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# -*- coding: utf-8 -*- 

 

u'''Functions to handle collections and sequences of C{LatLon} points 

specified as 2-d U{NumPy<https://www.NumPy.org>}, C{arrays} or tuples as 

C{LatLon} or as C{pseudo-x/-y} pairs. 

 

C{NumPy} arrays are assumed to contain rows of points with a lat-, a 

longitude -and possibly other- values in different columns. While 

iterating over the array rows, create an instance of a given C{LatLon} 

class "on-the-fly" for each row with the row's lat- and longitude. 

 

The original C{NumPy} array is read-accessed only and never duplicated, 

except to create a I{subset} of the original array. 

 

For example, to process a C{NumPy} array, wrap the array by instantiating 

class L{Numpy2LatLon} and specifying the column index for the lat- and 

longitude in each row. Then, pass the L{Numpy2LatLon} instance to any 

L{pygeodesy} function or method accepting a I{points} argument. 

 

Similarly, class L{Tuple2LatLon} is used to instantiate a C{LatLon} 

for each 2+tuple in a list, tuple or sequence of such 2+tuples from 

the index for the lat- and longitude index in each 2+tuple. 

 

@newfield example: Example, Examples 

''' 

 

from pygeodesy.dms import F_D, latDMS, lonDMS 

from pygeodesy.fmath import EPS, favg, fdot, Fsum, fsum, isint, \ 

_IsNotError, map1, scalar 

from pygeodesy.formy import equirectangular_, points2 

from pygeodesy.lazily import _ALL_LAZY 

from pygeodesy.named import Bounds2Tuple, Bounds4Tuple, classname, inStr, \ 

LatLon2Tuple, NearestOn3Tuple, NearestOn5Tuple, \ 

PhiLam2Tuple, Point3Tuple, Shape2Tuple, \ 

nameof, _xnamed 

from pygeodesy.utily import PI_2, R_M, degrees90, degrees180, degrees360, \ 

degrees2m, issequence, property_RO, \ 

unroll180, unrollPI, wrap90, wrap180, _TypeError 

from pygeodesy.vector3d import CrossError, crosserrors 

 

try: 

from collections import Sequence as _Sequence # immutable 

except ImportError: 

_Sequence = object # XXX or tuple 

from inspect import isclass 

from math import atan2, cos, fmod, hypot, radians, sin 

 

__all__ = _ALL_LAZY.points 

__version__ = '19.12.16' 

 

 

class LatLon_(object): # XXX imported by heights._HeightBase.height 

'''Low-overhead C{LatLon} class for L{Numpy2LatLon} and L{Tuple2LatLon}. 

''' 

# __slots__ efficiency is voided if the __slots__ class attribute 

# is used in a subclass of a class with the traditional __dict__, 

# see <https://docs.Python.org/2/reference/datamodel.html#slots> 

# and __slots__ must be repeated in sub-classes, see "Problems 

# with __slots__" in Luciano Ramalho, "Fluent Python", page 

# 276+, O'Reilly, 2016, also at <https://Books.Google.ie/ 

# books?id=bIZHCgAAQBAJ&lpg=PP1&dq=fluent%20python&pg= 

# PT364#v=onepage&q=“Problems%20with%20__slots__”&f=false> 

__slots__ = ('lat', 'lon', 'name', 'height') 

 

def __init__(self, lat, lon, name='', height=0): 

'''Creat a new, mininal, low-overhead L{LatLon_} instance, 

without heigth and datum. 

 

@param lat: Latitude (C{degrees}). 

@param lon: Longitude (C{degrees}). 

@keyword name: Optional name (C{str}). 

 

@note: The lat- and longitude are taken as-given, 

un-clipped and un-validated. 

''' 

self.lat = float(lat) 

self.lon = float(lon) 

self.name = str(name) 

self.height = height 

 

def __eq__(self, other): 

return isinstance(other, LatLon_) and \ 

other.lat == self.lat and \ 

other.lon == self.lon 

 

def __ne__(self, other): 

return not self.__eq__(other) 

 

def __repr__(self): 

return self.toStr2() 

 

def __str__(self): 

return self.toStr() 

 

def classof(self, *args, **kwds): 

'''Instantiate this very class. 

 

@param args: Optional, positional arguments. 

@keyword kwds: Optional, keyword arguments. 

 

@return: New instance (C{self.__class__}). 

''' 

if 'name' in kwds: 

return self.__class__(*args, **kwds) 

else: 

return self.__class__(name=self.name, *args, **kwds) 

 

def others(self, other, name='other'): 

'''Check this and an other instance for type compatiblility. 

 

@param other: The other instance (any C{type}). 

@keyword name: Optional, name for other (C{str}). 

 

@return: C{None}. 

 

@raise TypeError: Incompatible B{C{other}} C{type}. 

''' 

if not (isinstance(other, self.__class__) or 

(hasattr(other, 'lat') and hasattr(other, 'lon'))): 

raise TypeError('type(%s) mismatch: %s vs %s' % (name, 

classname(other), classname(self))) 

 

def points(self, points, closed=False, base=None): 

'''DEPRECATED, use method C{points2}. 

''' 

return points2(points, closed=closed, base=base) 

 

def points2(self, points, closed=False, base=None): 

return points2(points, closed=closed, base=base) 

 

points.__doc__ = points2.__doc__ 

 

def to2ab(self): 

'''Return the lat- and longitude in C{radians}. 

 

@return: A L{PhiLam2Tuple}C{(phi, lam)}. 

''' 

return PhiLam2Tuple(radians(self.lat), radians(self.lon)) 

 

def toStr(self, form=F_D, prec=6, sep=', ', **kwds): 

'''This L{LatLon_} as a string "<degrees>, <degrees>". 

 

@keyword form: Optional format, F_D, F_DM, F_DMS for 

deg°, deg°min′, deg°min′sec″ (C{str}). 

@keyword prec: Optional number of decimal digits (0..8 or C{None}). 

@keyword sep: Optional separator to join (C{str}). 

@keyword kwds: Optional, keyword arguments. 

 

@return: Instance (C{str}). 

''' 

t = [latDMS(self.lat, form=form, prec=prec), 

lonDMS(self.lon, form=form, prec=prec)] 

if self.height: 

t += ['%+.2f' % (self.height,)] 

if self.name: 

t += [repr(self.name)] 

if kwds: 

t += ['%s=%s' % _ for _ in sorted(kwds.items())] 

return sep.join(t) 

 

def toStr2(self, **kwds): 

'''This L{LatLon_} as a string "class(<degrees>, ...)". 

 

@keyword kwds: Optional, keyword arguments. 

