def _xyhs3(atype, m, knots, off=True):
# convert knot C{LatLon}s to tuples or C{NumPy} arrays and C{SciPy} sphericals
xs, ys, hs = zip(*_xyhs(knots, off=off)) # PYCHOK unzip
n = len(hs)
if n < m:
raise HeightError('insufficient %s: %s, need %s' % ('knots', n, m))
return map1(atype, xs, ys, hs)
def _xyhs3(atype, m, knots, off=True):
# convert knot C{LatLon}s to tuples or C{NumPy} arrays and C{SciPy} sphericals
xs, ys, hs = zip(*_xyhs(knots, off=off, name=_knots_)) # PYCHOK unzip
n = len(hs)
if n < m:
raise _insufficientError(m, knots=n)
return map1(atype, xs, ys, hs)
def cross(self, other, raiser=None): # raiser=NN
'''Compute the cross product of this and an other vector.
@arg other: The other vector (L{Vector3d}).
@kwarg raiser: Optional, L{CrossError} label if raised (C{str}).
@return: Cross product (L{Vector3d}).
@raise CrossError: Zero or near-zero cross product and both
B{C{raiser}} and L{crosserrors} set.
@raise TypeError: Incompatible B{C{other}} C{type}.
'''
self.others(other)
x = self.y * other.z - self.z * other.y
y = self.z * other.x - self.x * other.z
z = self.x * other.y - self.y * other.x
if raiser and self.crosserrors and max(map1(abs, x, y, z)) < EPS:
t = _coincident_ if self.isequalTo(other) else _colinear_
r = getattr(other, '_fromll', None) or other
raise CrossError(raiser, r, txt=t)
return self.classof(x, y, z)
def isequalTo(self, other, eps=None):
'''Compare this point with an other point, I{ignoring} height.
@arg other: The other point (C{LatLon}).
@kwarg eps: Tolerance for equality (C{degrees}).
@return: C{True} if both points are identical,
I{ignoring} height, C{False} otherwise.
@raise TypeError: The B{C{other}} point is not C{LatLon}
or mismatch of the B{C{other}} and
this C{class} or C{type}.
@raise ValueError: Invalid B{C{eps}}.
@see: Method L{isequalTo3}.
@example:
>>> p = LatLon(52.205, 0.119)
>>> q = LatLon(52.205, 0.119)
>>> e = p.isequalTo(q) # True
'''
self.others(other)
e = _0_0 if eps in (None, 0, _0_0) else Scalar_(eps, name='eps')
if e > 0:
return max(map1(abs, self.lat - other.lat,
self.lon - other.lon)) < e
else:
return self.lat == other.lat and \
self.lon == other.lon
def _exs(n, points): # iterate over spherical edge excess
a1, b1 = points[n - 1].philam
ta1 = tan_2(a1)
for i in range(n):
a2, b2 = points[i].philam
db, b2 = unrollPI(b1, b2, wrap=wrap)
ta2, tdb = map1(tan_2, a2, db)
yield atan2(tdb * (ta1 + ta2), 1 + ta1 * ta2)
ta1, b1 = ta2, b2
def _to4lldn(latlon, lon, datum, name):
'''(INTERNAL) Return 4-tuple (C{lat, lon, datum, name}).
'''
try:
# if lon is not None:
# raise AttributeError
lat, lon = map1(float, latlon.lat, latlon.lon)
_xinstanceof(_LLEB, LatLonDatum5Tuple, latlon=latlon)
d = datum or latlon.datum
except AttributeError:
lat, lon = parseDMS2(latlon, lon)
d = datum or Datums.WGS84
return lat, lon, d, (name or nameof(latlon))
def _xyzn4(xyz, y, z, Error=TypeError): # imported by .ecef.py
'''(INTERNAL) Get an C{(x, y, z, name)} 4-tuple.
'''
try:
t = xyz.x, xyz.y, xyz.z
except AttributeError:
t = xyz, y, z
try:
x, y, z = map1(float, *t)
except (TypeError, ValueError) as x:
raise Error('%s invalid: %r, %s' % ('xyz, y or z', t, x))
return x, y, z, getattr(xyz, 'name', '')
def _xyzn4(xyz, y, z, Error=_TypeError): # imported by .ecef
'''(INTERNAL) Get an C{(x, y, z, name)} 4-tuple.
