# Coverage for pygeodesy/points.py : 90%

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1422 1423 1424 1425 1426 1427 1428 1429 1430 1431 1432 1433 1434 1435 1436 1437 1438 1439 1440 1441 1442 1443 1444 1445 1446 1447 1448 1449 1450 1451 1452 1453 1454 1455 1456 1457 1458 1459 1460 1461 1462 1463 1464 1465 1466 1467 1468 1469 1470 1471 1472 1473 1474 1475 1476 1477 1478 1479 1480 1481 1482 1483 1484 1485 1486 1487 1488 1489 1490 1491 1492 1493 1494 1495 1496 1497 1498 1499 1500 1501 1502 1503 1504 1505 1506 1507 1508 1509 1510 1511 1512 1513 1514 1515 1516 1517 1518 1519 1520 1521 1522 1523 1524 1525 1526 | # -*- 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 EPS, R_M, isint, _isnotError, issequence, \ map1, property_doc_, property_RO, scalar, \ _Sequence, _TypeError, _xcopy, _xkwds from pygeodesy.dms import F_D, latDMS, lonDMS, parseDMS2 from pygeodesy.fmath import favg, fdot, Fsum, fsum from pygeodesy.formy import equirectangular_, latlon2n_xyz, points2 from pygeodesy.lazily import _ALL_LAZY from pygeodesy.named import Bounds2Tuple, Bounds4Tuple, classname, \ LatLon2Tuple, NearestOn3Tuple, NearestOn5Tuple, \ PhiLam2Tuple, Point3Tuple, Shape2Tuple, \ nameof, notOverloaded, Vector4Tuple, _xnamed from pygeodesy.nvectorBase import NvectorBase, _N_vector_ from pygeodesy.streprs import instr, pairs from pygeodesy.utily import PI_2, degrees90, degrees180, degrees360, degrees2m, \ unroll180, unrollPI, wrap90, wrap180 from pygeodesy.vector3d import CrossError, crosserrors from inspect import isclass from math import atan2, cos, fmod, hypot, radians, sin __all__ = _ALL_LAZY.points __version__ = '20.03.23' class LatLon_(object): # XXX imported by heights._HeightBase.height '''Low-overhead C{LatLon} class for L{Numpy2LatLon} and L{Tuple2LatLon}. ''' # __slots__ efficiency is voided if the __slots__ class attribute # is used in a subclass of a class with the traditional __dict__, # see <https://docs.Python.org/2/reference/datamodel.html#slots> # and __slots__ must be repeated in sub-classes, see "Problems # with __slots__" in Luciano Ramalho, "Fluent Python", page # 276+, O'Reilly, 2016, also at <https://Books.Google.ie/ # books?id=bIZHCgAAQBAJ&lpg=PP1&dq=fluent%20python&pg= # PT364#v=onepage&q=“Problems%20with%20__slots__”&f=false> __slots__ = ('lat', 'lon', 'name', 'height') def __init__(self, lat, lon, name='', height=0): '''Creat a new, mininal, low-overhead L{LatLon_} instance, without heigth and datum. @arg lat: Latitude (C{degrees}). @arg lon: Longitude (C{degrees}). @kwarg name: Optional name (C{str}). @note: The lat- and longitude are taken as-given, un-clipped and un-validated . ''' try: 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 def __eq__(self, other): return isinstance(other, LatLon_) and \ other.lat == self.lat and \ other.lon == self.lon def __ne__(self, other): return not self.__eq__(other) def __repr__(self): return self.toStr2() def __str__(self): return self.toStr() def classof(self, *args, **kwds): '''Instantiate this very class. @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) @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'): '''Check this and an other instance for type compatiblility. @arg other: The other instance (any C{type}). @kwarg name: Optional, name for other (C{str}). @return: C{None}. @raise TypeError: Incompatible B{C{other}} C{type}. ''' if not (isinstance(other, self.