 

@return: Class instance (C{str}). 

''' 

return '%s(%s)' % (classname(self), self.toStr(**kwds)) 

 

 

class _Basequence(_Sequence): # immutable, on purpose 

'''(INTERNAL) Base class. 

''' 

_array = [] 

_epsilon = EPS 

_itemname = 'point' 

 

def _contains(self, point): 

'''(INTERNAL) Check for a matching point. 

''' 

for _ in self._findall(point, ()): 

return True 

return False 

 

def _count(self, point): 

'''(INTERNAL) Count the number of matching points. 

''' 

n = 0 

for _ in self._findall(point, ()): 

n += 1 

return n 

 

def _find(self, point, start_end): 

'''(INTERNAL) Find the first matching point index. 

''' 

for i in self._findall(point, start_end): 

return i 

return -1 

 

def _findall(self, unused, start_end): # PYCHOK unused 

'''Must be overloaded. 

''' 

raise NotImplementedError('method: %s' % ('_findall',)) 

 

def _getitem(self, index): 

'''(INTERNAL) Return point [index] or return a slice. 

''' 

# Luciano Ramalho, "Fluent Python", page 290+, O'Reilly, 2016 

if isinstance(index, slice): 

# XXX an numpy.array slice is a view, not a copy 

return self.__class__(self._array[index], **self._slicekwds()) 

else: 

return self.point(self._array[index]) 

 

def _index(self, point, start_end): 

'''(INTERNAL) Find the first matching point index. 

''' 

for i in self._findall(point, start_end): 

return i 

raise ValueError('%s not found: %r' % (self._itemname, point)) 

 

def _iter(self): 

'''(INTERNAL) Yield all points. 

''' 

for i in range(len(self)): 

yield self.point(self._array[i]) 

 

def point(self, unused): # PYCHOK unused 

'''Must be overloaded. 

''' 

raise NotImplementedError('method: %s' % ('point',)) 

 

def _range(self, start=None, end=None, step=1): 

'''(INTERNAL) Return the range. 

''' 

if step > 0: 

if start is None: 

start = 0 

if end is None: 

end = len(self) 

elif step < 0: 

if start is None: 

start = len(self) - 1 

if end is None: 

end = -1 

else: 

raise ValueError('%s invalid: %r' % ('step', step)) 

return range(start, end, step) 

 

def _repr(self): 

'''(INTERNAL) Return a string representation. 

''' 

# XXX use Python 3+ reprlib.repr 

t = repr(self._array[:1]) # only first row 

t = '%s ...%s[%s]' % (t[:-1], t[-1:], len(self)) 

t = ' '.join(t.split()) # coalesce spaces 

return inStr(self, t, **self._slicekwds()) 

 

def _reversed(self): # PYCHOK false 

'''(INTERNAL) Yield all points in reverse order. 

''' 

for i in range(len(self) - 1, -1): 

yield self.point(self._array[i]) 

 

def _rfind(self, point, start_end): 

'''(INTERNAL) Find the last matching point index. 

''' 

def _r3(start=None, end=None, step=-1): 

return (start, end, step) # PYCHOK returns 

 

for i in self._findall(point, _r3(*start_end)): 

return i 

return -1 

 

def _slicekwds(self): 

'''(INTERNAL) Should be overloaded. 

''' 

return {} 

 

def _zeros(self, *zeros): 

'''(INTERNAL) Check for near-zero values. 

''' 

return all(abs(z) <= self._epsilon for z in zeros) 

 

@property 

def epsilon(self): 

'''Get the tolerance for equality tests (C{float}). 

''' 

return self._epsilon 

 

@epsilon.setter # PYCHOK setter! 

def epsilon(self, tol): 

'''Set the tolerance for equality tests. 

 

@param tol: New tolerance (C{scalar}). 

 

@raise TypeError: Non-scalar B{C{tol}}. 

 

@raise ValueError: Out-of-bounds B{C{tol}}. 

''' 

self._epsilon = scalar(tol, 0.0, name='tolerance') 

 

@property_RO 

def isNumpy2(self): 

'''Is this a Numpy2 wrapper? 

''' 

return False # isinstance(self, (Numpy2LatLon, ...)) 

 

@property_RO 

def isPoints2(self): 

'''Is this a LatLon2 wrapper/converter? 

''' 

return False # isinstance(self, (LatLon2psxy, ...)) 

 

@property_RO 

def isTuple2(self): 

'''Is this a Tuple2 wrapper? 

''' 

return False # isinstance(self, (Tuple2LatLon, ...)) 

 

 

class _Array2LatLon(_Basequence): # immutable, on purpose 

'''Base class for Numpy2LatLon or Tuple2LatLon. 

''' 

_array = () 

_ilat = 0 # row column index 

_ilon = 0 # row column index 

_LatLon = LatLon_ # default 

_shape = () 

 

def __init__(self, array, ilat=0, ilon=1, LatLon=None, shape=()): 

'''Handle a C{NumPy} or C{Tuple} array as a sequence of C{LatLon} points. 

''' 

ais = ('ilat', ilat), ('ilon', ilon) 

 

if len(shape) != 2 or shape[0] < 1 or shape[1] < len(ais): 

raise IndexError('%s invalid: %r' % ('array shape', shape)) 

 

self._array = array 

self._shape = Shape2Tuple(*shape) 

 

# check the point class 

if LatLon is not None: 

if isclass(LatLon) and all(hasattr(LatLon, a) for a in LatLon_.__slots__): 

self._LatLon = LatLon 

else: 

raise _IsNotError('valid', LatLon=LatLon) 

 

# check the attr indices 

for n, (ai, i) in enumerate(ais): 

if not isint(i): 

raise _IsNotError(int.__name__, **{ai: i}) 

i = int(i) 

if not 0 <= i < shape[1]: 

raise _IsNotError('valid', Error=ValueError, **{ai: i}) 

for aj, j in ais[:n]: 

if int(j) == i: 

raise ValueError('%s == %s == %s' % (ai, aj, i)) 

setattr(self, '_' + ai, i) 

 

def __contains__(self, latlon): 

'''Check for a specific lat-/longitude. 

 

@param latlon: Point (C{LatLon}, L{LatLon2Tuple} or 2-tuple 

C{(lat, lon)}). 

 

@return: C{True} if B{C{latlon}} is present, C{False} otherwise. 

 

@raise TypeError: Invalid B{C{latlon}}. 

''' 

return self._contains(latlon) 

 

def __getitem__(self, index): 

'''Return row[index] as C{LatLon} or return a L{Numpy2LatLon} slice. 

''' 

return self._getitem(index) 

 

def __iter__(self): 

'''Yield rows as C{LatLon}. 