'''
try:
t = xyz.x, xyz.y, xyz.z
except AttributeError:
t = xyz, y, z
try:
x, y, z = map1(float, *t)
except (TypeError, ValueError) as x:
d = dict(zip(('xyz', _y_, _z_), t))
raise Error(txt=str(x), **d)
return x, y, z, getattr(xyz, _name_, NN)
def _llhn4(latlonh, lon, height, suffix):
'''(INTERNAL) Get C{lat, lon, h, name} as C{4-tuple}.
'''
try:
llh = latlonh.lat, latlonh.lon, getattr(latlonh, 'height',
getattr(latlonh, 'h', height))
except AttributeError:
llh = latlonh, lon, height
try:
lat, lon, h = map1(float, *llh)
except (TypeError, ValueError) as x:
t = 'lat_, lon_ or height_'.replace('_', suffix)
raise EcefError('%s invalid: %r, %s' % (t, llh, x))
if abs(lat) > 90:
raise EcefError('%s%s out of range: %.6g' % ('lat', suffix, lat))
return lat, lon, h, getattr(latlonh, 'name', '')
def date2epoch(year, month, day):
'''Return the reference frame C{epoch} for a calendar day.
@arg year: Year of the date (C{scalar}).
@arg month: Month in the B{C{year}} (C{scalar}, 1..12).
@arg day: Day in the B{C{month}} (C{scalar}, 1..31).
@return: Epoch, the fractional year (C{float}).
@raise TRFError: Invalid B{C{year}}, B{C{month}} or B{C{day}}.
@note: Any B{C{year}} is considered a leap year, i.e. having
29 days in February.
'''
try:
y, m, d = map1(int, year, month, day)
if y > 0 and 1 <= m <= 12 and 1 <= d <= _mDays[m]:
return y + float(sum(_mDays[:m]) + d) / 366.0
except (ValueError, TypeError):
pass
raise TRFError('%s invalid: %s-%s-%s' % ('date', year, month, day))
def date2epoch(year, month, day):
'''Return the reference frame C{epoch} for a calendar day.
@arg year: Year of the date (C{scalar}).
@arg month: Month in the B{C{year}} (C{scalar}, 1..12).
@arg day: Day in the B{C{month}} (C{scalar}, 1..31).
@return: Epoch, the fractional year (C{float}).
@raise TRFError: Invalid B{C{year}}, B{C{month}} or B{C{day}}.
@note: Any B{C{year}} is considered a leap year, i.e. having
29 days in February.
'''
try:
y, m, d = map1(int, year, month, day)
if y > 0 and 1 <= m <= 12 and 1 <= d <= _mDays[m]:
return Epoch(y + float(sum(_mDays[:m]) + d) / _366_0, low=0)
t = NN # _invalid_
except (TRFError, TypeError, ValueError) as x:
t = str(x)
raise TRFError(year=year, month=month, day=day, txt=t)
def toOsgr(latlon,
lon=None,
datum=Datums.WGS84,
Osgr=Osgr,
name=NN,
**Osgr_kwds):
'''Convert a lat-/longitude point to an OSGR coordinate.
@arg latlon: Latitude (C{degrees}) or an (ellipsoidal) geodetic
C{LatLon} point.
@kwarg lon: Optional longitude in degrees (scalar or C{None}).
@kwarg datum: Optional datum to convert B{C{lat, lon}} from
(L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or
L{a_f2Tuple}).
@kwarg Osgr: Optional class to return the OSGR coordinate
(L{Osgr}) or C{None}.
@kwarg name: Optional B{C{Osgr}} name (C{str}).
@kwarg Osgr_kwds: Optional, additional B{C{Osgr}} keyword
arguments, ignored if B{C{Osgr=None}}.
@return: The OSGR coordinate (B{C{Osgr}}) or an
L{EasNor2Tuple}C{(easting, northing)} if B{C{Osgr}}
is C{None}.
@raise OSGRError: Invalid B{C{latlon}} or B{C{lon}}.
@raise TypeError: Non-ellipsoidal B{C{latlon}} or invalid
B{C{datum}} or conversion failed.
