Coverage for pygeodesy/points.py: 92%
610 statements
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« prev ^ index » next coverage.py v7.2.2, created at 2023-08-06 15:27 -0400
2# -*- coding: utf-8 -*-
4u'''Utilities for point lists, tuples, etc.
6Functions to handle collections and sequences of C{LatLon} points
7specified as 2-d U{NumPy<https://www.NumPy.org>}, C{arrays} or tuples
8as C{LatLon} or as C{pseudo-x/-y} pairs.
10C{NumPy} arrays are assumed to contain rows of points with a lat-, a
11longitude -and possibly other- values in different columns. While
12iterating over the array rows, create an instance of a given C{LatLon}
13class "on-the-fly" for each row with the row's lat- and longitude.
15The original C{NumPy} array is read-accessed only and never duplicated,
16except to return a I{subset} of the original array.
18For example, to process a C{NumPy} array, wrap the array by instantiating
19class L{Numpy2LatLon} and specifying the column index for the lat- and
20longitude in each row. Then, pass the L{Numpy2LatLon} instance to any
21L{pygeodesy} function or method accepting a I{points} argument.
23Similarly, class L{Tuple2LatLon} is used to instantiate a C{LatLon} from
24each 2+tuple in a sequence of such 2+tuples using the C{ilat} lat- and
25C{ilon} longitude index in each 2+tuple.
26'''
28from pygeodesy.basics import isclass, isint, isscalar, issequence, \
29 issubclassof, _Sequence, _xcopy, _xdup, \
30 _xinstanceof
31from pygeodesy.constants import EPS, EPS1, PI_2, R_M, isnear0, isnear1, \
32 _umod_360, _0_0, _0_5, _1_0, _2_0, _6_0, \
33 _90_0, _N_90_0, _180_0, _360_0
34# from pygeodesy.datums import _spherical_datum # from .formy
35from pygeodesy.dms import F_D, latDMS, lonDMS, parseDMS, S_DEG, S_DMS, \
36 S_MIN, S_SEC, S_SEP
37from pygeodesy.errors import CrossError, crosserrors, _IndexError, \
38 _IsnotError, _TypeError, _ValueError, \
39 _xattr, _xkwds, _xkwds_pop
40from pygeodesy.fmath import favg, fdot, hypot, Fsum, fsum
41# from pygeodesy.fsums import Fsum, fsum # from .fmath
42from pygeodesy.formy import _bearingTo2, equirectangular_, _isequalTo, \
43 isnormal, latlon2n_xyz, normal, _spherical_datum
44from pygeodesy.interns import NN, _colinear_, _COMMASPACE_, _composite_, \
45 _DEQUALSPACED_, _ELLIPSIS_, _EW_, _immutable_, \
46 _lat_, _lon_, _LatLon_, _near_, _no_, _not_, \
47 _NS_, _point_, _SPACE_, _UNDER_, _valid_
48from pygeodesy.iters import LatLon2PsxyIter, PointsIter, points2
49from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS
50from pygeodesy.named import classname, nameof, notImplemented, notOverloaded, \
51 _NamedTuple, _xnamed, _xother3, _xotherError
52from pygeodesy.namedTuples import Bounds2Tuple, Bounds4Tuple, \
53 LatLon2Tuple, NearestOn3Tuple, \
54 NearestOn5Tuple, PhiLam2Tuple, \
55 Point3Tuple, Vector3Tuple, Vector4Tuple
56from pygeodesy.nvectorBase import NvectorBase, _N_vector_
57from pygeodesy.props import deprecated_method, Property, Property_RO, \
58 property_doc_, property_RO, _update_all
59from pygeodesy.streprs import Fmt, hstr, instr, pairs
60from pygeodesy.units import Number_, Radius, Scalar, Scalar_
61from pygeodesy.utily import atan2b, degrees90, degrees180, degrees2m, \
62 unroll180, _unrollon, unrollPI, _Wrap, wrap180
64from math import cos, fabs, fmod, radians, sin
66__all__ = _ALL_LAZY.points
67__version__ = '23.08.04'
69_ilat_ = 'ilat'
70_ilon_ = 'ilon'
71_ncols_ = 'ncols'
72_nrows_ = 'nrows'
75class LatLon_(object): # XXX in heights._HeightBase.height
76 '''Low-overhead C{LatLon} class for L{Numpy2LatLon} and L{Tuple2LatLon}.
77 '''
78 # __slots__ efficiency is voided if the __slots__ class attribute
79 # is used in a subclass of a class with the traditional __dict__,
80 # see <https://docs.Python.org/2/reference/datamodel.html#slots>
81 # and __slots__ must be repeated in sub-classes, see "Problems
82 # with __slots__" in Luciano Ramalho, "Fluent Python", page
83 # 276+, O'Reilly, 2016, also at <https://Books.Google.ie/
84 # books?id=bIZHCgAAQBAJ&lpg=PP1&dq=fluent%20python&pg=
85 # PT364#v=onepage&q=“Problems%20with%20__slots__”&f=false>
86 #
87 # __slots__ = (_lat_, _lon_, _height_, _datum_, _name_)
88 # Property_RO = property_RO # no __dict__ with __slots__!
89 #
90 # However, sys.getsizeof(LatLon_(1, 2)) is 72-88 with __slots__
91 # but only 48-56 bytes without in Python 2.7.18+ and Python 3+.
93 def __init__(self, latlonh, lon=None, name=NN, height=0,
94 datum=None, wrap=False):
95 '''Creat a new, mininal, low-overhead L{LatLon_} instance.
97 @arg latlonh: Latitude (C{degrees} or DMS C{str} with N or S suffix) or
98 a previous C{LatLon} instance provided C{B{lon}=None}.
99 @kwarg lon: Longitude (C{degrees} or DMS C{str} with E or W suffix) or
100 C(None), indicating B{C{latlonh}} is a C{LatLon}.
101 @kwarg name: Optional name (C{str}).
102 @kwarg height: Optional height (C{meter}, conventionally).
103 @kwarg datum: Optional datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2},
104 L{a_f2Tuple} or I{scalar} radius) or C{None}.
105 @kwarg wrap: If C{True}, wrap or I{normalize} B{C{lat}} and B{C{lon}}
106 (C{bool}).
108 @raise TypeError: Invalid B{C{datum}} or B{C{latlonh}} not a C{LatLon}.
110 @note: The lat- and longitude are taken as-given,
111 un-clipped and un-validated .
112 '''
113 if lon is None: # PYCHOK no cover
114 try:
115 ll = latlonh.lat, latlonh.lon
116 height = _xattr(latlonh, height=height)
117 except AttributeError:
118 raise _IsnotError(_LatLon_, latlonh=latlonh)
119 if wrap:
120 ll = _Wrap.latlon(*ll)
121 elif wrap: # PYCHOK no cover
122 ll = _Wrap.latlonDMS2(latlonh, lon)
123 else: # must be latNS, lonEW
124 ll = parseDMS(latlonh, suffix=_NS_), parseDMS(lon, suffix=_EW_)
126 self.lat, self.lon = ll
127 self.name = str(name) if name else NN
128 self.height = height
129 self.datum = datum if datum is None else \
130 _spherical_datum(datum, name=self.name)
132 def __eq__(self, other):
133 return isinstance(other, LatLon_) and \
134 other.lat == self.lat and \
135 other.lon == self.lon
137 def __ne__(self, other):
138 return not self.__eq__(other)
140 def __repr__(self):
141 return self.toRepr()
143 def __str__(self):
144 return self.toStr()
146 def classof(self, *args, **kwds):
147 '''Instantiate this very class.
149 @arg args: Optional, positional arguments.
150 @kwarg kwds: Optional, keyword arguments.
152 @return: New instance (C{self.__class__}).
153 '''
154 return _xnamed(self.__class__(*args, **kwds), self.name)
156 def copy(self, deep=False):
157 '''Make a shallow or deep copy of this instance.
159 @kwarg deep: If C{True} make a deep, otherwise a
160 shallow copy (C{bool}).
162 @return: The copy (C{This} (sub-)class).
163 '''
164 return _xcopy(self, deep=deep)
166 def dup(self, **items):
167 '''Duplicate this instance, replacing some items.
169 @kwarg items: Attributes to be changed (C{any}).
171 @return: The duplicate (C{This} (sub-)class).
173 @raise AttributeError: Some B{C{items}} invalid.
174 '''
175 d = _xdup(self, **items)
176 if items:
177 _update_all(d)
178 return d
180 def heightStr(self, prec=-2):
181 '''Return a string for the height B{C{height}}.
183 @kwarg prec: Number of (decimal) digits, unstripped (C{int}).
185 @see: Function L{pygeodesy.hstr}.
186 '''
187 return hstr(self.height, prec=prec)
189 def intermediateTo(self, other, fraction, height=None, wrap=False):
190 '''Locate the point at a given fraction between (or along) this
191 and an other point.
193 @arg other: The other point (C{LatLon}).
194 @arg fraction: Fraction between both points (C{float},
195 0.0 for this and 1.0 for the other point).
196 @kwarg height: Optional height (C{meter}), overriding the
197 intermediate height.
198 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll
199 the B{C{other}} point (C{bool}).
201 @return: Intermediate point (this C{LatLon}).
203 @raise TypeError: Incompatible B{C{other}} C{type}.
204 '''
205 f = Scalar(fraction=fraction)
206 if isnear0(f):
207 r = self
208 elif isnear1(f) and not wrap:
209 r = self.others(other)
210 else:
211 p = self.others(other)
212 h = favg(self.height, p.height, f=f) if height is None else height
213 _, lat, lon = _Wrap.latlon3(self.lon, p.lat, p.lon, wrap=wrap)
214 r = self.classof(favg(self.lat, lat, f=f),
215 favg(self.lon, lon, f=f),
216 height=h, datum=self.datum,
217 name=self.intermediateTo.__name__)
218 return r
220 @Property_RO # PYCHOK no cover
221 def isEllipsoidal(self):
222 '''Check whether this point is ellipsoidal (C{bool} or C{None} if unknown).
223 '''
224 return self.datum.isEllipsoidal if self.datum else None
226 @Property_RO # PYCHOK no cover
227 def isEllipsoidalLatLon(self):
228 '''Get C{LatLon} base.
