# Coverage for pygeodesy/points.py : 94%

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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 | # -*- 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.basics import isclass, isint, issequence, map1, \ property_doc_, property_RO, _Sequence, \ _xcopy, _xinstanceof, _xkwds 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_pop from pygeodesy.fmath import favg, fdot, Fsum, fsum from pygeodesy.formy import equirectangular_, latlon2n_xyz, points2 from pygeodesy.interns import EPS, NN, PI_2, R_M, _colinear_, _COMMA_SPACE_, \ _datum_, _height_, _item_ps, _item_sq, _lat_, \ _lon_, _name_, _point_, _SPACE_, _UNDERSCORE_, \ _valid_, _x_, _y_, _0_0, _0_5, _1_0, _3_0, \ _90_0, _180_0, _360_0 from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY from pygeodesy.named import classname, _NamedTuple, nameof, \ notImplemented, notOverloaded, _Pass, \ _xnamed, _xother3, _xotherError from pygeodesy.namedTuples import Bounds2Tuple, Bounds4Tuple, \ LatLon2Tuple, NearestOn3Tuple, \ PhiLam2Tuple, Vector4Tuple from pygeodesy.nvectorBase import NvectorBase, _N_vector_ from pygeodesy.streprs import hstr, instr, pairs from pygeodesy.units import Degrees, Lat, Lon, Meter, Number_, \ Radius, Scalar_ from pygeodesy.utily import atan2b, degrees90, degrees180, degrees2m, \ unroll180, unrollPI, wrap90, wrap180 from math import cos, fmod, hypot, radians, sin __all__ = _ALL_LAZY.points __version__ = '20.09.26' 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_, _datum_) def __init__(self, lat, lon, name=NN, height=0, datum=None): '''Creat a new, mininal, low-overhead L{LatLon_} instance, without heigth 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__}). ''' if 'name' in kwds: return self.__class__(*args, **kwds) else: return self.__class__(name=self.name, *args, **kwds) 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) @property_RO def latlon(self): '''Get the lat- and longitude in C{degrees} (L{LatLon2Tuple}C{(lat, lon)}). ''' return LatLon2Tuple(self.lat, self.lon) @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) def others(self, *other, **name_other_up): # see .named._namedBase.others '''Refined class comparison. @arg other: The other instance (L{any}). @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)) @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) 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 to2ab(self): # PYCHOK no cover '''DEPRECATED, use property C{philam}. @return: A L{PhiLam2Tuple}C{(phi, lam)}. ''' 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 B{C{Nvector=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: r = Nvector(x, y, z, h=r.h, **_xkwds(Nvector_kwds, 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 _item_ps(classname(self), self.toStr(**kwds)) toStr2 = toRepr # PYCHOK for backward compatibility '''DEPRECATED, used method L{LatLon_.toRepr}.''' def toStr(self, form=F_D, prec=6, sep=_COMMA_SPACE_, **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) 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, self._findall, 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}. @arg attrs: Optional arguments. ''' notOverloaded(self, self.point, *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 = '%s ... %s[%s]' % (t[:-1], 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) # 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 _ValueError(ai, i) for aj, j in ais[:n]: if int(j) == i: raise _ValueError(' == '.join(map1(str, ai, aj, i))) setattr(self, _UNDERSCORE_ + 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 unused '''(INTERNAL) I{Must be implemented/overloaded}. ''' notImplemented(self, self._subset, 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(_item_sq(indices=i), v) elif not 0 <= v < n: raise _IndexError(_item_sq(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 = radius self._deg2m = degrees2m(_1_0, radius) 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, ...)) # next = __iter__ 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 Point3Tuple(_NamedTuple): '''3-Tuple C{(x, y, ll)} in C{meter}, C{meter} and C{LatLon}. ''' _Names_ = (_x_, _y_, 'll') _Units_ = ( Meter, Meter, _Pass) 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 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) ''' _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): # 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_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 _areaError(pts, near_=NN): # imported by .ellipsoidalKarney '''(INTERNAL) Area issue. ''' return _ValueError(near_ + 'zero or polar area', txt='%s ...' % (pts[:3],)) 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}). @kwarg wrap: Wrap lat-, wrap and unroll longitudes (C{bool}). @return: Approximate area (C{meter}, same units as B{C{radius}}, I{squared}). @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) * 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}. @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 r = Bounds4Tuple(loy, lox, hiy, hix) if LatLon is None else \ Bounds2Tuple(LatLon(loy, lox), LatLon(hiy, hix)) # PYCHOK inconsistent return r 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 (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 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. ''' # 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 _areaError(points, near_='near-') 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. @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, _ = _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(points) 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, 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_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(points=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)) 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_0): x += _360_0 elif x >= (x0 + _180_0): x -= _360_0 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. @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. ''' 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 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: Yield 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>}. ''' for ll in ((_0_0, lon1), (_90_0, lon1), (_0_0, lon2), (-_90_0, lon2)): yield LatLon(*ll, **LatLon_kwds) if closed: yield LatLon(_0_0, lon1, **LatLon_kwds) 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 (L{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 B{C{LatLon}} is C{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}. ''' 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) / hypot2(dx, dy) i, m = _imdex2(closed, n) p2 = c = points[i] u2 = u = _0_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_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), 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}. ''' 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_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=radius) def quadOf(lat1, lon1, lat2, lon2, closed=False, LatLon=LatLon_, **LatLon_kwds): '''Generate a quadrilateral path or polygon from two points. @arg lat1: Lower latitude (C{degrees90}). @arg lon1: Left longitude (C{degrees180}). @arg lat2: Upper latitude (C{degrees90}). @arg lon2: Right 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: Yield 4 or 5 B{C{LatLon}} instances outlining the quadrilateral. ''' for ll in ((lat1, lon1), (lat2, lon1), (lat2, lon2), (lat1, lon2)): yield LatLon(*ll, **LatLon_kwds) if closed: yield LatLon(lat1, lon1, **LatLon_kwds) __all__ += _ALL_DOCS(NearestOn5Tuple, Point3Tuple, Shape2Tuple) # **) 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.