@example:
>>> p = LatLon(52.65798, 1.71605)
>>> r = toOsgr(p) # TG 51409 13177
>>> # for conversion of (historical) OSGB36 lat-/longitude:
>>> r = toOsgr(52.65757, 1.71791, datum=Datums.OSGB36)
'''
if not isinstance(latlon, _LLEB):
# XXX fix failing _LLEB.convertDatum()
latlon = _LLEB(*parseDMS2(latlon, lon), datum=datum)
elif lon is not None:
raise OSGRError(lon=lon, txt='not %s' % (None, ))
elif not name: # use latlon.name
name = nameof(latlon)
# if necessary, convert to OSGB36 first
ll = _ll2datum(latlon, _Datums_OSGB36, _latlon_)
try:
a, b = ll.philam
except AttributeError:
a, b = map1(radians, ll.lat, ll.lon)
sa, ca = sincos2(a)
E = _Datums_OSGB36.ellipsoid
s = E.e2s2(sa) # r, v = E.roc2_(sa, _F0); r = v / r
v = E.a * _F0 / sqrt(s) # nu
r = s / E.e12 # nu / rho == v / (v * E.e12 / s) == s / E.e12
x2 = r - 1 # η2
ta = tan(a)
ca3, ca5 = fpowers(ca, 5, 3) # PYCHOK false!
ta2, ta4 = fpowers(ta, 4, 2) # PYCHOK false!
vsa = v * sa
I4 = (E.b * _F0 * _M(E.Mabcd, a) + _N0, (vsa / 2) * ca,
(vsa / 24) * ca3 * fsum_(5, -ta2, 9 * x2),
(vsa / 720) * ca5 * fsum_(61, ta4, -58 * ta2))
V4 = (_E0, (v * ca), (v / 6) * ca3 * (r - ta2), (v / 120) * ca5 * fdot(
(-18, 1, 14, -58), ta2, 5 + ta4, x2, ta2 * x2))
d, d2, d3, d4, d5, d6 = fpowers(b - _B0, 6) # PYCHOK false!
n = fdot(I4, 1, d2, d4, d6)
e = fdot(V4, 1, d, d3, d5)
if Osgr is None:
r = _EasNor2Tuple(e, n)
else:
r = Osgr(e, n, datum=_Datums_OSGB36, **Osgr_kwds)
if lon is None and isinstance(latlon, _LLEB):
r._latlon = latlon # XXX weakref(latlon)?
return _xnamed(r, name)
def intersection(start1,
end1,
start2,
end2,
height=None,
wrap=False,
LatLon=LatLon,
**LatLon_kwds):
'''Compute the intersection point of two paths both defined
by two points or a start point and bearing from North.
@arg start1: Start point of the first path (L{LatLon}).
@arg end1: End point ofthe first path (L{LatLon}) or
the initial bearing at the first start point
(compass C{degrees360}).
@arg start2: Start point of the second path (L{LatLon}).
@arg end2: End point of the second path (L{LatLon}) or
the initial bearing at the second start point
(compass C{degrees360}).
@kwarg height: Optional height for the intersection point,
overriding the mean height (C{meter}).
@kwarg wrap: Wrap and unroll longitudes (C{bool}).
@kwarg LatLon: Optional class to return the intersection
point (L{LatLon}) or C{None}.
@kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword
arguments, ignored if B{C{LatLon=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
or invalid B{C{height}}.
@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.philam
a2, b2 = start2.philam
db, b2 = unrollPI(b1, b2, wrap=wrap)
r12 = haversine_(a2, a1, db)
if abs(r12) < EPS: # [nearly] coincident points
a, b = 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) # PYCHOK PhiLam2Tuple
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.philam
# choose intersection similar to sphericalNvector
d1 = _xdot(d1, a1, b1, a, b, wrap)
if d1:
d2 = _xdot(d2, a2, b2, a, b, wrap)
if (d2 < 0 and d1 > 0) or (d2 > 0 and d1 < 0):
a, b = antipode_(a, b) # PYCHOK PhiLam2Tuple
h = fmean(hs) if height is None else Height(height)
return _latlon3(degrees90(a), degrees180(b), h, intersection, LatLon,
**LatLon_kwds)
def _trilaterate(point1,
distance1,
point2,
distance2,
point3,
distance3,
radius=R_M,
height=None,
useZ=False,
**LatLon_LatLon_kwds):
# (INTERNAL) Locate a point at given distances from
# three other points, see LatLon.triangulate above
def _nd2(p, d, r, _i_, *qs): # .toNvector and angular distance squared
for q in qs:
if p.isequalTo(q, EPS):
raise _ValueError(points=p, txt=_coincident_)
return p.toNvector(), (Scalar(d, name=_distance_ + _i_) / r)**2
r = Radius_(radius)
n1, r12 = _nd2(point1, distance1, r, _1_)
n2, r22 = _nd2(point2, distance2, r, _2_, point1)
n3, r32 = _nd2(point3, distance3, r, _3_, point1, point2)
# the following uses x,y coordinate system with origin at n1, x axis n1->n2
y = n3.minus(n1)
x = n2.minus(n1)
z = None
d = x.length # distance n1->n2
if d > EPS_2: # and y.length > EPS_2:
X = x.unit() # unit vector in x direction n1->n2
i = X.dot(y) # signed magnitude of x component of n1->n3
Y = y.minus(X.times(i)).unit() # unit vector in y direction
j = Y.dot(y) # signed magnitude of y component of n1->n3
if abs(j) > EPS_2:
# courtesy Carlos Freitas <https://GitHub.com/mrJean1/PyGeodesy/issues/33>
x = fsum_(r12, -r22, d**2) / (2 * d) # n1->intersection x- and ...
