# Coverage for pygeodesy/points.py : 95%

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1622 1623 1624 1625 1626 1627 1628 1629 1630 1631 1632 1633 1634 1635 1636 1637 1638 1639 1640 1641 1642 1643 1644 1645 1646 1647 1648 1649 1650 1651 1652 1653 1654 1655 1656 1657 1658 1659 1660 1661 1662 1663 1664 1665 1666 1667 1668 1669 1670 1671 1672 1673 1674 1675 1676 1677 1678 1679 1680 1681 1682 1683 1684 1685 1686 1687 1688 1689 1690 1691 1692 1693 1694 1695 1696 1697 1698 1699 1700 1701 1702 1703 1704 1705 1706 1707 1708 1709 1710 1711 1712 1713 1714 1715 1716 1717 1718 1719 1720 1721 1722 1723 1724 1725 1726 1727 1728 1729 1730 1731 1732 1733 1734 1735 1736 1737 1738 1739 1740 | # -*- coding: utf-8 -*- u'''Utilities for point lists, tuples, etc. 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. ''' from pygeodesy.basics import isclass, isint, isnear0, isscalar, \ issequence, issubclassof, map1, \ _Sequence, _xcopy, _xinstanceof from pygeodesy.datums import _spherical_datum from pygeodesy.dms import F_D, latDMS, lonDMS, parseDMS2 from pygeodesy.errors import CrossError, crosserrors, _IndexError, \ _IsnotError, _TypeError, _ValueError, \ _xkwds, _xkwds_pop from pygeodesy.fmath import favg, fdot, Fsum, fsum, hypot from pygeodesy.formy import _bearingTo2, equirectangular_, latlon2n_xyz from pygeodesy.interns import EPS, EPS1, NN, PI_2, R_M, _angle_, \ _colinear_, _COMMASPACE_, _DASH_, _DEQUALSPACED_, \ _distance_, _ELLIPSIS_, _height_, _lat_, _lon_, \ _near_, _not_, _point_, _SPACE_, _UNDER_, _valid_, \ _0_0, _0_5, _1_0, _3_0, _90_0, _180_0, _360_0 from pygeodesy.iters import LatLon2PsxyIter, PointsIter, points2 from pygeodesy.lazily import _ALL_LAZY from pygeodesy.named import classname, nameof, notImplemented, notOverloaded, \ _NamedTuple, _xnamed, _xother3, _xotherError from pygeodesy.namedTuples import Bounds2Tuple, Bounds4Tuple, \ LatLon2Tuple, NearestOn3Tuple, \ PhiLam2Tuple, Point3Tuple, Vector4Tuple from pygeodesy.nvectorBase import NvectorBase, _N_vector_ from pygeodesy.props import deprecated_method, Property_RO, property_doc_, \ property_RO from pygeodesy.streprs import Fmt, hstr, instr, pairs from pygeodesy.units import Degrees, Lat, Lon, Number_, Radius, Scalar_ from pygeodesy.utily import atan2b, degrees90, degrees180, degrees2m, \ unroll180, unrollPI, wrap90, wrap180 from math import cos, fmod, radians, sin __all__ = _ALL_LAZY.points __version__ = '21.07.31' _fin_ = 'fin' _ilat_ = 'ilat' _ilon_ = 'ilon' _ncols_ = 'ncols' _nrows_ = 'nrows' 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_, _height_, _datum_, _name_) # Property_RO = property_RO # no __dict__ with __slots__ # # However, sys.getsizeof(LatLon_(1, 2)) is 72-88 with __slots__ # and only 48-64 bytes without in Python 2.7.18+ and Python 3+. def __init__(self, lat, lon, name=NN, height=0, datum=None): '''Creat a new, mininal, low-overhead L{LatLon_} instance, without height and datum. @arg lat: Latitude (C{degrees}). @arg lon: Longitude (C{degrees}). @kwarg name: Optional name (C{str}). @kwarg height: Optional height (C{float} or C{int}). @kwarg datum: Optional datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2}, L{a_f2Tuple} or I{scalar} radius) or C{None}. @raise TypeError: Invalid B{C{datum}}. @note: The lat- and longitude are taken as-given, un-clipped and un-validated . ''' try: # most common use case self.lat, self.lon = float(lat), float(lon) except (TypeError, ValueError): self.lat, self.lon = parseDMS2(lat, lon, clipLat=0, clipLon=0) # PYCHOK LatLon2Tuple self.name = str(name) self.height = height self.datum = datum if datum is None else \ _spherical_datum(datum, name=self.name) 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.toRepr() def __str__(self): return self.toStr() def classof(self, *args, **kwds): '''Instantiate this very class. @arg args: Optional, positional arguments. @kwarg kwds: Optional, keyword arguments. @return: New instance (C{self.