''' 

return self._iter() 

 

def __len__(self): 

'''Return the number of rows. 

''' 

return self._shape[0] 

 

def __repr__(self): 

'''Return a string representation. 

''' 

return self._repr() 

 

def __reversed__(self): # PYCHOK false 

'''Yield rows as C{LatLon} in reverse order. 

''' 

return self._reversed() 

 

__str__ = __repr__ 

 

def count(self, latlon): 

'''Count the number of rows with a specific lat-/longitude. 

 

@param latlon: Point (C{LatLon}, L{LatLon2Tuple} or 2-tuple 

C{(lat, lon)}). 

 

@return: Count (C{int}). 

 

@raise TypeError: Invalid B{C{latlon}}. 

''' 

return self._count(latlon) 

 

def find(self, latlon, *start_end): 

'''Find the first row with a specific lat-/longitude. 

 

@param latlon: Point (C{LatLon}) or 2-tuple (lat, lon). 

@param start_end: Optional C{[start[, end]]} index (integers). 

 

@return: Index or -1 if not found (C{int}). 

 

@raise TypeError: Invalid B{C{latlon}}. 

''' 

return self._find(latlon, start_end) 

 

def _findall(self, latlon, start_end): 

'''(INTERNAL) Yield indices of all matching rows. 

''' 

try: 

lat, lon = latlon.lat, latlon.lon 

except AttributeError: 

try: 

lat, lon = latlon 

except (TypeError, ValueError): 

raise _IsNotError('valid', latlon=latlon) 

 

for i in self._range(*start_end): 

row = self._array[i] 

if self._zeros(row[self._ilat] - lat, 

row[self._ilon] - lon): 

yield i 

 

def findall(self, latlon, *start_end): 

'''Yield indices of all rows with a specific lat-/longitude. 

 

@param latlon: Point (C{LatLon}, L{LatLon2Tuple} or 2-tuple 

C{(lat, lon)}). 

@param start_end: Optional C{[start[, end]]} index (C{int}). 

 

@return: Indices (C{iterable}). 

 

@raise TypeError: Invalid B{C{latlon}}. 

''' 

return self._findall(latlon, start_end) 

 

def index(self, latlon, *start_end): # PYCHOK Python 2- issue 

'''Find index of the first row with a specific lat-/longitude. 

 

@param latlon: Point (C{LatLon}, L{LatLon2Tuple} or 2-tuple 

C{(lat, lon)}). 

@param start_end: Optional C{[start[, end]]} index (C{int}). 

 

@return: Index (C{int}). 

 

@raise TypeError: Invalid B{C{latlon}}. 

 

@raise ValueError: Point not found. 

''' 

return self._index(latlon, start_end) 

 

@property_RO 

def ilat(self): 

'''Get the latitudes column index (C{int}). 

''' 

return self._ilat 

 

@property_RO 

def ilon(self): 

'''Get the longitudes column index (C{int}). 

''' 

return self._ilon 

 

# next = __iter__ 

 

def point(self, row): 

'''Instantiate a point C{LatLon}. 

 

@param row: Array row (numpy.array). 

 

@return: Point (C{LatLon}). 

''' 

return self._LatLon(row[self._ilat], row[self._ilon]) 

 

def rfind(self, latlon, *start_end): 

'''Find the last row with a specific lat-/longitude. 

 

@param latlon: Point (C{LatLon}, L{LatLon2Tuple} or 2-tuple 

C{(lat, lon)}). 

@param start_end: Optional C{[start[, end]]} index (C{int}). 

 

@note: Keyword order, first stop, then start. 

 

@return: Index or -1 if not found (C{int}). 

 

@raise TypeError: Invalid B{C{latlon}}. 

''' 

return self._rfind(latlon, start_end) 

 

def _slicekwds(self): 

'''(INTERNAL) Slice kwds. 

''' 

return dict(ilat=self._ilat, ilon=self._ilon) 

 

@property_RO 

def shape(self): 

'''Get the shape of the C{NumPy} array or the C{Tuples} as 

L{Shape2Tuple}C{(nrows, ncols)}. 

''' 

return self._shape 

 

def _subset(self, indices): # PYCHOK unused 

'''Must be overloaded. 

''' 

raise NotImplementedError('method: %s' % ('_subset',)) 

 

def subset(self, indices): 

'''Return a subset of the C{NumPy} array. 

 

@param indices: Row indices (C{range} or C{int}[]). 

 

@note: A C{subset} is different from a C{slice} in 2 ways: 

(a) the C{subset} is typically specified as a list of 

(un-)ordered indices and (b) the C{subset} allocates 

a new, separate C{NumPy} array while a C{slice} is 

just an other C{view} of the original C{NumPy} array. 

 

@return: Sub-array (C{numpy.array}). 

 

@raise IndexError: Out-of-range B{C{indices}} value. 

 

@raise TypeError: If B{C{indices}} is not a C{range} 

nor an C{int}[]. 

''' 

if not issequence(indices, tuple): # NO tuple, only list 

# and range work properly to get Numpy array sub-sets 

raise _IsNotError('valid', indices=type(indices)) 

 

n = len(self) 

for i, v in enumerate(indices): 

if not isint(v): 

raise TypeError('%s[%s] not valid: %r' % ('indices', i, v)) 

elif not 0 <= v < n: 

raise IndexError('%s[%s] not valid: %r' % ('indices', i, v)) 

 

return self._subset(indices) 

 

 

class LatLon2psxy(_Basequence): 

'''Wrapper for C{LatLon} points as "on-the-fly" pseudo-xy coordinates. 

''' 

_closed = False 

_len = 0 

_deg2m = None # default, keep degrees 

_radius = None 

_wrap = True 

 

def __init__(self, latlons, closed=False, radius=None, wrap=True): 

'''Handle C{LatLon} points as pseudo-xy coordinates. 

 

@note: The C{LatLon} latitude is considered the I{pseudo-y} 

and longitude the I{pseudo-x} coordinate, likewise 

for L{LatLon2Tuple}. However, 2-tuples C{(x, y)} are 

considered as I{(longitude, latitude)}. 

 

@param latlons: Points C{list}, C{sequence}, C{set}, C{tuple}, 

etc. (C{LatLon[]}). 

@keyword closed: Optionally, close the polygon (C{bool}). 

@keyword radius: Optional, mean earth radius (C{meter}). 

@keyword wrap: Wrap lat- and longitudes (C{bool}). 

 

@raise TypeError: Some B{C{latlons}} are not C{LatLon}. 

 

@raise ValueError: Insufficient number of B{C{latlons}}. 