229 '''
230 return False
232 def isequalTo(self, other, eps=None):
233 '''Compare this point with an other point, I{ignoring} height.
235 @arg other: The other point (C{LatLon}).
236 @kwarg eps: Tolerance for equality (C{degrees}).
238 @return: C{True} if both points are identical,
239 I{ignoring} height, C{False} otherwise.
241 @raise UnitError: Invalid B{C{eps}}.
242 '''
243 return _isequalTo(self, self.others(other), eps=eps)
245 @Property_RO
246 def isnormal(self):
247 '''Return C{True} if this point is normal (C{bool}),
248 meaning C{abs(lat) <= 90} and C{abs(lon) <= 180}.
250 @see: Methods L{normal}, L{toNormal} and functions
251 L{pygeodesy.isnormal} and L{pygeodesy.normal}.
252 '''
253 return isnormal(self.lat, self.lon, eps=0)
255 @Property_RO
256 def isSpherical(self): # PYCHOK no cover
257 '''Check whether this point is spherical (C{bool} or C{None} if unknown).
258 '''
259 return self.datum.isSpherical if self.datum else None
261 @Property_RO
262 def lam(self):
263 '''Get the longitude (B{C{radians}}).
264 '''
265 return radians(self.lon)
267 @Property
268 def latlon(self):
269 '''Get the lat- and longitude in C{degrees} (L{LatLon2Tuple}C{(lat, lon)}).
270 '''
271 return LatLon2Tuple(self.lat, self.lon, name=self.name)
273 @latlon.setter # PYCHOK setter!
274 def latlon(self, latlon):
275 '''Set the lat- and longitude.
277 @arg latlon: New lat- and longitude in C{degrees} (C{2-tuple} or {-list}).
278 '''
279 if self.latlon != latlon[:2]:
280 _update_all(self)
281 self.lat, self.lon = latlon[:2]
283 @Property_RO
284 def latlonheight(self):
285 '''Get the lat-, longitude and height (L{LatLon3Tuple}C{(lat, lon, height)}).
286 '''
287 return self.latlon.to3Tuple(self.height)
289 @Property_RO
290 def _N_vector(self):
291 '''(INTERNAL) Get the minimal, low-overhead (C{nvectorBase._N_vector_})
292 '''
293 return _N_vector_(*latlon2n_xyz(self.lat, self.lon),
294 h=self.height, name=self.name)
296 def others(self, *other, **name_other_up): # see .named._namedBase.others
297 '''Refined class comparison.
299 @arg other: The other instance (any C{type}).
300 @kwarg name_other_up: Overriding C{name=other} and C{up=1}
301 keyword arguments.
303 @return: The B{C{other}} if compatible.
305 @raise TypeError: Incompatible B{C{other}} C{type}.
306 '''
307 other, name, up = _xother3(self, other, **name_other_up)
308 if isinstance(other, self.__class__) or (hasattr(other, _lat_)
309 and hasattr(other, _lon_)):
310 return other
311 raise _xotherError(self, other, name=name, up=up + 1)
313 def normal(self):
314 '''Normalize this point I{in-place} to C{abs(lat) <= 90} and
315 C{abs(lon) <= 180}.
317 @return: C{True} if this point was I{normal}, C{False} if it
318 wasn't (but is now).
320 @see: Property L{isnormal} and method L{toNormal}.
321 '''
322 n = self.isnormal
323 if not n:
324 self.latlon = normal(*self.latlon)
325 return n
327 @Property_RO
328 def phi(self):
329 '''Get the latitude (B{C{radians}}).
330 '''
331 return radians(self.lat)
333 @Property_RO
334 def philam(self):
335 '''Get the lat- and longitude (L{PhiLam2Tuple}C{(phi, lam)}).
336 '''
337 return PhiLam2Tuple(self.phi, self.lam, name=self.name)
339 @Property_RO
340 def philamheight(self):
341 '''Get the lat-, longitude in C{radians} and height (L{PhiLam3Tuple}C{(phi, lam, height)}).
342 '''
343 return self.philam.to3Tuple(self.height)
345 @deprecated_method
346 def points(self, points, closed=False, base=None): # PYCHOK no cover
347 '''DEPRECATED, use method C{points2}.'''
348 return points2(points, closed=closed, base=base)
350 def points2(self, points, closed=False, base=None):
351 '''Check a path or polygon represented by points.
353 @arg points: The path or polygon points (C{LatLon}[])
354 @kwarg closed: Optionally, consider the polygon closed,
355 ignoring any duplicate or closing final
356 B{C{points}} (C{bool}).
357 @kwarg base: Optionally, check all B{C{points}} against
358 this base class, if C{None} don't check.
360 @return: A L{Points2Tuple}C{(number, points)} with the number
361 of points and the points C{list} or C{tuple}.
363 @raise PointsError: Insufficient number of B{C{points}}.
365 @raise TypeError: Some B{C{points}} are not B{C{base}}.
366 '''
367 return points2(points, closed=closed, base=base)
369 def PointsIter(self, points, loop=0, dedup=False):
370 '''Return a points iterator.
372 @arg points: The path or polygon points (C{LatLon}[])
373 @kwarg loop: Number of loop-back points (non-negative C{int}).
374 @kwarg dedup: Skip duplicate points (C{bool}).
376 @return: A new C{PointsIter} iterator.
378 @raise PointsError: Insufficient number of B{C{points}}.
379 '''
380 return PointsIter(points, base=self, loop=loop, dedup=dedup)
382 @deprecated_method
383 def to2ab(self): # PYCHOK no cover
384 '''DEPRECATED, use property L{philam}.'''
385 return self.philam
387 def toNormal(self, deep=False, name=NN):
388 '''Get a copy of this point normalized to C{abs(lat) <= 90}
389 and C{abs(lon) <= 180}.
391 @kwarg deep: If C{True} make a deep, otherwise a
392 shallow copy (C{bool}).
393 @kwarg name: Optional name of the copy (C{str}).
395 @return: A copy of this point, I{normalized} and
396 optionally renamed (C{LatLon}).
398 @see: Property L{isnormal}, method L{normal} and
399 function L{pygeodesy.normal}.
400 '''
401 ll = self.copy(deep=deep)
402 _ = ll.normal()
403 if name:
404 ll.name = str(name)
405 return ll
407 def toNvector(self, h=None, Nvector=NvectorBase, **Nvector_kwds):
408 '''Convert this point to C{n-vector} (normal to the earth's
409 surface) components, I{including height}.
411 @kwarg h: Optional height, overriding this point's height
412 (C{meter}).
413 @kwarg Nvector: Optional class to return the C{n-vector}
414 components (C{Nvector}) or C{None}.
415 @kwarg Nvector_kwds: Optional, additional B{C{Nvector}} keyword
416 arguments, ignored if C{B{Nvector} is None}.
418 @return: The C{n-vector} components B{C{Nvector}} or if
419 B{C{Nvector}} is C{None}, a L{Vector4Tuple}C{(x,
420 y, z, h)}.
422 @raise TypeError: Invalid B{C{Nvector}} or B{C{Nvector_kwds}}
423 argument.
424 '''
425 x, y, z = latlon2n_xyz(self.lat, self.lon)
426 r = Vector4Tuple(x, y, z, self.height if h is None else h)
427 if Nvector is not None:
428 r = Nvector(x, y, z, **_xkwds(Nvector_kwds, h=r.h, ll=self))
429 return _xnamed(r, self.name)
431 def toRepr(self, **kwds):
432 '''This L{LatLon_} as a string "class(<degrees>, ...)".
434 @kwarg kwds: Optional, keyword arguments.
436 @return: Class instance (C{str}).
437 '''
438 _ = _xkwds_pop(kwds, std=None) # PYCHOK std unused
439 return Fmt.PAREN(classname(self), self.toStr(**kwds))
441 def toStr(self, form=F_D, joined=_COMMASPACE_, **prec_sep_s_D_M_S_kwds):
442 '''Convert this point to a "lat, lon[, height][, name][, ...]" string,
443 formatted in the given C{B{form}at}.
445 @kwarg form: The lat-/longitude C{B{form}at} to use (C{str}), see
446 functions L{pygeodesy.latDMS} or L{pygeodesy.lonDMS}.
447 @kwarg joined: Separator to join the lat-, longitude, heigth, name
448 and other strings (C{str} or C{None} or C{NN} for
449 non-joined).
450 @kwarg prec_sep_s_D_M_S_kwds: Optional C{B{prec}ision}, C{B{sep}arator},
451 B{C{s_D}}, B{C{s_M}}, B{C{s_S}}, B{C{s_DMS}} and possibly
452 other keyword arguments, see functions L{pygeodesy.latDMS}
453 or L{pygeodesy.lonDMS}.
455 @return: This point in the specified C{B{form}at}, etc. (C{str} or
456 a 2- or 3+tuple C{(lat_str, lon_str[, height_str][, name_str][,
457 ...])} if C{B{joined}=NN} or C{B{joined}=None} and with the
458 C{height_str} and C{name_str} only included if non-zero
459 respectively non-empty).
461 @see: Function L{pygeodesy.latDMS} or L{pygeodesy.lonDMS} for more
462 details about keyword arguments C{B{form}at}, C{B{prec}ision},
463 C{B{sep}arator}, B{C{s_D}}, B{C{s_M}}, B{C{s_S}} and B{C{s_DMS}}.
464 '''
465 def _t3(prec=None, sep=S_SEP, s_D=S_DEG, s_M=S_MIN, s_S=S_SEC, s_DMS=S_DMS, **kwds):
466 return dict(prec=prec, sep=sep, s_D=s_D, s_M=s_M, s_S=s_S, s_DMS=s_DMS), kwds, prec
468 prec_sep_s_D_M_S, kwds, prec = _t3(**prec_sep_s_D_M_S_kwds)
469 t = (latDMS(self.lat, form=form, **prec_sep_s_D_M_S),
470 lonDMS(self.lon, form=form, **prec_sep_s_D_M_S))
471 if self.height:
472 t += (self.heightStr(),)
473 if self.name:
474 t += (repr(self.name),)
475 if kwds:
476 t += pairs(kwds) if prec is None else pairs(kwds, prec=prec)
477 return joined.join(t) if joined else t
479 @deprecated_method
480 def toStr2(self, **kwds): # PYCHOK no cover
481 '''DEPRECATED, used method L{toRepr}.'''