__class__}). ''' return _xnamed(self.__class__(*args, **kwds), self.name) def copy(self, deep=False): '''Make a shallow or deep copy of this instance. @kwarg deep: If C{True} make a deep, otherwise a shallow copy (C{bool}). @return: The copy (C{This class} or subclass thereof). ''' return _xcopy(self, deep=deep) def heightStr(self, prec=-2): '''Return a string for the height B{C{height}}. @kwarg prec: Optional number of decimals, unstripped (C{int}). @see: Function L{hstr}. ''' return hstr(self.height, prec=prec) 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 UnitError: Invalid B{C{eps}}. ''' self.others(other) if eps: return max(abs(self.lat - other.lat), abs(self.lon - other.lon)) < Scalar_(eps=eps) else: return self.lat == other.lat and \ self.lon == other.lon @Property_RO def latlon(self): '''Get the lat- and longitude in C{degrees} (L{LatLon2Tuple}C{(lat, lon)}). ''' return LatLon2Tuple(self.lat, self.lon, name=self.name) @Property_RO def latlonheight(self): '''Get the lat-, longitude and height (L{LatLon3Tuple}C{(lat, lon, height)}). ''' return self.latlon.to3Tuple(self.height) @Property_RO def _N_vector(self): '''(INTERNAL) Get the minimal, low-overhead (C{nvectorBase._N_vector_}) ''' return _N_vector_(*latlon2n_xyz(self.lat, self.lon), h=self.height, name=self.name) def others(self, *other, **name_other_up): # see .named._namedBase.others '''Refined class comparison. @arg other: The other instance (any C{type}). @kwarg name_other_up: Overriding C{name=other} and C{up=1} keyword arguments. @return: The B{C{other}} if compatible. @raise TypeError: Incompatible B{C{other}} C{type}. ''' other, name, up = _xother3(self, other, **name_other_up) if isinstance(other, self.__class__) or (hasattr(other, _lat_) and hasattr(other, _lon_)): return other raise _xotherError(self, other, name=name, up=up + 1) @Property_RO def philam(self): '''Get the lat- and longitude in C{radians} (L{PhiLam2Tuple}C{(phi, lam)}). ''' return PhiLam2Tuple(radians(self.lat), radians(self.lon), name=self.name) @Property_RO def philamheight(self): '''Get the lat-, longitude in C{radians} and height (L{PhiLam3Tuple}C{(phi, lam, height)}). ''' return self.philam.to3Tuple(self.height) @deprecated_method def points(self, points, closed=False, base=None): # PYCHOK no cover '''DEPRECATED, use method C{points2}.''' return points2(points, closed=closed, base=base) def points2(self, points, closed=False, base=None): '''Check a path or polygon represented by points. @arg points: The path or polygon points (C{LatLon}[]) @kwarg closed: Optionally, consider the polygon closed, ignoring any duplicate or closing final B{C{points}} (C{bool}). @kwarg base: Optionally, check all B{C{points}} against this base class, if C{None} don't check. @return: A L{Points2Tuple}C{(number, points)} with the number of points and the points C{list} or C{tuple}. @raise PointsError: Insufficient number of B{C{points}}. @raise TypeError: Some B{C{points}} are not B{C{base}}. ''' return points2(points, closed=closed, base=base) def PointsIter(self, points, loop=0, dedup=False): '''Return a points iterator. @arg points: The path or polygon points (C{LatLon}[]) @kwarg loop: Number of loop-back points (non-negative C{int}). @kwarg dedup: Skip duplicate points (C{bool}). @return: A new C{PointsIter} iterator. @raise PointsError: Insufficient number of B{C{points}}. ''' return PointsIter(points, loop=loop, base=self, dedup=dedup) @deprecated_method def to2ab(self): # PYCHOK no cover '''DEPRECATED, use property L{philam}.''' return self.philam def toNvector(self, h=None, Nvector=NvectorBase, **Nvector_kwds): '''Convert this point to C{n-vector} (normal to the earth's surface) components, I{including height}. @kwarg h: Optional height, overriding this point's height (C{meter}). @kwarg Nvector: Optional class to return the C{n-vector} components (C{Nvector}) or C{None}. @kwarg Nvector_kwds: Optional, additional B{C{Nvector}} keyword arguments, ignored if C{B{Nvector} is None}. @return: The C{n-vector} components B{C{Nvector}} or if B{C{Nvector}} is C{None}, a L{Vector4Tuple}C{(x, y, z, h)}. @raise TypeError: Invalid B{C{Nvector}} or B{C{Nvector_kwds}}. ''' x, y, z = latlon2n_xyz(self.lat, self.lon) r = Vector4Tuple(x, y, z, self.height if h is None else h) if Nvector is not None: r = Nvector(x, y, z, **_xkwds(Nvector_kwds, h=r.h, ll=self)) return _xnamed(r, self.name) def toRepr(self, **kwds): '''This L{LatLon_} as a string "class(<degrees>, ...)". @kwarg kwds: Optional, keyword arguments. @return: Class instance (C{str}). ''' _ = _xkwds_pop(kwds, std=None) # PYCHOK std unused return Fmt.PAREN(classname(self), self.toStr(**kwds)) def toStr(self, form=F_D, prec=6, sep=_COMMASPACE_, **kwds): '''This L{LatLon_} as a string "<degrees>, <degrees>". @kwarg form: Optional format, F_D, F_DM, F_DMS for deg°, deg°min′, deg°min′sec″ (C{str}). @kwarg prec: Optional number of decimal digits (0..8 or C{None}). @kwarg sep: Optional separator to join (C{str}). @kwarg 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 += (self.heightStr(),) if self.name: t += (repr(self.name),) if kwds: t += pairs(kwds, prec=prec) return sep.join(t) @deprecated_method def toStr2(self, **kwds): # PYCHOK no cover '''DEPRECATED, used method L{toRepr}.''' return self.toRepr(**kwds) try: _LatLon_attrs = LatLon_.__slots__ # PYCHOK no __slots__ except AttributeError: _LatLon_attrs = tuple(LatLon_(0, 0).__dict__.keys()) def _isLatLon_(LL): '''(INTERANL) Check attributes of class C{LL}. ''' return issubclassof(LL, LatLon_) or (isclass(LL) and all(hasattr(LL, a) for a in _LatLon_attrs)) 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 copy(self, deep=False): '''Make a shallow or deep copy of this instance. @kwarg deep: If C{True} make a deep, otherwise a shallow copy (C{bool}). @return: The copy (C{This class} or subclass thereof). ''' return _xcopy(self, deep=deep) def _count(self, point): '''(INTERNAL) Count the number of matching points. ''' n = 0 for _ in self._findall(point, ()): n += 1 return n @property_doc_(''' the equality tolerance (C{float}).''') 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. @arg tol: New tolerance (C{scalar}). @raise TypeError: Non-scalar B{C{tol}}. @raise ValueError: Out-of-bounds B{C{tol}}. ''' self._epsilon = Scalar_(tol, name='tolerance') 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, point, start_end): # PYCHOK no cover '''(INTERNAL) I{Must be implemented/overloaded}. ''' notImplemented(self, point, start_end) 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 _IndexError(self._itemname, point, txt=_not_('found')) @property_RO def isNumpy2(self): # PYCHOK no cover '''Is this a Numpy2 wrapper? ''' return False # isinstance(self, (Numpy2LatLon, ...)) @property_RO def isPoints2(self): # PYCHOK no cover '''Is this a LatLon2 wrapper/converter? ''' return False # isinstance(self, (LatLon2psxy, ...)) @property_RO def isTuple2(self): # PYCHOK no cover '''Is this a Tuple2 wrapper? ''' return False # isinstance(self, (Tuple2LatLon, ...)) def _iter(self): '''(INTERNAL) Yield all points. ''' for i in range(len(self)): yield self.point(self._array[i]) def point(self, *attrs): # PYCHOK no cover '''(INTERNAL) I{Must be overloaded}, see function C{notOverloaded}. @arg attrs: Optional arguments. ''' notOverloaded(self, *attrs) 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(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 = _SPACE_(t[:-1], _ELLIPSIS_, Fmt.SQUARE(t[-1:], len(self))) t = _SPACE_.