def __init__(self, a_ellipsoid, f, name):
'''(INTERNAL) New C{Ecef...}.
'''
try:
E = a_ellipsoid
if f is None:
if isinstance(E, Datum):
self._datum = E
E = E.ellipsoid
elif not isinstance(E, Ellipsoid):
raise TypeError
self.name = E.name
elif isscalar(E) and isscalar(f):
a = float(E)
f_ = (1.0 / f) if f else 0 # sphere
b = None if f_ else a
E = Ellipsoid(a, b, f_, name='_' + name)
else:
raise ValueError
if not (E.a > 0 and E.f < 1):
raise ValueError
except (TypeError, ValueError):
t = unStr(self.classname, a=E, f=f)
raise EcefError('%s invalid: %s' % ('ellipsoid', t))
self._E = E
if name:
self.name = name
def _height(self, lats, lons, Error=HeightError):
if isscalar(lats) and isscalar(lons):
llis = LatLon_(lats, lons)
else:
n, lats = len2(lats)
m, lons = len2(lons)
if n != m:
raise Error('non-matching %s: %s vs %s' % ('len', n, m))
llis = [LatLon_(*ll) for ll in zip(lats, lons)]
return self(llis) # __call__(lli) or __call__(llis)
def _x3d2(start, end, wrap, n, hs):
# see <https://www.EdWilliams.org/intersect.htm> (5) ff
a1, b1 = start.to2ab()
if isscalar(end): # bearing, make a point
a2, b2 = _destination2_(a1, b1, PI_4, radians(end))
else: # must be a point
_Trll.others(end, name='end' + n)
hs.append(end.height)
a2, b2 = end.to2ab()
db, b2 = unrollPI(b1, b2, wrap=wrap)
if max(abs(db), abs(a2 - a1)) < EPS:
raise ValueError('intersection %s%s null: %r' % ('path', n, (start, end)))
# note, in EdWilliams.org/avform.htm W is + and E is -
b21, b12 = db * 0.5, -(b1 + b2) * 0.5
sb21, cb21, sb12, cb12, \
sa21, _, sa12, _ = sincos2(b21, b12, a1 - a2, a1 + a2)
x = Vector3d(sa21 * sb12 * cb21 - sa12 * cb12 * sb21,
sa21 * cb12 * cb21 + sa12 * sb12 * sb21,
cos(a1) * cos(a2) * sin(db), ll=start)
return x.unit(), (db, (a2 - a1)) # negated d
def fractional(points, fi, LatLon=None):
'''Return the point at a given fractional index.
@param points: The points (C{LatLon}[], C{Numpy2LatLon}[],
C{Tuple2LatLon}[] or C{other}[]).
@param fi: The fractional index (C{int} or C{float}).
@keyword LatLon: Optional (sub-)class to return the
I{intermediate} point (C{LatLon}) or
C{None}.
@return: The B{C{points}}[B{C{fi}}] if fractional index
B{C{fi}} is C{int}, otherwise the intermediate
point at C{float} B{C{fi}} (B{C{LatLon}} or a
L{LatLon2Tuple}C{(lat, lon)} if B{C{LatLon}} is
C{None}).
@raise IndexError: Fractional index B{C{fi}} invalid or
B{C{points}} not subscriptable.
'''
try:
if not (isscalar(fi) and 0 <= fi < len(points)):
raise IndexError
p = _fractional(points, fi)
except (IndexError, TypeError):
raise IndexError('%s invalid: %r' % ('fractional', fi))
if LatLon and isinstance(p, LatLon2Tuple):
p = LatLon(*p)
return p
def toStr(self, prec=3, sep=' ', radius=False): # PYCHOK expected
'''Return a string representation of this WM coordinate.
@keyword prec: Optional number of decimals, unstripped (C{int}).
@keyword sep: Optional separator to join (C{str}).
@keyword radius: Optionally, include radius (C{bool} or C{scalar}).
@return: This WM as "meter meter" (C{str}) plus " radius"
if B{C{radius}} is C{True} or C{scalar}.
@raise WebMercatorError: Invalid B{C{radius}}.
@example:
>>> w = Wm(448251, 5411932.0001)
>>> w.toStr(4) # 448251.0 5411932.0001
>>> w.toStr(sep=', ') # 448251, 5411932
'''
fs = self._x, self._y
if radius in (False, None):
pass
elif radius is True:
fs += (self._radius,)
elif isscalar(radius):
fs += (radius,)
else:
raise WebMercatorError('% invalid: %r' % ('radius', radius))
return fStr(fs, prec=prec, sep=sep)
def _fraction(fraction):
f = 1 # int, no fractional indices
if fraction is None:
pass
elif not (isscalar(fraction) and EPS < fraction <= 1):
raise FrechetError('%s invalid: %r' % ('fraction', fraction))
elif fraction < EPS1:
f = float(fraction)
return f
def __init__(self, knots, weight=None, name=''):
'''New L{HeightLSQBiSpline} interpolator.
@param knots: The points with known height (C{LatLon}s).
@keyword weight: Optional weight or weights for each B{C{knot}}
(C{scalar} or C{scalar}s).
@keyword name: Optional height interpolator name (C{str}).
@raise HeightError: Insufficient number of B{C{knots}} or
B{C{weight}}s or invalid B{C{knot}} or B{C{weight}}.
@raise ImportError: Package C{numpy} or C{scipy} not found
or not installed.
@raise SciPyError: A C{LSQSphereBivariateSpline} issue.
@raise SciPyWarning: A C{LSQSphereBivariateSpline} warning
as exception.