482 return self.toRepr(**kwds)
485def _isLatLon(inst):
486 '''(INTERNAL) Check a C{LatLon} or C{LatLon_} instance.
487 '''
488 return isinstance(inst, (LatLon_, _MODS.latlonBase.LatLonBase))
491def _isLatLon_(LL):
492 '''(INTERNAL) Check a (sub-)class of C{LatLon_}.
493 '''
494 return issubclassof(LL, LatLon_) or (isclass(LL) and
495 all(hasattr(LL, a) for a in _ALL_ATTRS_))
498# get all pseudo-slots for class C{LatLon_}
499_ALL_ATTRS_ = tuple(LatLon_(0, 0).__dict__.keys())
502class _Basequence(_Sequence): # immutable, on purpose
503 '''(INTERNAL) Base class.
504 '''
505 _array = []
506 _epsilon = EPS
507 _itemname = _point_
509 def _contains(self, point):
510 '''(INTERNAL) Check for a matching point.
511 '''
512 return any(self._findall(point, ()))
514 def copy(self, deep=False): # PYCHOK no cover
515 '''Make a shallow or deep copy of this instance.
517 @kwarg deep: If C{True} make a deep, otherwise a
518 shallow copy (C{bool}).
520 @return: The copy (C{This class} or subclass thereof).
521 '''
522 return _xcopy(self, deep=deep)
524 def _count(self, point):
525 '''(INTERNAL) Count the number of matching points.
526 '''
527 return sum(1 for _ in self._findall(point, ())) # NOT len()!
529 def dup(self, **items): # PYCHOK no cover
530 '''Duplicate this instance, I{without replacing items}.
532 @kwarg items: No attributes (I{not allowed}).
534 @return: The duplicate (C{This} (sub-)class).
536 @raise TypeError: Any B{C{items}} invalid.
537 '''
538 if items:
539 t = _SPACE_(classname(self), _immutable_)
540 raise _TypeError(txt=t, this=self, **items)
541 return _xdup(self)
543 @property_doc_(''' the equality tolerance (C{float}).''')
544 def epsilon(self):
545 '''Get the tolerance for equality tests (C{float}).
546 '''
547 return self._epsilon
549 @epsilon.setter # PYCHOK setter!
550 def epsilon(self, tol):
551 '''Set the tolerance for equality tests (C{scalar}).
553 @raise UnitError: Non-scalar or invalid B{C{tol}}.
554 '''
555 self._epsilon = Scalar_(tolerance=tol)
557 def _find(self, point, start_end):
558 '''(INTERNAL) Find the first matching point index.
559 '''
560 for i in self._findall(point, start_end):
561 return i
562 return -1
564 def _findall(self, point, start_end): # PYCHOK no cover
565 '''(INTERNAL) I{Must be implemented/overloaded}.
566 '''
567 notImplemented(self, point, start_end)
569 def _getitem(self, index):
570 '''(INTERNAL) Return point [index] or return a slice.
571 '''
572 # Luciano Ramalho, "Fluent Python", page 290+, O'Reilly, 2016
573 if isinstance(index, slice):
574 # XXX an numpy.[nd]array slice is a view, not a copy
575 return self.__class__(self._array[index], **self._slicekwds())
576 else:
577 return self.point(self._array[index])
579 def _index(self, point, start_end):
580 '''(INTERNAL) Find the first matching point index.
581 '''
582 for i in self._findall(point, start_end):
583 return i
584 raise _IndexError(self._itemname, point, txt=_not_('found'))
586 @property_RO
587 def isNumpy2(self): # PYCHOK no cover
588 '''Is this a Numpy2 wrapper?
589 '''
590 return False # isinstance(self, (Numpy2LatLon, ...))
592 @property_RO
593 def isPoints2(self): # PYCHOK no cover
594 '''Is this a LatLon2 wrapper/converter?
595 '''
596 return False # isinstance(self, (LatLon2psxy, ...))
598 @property_RO
599 def isTuple2(self): # PYCHOK no cover
600 '''Is this a Tuple2 wrapper?
601 '''
602 return False # isinstance(self, (Tuple2LatLon, ...))
604 def _iter(self):
605 '''(INTERNAL) Yield all points.
606 '''
607 _array, _point = self._array, self.point
608 for i in range(len(self)):
609 yield _point(_array[i])
611 def point(self, *attrs): # PYCHOK no cover
612 '''(INTERNAL) I{Must be overloaded}, see function C{notOverloaded in}.
614 @arg attrs: Optional arguments.
615 '''
616 notOverloaded(self, *attrs)
618 def _range(self, start=None, end=None, step=1):
619 '''(INTERNAL) Return the range.
620 '''
621 if step > 0:
622 if start is None:
623 start = 0
624 if end is None:
625 end = len(self)
626 elif step < 0:
627 if start is None:
628 start = len(self) - 1
629 if end is None:
630 end = -1
631 else:
632 raise _ValueError(step=step)
633 return range(start, end, step)
635 def _repr(self):
636 '''(INTERNAL) Return a string representation.
637 '''
638 # XXX use Python 3+ reprlib.repr
639 t = repr(self._array[:1]) # only first row
640 t = _SPACE_(t[:-1], _ELLIPSIS_, Fmt.SQUARE(t[-1:], len(self)))
641 t = _SPACE_.join(t.split()) # coalesce spaces
642 return instr(self, t, **self._slicekwds())
644 def _reversed(self): # PYCHOK false
645 '''(INTERNAL) Yield all points in reverse order.
646 '''
647 _array, point = self._array, self.point
648 for i in range(len(self) - 1, -1, -1):
649 yield point(_array[i])
651 def _rfind(self, point, start_end):
652 '''(INTERNAL) Find the last matching point index.
653 '''
654 def _r3(start=None, end=None, step=-1):
655 return (start, end, step) # PYCHOK returns
657 for i in self._findall(point, _r3(*start_end)):
658 return i
659 return -1
661 def _slicekwds(self): # PYCHOK no cover
662 '''(INTERNAL) I{Should be overloaded}.
663 '''
664 return {}
667class _Array2LatLon(_Basequence): # immutable, on purpose
668 '''(INTERNAL) Base class for Numpy2LatLon or Tuple2LatLon.
669 '''
670 _array = ()
671 _ilat = 0 # row column index
672 _ilon = 0 # row column index
673 _LatLon = LatLon_ # default
674 _shape = ()
676 def __init__(self, array, ilat=0, ilon=1, LatLon=None, shape=()):
677 '''Handle a C{NumPy} or C{Tuple} array as a sequence of C{LatLon} points.
678 '''
679 ais = (_ilat_, ilat), (_ilon_, ilon)
681 if len(shape) != 2 or shape[0] < 1 or shape[1] < len(ais):
682 raise _IndexError('array.shape', shape)
684 self._array = array
685 self._shape = Shape2Tuple(shape) # *shape
687 if LatLon: # check the point class
688 if not _isLatLon_(LatLon):
689 raise _IsnotError(_valid_, LatLon=LatLon)
690 self._LatLon = LatLon
692 # check the attr indices
693 for n, (ai, i) in enumerate(ais):
694 if not isint(i):
695 raise _IsnotError(int.__name__, **{ai: i})
696 i = int(i)
697 if not 0 <= i < shape[1]:
698 raise _ValueError(ai, i)
699 for aj, j in ais[:n]:
700 if int(j) == i:
701 raise _ValueError(_DEQUALSPACED_(ai, aj, i))
702 setattr(self, NN(_UNDER_, ai), i)
704 def __contains__(self, latlon):
705 '''Check for a specific lat-/longitude.
707 @arg latlon: Point (C{LatLon}, L{LatLon2Tuple} or 2-tuple
708 C{(lat, lon)}).
710 @return: C{True} if B{C{latlon}} is present, C{False} otherwise.
712 @raise TypeError: Invalid B{C{latlon}}.
713 '''
714 return self._contains(latlon)
716 def __getitem__(self, index):
717 '''Return row[index] as C{LatLon} or return a L{Numpy2LatLon} slice.
718 '''
719 return self._getitem(index)
721 def __iter__(self):
722 '''Yield rows as C{LatLon}.
723 '''
724 return self._iter()
726 def __len__(self):
727 '''Return the number of rows.
728 '''
729 return self._shape[0]
731 def __repr__(self):
732 '''Return a string representation.
733 '''
734 return self._repr()
736 def __reversed__(self): # PYCHOK false
737 '''Yield rows as C{LatLon} in reverse order.
738 '''
739 return self._reversed()
741 __str__ = __repr__
743 def count(self, latlon):
744 '''Count the number of rows with a specific lat-/longitude.
746 @arg latlon: Point (C{LatLon}, L{LatLon2Tuple} or 2-tuple
747 C{(lat, lon)}).
749 @return: Count (C{int}).
751 @raise TypeError: Invalid B{C{latlon}}.
752 '''
753 return self._count(latlon)
755 def find(self, latlon, *start_end):
756 '''Find the first row with a specific lat-/longitude.
758 @arg latlon: Point (C{LatLon}) or 2-tuple (lat, lon).
759 @arg start_end: Optional C{[start[, end]]} index (integers).
761 @return: Index or -1 if not found (C{int}).
763 @raise TypeError: Invalid B{C{latlon}}.
764 '''
765 return self._find(latlon, start_end)
767 def _findall(self, latlon, start_end):
768 '''(INTERNAL) Yield indices of all matching rows.
769 '''
770 try:
771 lat, lon = latlon.lat, latlon.lon
772 except AttributeError:
773 try:
774 lat, lon = latlon
775 except (TypeError, ValueError):
776 raise _IsnotError(_valid_, latlon=latlon)
778 _ilat, _ilon = self._ilat, self._ilon
779 _array, _eps = self._array, self._epsilon
780 for i in self._range(*start_end):
781 row = _array[i]
782 if fabs(row[_ilat] - lat) <= _eps and \
783 fabs(row[_ilon] - lon) <= _eps:
784 yield i
786 def findall(self, latlon, *start_end):
787 '''Yield indices of all rows with a specific lat-/longitude.