__class__) or (hasattr(other, 'lat') and hasattr(other, 'lon'))): raise TypeError('type(%s) mismatch: %s vs %s' % (name, classname(other), classname(self))) @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): '''DEPRECATED, use method C{points2}. ''' return points2(points, closed=closed, base=base) # PYCHOK no cover 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 TypeError: Some B{C{points}} are not B{C{base}}. @raise ValueError: Insufficient number of B{C{points}}. ''' 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 toStr(self, form=F_D, prec=6, sep=', ', **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 += ('%+.2f' % (self.height,),) if self.name: t += (repr(self.name),) if kwds: t += pairs(kwds.items(), prec=prec) return sep.join(t) def toStr2(self, **kwds): '''This L{LatLon_} as a string "class(<degrees>, ...)". @kwarg kwds: Optional, keyword arguments. @return: Class instance (C{str}). ''' return '%s(%s)' % (classname(self), self.toStr(**kwds)) class _Basequence(_Sequence): # immutable, on purpose '''(INTERNAL) Base class. ''' _array = [] _epsilon = EPS _itemname = 'point' def _contains(self, point): '''(INTERNAL) Check for a matching point. ''' for _ in self._findall(point, ()): return True return False def 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 def _find(self, point, start_end): '''(INTERNAL) Find the first matching point index. ''' for i in self._findall(point, start_end): return i return -1 def _findall(self, unused, start_end): # PYCHOK unused '''Must be overloaded. ''' raise NotImplementedError('method: %s' % ('_findall',)) def _getitem(self, index): '''(INTERNAL) Return point [index] or return a slice. ''' # Luciano Ramalho, "Fluent Python", page 290+, O'Reilly, 2016 if isinstance(index, slice): # XXX an numpy.array slice is a view, not a copy return self.__class__(self._array[index], **self._slicekwds()) else: return self.point(self._array[index]) def _index(self, point, start_end): '''(INTERNAL) Find the first matching point index. ''' for i in self._findall(point, start_end): return i raise ValueError('%s not found: %r' % (self._itemname, point)) def _iter(self): '''(INTERNAL) Yield all points. ''' for i in range(len(self)): yield self.point(self._array[i]) def point(self, *attrs): '''(INTERNAL) Must be overloaded. @arg attrs: Optional arguments. ''' notOverloaded(self, self.point.__name__, *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('%s invalid: %r' % ('step', step)) return range(start, end, step) def _repr(self): '''(INTERNAL) Return a string representation. ''' # XXX use Python 3+ reprlib.repr t = repr(self._array[:1]) # only first row t = '%s ...%s[%s]' % (t[:-1], t[-1:], len(self)) t = ' '.join(t.split()) # coalesce spaces return instr(self, t, **self._slicekwds()) def _reversed(self): # PYCHOK false '''(INTERNAL) Yield all points in reverse order. ''' for i in range(len(self) - 1, -1): yield self.point(self._array[i]) def _rfind(self, point, start_end): '''(INTERNAL) Find the last matching point index. ''' def _r3(start=None, end=None, step=-1): return (start, end, step) # PYCHOK returns for i in self._findall(point, _r3(*start_end)): return i return -1 def _slicekwds(self): # PYCHOK no cover '''(INTERNAL) Should be overloaded. ''' return {} def _zeros(self, *zeros): '''(INTERNAL) Check for near-zero values. ''' return all(abs(z) <= self._epsilon for z in zeros) @property_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, 0.0, name='tolerance') @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, ...)) class _Array2LatLon(_Basequence): # immutable, on purpose '''Base class for Numpy2LatLon or Tuple2LatLon. ''' _array = () _ilat = 0 # row column