'''
np, spi = self._NumSciPy()
xs, ys, hs = self._xyhs3(knots)
m = len(hs)
if not weight:
w = None # default
elif isscalar(weight):
w = float(weight)
if w <= 0:
raise HeightError('invalid %s: %.6f' % ('weight', w))
else:
n, w = len2(weight)
if n != m:
raise HeightError('invalid %s: %s, not %s' %
('number of weights', n, m))
w = np.array(map(float, w))
for i in range(m):
if w[i] <= 0:
raise HeightError('invalid %s[%s]: %.6f' %
('weight', i, w[i]))
try:
T = 1.0e-4 # like SciPy example
ps = np.array(_ordedup(xs, T, PI2 - T))
ts = np.array(_ordedup(ys, T, PI - T))
self._ev = spi.LSQSphereBivariateSpline(ys,
xs,
hs,
ts,
ps,
eps=EPS,
w=w).ev
except Exception as x:
raise _SciPyIssue(x)
if name:
self.name = name
def times(self, factor):
'''Multiply this vector by a scalar.
@param factor: Scale factor (C{scalar}).
@return: New, scaled vector (L{Vector3d}).
@raise TypeError: Non-scalar B{C{factor}}.
'''
if not isscalar(factor):
raise _IsNotError('scalar', factor=factor)
return self.classof(self.x * factor, self.y * factor, self.z * factor)
def _gc3(self, start, end, namend, raiser='points'):
'''(INTERNAL) Return great circle, start and end Nvectors.
'''
s = start.toNvector()
if isscalar(end): # bearing
gc = s.greatCircle(end)
e = None
else:
self.others(end, name=namend)
e = end.toNvector()
gc = s.cross(e, raiser=raiser) # XXX .unit()?
return gc, s, e
def dividedBy(self, factor):
'''Divide this vector by a scalar.
@param factor: The divisor (C{scalar}).
@return: New, scaled vector (L{Vector3d}).
@raise TypeError: Non-scalar B{C{factor}}.
@raise VectorError: Invalid or zero B{C{factor}}.
'''
if not isscalar(factor):
raise _IsNotError('scalar', factor=factor)
try:
return self.times(1.0 / factor)
except (ValueError, ZeroDivisionError):
raise VectorError('%s invalid: %r' % ('factor', factor))
def _to3zBhp(zone,
band,
hemipole=''): # imported by .epsg, .ups, .utm, .utmups
'''Parse UTM/UPS zone, Band letter and hemisphere/pole letter.
@param zone: Zone with/-out Band (C{scalar} or C{str}).
@keyword band: Optional (longitudinal/polar) Band letter (C{str}).
@keyword hemipole: Optional hemisphere/pole letter (C{str}).
@return: 3-Tuple (C{zone, Band, hemisphere/pole}) as (C{int,
str, 'N'|'S'}) where C{zone} is C{0} for UPS or
C{1..60} for UTM and C{Band} is C{'A'..'Z'} I{NOT}
checked for valid UTM/UPS bands.
@raise ValueError: Invalid B{C{zone}}, B{C{band}} or B{C{hemipole}}.
'''
B = band
try:
z = _UTMUPS_ZONE_INVALID
if isscalar(zone) or zone.isdigit():
z = int(zone)
elif zone and isinstance(zone, _Strs):
if len(zone) > 1:
B = zone[-1:]
z = int(zone[:-1])
elif zone in 'AaBbYyZz': # single letter
B = zone
z = _UPS_ZONE
if _UTMUPS_ZONE_MIN <= z <= _UTMUPS_ZONE_MAX:
hp = hemipole[:1].upper()
if hp in ('N', 'S') or not hp:
B = B.upper()
if B.isalpha():
return z, B, (hp or ('S' if B < 'N' else 'N'))
elif not B:
return z, B, hp
except (AttributeError, TypeError, ValueError):
pass
raise ValueError('%s, %s or %s invalid: %r' % ('zone', 'band', 'hemipole',
(zone, B, hemipole)))
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 to return the intersection
point (L{LatLon}) or C{None}.
@return: The intersection point (B{C{LatLon}}) or a
L{LatLon3Tuple}C{(lat, lon, height)} if B{C{LatLon}}
is C{None}. An alternate intersection point might
be the L{antipode} to the returned result.
@raise TypeError: A B{C{start}} or B{C{end}} point 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')
hs = [start1.height, start2. height]
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 <https://www.EdWilliams.org/avform.htm#Intersection>
elif isscalar(end1) and isscalar(end2): # both bearings
sa1, ca1, sa2, ca2, sr12, cr12 = sincos2(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
# <https://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, cx1, sx2, cx2 = sincos2(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)))
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', hs)
x2, d2 = _x3d2(start2, end2, wrap, '2', hs)
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 = fmean(hs) if height is None else height
r = LatLon3Tuple(a, b, h) if LatLon is None else \
LatLon(a, b, height=h)
return _xnamed(r, intersection.__name__)
def _2epoch(epoch): # imported by .ellipsoidalBase.py
'''(INTERNAL) Validate an C{epoch}.
'''
if isscalar(epoch) and epoch > 0: # XXX 1970?
return _F(epoch)
raise _IsNotError('scalar', epoch=epoch)
def _2epoch(epoch): # imported by .ellipsoidalBase.py
'''(INTERNAL) Validate an C{epoch}.
'''
if isscalar(epoch) and epoch > 0: # XXX 1970?
return _F(epoch)
raise TypeError('%s not %s: %r' % ('epoch', 'scalar', epoch))