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, -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): # PYCHOK no cover '''(INTERNAL) I{Should be overloaded}. ''' return {} def _zeros(self, *zeros): '''(INTERNAL) Check for near-zero values. ''' return all(abs(z) <= self._epsilon for z in zeros) 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('array.shape', shape) self._array = array self._shape = Shape2Tuple(*shape) if LatLon: # check the point class if _isLatLon_(LatLon): 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 _ValueError(ai, i) for aj, j in ais[:n]: if int(j) == i: raise _ValueError(_DEQUALSPACED_(ai, aj, i)) setattr(self, NN(_UNDER_, ai), i) def __contains__(self, latlon): '''Check for a specific lat-/longitude. @arg 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. @arg 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. @arg latlon: Point (C{LatLon}) or 2-tuple (lat, lon). @arg 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. @arg latlon: Point (C{LatLon}, L{LatLon2Tuple} or 2-tuple C{(lat, lon)}). @arg 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. @arg latlon: Point (C{LatLon}, L{LatLon2Tuple} or 2-tuple C{(lat, lon)}). @arg start_end: Optional C{[start[, end]]} index (C{int}). @return: Index (C{int}). @raise IndexError: Point not found. @raise TypeError: Invalid B{C{latlon}}. ''' 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): # PYCHOK *attrs '''Instantiate a point C{LatLon}. @arg 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. @arg latlon: Point (C{LatLon}, L{LatLon2Tuple} or 2-tuple C{(lat, lon)}). @arg 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 no cover '''(INTERNAL) I{Must be implemented/overloaded}. ''' notImplemented(self, indices) def subset(self, indices): '''Return a subset of the C{NumPy} array. @arg 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(Fmt.SQUARE(indices=i), v) elif not 0 <= v < n: raise _IndexError(Fmt.SQUARE(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)}. @arg latlons: Points C{list}, C{sequence}, C{set}, C{tuple}, etc. (C{LatLon[]}). @kwarg closed: Optionally, close the polygon (C{bool}). @kwarg radius: Mean earth radius (C{meter}). @kwarg wrap: Wrap lat- and longitudes (C{bool}). @raise PointsError: Insufficient number of B{C{latlons}}. @raise TypeError: Some B{C{points}} are not B{C{base}}. ''' self._closed = closed self._len, self._array = points2(latlons, closed=closed) if radius: self._radius = r = Radius(radius) self._deg2m = degrees2m(_1_0, r) self._wrap = wrap def __contains__(self, xy): '''Check for a matching point. @arg 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. @arg 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. @arg xy: Point (C{LatLon}, L{LatLon2Tuple} or 2-tuple C{(x, y)}) in (C{degrees}. @arg 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[:2] except (IndexError, 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. @arg xy: Point (C{LatLon}, L{LatLon2Tuple} or 2-tuple C{(x, y)}) in (C{degrees}. @arg 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. @arg xy: Point (C{LatLon}) or 2-tuple (x, y) in (C{degrees}). @arg start_end: Optional C{[start[, end]]} index (C{int}). @return: Index (C{int}). @raise IndexError: Point not found. @raise TypeError: Invalid B{C{xy}}. ''' return self._index(xy, start_end) @property_RO def isPoints2(self): '''Is this a LatLon2 wrapper/converter? ''' return True # isinstance(self, (LatLon2psxy, ...)) def point(self, ll): # PYCHOK *attrs '''Create a pseudo-xy. @arg 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. @arg xy: Point (C{LatLon}, L{LatLon2Tuple} or 2-tuple C{(x, y)}) in (C{degrees}. @arg 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 NearestOn5Tuple(_NamedTuple): '''5-Tuple C{(lat, lon, distance, angle, height)} all in C{degrees}, except C{height}. The C{distance} is the L{equirectangular_} distance between the closest and the reference B{C{point}} in C{degrees}. The C{angle} from the reference B{C{point}} to the closest point is in compass C{degrees360}, see function L{compassAngle}. The C{height} is the (interpolated) height at the closest