''' 

self._closed = closed 

self._len, self._array = points2(latlons, closed=closed) 

if radius: 

self._radius = radius 

self._deg2m = degrees2m(1.0, radius) 

self._wrap = wrap 

 

def __contains__(self, xy): 

'''Check for a matching point. 

 

@param xy: Point (C{LatLon}, L{LatLon2Tuple} or 2-tuple 

C{(x, y)}) in (C{degrees}. 

 

@return: C{True} if B{C{xy}} is present, C{False} otherwise. 

 

@raise TypeError: Invalid B{C{xy}}. 

''' 

return self._contains(xy) 

 

def __getitem__(self, index): 

'''Return the pseudo-xy or return a L{LatLon2psxy} slice. 

''' 

return self._getitem(index) 

 

def __iter__(self): 

'''Yield all pseudo-xy's. 

''' 

return self._iter() 

 

def __len__(self): 

'''Return the number of pseudo-xy's. 

''' 

return self._len 

 

def __repr__(self): 

'''Return a string representation. 

''' 

return self._repr() 

 

def __reversed__(self): # PYCHOK false 

'''Yield all pseudo-xy's in reverse order. 

''' 

return self._reversed() 

 

__str__ = __repr__ 

 

def count(self, xy): 

'''Count the number of matching points. 

 

@param xy: Point (C{LatLon}, L{LatLon2Tuple} or 2-tuple 

C{(x, y)}) in (C{degrees}. 

 

@return: Count (C{int}). 

 

@raise TypeError: Invalid B{C{xy}}. 

''' 

return self._count(xy) 

 

def find(self, xy, *start_end): 

'''Find the first matching point. 

 

@param xy: Point (C{LatLon}, L{LatLon2Tuple} or 2-tuple 

C{(x, y)}) in (C{degrees}. 

@param start_end: Optional C{[start[, end]]} index (C{int}). 

 

@return: Index or -1 if not found (C{int}). 

 

@raise TypeError: Invalid B{C{xy}}. 

''' 

return self._find(xy, start_end) 

 

def _findall(self, xy, start_end): 

'''(INTERNAL) Yield indices of all matching points. 

''' 

try: 

x, y = xy.lon, xy.lat 

 

def _3xyll(ll): # match LatLon 

return ll.lon, ll.lat, ll 

 

except AttributeError: 

try: 

x, y = xy 

except (TypeError, ValueError): 

raise _IsNotError('valid', xy=xy) 

 

def _3xyll(ll): # PYCHOK expected 

return self.point(ll) 

 

for i in self._range(*start_end): 

xi, yi, _ = _3xyll(self._array[i]) 

if self._zeros(xi - x, yi - y): 

yield i 

 

def findall(self, xy, *start_end): 

'''Yield indices of all matching points. 

 

@param xy: Point (C{LatLon}, L{LatLon2Tuple} or 2-tuple 

C{(x, y)}) in (C{degrees}. 

@param start_end: Optional C{[start[, end]]} index (C{int}). 

 

@return: Indices (C{iterator}). 

 

@raise TypeError: Invalid B{C{xy}}. 

''' 

return self._findall(xy, start_end) 

 

def index(self, xy, *start_end): # PYCHOK Python 2- issue 

'''Find the first matching point. 

 

@param xy: Point (C{LatLon}) or 2-tuple (x, y) in (C{degrees}). 

@param start_end: Optional C{[start[, end]]} index (C{int}). 

 

@return: Index (C{int}). 

 

@raise TypeError: Invalid B{C{xy}}. 

 

@raise ValueError: Point not found. 

''' 

return self._index(xy, start_end) 

 

@property_RO 

def isPoints2(self): 

'''Is this a LatLon2 wrapper/converter? 

''' 

return True # isinstance(self, (LatLon2psxy, ...)) 

 

# next = __iter__ 

 

def point(self, ll): 

'''Create a pseudo-xy. 

 

@param ll: Point (C{LatLon}). 

 

@return: An L{Point3Tuple}C{(x, y, ll)}. 

''' 

x, y = ll.lon, ll.lat # note, x, y = lon, lat 

if self._wrap: 

x, y = wrap180(x), wrap90(y) 

if self._deg2m: # convert degrees to meter (or radians) 

x *= self._deg2m 

y *= self._deg2m 

return Point3Tuple(x, y, ll) 

 

def rfind(self, xy, *start_end): 

'''Find the last matching point. 

 

@param xy: Point (C{LatLon}, L{LatLon2Tuple} or 2-tuple 

C{(x, y)}) in (C{degrees}. 

@param start_end: Optional C{[start[, end]]} index (C{int}). 

 

@return: Index or -1 if not found (C{int}). 

 

@raise TypeError: Invalid B{C{xy}}. 

''' 

return self._rfind(xy, start_end) 

 

def _slicekwds(self): 

'''(INTERNAL) Slice kwds. 

''' 

return dict(closed=self._closed, radius=self._radius, wrap=self._wrap) 

 

 

class Numpy2LatLon(_Array2LatLon): # immutable, on purpose 

'''Wrapper for C{NumPy} arrays as "on-the-fly" C{LatLon} points. 

''' 

def __init__(self, array, ilat=0, ilon=1, LatLon=None): 

'''Handle a C{NumPy} array as a sequence of C{LatLon} points. 

 

@param array: C{NumPy} array (C{numpy.array}). 

@keyword ilat: Optional index of the latitudes column (C{int}). 

@keyword ilon: Optional index of the longitudes column (C{int}). 

@keyword LatLon: Optional C{LatLon} (sub-)class to use (L{LatLon_}). 

 

@raise IndexError: If B{C{array.shape}} is not (1+, 2+). 

 

@raise TypeError: If B{C{array}} is not a C{NumPy} array or 

C{LatLon} is not a class with C{lat} 

and C{lon} attributes. 

 

@raise ValueError: If the B{C{ilat}} and/or B{C{ilon}} values 

are the same or out of range. 

 

@example: 

 

>>> type(array) 

<type 'numpy.ndarray'> # <class ...> in Python 3+ 

>>> points = Numpy2LatLon(array, lat=0, lon=1) 

>>> simply = simplifyRDP(points, ...) 

>>> type(simply) 

<type 'numpy.ndarray'> # <class ...> in Python 3+ 

>>> sliced = points[1:-1] 

>>> type(sliced) 

<class '...Numpy2LatLon'> 

''' 

try: # get shape and check some other numpy.array attrs 

s, _, _ = array.shape, array.nbytes, array.ndim # PYCHOK expected 

except AttributeError: 

raise _IsNotError('NumPy', array=type(array)) 

 

_Array2LatLon.__init__(self, array, ilat=ilat, ilon=ilon, 

LatLon=LatLon, shape=s) 

 

@property_RO 

def isNumpy2(self): 

'''Is this a Numpy2 wrapper? 

