPI2, end1, end2)
x1, x2 = map1(
wrapPI,
t13 - t12, # angle 2-1-3
t21 - t23) # angle 1-2-3
sx1, sx2 = map1(sin, x1, x2)
if sx1 == 0 and sx2 == 0: # max(abs(sx1), abs(sx2)) < EPS
raise ValueError('intersection %s: %r vs %r' % ('infinite',
(start1, end1),
(start2, end2)))
sx3 = sx1 * sx2
# if sx3 < 0:
# raise ValueError('intersection %s: %r vs %r' % ('ambiguous',
# (start1, end1), (start2, end2)))
cx1, cx2 = map1(cos, x1, x2)
x3 = acos1(cr12 * sx3 - cx2 * cx1)
r13 = atan2(sr12 * sx3, cx2 + cx1 * cos(x3))
a, b = _destination2(a1, b1, r13, t13)
# choose antipode for opposing bearings
if _xb(a1, b1, end1, a, b, wrap) < 0 or \
_xb(a2, b2, end2, a, b, wrap) < 0:
a, b = antipode(a, b)
else: # end point(s) or bearing(s)
x1, d1 = _x3d2(start1, end1, wrap, '1')
x2, d2 = _x3d2(start2, end2, wrap, '2')
x = x1.cross(x2)
if x.length < EPS: # [nearly] colinear or parallel paths
raise ValueError('intersection %s: %r vs %r' % ('colinear',
(start1, end1),
(start2, end2)))
a, b = x.to2ll()
# choose intersection similar to sphericalNvector
d1 = _xdot(d1, a1, b1, a, b, wrap)
d2 = _xdot(d2, a2, b2, a, b, wrap)
if (d1 < 0 and d2 > 0) or (d1 > 0 and d2 < 0):
a, b = antipode(a, b)
h = start1._havg(start2) if height is None else height
return (a, b, h) if LatLon is None else LatLon(a, b, height=h)