point in C{meter} or C{0}. ''' _Names_ = (_lat_, _lon_, _distance_, _angle_, _height_) _Units_ = ( Lat, Lon, Degrees, Degrees, Degrees) 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. @arg array: C{NumPy} array (C{numpy.array}). @kwarg ilat: Optional index of the latitudes column (C{int}). @kwarg ilon: Optional index of the longitudes column (C{int}). @kwarg LatLon: Optional C{LatLon} 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 Shape2Tuple(_NamedTuple): '''2-Tuple C{(nrows, ncols)}, the number of rows and columns, both C{int}. ''' _Names_ = (_nrows_, _ncols_) _Units_ = ( Number_, Number_) 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. @arg tuples: The C{list}, C{tuple} or C{sequence} of tuples (C{tuple}[]). @kwarg ilat: Optional index of the latitudes value (C{int}). @kwarg ilon: Optional index of the longitudes value (C{int}). @kwarg LatLon: Optional C{LatLon} class to use (L{LatLon_}). @raise IndexError: If C{(len(B{tuples}), min(len(t) for t in B{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) ''' _xinstanceof(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): '''(INTERNAL) Approximate the area in radians squared, I{signed}. ''' if adjust: # approximate trapezoid by a rectangle, adjusting # the top width by the cosine of the latitudinal # average and bottom width by some fudge factor def _adjust(w, h): c = cos(h) if abs(h) < PI_2 else _0_0 return w * h * (c + 1.2876) * _0_5 else: def _adjust(w, h): # PYCHOK expected return w * h # setting radius=1 converts degrees to radians Ps = LatLon2PsxyIter(points, wrap=wrap, radius=_1_0, loop=1) x1, y1, ll = Ps[0] pts = [ll] A2 = Fsum() # trapezoidal area in radians**2 for i, p in Ps.enumerate(closed=True): x2, y2, ll = p if 0 < i < 4: pts.append(ll) w, x2 = unrollPI(x1, x2, wrap=wrap if i else False) A2 += _adjust(w, (y2 + y1) * _0_5) x1, y1 = x2, y2 return A2.fsum(), tuple(pts) def _areaError(pts, near_=NN): # imported by .ellipsoidalKarney '''(INTERNAL) Area issue. ''' t = _ELLIPSIS_(pts[:3], NN) return _ValueError(NN(near_, 'zero or polar area'), txt=t) def areaOf(points, adjust=True, radius=R_M, wrap=True): '''Approximate the area of a polygon. @arg points: The polygon points (C{LatLon}[]). @kwarg adjust: Adjust the wrapped, unrolled longitudinal delta by the cosine of the mean latitude (C{bool}). @kwarg radius: Mean earth radius (C{meter}) or C{None}. @kwarg wrap: Wrap lat-, wrap and unroll longitudes (C{bool}). @return: Approximate area (I{square} C{meter}, same units as B{C{radius}} or C{radians} I{squared} if B{C{radius}} is C{None}). @raise PointsError: Insufficient number of B{C{points}} @raise TypeError: Some B{C{points}} are not C{LatLon}. @raise ValueError: Invalid B{C{radius}}. @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) if radius is None else (abs(a) * Radius(radius)**2) def boundsOf(points, wrap=True, LatLon=None): '''Determine the lower-left SW and upper-right NE corners of a path or polygon. @arg points: The path or polygon points (C{LatLon}[]). @kwarg wrap: Wrap lat- and longitudes (C{bool}). @kwarg LatLon: Optional class to return the C{bounds} corners (C{LatLon}) or C{None}. @return: A L{Bounds2Tuple}C{(latlonSW, latlonNE)} as B{C{LatLon}}s if B{C{LatLon}} is C{None} a L{Bounds4Tuple}C{(latS, lonW, latN, lonE)}. @raise PointsError: Insufficient number of B{C{points}} @raise TypeError: Some B{C{points}} are not C{LatLon}. @see: Function L{quadOf}. @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 ''' Ps = LatLon2PsxyIter(points, wrap=wrap, loop=1) lox, loy, _ = hix, hiy, _ = Ps[0] for x, y, _ in Ps.iterate(closed=False): # [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. @arg points: The polygon points (C{LatLon}[]). @kwarg wrap: Wrap lat-, wrap and unroll longitudes (C{bool}). @kwarg LatLon: Optional class to return the centroid (C{LatLon}) or C{None}. @return: Centroid (B{C{LatLon}}) or a