''' 

return True # isinstance(self, (Numpy2LatLon, ...)) 

 

def _subset(self, indices): 

return self._array[indices] # NumPy special 

 

 

class Tuple2LatLon(_Array2LatLon): 

'''Wrapper for tuple sequences as "on-the-fly" C{LatLon} points. 

''' 

def __init__(self, tuples, ilat=0, ilon=1, LatLon=None): 

'''Handle a list of tuples, each containing a lat- and longitude 

and perhaps other values as a sequence of C{LatLon} points. 

 

@param tuples: The C{list}, C{tuple} or C{sequence} of tuples (C{tuple}[]). 

@keyword ilat: Optional index of the latitudes value (C{int}). 

@keyword ilon: Optional index of the longitudes value (C{int}). 

@keyword LatLon: Optional C{LatLon} (sub-)class to use (L{LatLon_}). 

 

@raise IndexError: If I{(len(B{C{tuples}}), min(len(t) for t 

in B{C{tuples}}))} is not (1+, 2+). 

 

@raise TypeError: If B{C{tuples}} is not a C{list}, C{tuple} 

or C{sequence} or if B{C{LatLon}} is not a 

C{LatLon} with C{lat}, C{lon} and C{name} 

attributes. 

 

@raise ValueError: If the B{C{ilat}} and/or B{C{ilon}} values 

are the same or out of range. 

 

@example: 

 

>>> tuples = [(0, 1), (2, 3), (4, 5)] 

>>> type(tuples) 

<type 'list'> # <class ...> in Python 3+ 

>>> points = Tuple2LatLon(tuples, lat=0, lon=1) 

>>> simply = simplifyRW(points, 0.5, ...) 

>>> type(simply) 

<type 'list'> # <class ...> in Python 3+ 

>>> simply 

[(0, 1), (4, 5)] 

>>> sliced = points[1:-1] 

>>> type(sliced) 

<class '...Tuple2LatLon'> 

>>> sliced 

...Tuple2LatLon([(2, 3), ...][1], ilat=0, ilon=1) 

 

>>> closest, _ = nearestOn2(LatLon_(2, 1), points, adjust=False) 

>>> closest 

LatLon_(lat=1.0, lon=2.0) 

 

>>> closest, _ = nearestOn2(LatLon_(3, 2), points) 

>>> closest 

LatLon_(lat=2.001162, lon=3.001162) 

''' 

_TypeError(list, tuple, tuples=tuples) 

s = len(tuples), min(len(_) for _ in tuples) 

_Array2LatLon.__init__(self, tuples, ilat=ilat, ilon=ilon, 

LatLon=LatLon, shape=s) 

 

@property_RO 

def isTuple2(self): 

'''Is this a Tuple2 wrapper? 

''' 

return True # isinstance(self, (Tuple2LatLon, ...)) 

 

def _subset(self, indices): 

return type(self._array)(self._array[i] for i in indices) 

 

 

def _area2(points, adjust, wrap): 

# return the signed area in radians squared 

 

# setting radius=1 converts degrees to radians 

pts = LatLon2psxy(points, closed=True, radius=1, wrap=wrap) 

 

def _rads2(n, pts): # trapezoidal areas in rads**2 

x1, y1, _ = pts[n-1] 

for i in range(n): 

x2, y2, _ = pts[i] 

w, x2 = unrollPI(x1, x2, wrap=wrap if i < (n - 1) else False) 

# approximate trapezoid by a rectangle, adjusting 

# the top width by the cosine of the latitudinal 

# average and bottom width by some fudge factor 

h = (y2 + y1) * 0.5 

if adjust: 

c = cos(h) if abs(h) < PI_2 else 0 

w *= (c + 1.2876) * 0.5 

yield h * w # signed trapezoidal area 

 

x1, y1 = x2, y2 

 

return fsum(_rads2(len(pts), pts)), pts 

 

 

def areaOf(points, adjust=True, radius=R_M, wrap=True): 

'''Approximate the area of a polygon. 

 

@param points: The polygon points (C{LatLon}[]). 

@keyword adjust: Adjust the wrapped, unrolled longitudinal delta 

by the cosine of the mean latitude (C{bool}). 

@keyword radius: Optional, mean earth radius (C{meter}). 

@keyword wrap: Wrap lat-, wrap and unroll longitudes (C{bool}). 

 

@return: Approximate area (C{meter}, same units as B{C{radius}}, 

I{squared}). 

 

@raise TypeError: Some B{C{points}} are not C{LatLon}. 

 

@raise ValueError: Insufficient number of B{C{points}}. 

 

@note: This area approximation has limited accuracy and is 

ill-suited for regions exceeding several hundred Km 

or Miles or with near-polar latitudes. 

 

@see: L{sphericalNvector.areaOf}, L{sphericalTrigonometry.areaOf} 

and L{ellipsoidalKarney.areaOf}. 

''' 

a, _ = _area2(points, adjust, wrap) 

return abs(a) * float(radius)**2 

 

 

def boundsOf(points, wrap=True, LatLon=None): 

'''Determine the lower-left SW and upper-right NE corners of a 

path or polygon. 

 

@param points: The path or polygon points (C{LatLon}[]). 

@keyword wrap: Wrap lat- and longitudes (C{bool}). 

@keyword LatLon: Optional (sub-)class to return the C{bounds} 

corners (C{LatLon}) or C{None}. 

 

@return: A L{Bounds2Tuple}C{(latlonSW, latlonNE)} as B{C{LatLon}} 

or a L{Bounds4Tuple}C{(latS, lonW, latN, lonE)} if 

B{C{LatLon}} is C{None}. 

 

@raise TypeError: Some B{C{points}} are not C{LatLon}. 

 

@raise ValueError: Insufficient number of B{C{points}}. 

 

@example: 

 

>>> b = LatLon(45,1), LatLon(45,2), LatLon(46,2), LatLon(46,1) 

>>> boundsOf(b) # False 

>>> 45.0, 1.0, 46.0, 2.0 

''' 

pts = LatLon2psxy(points, closed=False, radius=None, wrap=wrap) 

 

lox, loy, _ = hix, hiy, _ = pts[0] 

 

for x, y, _ in pts: # [1:] 

if lox > x: 

lox = x 

elif hix < x: 

hix = x 

 

if loy > y: 

loy = y 

elif hiy < y: 

hiy = y 

 

return Bounds4Tuple(loy, lox, hiy, hix) if LatLon is None else \ 

Bounds2Tuple(LatLon(loy, lox), LatLon(hiy, hix)) # PYCHOK inconsistent 

 

 

def centroidOf(points, wrap=True, LatLon=None): 

'''Determine the centroid of a polygon. 