789 @arg latlon: Point (C{LatLon}, L{LatLon2Tuple} or 2-tuple
790 C{(lat, lon)}).
791 @arg start_end: Optional C{[start[, end]]} index (C{int}).
793 @return: Indices (C{iterable}).
795 @raise TypeError: Invalid B{C{latlon}}.
796 '''
797 return self._findall(latlon, start_end)
799 def index(self, latlon, *start_end): # PYCHOK Python 2- issue
800 '''Find index of the first row with a specific lat-/longitude.
802 @arg latlon: Point (C{LatLon}, L{LatLon2Tuple} or 2-tuple
803 C{(lat, lon)}).
804 @arg start_end: Optional C{[start[, end]]} index (C{int}).
806 @return: Index (C{int}).
808 @raise IndexError: Point not found.
810 @raise TypeError: Invalid B{C{latlon}}.
811 '''
812 return self._index(latlon, start_end)
814 @Property_RO
815 def ilat(self):
816 '''Get the latitudes column index (C{int}).
817 '''
818 return self._ilat
820 @Property_RO
821 def ilon(self):
822 '''Get the longitudes column index (C{int}).
823 '''
824 return self._ilon
826# next = __iter__
828 def point(self, row): # PYCHOK *attrs
829 '''Instantiate a point C{LatLon}.
831 @arg row: Array row (numpy.array).
833 @return: Point (C{LatLon}).
834 '''
835 return self._LatLon(row[self._ilat], row[self._ilon])
837 def rfind(self, latlon, *start_end):
838 '''Find the last row with a specific lat-/longitude.
840 @arg latlon: Point (C{LatLon}, L{LatLon2Tuple} or 2-tuple
841 C{(lat, lon)}).
842 @arg start_end: Optional C{[start[, end]]} index (C{int}).
844 @note: Keyword order, first stop, then start.
846 @return: Index or -1 if not found (C{int}).
848 @raise TypeError: Invalid B{C{latlon}}.
849 '''
850 return self._rfind(latlon, start_end)
852 def _slicekwds(self):
853 '''(INTERNAL) Slice kwds.
854 '''
855 return dict(ilat=self._ilat, ilon=self._ilon)
857 @Property_RO
858 def shape(self):
859 '''Get the shape of the C{NumPy} array or the C{Tuples} as
860 L{Shape2Tuple}C{(nrows, ncols)}.
861 '''
862 return self._shape
864 def _subset(self, indices): # PYCHOK no cover
865 '''(INTERNAL) I{Must be implemented/overloaded}.
866 '''
867 notImplemented(self, indices)
869 def subset(self, indices):
870 '''Return a subset of the C{NumPy} array.
872 @arg indices: Row indices (C{range} or C{int}[]).
874 @note: A C{subset} is different from a C{slice} in 2 ways:
875 (a) the C{subset} is typically specified as a list of
876 (un-)ordered indices and (b) the C{subset} allocates
877 a new, separate C{NumPy} array while a C{slice} is
878 just an other C{view} of the original C{NumPy} array.
880 @return: Sub-array (C{numpy.array}).
882 @raise IndexError: Out-of-range B{C{indices}} value.
884 @raise TypeError: If B{C{indices}} is not a C{range}
885 nor an C{int}[].
886 '''
887 if not issequence(indices, tuple): # NO tuple, only list
888 # and range work properly to get Numpy array sub-sets
889 raise _IsnotError(_valid_, indices=type(indices))
891 n = len(self)
892 for i, v in enumerate(indices):
893 if not isint(v):
894 raise _TypeError(Fmt.SQUARE(indices=i), v)
895 elif not 0 <= v < n:
896 raise _IndexError(Fmt.SQUARE(indices=i), v)
898 return self._subset(indices)
901class LatLon2psxy(_Basequence):
902 '''Wrapper for C{LatLon} points as "on-the-fly" pseudo-xy coordinates.
903 '''
904 _closed = False
905 _len = 0
906 _deg2m = None # default, keep degrees
907 _radius = None
908 _wrap = True
910 def __init__(self, latlons, closed=False, radius=None, wrap=True):
911 '''Handle C{LatLon} points as pseudo-xy coordinates.
913 @note: The C{LatLon} latitude is considered the I{pseudo-y}
914 and longitude the I{pseudo-x} coordinate, likewise
915 for L{LatLon2Tuple}. However, 2-tuples C{(x, y)} are
916 considered as I{(longitude, latitude)}.
918 @arg latlons: Points C{list}, C{sequence}, C{set}, C{tuple},
919 etc. (C{LatLon[]}).
920 @kwarg closed: Optionally, close the polygon (C{bool}).
921 @kwarg radius: Mean earth radius (C{meter}).
922 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll
923 the B{C{latlons}} points (C{bool}).
925 @raise PointsError: Insufficient number of B{C{latlons}}.
927 @raise TypeError: Some B{C{points}} are not B{C{base}}.
928 '''
929 self._closed = closed
930 self._len, self._array = points2(latlons, closed=closed)
931 if radius:
932 self._radius = r = Radius(radius)
933 self._deg2m = degrees2m(_1_0, r)
934 if not wrap:
935 self._wrap = False
937 def __contains__(self, xy):
938 '''Check for a matching point.
940 @arg xy: Point (C{LatLon}, L{LatLon2Tuple} or 2-tuple
941 C{(x, y)}) in (C{degrees}.
943 @return: C{True} if B{C{xy}} is present, C{False} otherwise.
945 @raise TypeError: Invalid B{C{xy}}.
946 '''
947 return self._contains(xy)
949 def __getitem__(self, index):
950 '''Return the pseudo-xy or return a L{LatLon2psxy} slice.
951 '''
952 return self._getitem(index)
954 def __iter__(self):
955 '''Yield all pseudo-xy's.
956 '''
957 return self._iter()
959 def __len__(self):
960 '''Return the number of pseudo-xy's.
961 '''
962 return self._len
964 def __repr__(self):
965 '''Return a string representation.
966 '''
967 return self._repr()
969 def __reversed__(self): # PYCHOK false
970 '''Yield all pseudo-xy's in reverse order.
971 '''
972 return self._reversed()
974 __str__ = __repr__
976 def count(self, xy):
977 '''Count the number of matching points.
979 @arg xy: Point (C{LatLon}, L{LatLon2Tuple} or 2-tuple
980 C{(x, y)}) in (C{degrees}.
982 @return: Count (C{int}).
984 @raise TypeError: Invalid B{C{xy}}.
985 '''
986 return self._count(xy)
988 def find(self, xy, *start_end):
989 '''Find the first matching point.
991 @arg xy: Point (C{LatLon}, L{LatLon2Tuple} or 2-tuple
992 C{(x, y)}) in (C{degrees}.
993 @arg start_end: Optional C{[start[, end]]} index (C{int}).
995 @return: Index or -1 if not found (C{int}).
997 @raise TypeError: Invalid B{C{xy}}.
998 '''
999 return self._find(xy, start_end)
1001 def _findall(self, xy, start_end):
1002 '''(INTERNAL) Yield indices of all matching points.
1003 '''
1004 try:
1005 x, y = xy.lon, xy.lat
1007 def _x_y_ll3(ll): # match LatLon
1008 return ll.lon, ll.lat, ll
1010 except AttributeError:
1011 try:
1012 x, y = xy[:2]
1013 except (IndexError, TypeError, ValueError):
1014 raise _IsnotError(_valid_, xy=xy)
1016 _x_y_ll3 = self.point # PYCHOK expected
1018 _array, _eps = self._array, self._epsilon
1019 for i in self._range(*start_end):
1020 xi, yi, _ = _x_y_ll3(_array[i])
1021 if fabs(xi - x) <= _eps and \
1022 fabs(yi - y) <= _eps:
1023 yield i
1025 def findall(self, xy, *start_end):
1026 '''Yield indices of all matching points.
1028 @arg xy: Point (C{LatLon}, L{LatLon2Tuple} or 2-tuple
1029 C{(x, y)}) in (C{degrees}.
1030 @arg start_end: Optional C{[start[, end]]} index (C{int}).
1032 @return: Indices (C{iterator}).
1034 @raise TypeError: Invalid B{C{xy}}.
1035 '''
1036 return self._findall(xy, start_end)
1038 def index(self, xy, *start_end): # PYCHOK Python 2- issue
1039 '''Find the first matching point.
1041 @arg xy: Point (C{LatLon}) or 2-tuple (x, y) in (C{degrees}).
1042 @arg start_end: Optional C{[start[, end]]} index (C{int}).
1044 @return: Index (C{int}).
1046 @raise IndexError: Point not found.
1048 @raise TypeError: Invalid B{C{xy}}.
1049 '''
1050 return self._index(xy, start_end)
1052 @property_RO
1053 def isPoints2(self):
1054 '''Is this a LatLon2 wrapper/converter?
1055 '''
1056 return True # isinstance(self, (LatLon2psxy, ...))
1058 def point(self, ll): # PYCHOK *attrs
1059 '''Create a pseudo-xy.
1061 @arg ll: Point (C{LatLon}).
1063 @return: An L{Point3Tuple}C{(x, y, ll)}.
1064 '''
1065 x, y = ll.lon, ll.lat # note, x, y = lon, lat
1066 if self._wrap:
1067 y, x = _Wrap.latlon(y, x)
1068 d = self._deg2m
1069 if d: # convert degrees to meter (or radians)
1070 x *= d
1071 y *= d
1072 return Point3Tuple(x, y, ll)
1074 def rfind(self, xy, *start_end):
1075 '''Find the last matching point.
1077 @arg xy: Point (C{LatLon}, L{LatLon2Tuple} or 2-tuple
1078 C{(x, y)}) in (C{degrees}.
1079 @arg start_end: Optional C{[start[, end]]} index (C{int}).
1081 @return: Index or -1 if not found (C{int}).
1083 @raise TypeError: Invalid B{C{xy}}.
1084 '''
1085 return self._rfind(xy, start_end)
1087 def _slicekwds(self):
1088 '''(INTERNAL) Slice kwds.
1089 '''
1090 return dict(closed=self._closed, radius=self._radius, wrap=self._wrap)
1093class Numpy2LatLon(_Array2LatLon): # immutable, on purpose
1094 '''Wrapper for C{NumPy} arrays as "on-the-fly" C{LatLon} points.