L{LatLon2Tuple}C{(lat, lon)} if C{B{LatLon} is None}. @raise PointsError: Insufficient number of B{C{points}} @raise TypeError: Some B{C{points}} are not C{LatLon}. @raise ValueError: The B{C{points}} enclose a pole or near-zero area. @see: U{Centroid<https://WikiPedia.org/wiki/Centroid#Of_a_polygon>} and Paul Bourke's U{Calculating The Area And Centroid Of A Polygon <https://www.SEAS.UPenn.edu/~ese502/lab-content/extra_materials/ Polygon%20Area%20and%20Centroid.pdf>}, 1988. ''' A, X, Y = Fsum(), Fsum(), Fsum() # setting radius=1 converts degrees to radians Ps = LatLon2PsxyIter(points, wrap=wrap, radius=_1_0, loop=1) x1, y1, ll = Ps[0] pts = [ll] # for _areaError for i, p in Ps.enumerate(closed=True): x2, y2, ll = p if 0 < i < 4: pts.append(ll) if wrap and i != 0: _, x2 = unrollPI(x1, x2, wrap=wrap) 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 isnear0(A): raise _areaError(pts, near_=_DASH_(_near_, NN)) Y, X = degrees90(Y.fsum() / A), degrees180(X.fsum() / A) return LatLon2Tuple(Y, X) if LatLon is None else LatLon(Y, X) def _fractional(points, fi, fin=None): # wrap [n] to [0] '''(INTERNAL) Compute point at L{fractional} index. ''' i = int(fi) p = points[i] r = fi - float(i) if r > EPS: i += 1 q = points[0 if i == fin else i] if r < EPS1: p = LatLon2Tuple(favg(p.lat, q.lat, f=r), favg(p.lon, q.lon, f=r)) else: p = q return p def fractional(points, fi, LatLon=None, **LatLon_kwds): '''Return the point at a given I{fractional} index. @arg points: The points (C{LatLon}[], L{Numpy2LatLon}[], L{Tuple2LatLon}[] or C{other}[]). @arg fi: The fractional index (L{FIx}, C{float} or C{int}). @kwarg LatLon: Optional class to return the I{intermediate}, I{fractional} point (C{LatLon}) or C{None}. @kwarg LatLon_kwds: Optional B{C{LatLon}} keyword arguments, ignored of C{B{LatLon} is None}. @return: A B{C{LatLon}} or if B{C{LatLon}} is C{None}, a L{LatLon2Tuple}C{(lat, lon)} for C{B{points}[B{fi}]} if I{fractional} index B{C{fi}} is C{int}, otherwise the intermediate point between C{B{points}[int(B{fi})]} and C{B{points}[int(B{fi}) + 1]} for C{float} I{fractional} index B{C{fi}}. @raise IndexError: Fractional index B{C{fi}} invalid or B{C{points}} not subscriptable or not closed. @see: Class L{FIx} and method L{FIx.fractional}. ''' try: if not isscalar(fi) or fi < 0: raise IndexError p = _fractional(points, fi, fin=getattr(fi, _fin_, 0)) # see .units.FIx except (IndexError, TypeError): raise _IndexError(fractional.__name__, fi) if LatLon and isinstance(p, LatLon2Tuple): p = LatLon(*p, **LatLon_kwds) return p def isclockwise(points, adjust=False, wrap=True): '''Determine the direction of a path or polygon. @arg points: The path or polygon points (C{LatLon}[]). @kwarg adjust: Adjust the wrapped, unrolled longitudinal delta by the cosine of the mean latitude (C{bool}). @kwarg wrap: Wrap lat-, wrap and unroll longitudes (C{bool}). @return: C{True} if B{C{points}} are clockwise, C{False} otherwise. @raise PointsError: Insufficient number of B{C{points}} @raise TypeError: Some B{C{points}} are not C{LatLon}. @raise ValueError: 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 _areaError(pts) def isconvex(points, adjust=False, wrap=True): '''Determine whether a polygon is convex. @arg points: The polygon points (C{LatLon}[]). @kwarg adjust: Adjust the wrapped, unrolled longitudinal delta by the cosine of the mean latitude (C{bool}). @kwarg 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 PointsError: Insufficient number of B{C{points}} @raise TypeError: Some B{C{points}} are not C{LatLon}. @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 I{and clockwise}. @arg points: The polygon points (C{LatLon}[]). @kwarg adjust: Adjust the wrapped, unrolled longitudinal delta by the cosine of the mean latitude (C{bool}). @kwarg 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 PointsError: Insufficient number of B{C{points}} @raise