 

@param points: The polygon points (C{LatLon}[]). 

@keyword wrap: Wrap lat-, wrap and unroll longitudes (C{bool}). 

@keyword LatLon: Optional (sub-)class to return the centroid 

(L{LatLon}) or C{None}. 

 

@return: Centroid location (B{C{LatLon}}) or a 

L{LatLon2Tuple}C{(lat, lon)} if B{C{LatLon}} 

is C{None}. 

 

@raise TypeError: Some B{C{points}} are not C{LatLon}. 

 

@raise ValueError: Insufficient number of B{C{points}} or 

B{C{points}} enclose a pole or zero area. 

 

@see: U{Centroid<https://WikiPedia.org/wiki/Centroid#Of_a_polygon>} 

and U{Calculating The Area And Centroid Of A Polygon 

<https://www.Seas.UPenn.edu/~sys502/extra_materials/ 

Polygon%20Area%20and%20Centroid.pdf>}. 

''' 

# setting radius=1 converts degrees to radians 

pts = LatLon2psxy(points, closed=True, radius=1, wrap=wrap) 

n = len(pts) 

 

A, X, Y = Fsum(), Fsum(), Fsum() 

 

x1, y1, _ = pts[n-1] 

for i in range(n): 

x2, y2, _ = pts[i] 

if wrap and i < (n - 1): 

_, x2 = unrollPI(x1, x2, wrap=True) 

t = x1 * y2 - x2 * y1 

A += t 

X += t * (x1 + x2) 

Y += t * (y1 + y2) 

# XXX more elaborately: 

# t1, t2 = x1 * y2, -(x2 * y1) 

# A.fadd_(t1, t2) 

# X.fadd_(t1 * x1, t1 * x2, t2 * x1, t2 * x2) 

# Y.fadd_(t1 * y1, t1 * y2, t2 * y1, t2 * y2) 

x1, y1 = x2, y2 

 

A = A.fsum() * 3.0 # 6.0 / 2.0 

if abs(A) < EPS: 

raise ValueError('polar or zero area: %r' % (pts,)) 

Y, X = degrees90(Y.fsum() / A), degrees180(X.fsum() / A) 

return LatLon2Tuple(Y, X) if LatLon is None else LatLon(Y, X) 

 

 

def _imdex2(closed, n): # imported by sphericalNvector, -Trigonometry 

'''(INTERNAL) Return first and second index. 

''' 

return (n-1, 0) if closed else (0, 1) 

 

 

def isclockwise(points, adjust=False, wrap=True): 

'''Determine the direction of a path or polygon. 

 

@param points: The path or polygon points (C{LatLon}[]). 

@keyword adjust: Adjust the wrapped, unrolled longitudinal delta 

by the cosine of the mean latitude (C{bool}). 

@keyword wrap: Wrap lat-, wrap and unroll longitudes (C{bool}). 

 

@return: C{True} if B{C{points}} are clockwise, C{False} otherwise. 

 

@raise TypeError: Some B{C{points}} are not C{LatLon}. 

 

@raise ValueError: Insufficient number of B{C{points}} or the 

B{C{points}} enclose a pole or zero area. 

 

@example: 

 

>>> f = LatLon(45,1), LatLon(45,2), LatLon(46,2), LatLon(46,1) 

>>> isclockwise(f) # False 

>>> isclockwise(reversed(f)) # True 

''' 

a, pts = _area2(points, adjust, wrap) 

if a > 0: 

return True 

elif a < 0: 

return False 

# <https://blog.Element84.com/determining-if-a-spherical-polygon-contains-a-pole.html> 

raise ValueError('polar or zero area: %r' % (pts,)) 

 

 

def isconvex(points, adjust=False, wrap=True): 

'''Determine whether a polygon is convex. 

 

@param points: The polygon points (C{LatLon}[]). 

@keyword adjust: Adjust the wrapped, unrolled longitudinal delta 

by the cosine of the mean latitude (C{bool}). 

@keyword wrap: Wrap lat-, wrap and unroll longitudes (C{bool}). 

 

@return: C{True} if B{C{points}} are convex, C{False} otherwise. 

 

@raise CrossError: Some B{C{points}} are colinear. 

 

@raise TypeError: Some B{C{points}} are not C{LatLon}. 

 

@raise ValueError: Insufficient number of B{C{points}}. 

 

@example: 

 

>>> t = LatLon(45,1), LatLon(46,1), LatLon(46,2) 

>>> isconvex(t) # True 

 

>>> f = LatLon(45,1), LatLon(46,2), LatLon(45,2), LatLon(46,1) 

>>> isconvex(f) # False 

''' 

return bool(isconvex_(points, adjust=adjust, wrap=wrap)) 

 

 

def isconvex_(points, adjust=False, wrap=True): 

'''Determine whether a polygon is convex and clockwise. 

 

@param points: The polygon points (C{LatLon}[]). 

@keyword adjust: Adjust the wrapped, unrolled longitudinal delta 

by the cosine of the mean latitude (C{bool}). 

@keyword wrap: Wrap lat-, wrap and unroll longitudes (C{bool}). 

 

@return: C{+1} if B{C{points}} are convex clockwise, C{-1} for 

convex counter-clockwise B{C{points}}, C{0} otherwise. 

 

@raise CrossError: Some B{C{points}} are colinear. 

 

@raise TypeError: Some B{C{points}} are not C{LatLon}. 

 

@raise ValueError: Insufficient number of B{C{points}}. 