1095 '''
1096 def __init__(self, array, ilat=0, ilon=1, LatLon=None):
1097 '''Handle a C{NumPy} array as a sequence of C{LatLon} points.
1099 @arg array: C{NumPy} array (C{numpy.array}).
1100 @kwarg ilat: Optional index of the latitudes column (C{int}).
1101 @kwarg ilon: Optional index of the longitudes column (C{int}).
1102 @kwarg LatLon: Optional C{LatLon} class to use (L{LatLon_}).
1104 @raise IndexError: If B{C{array.shape}} is not (1+, 2+).
1106 @raise TypeError: If B{C{array}} is not a C{NumPy} array or
1107 C{LatLon} is not a class with C{lat}
1108 and C{lon} attributes.
1110 @raise ValueError: If the B{C{ilat}} and/or B{C{ilon}} values
1111 are the same or out of range.
1113 @example:
1115 >>> type(array)
1116 <type 'numpy.ndarray'> # <class ...> in Python 3+
1117 >>> points = Numpy2LatLon(array, lat=0, lon=1)
1118 >>> simply = simplifyRDP(points, ...)
1119 >>> type(simply)
1120 <type 'numpy.ndarray'> # <class ...> in Python 3+
1121 >>> sliced = points[1:-1]
1122 >>> type(sliced)
1123 <class '...Numpy2LatLon'>
1124 '''
1125 try: # get shape and check some other numpy.array attrs
1126 s, _, _ = array.shape, array.nbytes, array.ndim # PYCHOK expected
1127 except AttributeError:
1128 raise _IsnotError('NumPy', array=type(array))
1130 _Array2LatLon.__init__(self, array, ilat=ilat, ilon=ilon,
1131 LatLon=LatLon, shape=s)
1133 @property_RO
1134 def isNumpy2(self):
1135 '''Is this a Numpy2 wrapper?
1136 '''
1137 return True # isinstance(self, (Numpy2LatLon, ...))
1139 def _subset(self, indices):
1140 return self._array[indices] # NumPy special
1143class Shape2Tuple(_NamedTuple):
1144 '''2-Tuple C{(nrows, ncols)}, the number of rows and columns,
1145 both C{int}.
1146 '''
1147 _Names_ = (_nrows_, _ncols_)
1148 _Units_ = ( Number_, Number_)
1151class Tuple2LatLon(_Array2LatLon):
1152 '''Wrapper for tuple sequences as "on-the-fly" C{LatLon} points.
1153 '''
1154 def __init__(self, tuples, ilat=0, ilon=1, LatLon=None):
1155 '''Handle a list of tuples, each containing a lat- and longitude
1156 and perhaps other values as a sequence of C{LatLon} points.
1158 @arg tuples: The C{list}, C{tuple} or C{sequence} of tuples (C{tuple}[]).
1159 @kwarg ilat: Optional index of the latitudes value (C{int}).
1160 @kwarg ilon: Optional index of the longitudes value (C{int}).
1161 @kwarg LatLon: Optional C{LatLon} class to use (L{LatLon_}).
1163 @raise IndexError: If C{(len(B{tuples}), min(len(t) for t
1164 in B{tuples}))} is not (1+, 2+).
1166 @raise TypeError: If B{C{tuples}} is not a C{list}, C{tuple}
1167 or C{sequence} or if B{C{LatLon}} is not a
1168 C{LatLon} with C{lat}, C{lon} and C{name}
1169 attributes.
1171 @raise ValueError: If the B{C{ilat}} and/or B{C{ilon}} values
1172 are the same or out of range.
1174 @example:
1176 >>> tuples = [(0, 1), (2, 3), (4, 5)]
1177 >>> type(tuples)
1178 <type 'list'> # <class ...> in Python 3+
1179 >>> points = Tuple2LatLon(tuples, lat=0, lon=1)
1180 >>> simply = simplifyRW(points, 0.5, ...)
1181 >>> type(simply)
1182 <type 'list'> # <class ...> in Python 3+
1183 >>> simply
1184 [(0, 1), (4, 5)]
1185 >>> sliced = points[1:-1]
1186 >>> type(sliced)
1187 <class '...Tuple2LatLon'>
1188 >>> sliced
1189 ...Tuple2LatLon([(2, 3), ...][1], ilat=0, ilon=1)
1191 >>> closest, _ = nearestOn2(LatLon_(2, 1), points, adjust=False)
1192 >>> closest
1193 LatLon_(lat=1.0, lon=2.0)
1195 >>> closest, _ = nearestOn2(LatLon_(3, 2), points)
1196 >>> closest
1197 LatLon_(lat=2.001162, lon=3.001162)
1198 '''
1199 _xinstanceof(list, tuple, tuples=tuples)
1200 s = len(tuples), min(len(_) for _ in tuples)
1201 _Array2LatLon.__init__(self, tuples, ilat=ilat, ilon=ilon,
1202 LatLon=LatLon, shape=s)
1204 @property_RO
1205 def isTuple2(self):
1206 '''Is this a Tuple2 wrapper?
1207 '''
1208 return True # isinstance(self, (Tuple2LatLon, ...))
1210 def _subset(self, indices):
1211 return type(self._array)(self._array[i] for i in indices)
1214def _area2(points, adjust, wrap):
1215 '''(INTERNAL) Approximate the area in radians squared, I{signed}.
1216 '''
1217 if adjust:
1218 # approximate trapezoid by a rectangle, adjusting
1219 # the top width by the cosine of the latitudinal
1220 # average and bottom width by some fudge factor
1221 def _adjust(w, h):
1222 c = cos(h) if fabs(h) < PI_2 else _0_0
1223 return w * h * (c + 1.2876) * _0_5
1224 else:
1225 def _adjust(w, h): # PYCHOK expected
1226 return w * h
1228 # setting radius=1 converts degrees to radians
1229 Ps = LatLon2PsxyIter(points, loop=1, radius=_1_0, wrap=wrap)
1230 x1, y1, ll = Ps[0]
1231 pts = [ll] # for _areaError
1233 A2 = Fsum() # trapezoidal area in radians**2
1234 for p in Ps.iterate(closed=True):
1235 x2, y2, ll = p
1236 if len(pts) < 4:
1237 pts.append(ll)
1238 w, x2 = unrollPI(x1, x2, wrap=wrap and not Ps.looped)
1239 A2 += _adjust(w, (y2 + y1) * _0_5)
1240 x1, y1 = x2, y2
1242 return A2.fsum(), tuple(pts)
1245def _areaError(pts, near_=NN): # imported by .ellipsoidalKarney
1246 '''(INTERNAL) Area issue.
1247 '''
1248 t = _ELLIPSIS_(pts[:3], NN)
1249 return _ValueError(NN(near_, 'zero or polar area'), txt=t)
1252def areaOf(points, adjust=True, radius=R_M, wrap=True):
1253 '''Approximate the area of a polygon or composite.
1255 @arg points: The polygon points or clips (C{LatLon}[],
1256 L{BooleanFHP} or L{BooleanGH}).
1257 @kwarg adjust: Adjust the wrapped, unrolled longitudinal delta
1258 by the cosine of the mean latitude (C{bool}).
1259 @kwarg radius: Mean earth radius (C{meter}) or C{None}.
1260 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll
1261 the B{C{points}} (C{bool}).
1263 @return: Approximate area (I{square} C{meter}, same units as
1264 B{C{radius}} or C{radians} I{squared} if B{C{radius}}
1265 is C{None}).
1267 @raise PointsError: Insufficient number of B{C{points}}
1269 @raise TypeError: Some B{C{points}} are not C{LatLon}.
1271 @raise ValueError: Invalid B{C{radius}}.
1273 @note: This area approximation has limited accuracy and is
1274 ill-suited for regions exceeding several hundred Km
1275 or Miles or with near-polar latitudes.
1277 @see: L{sphericalNvector.areaOf}, L{sphericalTrigonometry.areaOf},
1278 L{ellipsoidalExact.areaOf} and L{ellipsoidalKarney.areaOf}.
1279 '''
1280 if _MODS.booleans.isBoolean(points):
1281 a = points._sum1(areaOf, adjust=adjust, radius=None, wrap=wrap)
1282 else:
1283 a, _ = _area2(points, adjust, wrap)
1284 return fabs(a if radius is None else (Radius(radius)**2 * a))
1287def boundsOf(points, wrap=False, LatLon=None): # was=True
1288 '''Determine the bottom-left SW and top-right NE corners of a
1289 path or polygon.
1291 @arg points: The path or polygon points (C{LatLon}[]).
1292 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll
1293 the B{C{points}} (C{bool}).
1294 @kwarg LatLon: Optional class to return the C{bounds}
1295 corners (C{LatLon}) or C{None}.
1297 @return: A L{Bounds2Tuple}C{(latlonSW, latlonNE)} as
1298 B{C{LatLon}}s if B{C{LatLon}} is C{None} a
1299 L{Bounds4Tuple}C{(latS, lonW, latN, lonE)}.
1301 @raise PointsError: Insufficient number of B{C{points}}
1303 @raise TypeError: Some B{C{points}} are not C{LatLon}.
1305 @see: Function L{quadOf}.
1307 @example:
1309 >>> b = LatLon(45,1), LatLon(45,2), LatLon(46,2), LatLon(46,1)
1310 >>> boundsOf(b) # False
1311 >>> 45.0, 1.0, 46.0, 2.0
1312 '''
1313 Ps = LatLon2PsxyIter(points, loop=1, wrap=wrap)
1314 w, s, _ = e, n, _ = Ps[0]
1316 v = w
1317 for x, y, _ in Ps.iterate(closed=False): # [1:]
1318 if wrap:
1319 _, x = unroll180(v, x, wrap=True)
1320 v = x
1322 if w > x:
1323 w = x
1324 elif e < x:
1325 e = x
1327 if s > y:
1328 s = y
1329 elif n < y:
1330 n = y
1332 return Bounds4Tuple(s, w, n, e) if LatLon is None else \
1333 Bounds2Tuple(LatLon(s, w), LatLon(n, e)) # PYCHOK inconsistent
1336def _distanceTo(Error, **name_points): # .frechet, .hausdorff, .heights
1337 '''(INTERNAL) Chech callable C{distanceTo} methods.
