Coverage for pygeodesy/ellipsoidalNvector.py: 99%
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2# -*- coding: utf-8 -*-
4u'''Ellipsoidal, C{N-vector}-based geodesy.
6Ellipsoidal classes geodetic (lat-/longitude) L{LatLon}, geocentric
7(ECEF) L{Cartesian}, DEPRECATED L{Ned} and L{Nvector} and functions
8L{meanOf}, L{sumOf} and DEPRECATED L{toNed}.
10Pure Python implementation of n-vector-based geodetic (lat-/longitude)
11methods by I{(C) Chris Veness 2011-2016} published under the same MIT
12Licence**, see U{Vector-based geodesy
13<https://www.Movable-Type.co.UK/scripts/latlong-vectors.html>}.
15These classes and functions work with: (a) geodesic (polar) lat-/longitude
16points on the earth's surface and (b) 3-D vectors used as n-vectors
17representing points on the earth's surface or vectors normal to the plane
18of a great circle.
20See also Kenneth Gade U{'A Non-singular Horizontal Position Representation'
21<https://www.NavLab.net/Publications/A_Nonsingular_Horizontal_Position_Representation.pdf>},
22The Journal of Navigation (2010), vol 63, nr 3, pp 395-417.
23'''
24# make sure int/int division yields float quotient, see .basics
25from __future__ import division as _; del _ # PYCHOK semicolon
27from pygeodesy.basics import issubclassof, map2, _xinstanceof
28from pygeodesy.datums import _ellipsoidal_datum, _spherical_datum, _WGS84
29# from pygeodesy.dms import toDMS # _MODS
30from pygeodesy.ellipsoidalBase import CartesianEllipsoidalBase, _TOL_M, \
31 LatLonEllipsoidalBase, _nearestOn
32from pygeodesy.errors import _IsnotError, _xkwds
33# from pygeodesy.fmath import fdot # from .nvectorBase
34from pygeodesy.interns import NN, _Nv00_, _COMMASPACE_
35from pygeodesy.interns import _down_, _east_, _north_, _pole_ # PYCHOK used!
36from pygeodesy.lazily import _ALL_LAZY, _ALL_MODS as _MODS, _ALL_OTHER
37# from pygeodesy.ltp import Ltp # _MODS
38from pygeodesy.ltpTuples import Aer as _Aer, Ned as _Ned, Ned4Tuple, \
39 sincos2d_, _xnamed
40# from pygeodesy.named import _xnamed # from .ltpTuples
41from pygeodesy.nvectorBase import fabs, fdot, NorthPole, LatLonNvectorBase, \
42 NvectorBase, sumOf as _sumOf
43from pygeodesy.props import deprecated_class, deprecated_function, \
44 deprecated_method, Property_RO
45from pygeodesy.streprs import Fmt, fstr, _xzipairs
46from pygeodesy.units import Bearing, Distance, Height, Scalar
47# from pygeodesy.utily import sincos2d_ # from .ltpTuples
49# from math import fabs # from .nvectorBase
51__all__ = _ALL_LAZY.ellipsoidalNvector
52__version__ = '23.03.19'
55class Ned(_Ned):
56 '''DEPRECATED, use class L{pygeodesy.Ned}.'''
58 def __init__(self, north, east, down, name=NN):
59 deprecated_class(self.__class__)
60 _Ned.__init__(self, north, east, down, name=name)
62 @deprecated_method # PYCHOK expected
63 def toRepr(self, prec=None, fmt=Fmt.SQUARE, sep=_COMMASPACE_, **unused):
64 '''DEPRECATED, use class L{pygeodesy.Ned}.
66 @kwarg prec: Number of (decimal) digits, unstripped (C{int}).
67 @kwarg fmt: Enclosing backets format (C{str}).
68 @kwarg sep: Separator between NEDs (C{str}).
70 @return: This Ned as "[L:f, B:degrees360, E:degrees90]" (C{str})
71 with length or slantrange C{L}, bearing or azimuth C{B}
72 and elevation C{E}.