TypeError: Some B{C{points}} are not C{LatLon}. @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, w): x21, x2 = unroll180(x1, x2, wrap=w) if adjust: y = radians(y1 + y2) * _0_5 x21 *= cos(y) if abs(y) < PI_2 else _0_0 return x21, x2 c, s = crosserrors(), 0 Ps = LatLon2PsxyIter(points, wrap=wrap, loop=2) x1, y1, _ = Ps[0] x2, y2, _ = Ps[1] x21, x2 = _unroll_adjust(x1, y1, x2, y2, False) for i, p in Ps.enumerate(closed=True): x3, y3, ll = p x32, x3 = _unroll_adjust(x2, y2, x3, y3, (wrap if i > 1 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 t = Fmt.SQUARE(points=i) raise CrossError(t, ll, txt=_colinear_) 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. @arg point: The point (C{LatLon} or 2-tuple C{(lat, lon)}). @arg points: The polygon points (C{LatLon}[]). @kwarg wrap: Wrap lat-, wrap and unroll longitudes (C{bool}). @return: C{True} if B{C{point}} is inside the polygon, C{False} otherwise. @raise PointsError: Insufficient number of B{C{points}} @raise TypeError: Some B{C{points}} are not C{LatLon}. @raise ValueError: Invalid B{C{point}}, lat- or longitude. @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) as x: raise _ValueError(point=point, txt=str(x)) if wrap: x0, y0 = wrap180(x0), wrap90(y0) def _dxy3(x1, x2, y2, w): dx, x2 = unroll180(x1, x2, wrap=w) return dx, x2, y2 else: x0 = fmod(x0, _360_0) # not x0 % 360 x0_180_ = x0 - _180_0 x0_180 = x0 + _180_0 def _dxy3(x1, x, y, unused): # PYCHOK expected x = float(x) % _360_0 if x < x0_180_: x += _360_0 elif x >= x0_180: x -= _360_0 return (x - x1), x, y Ps = LatLon2PsxyIter(points, wrap=wrap, loop=1) p = Ps[0] e = m = False S = Fsum() _, x1, y1 = _dxy3(x0, p.x, p.y, False) for i, p in Ps.enumerate(closed=True): dx, x2, y2 = _dxy3(x1, p.x, p.y, (wrap if i else False)) # 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 += 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. @arg points: The polygon points (C{LatLon}[]). @kwarg wrap: Wrap and unroll longitudes (C{bool}). @return: C{True} if the polygon encloses a pole, C{False} otherwise. @raise PointsError: 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. ''' def _cds(points, wrap): # iterate over course deltas Ps = PointsIter(points, loop=2) p2, p1 = Ps[0:2] b1, _ = _bearingTo2(p2, p1, wrap=wrap) for p2 in Ps.iterate(closed=True): if not p2.isequalTo(p1, EPS): b, b2 = _bearingTo2(p1, 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 # summation 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(points, wrap)) # XXX fix (intermittant) edge crossing pole - eg (85,90), (85,0), (85,-90) return abs(s) < 90 # "zero-ish" def luneOf(lon1, lon2, closed=False, LatLon=LatLon_, **LatLon_kwds): '''Generate an ellipsoidal or spherical U{lune <https://WikiPedia.org/wiki/Spherical_lune>}-shaped path or polygon. @arg lon1: Left longitude (C{degrees90}). @arg lon2: Right longitude (C{degrees90}). @kwarg closed: Optionally, close the path (C{bool}). @kwarg LatLon: Class to use (L{LatLon_}). @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments. @return: A tuple of 4 or 5 B{C{LatLon}} instances outlining the lune shape. @see: U{Latitude-longitude quadrangle <https://www.MathWorks.com/help/map/ref/areaquad.html>}. ''' t = (LatLon( _0_0, lon1, **LatLon_kwds), LatLon( _90_0, lon1, **LatLon_kwds), LatLon( _0_0, lon2, **LatLon_kwds), LatLon(-_90_0, lon2, **LatLon_kwds)) if closed: t += t[:1] return t 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}}. @arg point: The other, reference point (C{LatLon}). @arg points: The path or polygon points (C{LatLon}[]). @kwarg closed: Optionally, close the path or polygon (C{bool}). @kwarg wrap: Wrap and L{unroll180} longitudes and longitudinal delta (C{bool}) in function L{equirectangular_}. @kwarg LatLon: Optional class to return the closest point (C{LatLon}) or C{None}. @kwarg options: Other keyword arguments for function L{equirectangular_}. @return: A L{NearestOn3Tuple}C{(closest, distance, angle)} with the {closest} point (B{C{LatLon}}) or if C{B{LatLon} is None}, a L{NearestOn5Tuple}C{(lat, lon, distance, angle, height)}. The C{distance} is the L{equirectangular_} distance between the C{closest} and reference B{C{point}} in C{degrees}. The C{angle} from the reference B{C{point}} to the C{closest} is in compass C{degrees360}, like function L{compassAngle}. @raise LimitError: Lat- and/or longitudinal delta exceeds the B{C{limit}}, see function L{equirectangular_}. @raise PointsError: Insufficient number of B{C{points}} @raise TypeError: Some B{C{points}} are not C{LatLon}. @see: Function L{degrees2m} to convert C{degrees} to C{meter}. ''' def _d2yx(p2, p1, u, w): # w = wrap if (not closed or w < (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): # get height or default 0 return getattr(p, _height_, 0) or 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) / hypot2(dx, dy) Ps = PointsIter(points, loop=1) p1 = c = Ps[0] u1 = u = _0_0 d, dy, dx, _ = _d2yx(p1, point, u1, False) for i, p2 in Ps.enumerate(closed=closed): # iff wrapped, unroll lon1 (actually previous # lon2) like function unroll180/-PI would've w = False if closed and i == 0 else wrap d21, y21, x21, u2 = _d2yx(p2, p1, u1, w) if d21 > EPS: # distance point to p1, y01 and x01 inverted d2, y01, x01, _ = _d2yx(point, p1, u1, closed) 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_0 else: # p2 is closest p1, u1 = p2, u2 d2, y01, x01, _ = _d2yx(point, p1, u1, closed) if d2 < d: # p1 is closer, y01 and x01 inverted c, u, d, dy, dx = p1, u1, d2, -y01, -x01 p1, u1 = p2, u2 d, a, h = hypot(dx, dy), atan2b(dx, dy), _h(c) if LatLon is None: r = NearestOn5Tuple(c.lat, c.lon + u, d, a, h) else: r = LatLon(c.lat, c.lon + u, height=h) r = NearestOn3Tuple(r, 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. @arg points: The path or polygon points (C{LatLon}[]). @kwarg closed: Optionally, close the path or polygon (C{bool}). @kwarg adjust: Adjust the wrapped, unrolled longitudinal delta by the cosine of the mean latitude (C{bool}). @kwarg radius: Mean earth radius (C{meter}). @kwarg wrap: Wrap lat-, wrap and unroll longitudes (C{bool}). @return: Approximate perimeter (C{meter}, same units as B{C{radius}}). @raise PointsError: Insufficient number of B{C{points}} @raise TypeError: Some B{C{points}} are not C{LatLon}. @raise ValueError: Invalid B{C{radius}}. @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}. ''' def _degs(points, closed, wrap): # angular edge lengths in degrees Ps = LatLon2PsxyIter(points, wrap=wrap, loop=1) p1, u = Ps[0], _0_0 # previous x2's unroll/wrap for i, p2 in Ps.enumerate(closed=closed): w = False if closed and i == 0 else wrap # apply previous x2's unroll/wrap to new x1 _, dy, dx, u = equirectangular_(p1.y, p1.x + u, p2.y, p2.x, adjust=adjust, limit=None, wrap=w) # PYCHOK non-sequence yield hypot(dx, dy) p1 = p2 d = fsum(_degs(points, closed, wrap)) return degrees2m(d, radius=radius) def quadOf(latS, lonW, latN, lonE, closed=False, LatLon=LatLon_, **LatLon_kwds): '''Generate a quadrilateral path or polygon from two points. @arg latS: Southernmost latitude (C{degrees90}). @arg lonW: Westernmost longitude (C{degrees180}). @arg latN: Northernmost latitude (C{degrees90}). @arg lonE: Easternmost longitude (C{degrees180}). @kwarg closed: Optionally, close the path (C{bool}). @kwarg LatLon: Class to use (L{LatLon_}). @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments. @return: Return a tuple of 4 or 5 B{C{LatLon}} instances outlining the quadrilateral. @see: Function L{boundsOf}. ''' t = (LatLon(latS, lonW, **LatLon_kwds), LatLon(latN, lonW, **LatLon_kwds), LatLon(latN, lonE, **LatLon_kwds), LatLon(latS, lonE, **LatLon_kwds)) if closed: t += t[:1] return t # **) MIT License # # Copyright (C) 2016-2021 -- 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.