1338 '''
1339 name, ps = name_points.popitem()
1340 for i, p in enumerate(ps):
1341 if not callable(_xattr(p, distanceTo=None)):
1342 n = _distanceTo.__name__[1:]
1343 t = _SPACE_(_no_, callable.__name__, n)
1344 raise Error(Fmt.SQUARE(name, i), p, txt=t)
1345 return ps
1348def centroidOf(points, wrap=False, LatLon=None): # was=True
1349 '''Determine the centroid of a polygon.
1351 @arg points: The polygon points (C{LatLon}[]).
1352 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the
1353 B{C{points}} (C{bool}).
1354 @kwarg LatLon: Optional class to return the centroid (C{LatLon})
1355 or C{None}.
1357 @return: Centroid (B{C{LatLon}}) or a L{LatLon2Tuple}C{(lat, lon)}
1358 if C{B{LatLon} is None}.
1360 @raise PointsError: Insufficient number of B{C{points}}
1362 @raise TypeError: Some B{C{points}} are not C{LatLon}.
1364 @raise ValueError: The B{C{points}} enclose a pole or
1365 near-zero area.
1367 @see: U{Centroid<https://WikiPedia.org/wiki/Centroid#Of_a_polygon>} and
1368 Paul Bourke's U{Calculating The Area And Centroid Of A Polygon
1369 <https://www.SEAS.UPenn.edu/~ese502/lab-content/extra_materials/
1370 Polygon%20Area%20and%20Centroid.pdf>}, 1988.
1371 '''
1372 A, X, Y = Fsum(), Fsum(), Fsum()
1374 # setting radius=1 converts degrees to radians
1375 Ps = LatLon2PsxyIter(points, loop=1, radius=_1_0, wrap=wrap)
1376 x1, y1, ll = Ps[0]
1377 pts = [ll] # for _areaError
1378 for p in Ps.iterate(closed=True):
1379 x2, y2, ll = p
1380 if len(pts) < 4:
1381 pts.append(ll)
1382 if wrap and not Ps.looped:
1383 _, x2 = unrollPI(x1, x2, wrap=True)
1384 t = x1 * y2 - x2 * y1
1385 A += t
1386 X += t * (x1 + x2)
1387 Y += t * (y1 + y2)
1388 # XXX more elaborately:
1389 # t1, t2 = x1 * y2, -(x2 * y1)
1390 # A.fadd_(t1, t2)
1391 # X.fadd_(t1 * x1, t1 * x2, t2 * x1, t2 * x2)
1392 # Y.fadd_(t1 * y1, t1 * y2, t2 * y1, t2 * y2)
1393 x1, y1 = x2, y2
1395 a = A.fmul(_6_0).fover(_2_0)
1396 if isnear0(a):
1397 raise _areaError(pts, near_=_near_)
1398 y, x = degrees90(Y.fover(a)), degrees180(X.fover(a))
1399 return LatLon2Tuple(y, x) if LatLon is None else LatLon(y, x)
1402def fractional(points, fi, j=None, wrap=None, LatLon=None, Vector=None, **kwds):
1403 '''Return the point at a given I{fractional} index.
1405 @arg points: The points (C{LatLon}[], L{Numpy2LatLon}[],
1406 L{Tuple2LatLon}[], C{Cartesian}[], C{Vector3d}[],
1407 L{Vector3Tuple}[]).
1408 @arg fi: The fractional index (L{FIx}, C{float} or C{int}).
1409 @kwarg j: Optionally, index of the other point (C{int}).
1410 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the
1411 B{{points}} (C{bool}) or C{None} for a backward
1412 compatible L{LatLon2Tuple} or B{C{LatLon}} with
1413 averaged lat- and longitudes. Use C{True} or
1414 C{False} to get the I{fractional} point computed
1415 by method C{B{points}[fi].intermediateTo}.
1416 @kwarg LatLon: Optional class to return the I{intermediate},
1417 I{fractional} point (C{LatLon}) or C{None}.
1418 @kwarg Vector: Optional class to return the I{intermediate},
1419 I{fractional} point (C{Cartesian}, C{Vector3d})
1420 or C{None}.
1421 @kwarg kwds: Optional, additional B{C{LatLon}} I{or} B{C{Vector}}
1422 keyword arguments, ignored if both C{B{LatLon}} and
1423 C{B{Vector}} are C{None}.
1425 @return: A L{LatLon2Tuple}C{(lat, lon)} if B{C{wrap}}, B{C{LatLon}}
1426 and B{C{Vector}} all are C{None}, the defaults.
1428 An instance of B{C{LatLon}} if not C{None} I{or} an instance
1429 of B{C{Vector}} if not C{None}.
1431 Otherwise with B{C{wrap}} either C{True} or C{False} and
1432 B{C{LatLon}} and B{C{Vector}} both C{None}, an instance of
1433 B{C{points}}' (sub-)class C{intermediateTo} I{fractional}.
1435 Summarized as follows:
1437 >>> wrap | LatLon | Vector | returned type/value
1438 # -------+--------+--------+--------------+------
1439 # | | | LatLon2Tuple | favg
1440 # None | None | None | or** |
1441 # | | | Vector3Tuple | favg
1442 # None | LatLon | None | LatLon | favg
1443 # None | None | Vector | Vector | favg
1444 # -------+--------+--------+--------------+------
1445 # True | None | None | points' | .iTo
1446 # True | LatLon | None | LatLon | .iTo
1447 # True | None | Vector | Vector | .iTo
1448 # -------+--------+--------+--------------+------
1449 # False | None | None | points' | .iTo
1450 # False | LatLon | None | LatLon | .iTo
1451 # False | None | Vector | Vector | .iTo
1452 # _____
1453 # favg) averaged lat, lon or x, y, z values
1454 # .iTo) value from points[fi].intermediateTo
1455 # **) depends on base class of points[fi]
1457 @raise IndexError: Fractional index B{C{fi}} invalid or B{C{points}}
1458 not subscriptable or not closed.
1460 @raise TypeError: Invalid B{C{LatLon}}, B{C{Vector}} or B{C{kwds}}
1461 argument.
1463 @see: Class L{FIx} and method L{FIx.fractional}.
1464 '''
1465 if LatLon and Vector: # PYCHOK no cover
1466 kwds = _xkwds(kwds, fi=fi, LatLon=LatLon, Vector=Vector)
1467 raise _TypeError(txt=fractional.__name__, **kwds)
1468 w = wrap if LatLon else False # intermediateTo
1469 try:
1470 if not isscalar(fi) or fi < 0:
1471 raise IndexError
1472 n = _xattr(fi, fin=0)
1473 p = _fractional(points, fi, j, fin=n, wrap=w) # see .units.FIx
1474 if LatLon:
1475 p = LatLon(p.lat, p.lon, **kwds)
1476 elif Vector:
1477 p = Vector(p.x, p.y, p.z, **kwds)
1478 except (IndexError, TypeError):
1479 raise _IndexError(fi=fi, points=points, wrap=w, txt=fractional.__name__)
1480 return p
1483def _fractional(points, fi, j, fin=None, wrap=None): # in .frechet.py
1484 '''(INTERNAL) Compute point at L{fractional} index C{fi} and C{j}.
1485 '''
1486 i = int(fi)
1487 p = points[i]
1488 r = fi - float(i)
1489 if r > EPS: # EPS0?
1490 if j is None: # in .frechet.py
1491 j = i + 1
1492 if fin:
1493 j %= fin
1494 q = points[j]
1495 if r >= EPS1: # PYCHOK no cover
1496 p = q
1497 elif wrap is not None: # in (True, False)
1498 p = p.intermediateTo(q, r, wrap=wrap)
1499 elif _isLatLon(p): # backward compatible default
1500 p = LatLon2Tuple(favg(p.lat, q.lat, f=r),
1501 favg(p.lon, q.lon, f=r),
1502 name=fractional.__name__)
1503 else: # assume p and q are cartesian or vectorial
1504 z = p.z if p.z is q.z else favg(p.z, q.z, f=r)
1505 p = Vector3Tuple(favg(p.x, q.x, f=r),
1506 favg(p.y, q.y, f=r), z,
1507 name=fractional.__name__)
1508 return p
1511def isclockwise(points, adjust=False, wrap=True):
1512 '''Determine the direction of a path or polygon.
1514 @arg points: The path or polygon points (C{LatLon}[]).
1515 @kwarg adjust: Adjust the wrapped, unrolled longitudinal delta
1516 by the cosine of the mean latitude (C{bool}).
1517 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the
1518 B{C{points}} (C{bool}).
1520 @return: C{True} if B{C{points}} are clockwise, C{False} otherwise.
1522 @raise PointsError: Insufficient number of B{C{points}}
1524 @raise TypeError: Some B{C{points}} are not C{LatLon}.
1526 @raise ValueError: The B{C{points}} enclose a pole or zero area.
1528 @example:
1530 >>> f = LatLon(45,1), LatLon(45,2), LatLon(46,2), LatLon(46,1)
1531 >>> isclockwise(f) # False
1532 >>> isclockwise(reversed(f)) # True
1533 '''
1534 a, pts = _area2(points, adjust, wrap)
1535 if a > 0: # opposite of ellipsoidalExact and -Karney
1536 return True
1537 elif a < 0:
1538 return False
1539 # <https://blog.Element84.com/determining-if-a-spherical-polygon-contains-a-pole.html>
1540 raise _areaError(pts)
1543def isconvex(points, adjust=False, wrap=False): # was=True
1544 '''Determine whether a polygon is convex.
1546 @arg points: The polygon points (C{LatLon}[]).
1547 @kwarg adjust: Adjust the wrapped, unrolled longitudinal delta
1548 by the cosine of the mean latitude (C{bool}).
1549 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the
1550 B{C{points}} (C{bool}).
1552 @return: C{True} if B{C{points}} are convex, C{False} otherwise.
1554 @raise CrossError: Some B{C{points}} are colinear.
1556 @raise PointsError: Insufficient number of B{C{points}}
1558 @raise TypeError: Some B{C{points}} are not C{LatLon}.