73 '''
74 dms = _MODS.dms
75 t = (fstr(self.slantrange, prec=3 if prec is None else prec),
76 dms.toDMS(self.azimuth, form=dms.F_D, prec=prec, ddd=0),
77 dms.toDMS(self.elevation, form=dms.F_D, prec=prec, ddd=0))
78 return _xzipairs('LBE', t, sep=sep, fmt=fmt)
81class Cartesian(CartesianEllipsoidalBase):
82 '''Extended to convert geocentric, L{Cartesian} points to
83 L{Nvector} and n-vector-based, geodetic L{LatLon}.
84 '''
85 @Property_RO
86 def Ecef(self):
87 '''Get the ECEF I{class} (L{EcefVeness}), I{lazily}.
88 '''
89 return _MODS.ecef.EcefVeness
91 def toLatLon(self, **LatLon_and_kwds): # PYCHOK LatLon=LatLon, datum=None
92 '''Convert this cartesian to an C{Nvector}-based geodetic point.
94 @kwarg LatLon_and_kwds: Optional L{LatLon}, B{C{datum}} and other
95 keyword arguments. Use C{B{LatLon}=...} to
96 override this L{LatLon} class or specify
97 C{B{LatLon} is None}.
99 @return: The geodetic point (L{LatLon}) or if B{C{LatLon}} is set
100 to C{None}, an L{Ecef9Tuple}C{(x, y, z, lat, lon, height,
101 C, M, datum)} with C{C} and C{M} if available.
103 @raise TypeError: Invalid B{C{LatLon_and_kwds}}.
104 '''
105 kwds = _xkwds(LatLon_and_kwds, LatLon=LatLon, datum=self.datum)
106 return CartesianEllipsoidalBase.toLatLon(self, **kwds)
108 def toNvector(self, **Nvector_and_kwds): # PYCHOK Datums.WGS84
109 '''Convert this cartesian to L{Nvector} components, I{including height}.
111 @kwarg Nvector_and_kwds: Optional L{Nvector}, B{C{datum}} and other
112 keyword arguments. Use C{B{Nvector}=...} to
113 override this L{Nvector} class or specify
114 C{B{Nvector} is None}.
116 @return: The C{n-vector} components (L{Nvector}) or if B{C{Nvector}}
117 is set to C{None}, a L{Vector4Tuple}C{(x, y, z, h)}
119 @raise TypeError: Invalid B{C{Nvector_and_kwds}}.
121 @example:
123 >>> from ellipsoidalNvector import LatLon
124 >>> c = Cartesian(3980581, 97, 4966825)
125 >>> n = c.toNvector() # (0.62282, 0.000002, 0.78237, +0.24)
126 '''
127 kwds = _xkwds(Nvector_and_kwds, Nvector=Nvector, datum=self.datum)
128 return CartesianEllipsoidalBase.toNvector(self, **kwds)
131class LatLon(LatLonNvectorBase, LatLonEllipsoidalBase):
132 '''An n-vector-based, ellipsoidal L{LatLon} point.
134 @example:
136 >>> from ellipsoidalNvector import LatLon
137 >>> p = LatLon(52.205, 0.119) # height=0, datum=Datums.WGS84
138 '''
139 _Nv = None # cached toNvector (L{Nvector})
141 def _update(self, updated, *attrs, **setters): # PYCHOK args
142 '''(INTERNAL) Zap cached attributes if updated.
143 '''
144 if updated:
145 LatLonNvectorBase._update(self, updated, _Nv=self._Nv) # special case
146 LatLonEllipsoidalBase._update(self, updated, *attrs, **setters)
148# def crossTrackDistanceTo(self, start, end, radius=R_M):
149# '''Return the (signed) distance from this point to the great
150# circle defined by a start point and an end point or bearing.
151#
152# @arg start: Start point of great circle path (L{LatLon}).
153# @arg end: End point of great circle path (L{LatLon}) or
154# initial bearing (compass C{degrees360}) at the
155# start point.
156# @kwarg radius: Mean earth radius (C{meter}).
157#
158# @return: Distance to great circle, negative if to left or
159# positive if to right of path (C{meter}, same units
160# as B{C{radius}}).
161#
162# @raise TypeError: If B{C{start}} or B{C{end}} point is not L{LatLon}.