 

@example: 

 

>>> t = LatLon(45,1), LatLon(46,1), LatLon(46,2) 

>>> isconvex_(t) # +1 

 

>>> f = LatLon(45,1), LatLon(46,2), LatLon(45,2), LatLon(46,1) 

>>> isconvex_(f) # 0 

''' 

def _unroll_adjust(x1, y1, x2, y2, wrap): 

x21, x2 = unroll180(x1, x2, wrap=wrap) 

if adjust: 

y = radians(y1 + y2) * 0.5 

x21 *= cos(y) if abs(y) < PI_2 else 0 

return x21, x2 

 

pts = LatLon2psxy(points, closed=True, radius=None, wrap=wrap) 

c, n, s = crosserrors(), len(pts), 0 

 

x1, y1, _ = pts[n-2] 

x2, y2, _ = pts[n-1] 

x21, x2 = _unroll_adjust(x1, y1, x2, y2, False) 

 

for i in range(n): 

x3, y3, ll = pts[i] 

x32, x3 = _unroll_adjust(x2, y2, x3, y3, 

wrap if i < (n - 2) else False) 

 

# get the sign of the distance from point 

# x3, y3 to the line from x1, y1 to x2, y2 

# <https://WikiPedia.org/wiki/Distance_from_a_point_to_a_line> 

s3 = fdot((x3, y3, x1, y1), y2 - y1, -x21, -y2, x2) 

if s3 > 0: # x3, y3 on the right 

if s < 0: # non-convex 

return 0 

s = +1 

 

elif s3 < 0: # x3, y3 on the left 

if s > 0: # non-convex 

return 0 

s = -1 

 

elif c and fdot((x32, y1 - y2), y3 - y2, -x21) < 0: 

# colinear u-turn: x3, y3 not on the 

# opposite side of x2, y2 as x1, y1 

raise CrossError('%s %s: %r' % ('colinear', 'point', ll)) 

 

x1, y1, x2, y2, x21 = x2, y2, x3, y3, x32 

 

return s # all points on the same side 

 

 

def isenclosedBy(point, points, wrap=False): # MCCABE 15 

'''Determine whether a point is enclosed by a polygon. 

 

@param point: The point (C{LatLon} or 2-tuple C{(lat, lon)}). 

@param points: The polygon points (C{LatLon}[]). 

@keyword wrap: Wrap lat-, wrap and unroll longitudes (C{bool}). 

 

@return: C{True} if B{C{point}} is inside the polygon, C{False} 

otherwise. 

 

@raise TypeError: Some B{C{points}} are not C{LatLon}. 

 

@raise ValueError: Insufficient number of B{C{points}} or 

invalid B{C{point}}. 

 

@see: L{sphericalNvector.LatLon.isenclosedBy}, 

L{sphericalTrigonometry.LatLon.isenclosedBy} and 

U{MultiDop GeogContainPt<https://GitHub.com/NASA/MultiDop>} 

(U{Shapiro et al. 2009, JTECH 

<https://Journals.AMetSoc.org/doi/abs/10.1175/2009JTECHA1256.1>} 

and U{Potvin et al. 2012, JTECH 

<https://Journals.AMetSoc.org/doi/abs/10.1175/JTECH-D-11-00019.1>}). 

''' 

try: 

y0, x0 = point.lat, point.lon 

except AttributeError: 

try: 

y0, x0 = map1(float, *point[:2]) 

except (IndexError, TypeError, ValueError): 

raise ValueError('%s invalid: %r' % ('point', point)) 

 

pts = LatLon2psxy(points, closed=True, radius=None, wrap=wrap) 

n = len(pts) 

 

if wrap: 

x0, y0 = wrap180(x0), wrap90(y0) 

 

def _dxy(x1, i): 

x2, y2, _ = pts[i] 

dx, x2 = unroll180(x1, x2, wrap=i < (n - 1)) 

return dx, x2, y2 

 

else: 

x0 = fmod(x0, 360.0) # not x0 % 360 

 

def _dxy(x1, i): # PYCHOK expected 

x, y, _ = pts[i] 

x %= 360.0 

if x < (x0 - 180): 

x += 360 

elif x >= (x0 + 180): 

x -= 360 

return (x - x1), x, y 

 

e = m = False 

s = Fsum() 

 

_, x1, y1 = _dxy(x0, n - 1) 

for i in range(n): 

dx, x2, y2 = _dxy(x1, i) 

# ignore duplicate and near-duplicate pts 

if max(abs(dx), abs(y2 - y1)) > EPS: 

# determine if polygon edge (x1, y1)..(x2, y2) straddles 

# point (lat, lon) or is on boundary, but do not count 

# edges on boundary as more than one crossing 

if abs(dx) < 180 and (x1 < x0 <= x2 or x2 < x0 <= x1): 

m = not m 

dy = (x0 - x1) * (y2 - y1) - (y0 - y1) * dx 

if (dy > 0 and dx >= 0) or (dy < 0 and dx <= 0): 

e = not e 

 

s.fadd_(sin(radians(y2))) 

x1, y1 = x2, y2 

 

# An odd number of meridian crossings means, the polygon 

# contains a pole. Assume it is the pole on the hemisphere 

# containing the polygon mean point and if the polygon does 

# contain the North Pole, flip the result. 

if m and s.fsum() > 0: 

e = not e 

return e 

 

 

def ispolar(points, wrap=False): 

'''Check whether a polygon encloses a pole. 

 

@param points: The polygon points (C{LatLon}[]). 

@keyword wrap: Wrap and unroll longitudes (C{bool}). 

 

@return: C{True} if the polygon encloses a pole, C{False} 

otherwise. 

 

@raise ValueError: Insufficient number of B{C{points}}. 

 

@raise TypeError: Some B{C{points}} are not C{LatLon} or don't 

have C{bearingTo2}, C{initialBearingTo} 

and C{finalBearingTo} methods. 

''' 

n, points = points2(points, closed=True) 

 

def _cds(n, points): # iterate over course deltas 

p1 = points[n-1] 

try: # LatLon must have initial- and finalBearingTo 

b1, _ = p1.bearingTo2(points[0], wrap=wrap) 

except AttributeError: 

raise _IsNotError('.bearingTo2', points=p1) 

 

for i in range(n): 

p2 = points[i] 

if not p2.isequalTo(p1, EPS): 

b, b2 = p1.bearingTo2(p2, wrap=wrap) 

yield wrap180(b - b1) # (b - b1 + 540) % 360 - 180 

yield wrap180(b2 - b) # (b2 - b + 540) % 360 - 180 

p1, b1 = p2, b2 

 

# sum of course deltas around pole is 0° rather than normally ±360° 

# <https://blog.Element84.com/determining-if-a-spherical-polygon-contains-a-pole.html> 

s = fsum(_cds(n, points)) 

 

# XXX fix (intermittant) edge crossing pole - eg (85,90), (85,0), (85,-90) 

return abs(s) < 90 # "zero-ish" 

 

 

def nearestOn5(point, points, closed=False, wrap=False, LatLon=None, **options): 

'''Locate the point on a path or polygon closest to an other point. 

 

If the given point is within the extent of a polygon edge, 

the closest point is on that edge, otherwise the closest 

point is the nearest of that edge's end points. 

 

Distances are approximated by function L{equirectangular_}, 

subject to the supplied B{C{options}}. 

 

@param point: The other, reference point (C{LatLon}). 

@param points: The path or polygon points (C{LatLon}[]). 

@keyword closed: Optionally, close the path or polygon (C{bool}). 