1560 @example:
1562 >>> t = LatLon(45,1), LatLon(46,1), LatLon(46,2)
1563 >>> isconvex(t) # True
1565 >>> f = LatLon(45,1), LatLon(46,2), LatLon(45,2), LatLon(46,1)
1566 >>> isconvex(f) # False
1567 '''
1568 return bool(isconvex_(points, adjust=adjust, wrap=wrap))
1571def isconvex_(points, adjust=False, wrap=False): # was=True
1572 '''Determine whether a polygon is convex I{and clockwise}.
1574 @arg points: The polygon points (C{LatLon}[]).
1575 @kwarg adjust: Adjust the wrapped, unrolled longitudinal delta
1576 by the cosine of the mean latitude (C{bool}).
1577 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the
1578 B{C{points}} (C{bool}).
1580 @return: C{+1} if B{C{points}} are convex clockwise, C{-1} for
1581 convex counter-clockwise B{C{points}}, C{0} otherwise.
1583 @raise CrossError: Some B{C{points}} are colinear.
1585 @raise PointsError: Insufficient number of B{C{points}}
1587 @raise TypeError: Some B{C{points}} are not C{LatLon}.
1589 @example:
1591 >>> t = LatLon(45,1), LatLon(46,1), LatLon(46,2)
1592 >>> isconvex_(t) # +1
1594 >>> f = LatLon(45,1), LatLon(46,2), LatLon(45,2), LatLon(46,1)
1595 >>> isconvex_(f) # 0
1596 '''
1597 if adjust:
1598 def _unroll2(x1, x2, w, y1, y2):
1599 x21, x2 = unroll180(x1, x2, wrap=w)
1600 y = radians(y1 + y2) * _0_5
1601 x21 *= cos(y) if fabs(y) < PI_2 else _0_0
1602 return x21, x2
1603 else:
1604 def _unroll2(x1, x2, w, *unused): # PYCHOK expected
1605 return unroll180(x1, x2, wrap=w)
1607 c, s = crosserrors(), 0
1609 Ps = LatLon2PsxyIter(points, loop=2, wrap=wrap)
1610 x1, y1, _ = Ps[0]
1611 x2, y2, _ = Ps[1]
1613 x21, x2 = _unroll2(x1, x2, False, y1, y2)
1614 for i, p in Ps.enumerate(closed=True):
1615 x3, y3, ll = p
1616 x32, x3 = _unroll2(x2, x3, bool(wrap and not Ps.looped), y2, y3)
1618 # get the sign of the distance from point
1619 # x3, y3 to the line from x1, y1 to x2, y2
1620 # <https://WikiPedia.org/wiki/Distance_from_a_point_to_a_line>
1621 s3 = fdot((x3, y3, x1, y1), y2 - y1, -x21, -y2, x2)
1622 if s3 > 0: # x3, y3 on the right
1623 if s < 0: # non-convex
1624 return 0
1625 s = +1
1627 elif s3 < 0: # x3, y3 on the left
1628 if s > 0: # non-convex
1629 return 0
1630 s = -1
1632 elif c and fdot((x32, y1 - y2), y3 - y2, -x21) < 0: # PYCHOK no cover
1633 # colinear u-turn: x3, y3 not on the
1634 # opposite side of x2, y2 as x1, y1
1635 t = Fmt.SQUARE(points=i)
1636 raise CrossError(t, ll, txt=_colinear_)
1638 x1, y1, x2, y2, x21 = x2, y2, x3, y3, x32
1640 return s # all points on the same side
1643def isenclosedBy(point, points, wrap=False): # MCCABE 15
1644 '''Determine whether a point is enclosed by a polygon or composite.
1646 @arg point: The point (C{LatLon} or 2-tuple C{(lat, lon)}).
1647 @arg points: The polygon points or clips (C{LatLon}[], L{BooleanFHP}
1648 or L{BooleanGH}).
1649 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the
1650 B{C{points}} (C{bool}).
1652 @return: C{True} if the B{C{point}} is inside the polygon or
1653 composite, C{False} otherwise.
1655 @raise PointsError: Insufficient number of B{C{points}}
1657 @raise TypeError: Some B{C{points}} are not C{LatLon}.
1659 @raise ValueError: Invalid B{C{point}}, lat- or longitude.
1661 @see: Functions L{pygeodesy.isconvex} and L{pygeodesy.ispolar} especially
1662 if the B{C{points}} may enclose a pole or wrap around the earth
1663 I{longitudinally}, methods L{sphericalNvector.LatLon.isenclosedBy},
1664 L{sphericalTrigonometry.LatLon.isenclosedBy} and U{MultiDop
1665 GeogContainPt<https://GitHub.com/NASA/MultiDop>} (U{Shapiro et.al. 2009,
1666 JTECH<https://Journals.AMetSoc.org/doi/abs/10.1175/2009JTECHA1256.1>}
1667 and U{Potvin et al. 2012, JTECH <https://Journals.AMetSoc.org/doi/abs/
1668 10.1175/JTECH-D-11-00019.1>}).
1669 '''
1670 try:
1671 y0, x0 = point.lat, point.lon
1672 except AttributeError:
1673 try:
1674 y0, x0 = map(float, point[:2])
1675 except (IndexError, TypeError, ValueError) as x:
1676 raise _ValueError(point=point, cause=x)
1678 if wrap:
1679 y0, x0 = _Wrap.latlon(y0, x0)
1681 def _dxy3(x, x2, y2, Ps):
1682 dx, x2 = unroll180(x, x2, wrap=not Ps.looped)
1683 return dx, x2, y2
1685 else:
1686 x0 = fmod(x0, _360_0) # not x0 % 360!
1687 x0_180_ = x0 - _180_0
1688 x0_180 = x0 + _180_0
1690 def _dxy3(x1, x, y, unused): # PYCHOK expected
1691 x = _umod_360(float(x))
1692 if x < x0_180_:
1693 x += _360_0
1694 elif x >= x0_180:
1695 x -= _360_0
1696 return (x - x1), x, y
1698 if _MODS.booleans.isBoolean(points):
1699 return points._encloses(y0, x0, wrap=wrap)
1701 Ps = LatLon2PsxyIter(points, loop=1, wrap=wrap)
1702 p = Ps[0]
1703 e = m = False
1704 S = Fsum()
1706 _, x1, y1 = _dxy3(x0, p.x, p.y, False)
1707 for p in Ps.iterate(closed=True):
1708 dx, x2, y2 = _dxy3(x1, p.x, p.y, Ps)
1709 # ignore duplicate and near-duplicate pts
1710 if fabs(dx) > EPS or fabs(y2 - y1) > EPS:
1711 # determine if polygon edge (x1, y1)..(x2, y2) straddles
1712 # point (lat, lon) or is on boundary, but do not count
1713 # edges on boundary as more than one crossing
1714 if fabs(dx) < 180 and (x1 < x0 <= x2 or x2 < x0 <= x1):
1715 m = not m
1716 dy = (x0 - x1) * (y2 - y1) - (y0 - y1) * dx
1717 if (dy > 0 and dx >= 0) or (dy < 0 and dx <= 0):
1718 e = not e
1720 S += sin(radians(y2))
1721 x1, y1 = x2, y2
1723 # An odd number of meridian crossings means, the polygon
1724 # contains a pole. Assume it is the pole on the hemisphere
1725 # containing the polygon mean point and if the polygon does
1726 # contain the North Pole, flip the result.
1727 if m and S.fsum() > 0:
1728 e = not e
1729 return e
1732def ispolar(points, wrap=False):
1733 '''Check whether a polygon encloses a pole.
1735 @arg points: The polygon points (C{LatLon}[]).
1736 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll
1737 the B{C{points}} (C{bool}).
1739 @return: C{True} if the polygon encloses a pole, C{False}
1740 otherwise.
1742 @raise PointsError: Insufficient number of B{C{points}}
1744 @raise TypeError: Some B{C{points}} are not C{LatLon} or don't
1745 have C{bearingTo2}, C{initialBearingTo}
1746 and C{finalBearingTo} methods.
1747 '''
1748 def _cds(ps, w): # iterate over course deltas
1749 Ps = PointsIter(ps, loop=2, wrap=w)
1750 p2, p1 = Ps[0:2]
1751 b1, _ = _bearingTo2(p2, p1, wrap=False)
1752 for p2 in Ps.iterate(closed=True):
1753 if not p2.isequalTo(p1, EPS):
1754 if w and not Ps.looped:
1755 p2 = _unrollon(p1, p2)
1756 b, b2 = _bearingTo2(p1, p2, wrap=False)
1757 yield wrap180(b - b1) # (b - b1 + 540) % 360 - 180
1758 yield wrap180(b2 - b) # (b2 - b + 540) % 360 - 180
1759 p1, b1 = p2, b2
1761 # summation of course deltas around pole is 0° rather than normally ±360°
1762 # <https://blog.Element84.com/determining-if-a-spherical-polygon-contains-a-pole.html>
1763 s = fsum(_cds(points, wrap), floats=True)
1764 # XXX fix (intermittant) edge crossing pole - eg (85,90), (85,0), (85,-90)
1765 return fabs(s) < 90 # "zero-ish"
1768def luneOf(lon1, lon2, closed=False, LatLon=LatLon_, **LatLon_kwds):
1769 '''Generate an ellipsoidal or spherical U{lune
1770 <https://WikiPedia.org/wiki/Spherical_lune>}-shaped path or polygon.
1772 @arg lon1: Left longitude (C{degrees90}).
1773 @arg lon2: Right longitude (C{degrees90}).
1774 @kwarg closed: Optionally, close the path (C{bool}).
1775 @kwarg LatLon: Class to use (L{LatLon_}).
1776 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}}
1777 keyword arguments.
1779 @return: A tuple of 4 or 5 B{C{LatLon}} instances outlining
1780 the lune shape.
1782 @see: U{Latitude-longitude quadrangle
1783 <https://www.MathWorks.com/help/map/ref/areaquad.html>}.
1784 '''
1785 t = (LatLon( _0_0, lon1, **LatLon_kwds),
1786 LatLon( _90_0, lon1, **LatLon_kwds),
1787 LatLon( _0_0, lon2, **LatLon_kwds),
1788 LatLon(_N_90_0, lon2, **LatLon_kwds))
1789 if closed:
1790 t += t[:1]
1791 return t
1794def nearestOn5(point, points, closed=False, wrap=False, adjust=True,
1795 limit=9, **LatLon_and_kwds):
1796 '''Locate the point on a path or polygon closest to a reference point.