163#
164# @example:
165#
166# >>> p = LatLon(53.2611, -0.7972)
167#
168# >>> s = LatLon(53.3206, -1.7297)
169# >>> b = 96.0
170# >>> d = p.crossTrackDistanceTo(s, b) # -305.7
171#
172# >>> e = LatLon(53.1887, 0.1334)
173# >>> d = p.crossTrackDistanceTo(s, e) # -307.5
174# '''
175# self.others(start=start)
176#
177# if isscalar(end): # gc from point and bearing
178# gc = start.greatCircle(end)
179# else: # gc by two points
180# gc = start.toNvector().cross(end.toNvector())
181#
182# # (signed) angle between point and gc normal vector
183# v = self.toNvector()
184# a = gc.angleTo(v, vSign=v.cross(gc))
185# a = (-PI_2 - a) if a < 0 else (PI_2 - a)
186# return a * float(radius)
188 def deltaTo(self, other, Ned=Ned):
189 '''Calculate the local delta from this to an other point.
191 @note: This is a linear delta, I{unrelated} to a geodesic
192 on the ellipsoid.
194 @arg other: The other point (L{LatLon}).
195 @kwarg Ned: Class to use (L{pygeodesy.Ned} or
196 L{pygeodesy.Ned4Tuple}), overriding the
197 default DEPRECATED L{Ned}.
199 @return: Delta from this to the other point (B{C{Ned}}).
201 @raise TypeError: The B{C{other}} point is not L{LatLon} or
202 B{C{Ned}} is not L{pygeodesy.Ned} nor
203 L{pygeodesy.Ned4Tuple} nor DEPRECATED L{Ned}.
205 @raise ValueError: If ellipsoids are incompatible.
207 @example:
209 >>> a = LatLon(49.66618, 3.45063)
210 >>> b = LatLon(48.88667, 2.37472)
211 >>> delta = a.deltaTo(b) # [N:-86126, E:-78900, D:1069]
212 >>> d = delta.length # 116807.681 m
213 >>> b = delta.bearing # 222.493°
214 >>> e = delta.elevation # -0.5245°
215 '''
216 self.ellipsoids(other) # throws TypeError and ValueError
218 # get delta in cartesian frame
219 dc = other.toCartesian().minus(self.toCartesian())
220 # rotate dc to get delta in n-vector reference
221 # frame using the rotation matrix row vectors
222 ned_ = map2(dc.dot, self._rotation3)
223 if issubclassof(Ned, Ned4Tuple):
224 ned_ += (_MODS.ltp.Ltp(self, ecef=self.Ecef(self.datum)),)
225 elif not issubclassof(Ned, _Ned):
226 raise _IsnotError(Fmt.sub_class(_Ned, Ned4Tuple), Ned=Ned)
227 return Ned(*ned_, name=self.name)
229# def destination(self, distance, bearing, radius=R_M, height=None):
230# '''Return the destination point after traveling from this
231# point the given distance on the given initial bearing.
232#
233# @arg distance: Distance traveled (C{meter}, same units as
234# given earth B{C{radius}}).
235# @arg bearing: Initial bearing (compass C{degrees360}).
236# @kwarg radius: Mean earth radius (C{meter}).
237# @kwarg height: Optional height at destination point,
238# overriding default (C{meter}, same units
239# as B{C{radius}}).
240#
241# @return: Destination point (L{LatLon}).
242#
243# @example:
244#
245# >>> p = LatLon(51.4778, -0.0015)
246# >>> q = p.destination(7794, 300.7)
247# >>> q.toStr() # '51.5135°N, 000.0983°W' ?
248# '''
249# r = _angular(distance, radius) # angular distance in radians
250# # great circle by starting from this point on given bearing
251# gc = self.greatCircle(bearing)
252#
253# v1 = self.toNvector()
254# x = v1.times(cos(r)) # component of v2 parallel to v1
255# y = gc.cross(v1).times(sin(r)) # component of v2 perpendicular to v1
256#
257# v2 = x.plus(y).unit()
258# return v2.toLatLon(height=self.height if height is C{None} else height)
260 def destinationNed(self, delta):
261 '''Calculate the destination point using the supplied NED delta
262 from this point.
264 @arg delta: Delta from this to the other point in the local
265 tangent plane (LTP) of this point (L{Ned}).
267 @return: Destination point (L{LatLon}).