@keyword wrap: Wrap and L{unroll180} longitudes and longitudinal 

delta (C{bool}) in function L{equirectangular_}. 

@keyword LatLon: Optional (sub-)class to return the closest 

point (L{LatLon}) or C{None}. 

@keyword options: Other keyword arguments for function 

L{equirectangular_}. 

 

@return: A L{NearestOn3Tuple}C{(closest, distance, angle)} or 

a L{NearestOn5Tuple}C{(lat, lon, distance, angle, 

height)} if B{C{LatLon}} is C{None}. 

 

@raise LimitError: Lat- and/or longitudinal delta exceeds the 

B{C{limit}}, see function L{equirectangular_}. 

 

@raise TypeError: Some B{C{points}} are not C{LatLon}. 

 

@raise ValueError: Insufficient number of B{C{points}}. 

 

@see: Function L{degrees2m} to convert C{degrees} to C{meter}. 

''' 

n, points = points2(points, closed=closed) 

 

def _d2yx(p2, p1, u, i): 

w = wrap if (not closed or i < (n - 1)) else False 

# equirectangular_ returns a Distance4Tuple(distance 

# in degrees squared, delta lat, delta lon, p2.lon 

# unroll/wrap); the previous p2.lon unroll/wrap 

# is also applied to the next edge's p1.lon 

return equirectangular_(p1.lat, p1.lon + u, 

p2.lat, p2.lon, wrap=w, **options) 

 

def _h(p): 

try: # get height 

return p.height or 0 

except AttributeError: 

return 0 

 

# point (x, y) on axis rotated ccw by angle a: 

# x' = y * sin(a) + x * cos(a) 

# y' = y * cos(a) - x * sin(a) 

# 

# distance (w) along and perpendicular (h) to 

# a line thru point (dx, dy) and the origin: 

# w = (y * dy + x * dx) / hypot(dx, dy) 

# h = (y * dx - x * dy) / hypot(dx, dy) 

# 

# closest point on that line thru (dx, dy): 

# xc = dx * w / hypot(dx, dy) 

# yc = dy * w / hypot(dx, dy) 

# or 

# xc = dx * f 

# yc = dy * f 

# with 

# f = w / hypot(dx, dy) 

# or 

# f = (y * dy + x * dx) / (dx**2 + dy**2) 

 

i, m = _imdex2(closed, n) 

p2 = c = points[i] 

u2 = u = 0 

d, dy, dx, _ = _d2yx(p2, point, u2, i) 

for i in range(m, n): 

p1, u1, p2 = p2, u2, points[i] 

# iff wrapped, unroll lon1 (actually previous 

# lon2) like function unroll180/-PI would've 

d21, y21, x21, u2 = _d2yx(p2, p1, u1, i) 

if d21 > EPS: 

# distance point to p1, y01 and x01 inverted 

d2, y01, x01, _ = _d2yx(point, p1, u1, n) 

if d2 > EPS: 

w2 = y01 * y21 + x01 * x21 

if w2 > 0: 

if w2 < d21: 

# closest is between p1 and p2, use 

# original delta's, not y21 and x21 

f = w2 / d21 

p1 = LatLon_(favg(p1.lat, p2.lat, f=f), 

favg(p1.lon, p2.lon + u2, f=f), 

height=favg(_h(p1), _h(p2), f=f)) 

u1 = 0 

else: # p2 is closest 

p1, u1 = p2, u2 

d2, y01, x01, _ = _d2yx(point, p1, u1, n) 

if d2 < d: # p1 is closer, y01 and x01 inverted 

c, u, d, dy, dx = p1, u1, d2, -y01, -x01 

 

d, a, h = hypot(dx, dy), degrees360(atan2(dx, dy)), _h(c) 

if LatLon is None: 

r = NearestOn5Tuple(c.lat, c.lon + u, d, a, h) 

else: 

r = NearestOn3Tuple(LatLon(c.lat, c.lon + u, height=h), d, a) 

return _xnamed(r, nameof(point)) 

 

 

def perimeterOf(points, closed=False, adjust=True, radius=R_M, wrap=True): 

'''Approximate the perimeter of a path or polygon. 

 

@param points: The path or polygon points (C{LatLon}[]). 

@keyword closed: Optionally, close the path or polygon (C{bool}). 

@keyword adjust: Adjust the wrapped, unrolled longitudinal delta 

by the cosine of the mean latitude (C{bool}). 

@keyword radius: Optional, mean earth radius (C{meter}). 

@keyword wrap: Wrap lat-, wrap and unroll longitudes (C{bool}). 

 

@return: Approximate perimeter (C{meter}, same units as 

B{C{radius}}). 

 

@raise TypeError: Some B{C{points}} are not C{LatLon}. 

 

@raise ValueError: Insufficient number of B{C{points}}. 

 

@note: This perimeter is based on the L{equirectangular_} 

distance approximation and is ill-suited for regions 

exceeding several hundred Km or Miles or with 

near-polar latitudes. 

 

@see: L{sphericalTrigonometry.perimeterOf} and 

L{ellipsoidalKarney.perimeterOf}. 

''' 

pts = LatLon2psxy(points, closed=closed, radius=None, wrap=False) 

 

def _degs(n, pts, closed): # angular edge lengths in degrees 

i, m = _imdex2(closed, n) 

x1, y1, _ = pts[i] 

u = 0 # previous x2's unroll/wrap 

for i in range(m, n): 

x2, y2, _ = pts[i] 

w = wrap if (not closed or i < (n - 1)) else False 

# apply previous x2's unroll/wrap to new x1 

_, dy, dx, u = equirectangular_(y1, x1 + u, y2, x2, 

adjust=adjust, 

limit=None, 

wrap=w) 

yield hypot(dx, dy) 

x1, y1 = x2, y2 

 

d = fsum(_degs(len(pts), pts, closed)) 

return degrees2m(d, radius) 

 

# **) MIT License 

# 

# Copyright (C) 2016-2020 -- mrJean1 at Gmail -- All Rights Reserved. 

# 

# Permission is hereby granted, free of charge, to any person obtaining a 

# copy of this software and associated documentation files (the "Software"), 

# to deal in the Software without restriction, including without limitation 

# the rights to use, copy, modify, merge, publish, distribute, sublicense, 

# and/or sell copies of the Software, and to permit persons to whom the 

# Software is furnished to do so, subject to the following conditions: 

# 

# The above copyright notice and this permission notice shall be included 

# in all copies or substantial portions of the Software. 

# 

# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 

# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 

# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL 

# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR 

# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, 

# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR 

# OTHER DEALINGS IN THE SOFTWARE.