1798 The closest point on each polygon edge is either the nearest of that
1799 edge's end points or a point in between.
1801 @arg point: The reference point (C{LatLon}).
1802 @arg points: The path or polygon points (C{LatLon}[]).
1803 @kwarg closed: Optionally, close the path or polygon (C{bool}).
1804 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the
1805 B{C{points}} (C{bool}).
1806 @kwarg adjust: See function L{pygeodesy.equirectangular_} (C{bool}).
1807 @kwarg limit: See function L{pygeodesy.equirectangular_} (C{degrees}),
1808 default C{9 degrees} is about C{1,000 Kmeter} (for mean
1809 spherical earth radius L{R_KM}).
1810 @kwarg LatLon_and_kwds: Optional, C{B{LatLon}=None} class to use for
1811 the closest point and additional B{C{LatLon}} keyword
1812 arguments, ignored if C{B{LatLon}=None} or not given.
1814 @return: A L{NearestOn3Tuple}C{(closest, distance, angle)} with the
1815 {closest} point (B{C{LatLon}}) or if C{B{LatLon} is None},
1816 a L{NearestOn5Tuple}C{(lat, lon, distance, angle, height)}.
1817 The C{distance} is the L{pygeodesy.equirectangular} distance
1818 between the C{closest} and reference B{C{point}} in C{degrees}.
1819 The C{angle} from the B{C{point}} to the C{closest} is in
1820 compass C{degrees}, like function L{pygeodesy.compassAngle}.
1822 @raise LimitError: Lat- and/or longitudinal delta exceeds the B{C{limit}},
1823 see function L{pygeodesy.equirectangular_}.
1825 @raise PointsError: Insufficient number of B{C{points}}
1827 @raise TypeError: Some B{C{points}} are not C{LatLon}.
1829 @note: Distances are I{approximated} by function L{pygeodesy.equirectangular_}.
1830 For more accuracy use one of the C{LatLon.nearestOn6} methods.
1832 @see: Function L{pygeodesy.degrees2m}.
1833 '''
1834 def _d2yx4(p2, p1, u, alw):
1835 # w = wrap if (i < (n - 1) or not closed) else False
1836 # equirectangular_ returns a Distance4Tuple(distance
1837 # in degrees squared, delta lat, delta lon, p2.lon
1838 # unroll/wrap'd); the previous p2.lon unroll/wrap'd
1839 # is also applied to the next edge's p1.lon
1840 return equirectangular_(p1.lat, p1.lon + u,
1841 p2.lat, p2.lon, **alw)
1843 def _h(p): # get height or default 0
1844 return _xattr(p, height=0) or 0
1846 # 3-D version used in .vector3d._nearestOn2
1847 #
1848 # point (x, y) on axis rotated ccw by angle a:
1849 # x' = y * sin(a) + x * cos(a)
1850 # y' = y * cos(a) - x * sin(a)
1851 #
1852 # distance (w) along and (h) perpendicular to
1853 # a line thru point (dx, dy) and the origin:
1854 # w = (y * dy + x * dx) / hypot(dx, dy)
1855 # h = (y * dx - x * dy) / hypot(dx, dy)
1856 #
1857 # closest point on that line thru (dx, dy):
1858 # xc = dx * w / hypot(dx, dy)
1859 # yc = dy * w / hypot(dx, dy)
1860 # or
1861 # xc = dx * f
1862 # yc = dy * f
1863 # with
1864 # f = w / hypot(dx, dy)
1865 # or
1866 # f = (y * dy + x * dx) / hypot2(dx, dy)
1867 #
1868 # i.e. no need for sqrt or hypot
1870 Ps = PointsIter(points, loop=1, wrap=wrap)
1871 p1 = c = Ps[0]
1872 u1 = u = _0_0
1873 kw = dict(adjust=adjust, limit=limit, wrap=False)
1874 d, dy, dx, _ = _d2yx4(p1, point, u1, kw)
1875 for p2 in Ps.iterate(closed=closed):
1876 # iff wrapped, unroll lon1 (actually previous
1877 # lon2) like function unroll180/-PI would've
1878 if wrap:
1879 kw.update(wrap=not (closed and Ps.looped))
1880 d21, y21, x21, u2 = _d2yx4(p2, p1, u1, kw)
1881 if d21 > EPS:
1882 # distance point to p1, y01 and x01 negated
1883 d2, y01, x01, _ = _d2yx4(point, p1, u1, kw)
1884 if d2 > EPS:
1885 w2 = y01 * y21 + x01 * x21
1886 if w2 > 0:
1887 if w2 < d21:
1888 # closest is between p1 and p2, use
1889 # original delta's, not y21 and x21
1890 f = w2 / d21
1891 p1 = LatLon_(favg(p1.lat, p2.lat, f=f),
1892 favg(p1.lon, p2.lon + u2, f=f),
1893 height=favg(_h(p1), _h(p2), f=f))
1894 u1 = _0_0
1895 else: # p2 is closest
1896 p1, u1 = p2, u2
1897 d2, y01, x01, _ = _d2yx4(point, p1, u1, kw)
1898 if d2 < d: # p1 is closer, y01 and x01 negated
1899 c, u, d, dy, dx = p1, u1, d2, -y01, -x01
1900 p1, u1 = p2, u2
1902 a = atan2b(dx, dy)
1903 d = hypot(dx, dy)
1904 h = _h(c)
1905 n = nameof(point) or nearestOn5.__name__
1906 if LatLon_and_kwds:
1907 kwds = _xkwds(LatLon_and_kwds, height=h, name=n)
1908 LL = _xkwds_pop(kwds, LatLon=None)
1909 if LL is not None:
1910 r = LL(c.lat, c.lon + u, **kwds)
1911 return NearestOn3Tuple(r, d, a, name=n)
1912 return NearestOn5Tuple(c.lat, c.lon + u, d, a, h, name=n) # PYCHOK expected
1915def perimeterOf(points, closed=False, adjust=True, radius=R_M, wrap=True):
1916 '''I{Approximate} the perimeter of a path, polygon. or composite.
1918 @arg points: The path or polygon points or clips (C{LatLon}[],
1919 L{BooleanFHP} or L{BooleanGH}).
1920 @kwarg closed: Optionally, close the path or polygon (C{bool}).
1921 @kwarg adjust: Adjust the wrapped, unrolled longitudinal delta
1922 by the cosine of the mean latitude (C{bool}).
1923 @kwarg radius: Mean earth radius (C{meter}).
1924 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the
1925 B{C{points}} (C{bool}).
1927 @return: Approximate perimeter (C{meter}, same units as
1928 B{C{radius}}).
1930 @raise PointsError: Insufficient number of B{C{points}}
1932 @raise TypeError: Some B{C{points}} are not C{LatLon}.
1934 @raise ValueError: Invalid B{C{radius}} or C{B{closed}=False} with
1935 C{B{points}} a composite.
1937 @note: This perimeter is based on the L{pygeodesy.equirectangular_}
1938 distance approximation and is ill-suited for regions exceeding
1939 several hundred Km or Miles or with near-polar latitudes.
1941 @see: Functions L{sphericalTrigonometry.perimeterOf} and
1942 L{ellipsoidalKarney.perimeterOf}.
1943 '''
1944 def _degs(ps, c, a, w): # angular edge lengths in degrees
1945 Ps = LatLon2PsxyIter(ps, loop=1) # wrap=w
1946 p1, u = Ps[0], _0_0 # previous x2's unroll/wrap
1947 for p2 in Ps.iterate(closed=c):
1948 if w and c:
1949 w = not Ps.looped
1950 # apply previous x2's unroll/wrap'd to new x1
1951 _, dy, dx, u = equirectangular_(p1.y, p1.x + u,
1952 p2.y, p2.x,
1953 adjust=a, limit=None,
1954 wrap=w) # PYCHOK non-seq
1955 yield hypot(dx, dy)
1956 p1 = p2
1958 if _MODS.booleans.isBoolean(points):
1959 if not closed:
1960 notImplemented(None, closed=closed, points=_composite_)
1961 d = points._sum1(perimeterOf, closed=True, adjust=adjust,
1962 radius=radius, wrap=wrap)
1963 else:
1964 d = fsum(_degs(points, closed, adjust, wrap), floats=True)
1965 return degrees2m(d, radius=radius)
1968def quadOf(latS, lonW, latN, lonE, closed=False, LatLon=LatLon_, **LatLon_kwds):
1969 '''Generate a quadrilateral path or polygon from two points.
1971 @arg latS: Souther-nmost latitude (C{degrees90}).
1972 @arg lonW: Western-most longitude (C{degrees180}).
1973 @arg latN: Norther-nmost latitude (C{degrees90}).
1974 @arg lonE: Eastern-most longitude (C{degrees180}).
1975 @kwarg closed: Optionally, close the path (C{bool}).
1976 @kwarg LatLon: Class to use (L{LatLon_}).
1977 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}}
1978 keyword arguments.
1980 @return: Return a tuple of 4 or 5 B{C{LatLon}} instances
1981 outlining the quadrilateral.
1983 @see: Function L{boundsOf}.
1984 '''
1985 t = (LatLon(latS, lonW, **LatLon_kwds),
1986 LatLon(latN, lonW, **LatLon_kwds),
1987 LatLon(latN, lonE, **LatLon_kwds),
1988 LatLon(latS, lonE, **LatLon_kwds))
1989 if closed:
1990 t += t[:1]
1991 return t
1994__all__ += _ALL_DOCS(_Array2LatLon, _Basequence)
1996# **) MIT License
1997#
1998# Copyright (C) 2016-2023 -- mrJean1 at Gmail -- All Rights Reserved.
1999#
2000# Permission is hereby granted, free of charge, to any person obtaining a
2001# copy of this software and associated documentation files (the "Software"),
2002# to deal in the Software without restriction, including without limitation
2003# the rights to use, copy, modify, merge, publish, distribute, sublicense,
2004# and/or sell copies of the Software, and to permit persons to whom the
2005# Software is furnished to do so, subject to the following conditions:
2006#
2007# The above copyright notice and this permission notice shall be included
2008# in all copies or substantial portions of the Software.
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2010# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
2011# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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2016# OTHER DEALINGS IN THE SOFTWARE.