269 @raise TypeError: If B{C{delta}} is not L{pygeodesy.Ned} or
270 DEPRECATED L{Ned}.
272 @example:
274 >>> a = LatLon(49.66618, 3.45063)
275 >>> delta = Ned(-86126, -78900, 1069) # from Aer(222.493, -0.5245, 116807.681)
276 >>> b = a.destinationNed(delta) # 48.886669°N, 002.374721°E or 48°53′12.01″N, 002°22′29.0″E +0.20m
277 '''
278 _xinstanceof(_Ned, delta=delta)
280 nv, ev, dv = self._rotation3
281 # convert NED delta to standard coordinate frame of n-vector
282 dn = delta.ned
283 # rotate dn to get delta in cartesian (ECEF) coordinate
284 # reference frame using the rotation matrix column vectors
285 dc = Cartesian(fdot(dn, nv.x, ev.x, dv.x),
286 fdot(dn, nv.y, ev.y, dv.y),
287 fdot(dn, nv.z, ev.z, dv.z))
289 # apply (cartesian) delta to this Cartesian to obtain destination as cartesian
290 v = self.toCartesian().plus(dc)
291 return v.toLatLon(datum=self.datum, LatLon=self.classof) # Cartesian(v.x, v.y, v.z).toLatLon(...)
293 def distanceTo(self, other, radius=None, wrap=False):
294 '''I{Approximate} the distance from this to an other point.
296 @arg other: The other point (L{LatLon}).
297 @kwarg radius: Mean earth radius, ellipsoid or datum
298 (C{meter}, L{Ellipsoid}, L{Ellipsoid2},
299 L{Datum} or L{a_f2Tuple}), overriding the
300 mean radius C{R1} of this point's datum..
301 @kwarg wrap: Wrap/unroll the angular distance (C{bool}).
303 @return: Distance (C{meter}, same units as B{C{radius}}).
305 @raise TypeError: The B{C{other}} point is not L{LatLon}.
307 @raise ValueError: Invalid B{C{radius}}.
309 @example:
311 >>> p = LatLon(52.205, 0.119)
312 >>> q = LatLon(48.857, 2.351);
313 >>> d = p.distanceTo(q) # 404300
314 '''
315 self.others(other)
317 a = self._N_vector.angleTo(other._N_vector, wrap=wrap)
318 d = self.datum if radius is None else _spherical_datum(radius)
319 return fabs(a) * d.ellipsoid.R1 # see .utily.radians2m
321 @Property_RO
322 def Ecef(self):
323 '''Get the ECEF I{class} (L{EcefVeness}), I{lazily}.
324 '''
325 return _MODS.ecef.EcefVeness
327 @deprecated_method
328 def equals(self, other, eps=None): # PYCHOK no cover
329 '''DEPRECATED, use method L{isequalTo}.
330 '''
331 return self.isequalTo(other, eps=eps)
333 def isequalTo(self, other, eps=None):
334 '''Compare this point with an other point.
336 @arg other: The other point (L{LatLon}).
337 @kwarg eps: Optional margin (C{float}).
339 @return: C{True} if points are identical, including
340 datum, I{ignoring height}, C{False} otherwise.
342 @raise TypeError: The B{C{other}} point is not L{LatLon}.
344 @raise ValueError: Invalid B{C{eps}}.
346 @see: Method C{isequalTo3} to include I{height}.
348 @example:
350 >>> p = LatLon(52.205, 0.119)
351 >>> q = LatLon(52.205, 0.119)
352 >>> e = p.isequalTo(q) # True
353 '''
354 return LatLonEllipsoidalBase.isequalTo(self, other, eps=eps) \
355 if self.datum == other.datum else False
357# def greatCircle(self, bearing):
358# '''Return the great circle heading on the given bearing
359# from this point.
360#
361# Direction of vector is such that initial bearing vector
362# b = c × p, where p is representing this point.
363#
364# @arg bearing: Bearing from this point (compass C{degrees360}).
365#
366# @return: N-vector representing great circle (L{Nvector}).
367#
368# @example:
369#
370# >>> p = LatLon(53.3206, -1.7297)
371# >>> g = p.greatCircle(96.0)
372# >>> g.toStr() # '(-0.794, 0.129, 0.594)'
373# '''
374# a, b, _ = self.philamheight
375# t = radians(bearing)
376#
377# sa, ca, sb, cb, st, ct = sincos2_(a, b, t)
378# return self._xnamed(Nvector(sb * ct - sa * cb * st,
379# -cb * ct - sa * sb * st,
380# ca * st)
382# def initialBearingTo(self, other):
383# '''Return the initial bearing (forward azimuth) from this
384# to an other point.