index _ilon = 0 # row column index _LatLon = LatLon_ # default _shape = () def __init__(self, array, ilat=0, ilon=1, LatLon=None, shape=()): '''Handle a C{NumPy} or C{Tuple} array as a sequence of C{LatLon} points. ''' ais = ('ilat', ilat), ('ilon', ilon) if len(shape) != 2 or shape[0] < 1 or shape[1] < len(ais): raise IndexError('%s invalid: %r' % ('array shape', shape)) self._array = array self._shape = Shape2Tuple(*shape) # check the point class if LatLon is not None: if isclass(LatLon) and all(hasattr(LatLon, a) for a in LatLon_.__slots__): self._LatLon = LatLon else: raise _isnotError('valid', LatLon=LatLon) # check the attr indices for n, (ai, i) in enumerate(ais): if not isint(i): raise _isnotError(int.__name__, **{ai: i}) i = int(i) if not 0 <= i < shape[1]: raise _isnotError('valid', Error=ValueError, **{ai: i}) for aj, j in ais[:n]: if int(j) == i: raise ValueError('%s == %s == %s' % (ai, aj, i)) setattr(self, '_' + ai, i) def __contains__(self, latlon): '''Check for a specific lat-/longitude. @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 TypeError: Invalid B{C{latlon}}. @raise ValueError: Point not found. ''' return self._index(latlon, start_end) @property_RO def ilat(self): '''Get the latitudes column index (C{int}). ''' return self._ilat @property_RO def ilon(self): '''Get the longitudes column index (C{int}). ''' return self._ilon # next = __iter__ def point(self, row): # 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 '''Must be overloaded. ''' raise NotImplementedError('method: %s' % ('_subset',)) 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('%s[%s] not valid: %r' % ('indices', i, v)) elif not 0 <= v < n: raise IndexError('%s[%s] not valid: %r' % ('indices', i, v)) return self._subset(indices) class LatLon2psxy(_Basequence): '''Wrapper for C{LatLon} points as "on-the-fly" pseudo-xy coordinates. ''' _closed = False _len = 0 _deg2m = None # default, keep degrees _radius = None _wrap = True def __init__(self, latlons, closed=False, radius=None, wrap=True): '''Handle C{LatLon} points as pseudo-xy coordinates. @note: The C{LatLon} latitude is considered the I{pseudo-y} and longitude the I{pseudo-x} coordinate, likewise for L{LatLon2Tuple}. However, 2-tuples C{(x, y)} are considered as I{(longitude, latitude)}. @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 TypeError: Some B{C{latlons}} are not C{LatLon}. @raise ValueError: Insufficient number of B{C{latlons}}. ''' self._closed = closed self._len, self._array = points2(latlons, closed=closed) if radius: self._radius = radius self._deg2m = degrees2m(1.0, radius) self._wrap = wrap def __contains__(self, xy): '''Check for a matching point. @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 except (TypeError, ValueError): raise _isnotError('valid', xy=xy) def _3xyll(ll): # PYCHOK expected return self.point(ll) for i in self._range(*start_end): xi, yi, _ = _3xyll(self._array[i]) if self._zeros(xi - x, yi - y): yield i def findall(self, xy, *start_end): '''Yield indices of all matching points. @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 TypeError: Invalid B{C{xy}}. @raise ValueError: Point not found. ''' return self._index(xy, start_end) @property_RO def isPoints2(self): '''Is this a LatLon2 wrapper/converter? ''' return True # isinstance(self, (LatLon2psxy, ...)) # next = __iter__ def point(self, ll): # 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 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 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) ''' _TypeError(list, tuple, tuples=tuples) s = len(tuples), min(len(_) for _ in tuples) _Array2LatLon.