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 __init__(self, knots, datum=None, beta=2, wrap=False, name=''):
'''New L{HeightIDWhaversine} interpolator.
@param knots: The points with known height (C{LatLon}s).
@keyword datum: Optional datum (L{Datum} to use, overriding
the default C{B{knots}[0].datum}
@keyword beta: Inverse distance power (C{int} 1, 2, or 3).
@keyword wrap: Wrap and L{unroll180} longitudes (C{bool}).
@keyword name: Optional height interpolator name (C{str}).
@raise HeightError: Insufficient number of B{C{knots}} or
invalid B{C{knot}}, B{C{datum}} or
B{C{beta}}.
@raise ImportError: Package U{GeographicLib
<https://PyPI.org/project/geographiclib>} missing.
@raise TypeError: Invalid B{C{datum}}.
'''
n, self._lls = len2(knots)
if n < self._kmin:
raise HeightError('insufficient %s: %s, need %s' % ('knots', n, self._kmin))
try:
self._datum = self._lls[0].datum if datum is None else datum
if not isinstance(self.datum, Datum):
raise TypeError
except (AttributeError, TypeError):
raise TypeError('%s invalid: %r' % ('datum', self.datum or datum))
self._geodesic = self.datum.ellipsoid.geodesic
self.beta = beta
if wrap:
self._warp = True
if name:
self.name = name
def __init__(self, points, tolerance, radius, shortest,
indices, **options):
'''New C{Simplify} state.
'''
n, self.pts = len2(points)
if n > 0:
self.n = n
self.r = {0: True, n-1: True} # dict to avoid duplicates
if indices:
self.indices = True
if radius:
self.radius = float(radius)
if self.radius < self.eps:
raise ValueError('%s too small: %.6e' % ('radius', radius))
if options:
self.options = options
# tolerance converted to degrees squared
self.s2 = degrees(tolerance / self.radius)**2
if min(self.s2, tolerance) < self.eps:
raise ValueError('%s too small: %.6e' % ('tolerance', tolerance))
self.s2e = self.s2 + 1 # sentinel
# compute either the shortest or perpendicular distance
self.d2i = self.d2iS if shortest else self.d2iP # PYCHOK false
def sumOf(nvectors, Vector=None, h=None, **kwds):
'''Return the vectorial sum of two or more n-vectors.
@param nvectors: Vectors to be added (C{Nvector}[]).
@keyword Vector: Optional class for the vectorial sum
(C{Nvector}) or C{None}.
@keyword h: Optional height, overriding the mean height (C{meter}).
@keyword kwds: Optional, additional B{C{Vector}} keyword arguments,
ignored if C{B{Vector}=None}.
@return: Vectorial sum (B{C{Vector}}) or a L{Vector4Tuple}C{(x, y,
z, h)} if C{B{Vector}=None}.
@raise VectorError: No B{C{nvectors}}.
'''
n, nvectors = len2(nvectors)
if n < 1:
raise VectorError('no nvectors: %r' & (n, ))
if h is None:
h = fsum(v.h for v in nvectors) / float(n)
if Vector is None:
r = _sumOf(nvectors, Vector=Vector3Tuple)._4Tuple(h)
else:
r = _sumOf(nvectors, Vector=Vector, h=h, **kwds)
return r
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 clip(self, points, inull, closed): # MCCABE 19, clip points
np, self._points = len2(points)
if np > 0: # initial points, opened
p = self._points[0]
while np > 1 and _eq(self._points[np - 1], p):
np -= 1
if np < 3:
raise ValueError('too few %s: %s' % ('points', np))
no = ni = True # all out- or inside?
for e in self.clips():
# clip the points, closed
d2, p2 = self.dot2(np - 1)
for i in range(np):
d1, p1 = d2, p2
d2, p2 = self.dot2(i)
if d1 < 0: # p1 inside, ...
# self.append(p1, False, e)
if d2 < 0: # ... p2 inside
self.append(p2, inull)
else: # ... p2 outside
p = self.intersect(p1, p2, e)
self.append(p, inull)
if d2 > 0:
no = False
elif d2 < 0: # p1 out-, p2 inside
p = self.intersect(p1, p2, e)
self.append(p, inull)
self.append(p2, inull)
if d1 > 0:
no = ni = False
elif d1 > 0:
ni = False
if self._clipped: # replace points
self._points = self._clipped
self._clipped = []
np = len(self._points)
# no is True iff all points are on or at one
# side (left or right) of each clip edge,
# ni is True iff all points are on or on the
# right side (i.e. inside) of all clip edges
if no and not ni:
self._points = ()
np = 0
elif np > 1:
p = self._points[0]
if closed: # close clipped polygon
if _neq(self._points[np - 1], p):
self._points.append(p)
np += 1
elif not inull: # open clipped polygon
while np > 0 and _eq(self._points[np - 1], p):
np -= 1
return np
def __init__(self, corners):
n = ''
try:
n, cs = len2(corners)
if n == 2: # make a box
b, l, t, r = boundsOf(cs, wrap=False)
cs = LL_(b, l), LL_(t, l), LL_(t, r), LL_(b, r)
n, cs = points2(cs, closed=True)
self._corners = cs = cs[:n]
self._nc = n
self._cw = 1 if isclockwise(cs, adjust=False, wrap=False) else -1
if self._cw != isconvex_(cs, adjust=False, wrap=False):
raise ValueError
except ValueError:
raise ValueError('%s[%s] invalid: %r' % ('corners', n, corners))
self._clipped = self._points = []
def sumOf(vectors, Vector=Vector3d, **kwds):
'''Compute the vectorial sum of several vectors.