y = fsum_(r12, -r32, i**2, j**2, -2 * x * i) / (
2 * j) # ... y-component
# courtesy AleixDev <https://GitHub.com/mrJean1/PyGeodesy/issues/43>
z = fsum_(max(r12, r22, r32), -(x**2),
-(y**2)) # XXX not just r12!
if z > EPS:
n = n1.plus(X.times(x)).plus(Y.times(y))
if useZ: # include Z component
Z = X.cross(Y) # unit vector perpendicular to plane
n = n.plus(Z.times(sqrt(z)))
if height is None:
h = fidw((point1.height, point2.height, point3.height),
map1(fabs, distance1, distance2, distance3))
else:
h = Height(height)
kwds = _xkwds(LatLon_LatLon_kwds, height=h)
return n.toLatLon(**
kwds) # Nvector(n.x, n.y, n.z).toLatLon(...)
# no intersection, d < EPS_2 or abs(j) < EPS_2 or z < EPS
t = NN(_no_, _intersection_, _SPACE_)
raise IntersectionError(point1=point1,
distance1=distance1,
point2=point2,
distance2=distance2,
point3=point3,
distance3=distance3,
txt=unstr(t, z=z, useZ=useZ))
def _T(*fs):
'''(INTERNAL) Cache a tuple of single C{float}s.
'''
return map1(_F, *fs)
def utmupsValidate(coord, falsed=False, MGRS=False, Error=UTMUPSError):
'''Check a UTM or UPS coordinate.
@arg coord: The UTM or UPS coordinate (L{Utm}, L{Ups} or C{5+Tuple}).
@kwarg falsed: C{5+Tuple} easting and northing are falsed (C{bool}).
@kwarg MGRS: Increase easting and northing ranges (C{bool}).
@kwarg Error: Optional error to raise, overriding the default
(L{UTMUPSError}).
@return: C{None} if validation passed.
@raise Error: Validation failed.
@see: Function L{utmupsValidateOK}.
'''
def _en(en, lo, hi, ename): # U, Error
try:
if lo <= float(en) <= hi:
return
except (TypeError, ValueError):
pass
t = _SPACE_.join(
(_outside_, U, _range_, '[%.0F' % (lo, ), '%.0F]' % (hi, )))
raise Error(ename, en, txt=t)
if isinstance(coord, (Ups, Utm)):
hemi = coord.hemisphere
enMM = coord.falsed
elif isinstance(coord, (UtmUps5Tuple, UtmUps8Tuple)):
hemi = coord.hemipole
enMM = falsed
else:
raise _IsnotError(Error=Error,
coord=coord,
*map1(modulename, Utm, Ups, UtmUps5Tuple,
UtmUps8Tuple))
band = coord.band
zone = coord.zone
z, B, h = _to3zBhp(zone, band, hemipole=hemi)
if z == _UPS_ZONE: # UPS
import pygeodesy.ups as u # PYCHOK expected
U, M = _UPS_, _UpsMinMax
else: # UTM
import pygeodesy.utm as u # PYCHOK expected
U, M = _UTM_, _UtmMinMax
if MGRS:
U, s = _MGRS_, _MGRS_TILE
else:
s = 0
i = _NS_.find(h)
if i < 0 or z < _UTMUPS_ZONE_MIN \
or z > _UTMUPS_ZONE_MAX \
or B not in u._Bands:
t = '%s(%s%s %s)' % (U, z, B, h)
raise Error(coord=t, zone=zone, band=band, hemisphere=hemi)
if enMM:
_en(coord.easting, M.eMin[i] - s, M.eMax[i] + s,
_easting_) # PYCHOK .eMax .eMin
_en(coord.northing, M.nMin[i] - s, M.nMax[i] + s,
_northing_) # PYCHOK .nMax .nMin