__init__(self, tuples, ilat=ilat, ilon=ilon, LatLon=LatLon, shape=s) @property_RO def isTuple2(self): '''Is this a Tuple2 wrapper? ''' return True # isinstance(self, (Tuple2LatLon, ...)) def _subset(self, indices): return type(self._array)(self._array[i] for i in indices) def _area2(points, adjust, wrap): # return the signed area in radians squared # setting radius=1 converts degrees to radians pts = LatLon2psxy(points, closed=True, radius=1, wrap=wrap) def _rads2(n, pts): # trapezoidal areas in rads**2 x1, y1, _ = pts[n-1] for i in range(n): x2, y2, _ = pts[i] w, x2 = unrollPI(x1, x2, wrap=wrap if i < (n - 1) else False) # approximate trapezoid by a rectangle, adjusting # the top width by the cosine of the latitudinal # average and bottom width by some fudge factor h = (y2 + y1) * 0.5 if adjust: c = cos(h) if abs(h) < PI_2 else 0 w *= (c + 1.2876) * 0.5 yield h * w # signed trapezoidal area x1, y1 = x2, y2 return fsum(_rads2(len(pts), pts)), pts def areaOf(points, adjust=True, radius=R_M, wrap=True): '''Approximate the area of a polygon. @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 TypeError: Some B{C{points}} are not C{LatLon}. @raise ValueError: Insufficient number of B{C{points}}. @note: This area approximation has limited accuracy and is ill-suited for regions exceeding several hundred Km or Miles or with near-polar latitudes. @see: L{sphericalNvector.areaOf}, L{sphericalTrigonometry.areaOf} and L{ellipsoidalKarney.areaOf}. ''' a, _ = _area2(points, adjust, wrap) return abs(a) * float(radius)**2 def boundsOf(points, wrap=True, LatLon=None): '''Determine the lower-left SW and upper-right NE corners of a path or polygon. @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 TypeError: Some B{C{points}} are not C{LatLon}. @raise ValueError: Insufficient number of B{C{points}}. @example: >>> b = LatLon(45,1), LatLon(45,2), LatLon(46,2), LatLon(46,1) >>> boundsOf(b) # False >>> 45.0, 1.0, 46.0, 2.0 ''' pts = LatLon2psxy(points, closed=False, radius=None, wrap=wrap) lox, loy, _ = hix, hiy, _ = pts[0] for x, y, _ in pts: # [1:] if lox > x: lox = x elif hix < x: hix = x if loy > y: loy = y elif hiy < y: hiy = y return Bounds4Tuple(loy, lox, hiy, hix) if LatLon is None else \ Bounds2Tuple(LatLon(loy, lox), LatLon(hiy, hix)) # PYCHOK inconsistent def centroidOf(points, wrap=True, LatLon=None): '''Determine the centroid of a polygon. @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 TypeError: Some B{C{points}} are not C{LatLon}. @raise ValueError: Insufficient number of B{C{points}} or B{C{points}} enclose a pole or zero area. @see: U{Centroid<https://WikiPedia.org/wiki/Centroid#Of_a_polygon>} and U{Calculating The Area And Centroid Of A Polygon <https://www.Seas.UPenn.edu/~sys502/extra_materials/ Polygon%20Area%20and%20Centroid.pdf>}. ''' # setting radius=1 converts degrees to radians pts = LatLon2psxy(points, closed=True, radius=1, wrap=wrap) n = len(pts) A, X, Y = Fsum(), Fsum(), Fsum() x1, y1, _ = pts[n-1] for i in range(n): x2, y2, _ = pts[i] if wrap and i < (n - 1): _, x2 = unrollPI(x1, x2, wrap=True) t = x1 * y2 - x2 * y1 A += t X += t * (x1 + x2) Y += t * (y1 + y2) # XXX more elaborately: # t1, t2 = x1 * y2, -(x2 * y1) # A.fadd_(t1, t2) # X.fadd_(t1 * x1, t1 * x2, t2 * x1, t2 * x2) # Y.fadd_(t1 * y1, t1 * y2, t2 * y1, t2 * y2) x1, y1 = x2, y2 A = A.fsum() * 3.0 # 6.0 / 2.0 if abs(A) < EPS: raise ValueError('polar or zero area: %r' % (pts,)) Y, X = degrees90(Y.fsum() / A), degrees180(X.fsum() / A) return LatLon2Tuple(Y, X) if LatLon is None else LatLon(Y, X) def _imdex2(closed, n): # imported by sphericalNvector, -Trigonometry '''(INTERNAL) Return first and second index. ''' return (n-1, 0) if closed else (0, 1) def isclockwise(points, adjust=False, wrap=True): '''Determine the direction of a path or polygon. @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 TypeError: Some B{C{points}} are not C{LatLon}. @raise ValueError: Insufficient number of B{C{points}} or the B{C{points}} enclose a pole or zero area. @example: >>> f = LatLon(45,1), LatLon(45,2), LatLon(46,2), LatLon(46,1) >>> isclockwise(f) # False >>> isclockwise(reversed(f)) # True ''' a, pts = _area2(points, adjust, wrap) if a > 0: return True elif a < 0: return False # <https://blog.Element84.com/determining-if-a-spherical-polygon-contains-a-pole.html> raise ValueError('polar or zero area: %r' % (pts,)) def isconvex(points, adjust=False, wrap=True): '''Determine whether a polygon is convex. @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 TypeError: Some B{C{points}} are not C{LatLon}. @raise ValueError: Insufficient number of B{C{points}}. @example: >>> t = LatLon(45,1), LatLon(46,1), LatLon(46,2) >>> isconvex(t) # True >>> f = LatLon(45,1), LatLon(46,2), LatLon(45,2), LatLon(46,1) >>> isconvex(f) # False ''' return bool(isconvex_(points, adjust=adjust, wrap=wrap)) def isconvex_(points, adjust=False, wrap=True): '''Determine whether a polygon is convex and clockwise. @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 TypeError: Some B{C{points}} are not C{LatLon}. @raise ValueError: Insufficient number of B{C{points}}. @example: >>> t = LatLon(45,1), LatLon(46,1), LatLon(46,2) >>> isconvex_(t) # +1 >>> f = LatLon(45,1), LatLon(46,2), LatLon(45,2), LatLon(46,1) >>> isconvex_(f) # 0 ''' def _unroll_adjust(x1, y1, x2, y2, wrap): x21, x2 = unroll180(x1, x2, wrap=wrap) if adjust: y = radians(y1 + y2) * 0.5 x21 *= cos(y) if abs(y) < PI_2 else 0 return x21, x2 pts = LatLon2psxy(points, closed=True, radius=None, wrap=wrap) c, n, s = crosserrors(), len(pts), 0 x1, y1, _ = pts[n-2] x2, y2, _ = pts[n-1] x21, x2 = _unroll_adjust(x1, y1, x2, y2, False) for i in range(n): x3, y3, ll = pts[i] x32, x3 = _unroll_adjust(x2, y2, x3, y3, wrap if i < (n - 2) else False) # get the sign of the distance from point # x3, y3 to the line from x1, y1 to x2, y2 # <https://WikiPedia.org/wiki/Distance_from_a_point_to_a_line> s3 = fdot((x3, y3, x1, y1), y2 - y1, -x21, -y2, x2) if s3 > 0: # x3, y3 on the right if s < 0: # non-convex return 0 s = +1 elif s3 < 0: # x3, y3 on the left if s > 0: # non-convex return 0 s = -1 elif c and fdot((x32, y1 - y2), y3 - y2, -x21) < 0: # colinear u-turn: x3, y3 not on the # opposite side of x2, y2 as x1, y1 raise CrossError('%s %s: %r' % ('colinear', 'point', ll)) x1, y1, x2, y2, x21 = x2, y2, x3, y3, x32 return s # all points on the same side def isenclosedBy(point, points, wrap=False): # MCCABE 15 '''Determine whether a point is enclosed by a polygon. @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 TypeError: Some B{C{points}} are not C{LatLon}. @raise ValueError: Insufficient number of B{C{points}} or invalid B{C{point}}. @see: L{sphericalNvector.LatLon.isenclosedBy}, L{sphericalTrigonometry.LatLon.isenclosedBy} and U{MultiDop GeogContainPt<https://GitHub.com/NASA/MultiDop>} (U{Shapiro et al. 2009, JTECH <https://Journals.AMetSoc.org/doi/abs/10.1175/2009JTECHA1256.1>} and U{Potvin et al. 2012, JTECH <https://Journals.AMetSoc.org/doi/abs/10.1175/JTECH-D-11-00019.1>}). ''' try: y0, x0 = point.lat, point.lon except AttributeError: try: y0, x0 = map1(float, *point[:2]) except (IndexError, TypeError, ValueError): raise ValueError('%s invalid: %r' % ('point', point)) pts = LatLon2psxy(points, closed=True, radius=None, wrap=wrap) n = len(pts) if wrap: x0, y0 = wrap180(x0), wrap90(y0) def _dxy(x1, i): x2, y2, _ = pts[i] dx, x2 = unroll180(x1, x2, wrap=i < (n - 1)) return dx, x2, y2 else: x0 = fmod(x0, 360.0) # not x0 % 360 def _dxy(x1, i): # PYCHOK expected x, y, _ = pts[i] x %= 360.0 if x < (x0 - 180): x += 360 elif x >= (x0 + 180): x -= 360 return (x - x1), x, y e = m = False s = Fsum() _, x1, y1 = _dxy(x0, n - 1) for i in range(n): dx, x2, y2 = _dxy(x1, i) # ignore duplicate and near-duplicate pts if max(abs(dx), abs(y2 - y1)) > EPS: # determine if polygon edge (x1, y1)..(x2, y2) straddles # point (lat, lon) or is on boundary, but do not count # edges on boundary as more than one crossing if abs(dx) < 180 and (x1 < x0 <= x2 or x2 < x0 <= x1): m = not m dy = (x0 - x1) * (y2 - y1) - (y0 - y1) * dx if (dy > 0 and dx >= 0) or (dy < 0 and dx <= 0): e = not e s.fadd_(sin(radians(y2))) x1, y1 = x2, y2 # An odd number of meridian crossings means, the polygon # contains a pole. Assume it is the pole on the hemisphere # containing the polygon mean point and if the polygon does # contain the North Pole, flip the result. if m and s.fsum() > 0: e = not e return e def ispolar(points, wrap=False): '''Check whether a polygon encloses a pole. @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 ValueError: Insufficient number of B{C{points}}. @raise TypeError: Some B{C{points}} are not C{LatLon} or don't have C{bearingTo2}, C{initialBearingTo} and C{finalBearingTo} methods. ''' n, points = points2(points, closed=True) def _cds(n, points): # iterate over course deltas p1 = points[n-1] try: # LatLon must have initial- and finalBearingTo b1, _ = p1.bearingTo2(points[0], wrap=wrap) except AttributeError: raise _isnotError('.bearingTo2', points=p1) for i in range(n): p2 = points[i] if not p2.isequalTo(p1, EPS): b, b2 = p1.bearingTo2(p2, wrap=wrap) yield wrap180(b - b1) # (b - b1 + 540) % 360 - 180 yield wrap180(b2 - b) # (b2 - b + 540) % 360 - 180 p1, b1 = p2, b2 # sum of course deltas around pole is 0° rather than normally ±360° # <https://blog.Element84.com/determining-if-a-spherical-polygon-contains-a-pole.html> s = fsum(_cds(n, points)) # XXX fix (intermittant) edge crossing pole - eg (85,90), (85,0), (85,-90) return abs(s) < 90 # "zero-ish" def nearestOn5(point, points, closed=False, wrap=False, LatLon=None, **options): '''Locate the point on a path or polygon closest to an other point. If the given point is within the extent of a polygon edge, the closest point is on that edge, otherwise the closest point is the nearest of that edge's end points. Distances are approximated by function L{equirectangular_}, subject to the supplied B{C{options}}. @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 TypeError: Some B{C{points}} are not C{LatLon}. @raise ValueError: Insufficient number of B{C{points}}. @see: Function L{degrees2m} to convert C{degrees} to C{meter}. ''' n, points = points2(points, closed=closed) def _d2yx(p2, p1, u, i): w = wrap if (not closed or i < (n - 1)) else False # equirectangular_ returns a Distance4Tuple(distance # in degrees squared, delta lat, delta lon, p2.lon # unroll/wrap); the previous p2.lon unroll/wrap # is also applied to the next edge's p1.lon return equirectangular_(p1.lat, p1.lon + u, p2.lat, p2.lon, wrap=w, **options) def _h(p): try: # get height return p.height or 0 except AttributeError: return 0 # point (x, y) on axis rotated ccw by angle a: # x' = y * sin(a) + x * cos(a) # y' = y * cos(a) - x * sin(a) # # distance (w) along and perpendicular (h) to # a line thru point (dx, dy) and the origin: # w = (y * dy + x * dx) / hypot(dx, dy) # h = (y * dx - x * dy) / hypot(dx, dy) # # closest point on that line thru (dx, dy): # xc = dx * w / hypot(dx, dy) # yc = dy * w / hypot(dx, dy) # or # xc = dx * f # yc = dy * f # with # f = w / hypot(dx, dy) # or # f = (y * dy + x * dx) / hypot2(dx, dy) i, m = _imdex2(closed, n) p2 = c = points[i] u2 = u = 0 d, dy, dx, _ = _d2yx(p2, point, u2, i) for i in range(m, n): p1, u1, p2 = p2, u2, points[i] # iff wrapped, unroll lon1 (actually previous # lon2) like function unroll180/-PI would've d21, y21, x21, u2 = _d2yx(p2, p1, u1, i) if d21 > EPS: # distance point to p1, y01 and x01 inverted d2, y01, x01, _ = _d2yx(point, p1, u1, n) if d2 > EPS: w2 = y01 * y21 + x01 * x21 if w2 > 0: if w2 < d21: # closest is between p1 and p2, use # original delta's, not y21 and x21 f = w2 / d21 p1 = LatLon_(favg(p1.lat, p2.lat, f=f), favg(p1.lon, p2.lon + u2, f=f), height=favg(_h(p1), _h(p2), f=f)) u1 = 0 else: # p2 is closest p1, u1 = p2, u2 d2, y01, x01, _ = _d2yx(point, p1, u1, n) if d2 < d: # p1 is closer, y01 and x01 inverted c, u, d, dy, dx = p1, u1, d2, -y01, -x01 d, a, h = hypot(dx, dy), degrees360(atan2(dx, dy)), _h(c) if LatLon is None: r = NearestOn5Tuple(c.lat, c.lon + u, d, a, h) else: r = 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 TypeError: Some B{C{points}} are not C{LatLon}. @raise ValueError: Insufficient number of B{C{points}}. @note: This perimeter is based on the L{equirectangular_} distance approximation and is ill-suited for regions exceeding several hundred Km or Miles or with near-polar latitudes. @see: L{sphericalTrigonometry.perimeterOf} and L{ellipsoidalKarney.perimeterOf}. ''' pts = LatLon2psxy(points, closed=closed, radius=None, wrap=False) def _degs(n, pts, closed): # angular edge lengths in degrees i, m = _imdex2(closed, n) x1, y1, _ = pts[i] u = 0 # previous x2's unroll/wrap for i in range(m, n): x2, y2, _ = pts[i] w = wrap if (not closed or i < (n - 1)) else False # apply previous x2's unroll/wrap to new x1 _, dy, dx, u = equirectangular_(y1, x1 + u, y2, x2, adjust=adjust, limit=None, wrap=w) yield hypot(dx, dy) x1, y1 = x2, y2 d = fsum(_degs(len(pts), pts, closed)) return degrees2m(d, radius) # **) MIT License # # Copyright (C) 2016-2020 -- mrJean1 at Gmail -- All Rights Reserved. # # Permission is hereby granted, free of charge, to any person obtaining a # copy of this software and associated documentation files (the "Software"), # to deal in the Software without restriction, including without limitation # the rights to use, copy, modify, merge, publish, distribute, sublicense, # and/or sell copies of the Software, and to permit persons to whom the # Software is furnished to do so, subject to the following conditions: # # The above copyright notice and this permission notice shall be included # in all copies or substantial portions of the Software. # # THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS # OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, # FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL # THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR # OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, # ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR # OTHER DEALINGS IN THE SOFTWARE.