@param vectors: Vectors to be added (L{Vector3d}[]).
@keyword Vector: Optional class for the vectorial sum (L{Vector3d}).
@keyword kwds: Optional, additional B{C{Vector}} keyword arguments.
@return: Vectorial sum (B{C{Vector}}).
@raise VectorError: No B{C{vectors}}.
'''
n, vectors = len2(vectors)
if n < 1:
raise VectorError('no vectors: %r' & (n, ))
return Vector(fsum(v.x for v in vectors), fsum(v.y for v in vectors),
fsum(v.z for v in vectors), **kwds)
def sumOf(nvectors, Vector=Nvector, h=None, **kwds):
'''Return the vectorial sum of two or more n-vectors.
@param nvectors: Vectors to be added (L{Nvector}[]).
@keyword Vector: Optional class for the vectorial sum (L{Nvector}).
@keyword kwds: Optional, additional B{C{Vector}} keyword arguments.
@keyword h: Optional height, overriding the mean height (C{meter}).
@return: Vectorial sum (B{C{Vector}}).
@raise VectorError: No B{C{nvectors}}.
'''
n, nvectors = len2(nvectors)
if n < 1:
raise VectorError('no nvectors: %r' & (n, ))
if h is None:
h = fsum(v.h for v in nvectors) / float(n)
return _sumOf(nvectors, Vector=Vector, h=h, **kwds)
def _allis2(llis, m=1, Error=HeightError): # imported by .geoids
# dtermine return type and convert lli C{LatLon}s to list
if not isinstance(llis, tuple): # llis are *args
raise AssertionError('type(%s): %r' % ('*llis', llis))
n = len(llis)
if n == 1: # convert single lli to 1-item list
llis = llis[0]
try:
n, llis = len2(llis)
_as = _alist # return list of interpolated heights
except TypeError: # single lli
n, llis = 1, [llis]
_as = _ascalar # return single interpolated heights
else: # of 0, 2 or more llis
_as = _atuple # return tuple of interpolated heights
if n < m:
raise Error('insufficient %s: %s, need %s' % ('llis', n, m))
return _as, llis
def sumOf(vectors, Vector=Vector3d, **kwds):
'''Compute the vectorial sum of several vectors.
@param vectors: Vectors to be added (L{Vector3d}[]).
@keyword Vector: Optional class for the vectorial sum (L{Vector3d}).
@keyword kwds: Optional, additional B{C{Vector}} keyword arguments,
ignored if C{B{Vector}=None}.
@return: Vectorial sum (B{C{Vector}}).
@raise VectorError: No B{C{vectors}}.
'''
n, vectors = len2(vectors)
if n < 1:
raise VectorError('no vectors: %r' & (n, ))
r = Vector3Tuple(fsum(v.x for v in vectors), fsum(v.y for v in vectors),
fsum(v.z for v in vectors))
if Vector is not None:
r = Vector(r.x, r.y, r.z, **kwds) # PYCHOK x, y, z
return r
def __init__(self, AB, x, y):
'''(INTERNAL) New Alpha or Beta Krüger series
@param AB: Krüger Alpha or Beta series coefficients
(C{4-, 6- or 8-tuple}).
@param x: Eta angle (C{radians}).
@param y: Ksi angle (C{radians}).
'''
n, j2 = len2(range(2, len(AB) * 2 + 1, 2))
self._ab = AB
self._pq = map2(mul, j2, self._ab)
# assert len(self._ab) == len(self._pq) == n
x2 = map2(mul, j2, (x, ) * n)
self._chx = map2(cosh, x2)
self._shx = map2(sinh, x2)
# assert len(x2) == len(self._chx) == len(self._shx) == n
y2 = map2(mul, j2, (y, ) * n)
self._cy = map2(cos, y2)
self._sy = map2(sin, y2)
def points2(points, closed=True, base=None, Error=ValueError):
'''Check a polygon represented by points.
@param points: The polygon points (C{LatLon}[])
@keyword closed: Optionally, consider the polygon closed,
ignoring any duplicate or closing final
B{C{points}} (C{bool}).
@keyword base: Optionally, check the B{C{points}} against this
base class C{None}.
@keyword Error: Exception for raise (C{ValueError}).
@return: 2-Tuple (n, points) with the number (C{int}) of points
and the points C{list} or C{tuple}.
@raise TypeError: Some B{C{points}} are not C{LatLon}.
@raise Error: Insufficient number of B{C{points}}.
'''
n, points = len2(points)
if closed:
# remove duplicate or closing final points
while n > 1 and (points[n - 1] == points[0]
or points[n - 1] == points[n - 2]):
n -= 1
# XXX following line is unneeded if points
# are always indexed as ... i in range(n)
points = points[:n] # XXX numpy.array slice is a view!
if n < (3 if closed else 1):
raise Error('too few %s: %s' % ('points', n))
if base and not (isNumpy2(points) or isTuple2(points)):
for i in range(n):
base.others(points[i], name='%s[%s]' % ('points', i))
return n, points