385#
386# @arg other: The other point (L{LatLon}).
387#
388# @return: Initial bearing (compass C{degrees360}).
389#
390# @raise TypeError: The B{C{other}} point is not L{LatLon}.
391#
392# @example:
393#
394# >>> p1 = LatLon(52.205, 0.119)
395# >>> p2 = LatLon(48.857, 2.351)
396# >>> b = p1.bearingTo(p2) # 156.2
397# '''
398# self.others(other)
399#
400# v1 = self.toNvector()
401# v2 = other.toNvector()
402#
403# gc1 = v1.cross(v2) # gc through v1 & v2
404# gc2 = v1.cross(_NP3) # gc through v1 & North pole
405#
406# # bearing is (signed) angle between gc1 & gc2
407# return degrees360(gc1.angleTo(gc2, vSign=v1))
409 def intermediateTo(self, other, fraction, height=None, **unused): # PYCHOK wrap=False
410 '''Return the point at given fraction between this and
411 an other point.
413 @arg other: The other point (L{LatLon}).
414 @arg fraction: Fraction between both points (C{scalar},
415 0.0 at this to 1.0 at the other point.
416 @kwarg height: Optional height, overriding the fractional
417 height (C{meter}).
419 @return: Intermediate point (L{LatLon}).
421 @raise TypeError: The B{C{other}} point is not L{LatLon}.
423 @example:
425 >>> p = LatLon(52.205, 0.119)
426 >>> q = LatLon(48.857, 2.351)
427 >>> p = p.intermediateTo(q, 0.25) # 51.3721°N, 000.7073°E
428 '''
429 self.others(other)
431 f = Scalar(fraction=fraction)
432 i = self.toNvector().intermediateTo(other.toNvector(), f)
434 h = self._havg(other, f=f) if height is None else Height(height)
435 return i.toLatLon(height=h, LatLon=self.classof) # Nvector(i.x, i.y, i.z).toLatLon(...)
437 @Property_RO
438 def _rotation3(self):
439 '''(INTERNAL) Get the rotation matrix from n-vector coordinate frame axes.
440 '''
441 nv = self.toNvector() # local (n-vector) coordinate frame
443 dv = nv.negate() # down, opposite to n-vector
444 ev = NorthPole.cross(nv, raiser=_pole_).unit() # east, pointing perpendicular to the plane
445 nv = ev.cross(dv) # north, by right hand rule
446 return nv, ev, dv # matrix rows
448 def toCartesian(self, **Cartesian_and_kwds): # PYCHOK Cartesian=Cartesian, datum=None
449 '''Convert this point to an C{Nvector}-based geodetic point.
451 @kwarg Cartesian_and_kwds: Optional L{Cartesian}, B{C{datum}} and other
452 keyword arguments. Use C{B{Cartesian}=...}
453 to override this L{Cartesian} class or specify
454 C{B{Cartesian} is None}.
456 @return: The geodetic point (L{Cartesian}) or if B{C{Cartesian}} is set
457 to C{None}, an L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M,
458 datum)} with C{C} and C{M} if available.
460 @raise TypeError: Invalid B{C{Cartesian}} or other B{C{Cartesian_and_kwds}}.
461 '''
462 kwds = _xkwds(Cartesian_and_kwds, Cartesian=Cartesian, datum=self.datum)
463 return LatLonEllipsoidalBase.toCartesian(self, **kwds)
465 def toNvector(self, **Nvector_and_kwds): # PYCHOK signature
466 '''Convert this point to L{Nvector} components, I{including height}.
468 @kwarg Nvector_and_kwds: Optional L{Nvector}, B{C{datum}} and other
469 keyword arguments. Use C{B{Nvector}=...}
470 to override this L{Nvector} class or specify
471 C{B{Nvector} is None}.
473 @return: The C{n-vector} components (L{Nvector}) or if B{C{Nvector}}
474 is set to C{None}, a L{Vector4Tuple}C{(x, y, z, h)}.
476 @raise TypeError: Invalid B{C{Nvector}} or other B{C{Nvector_and_kwds}}.
478 @example:
480 >>> p = LatLon(45, 45)
481 >>> n = p.toNvector()
482 >>> n.toStr() # [0.50, 0.50, 0.70710]
483 '''
484 kwds = _xkwds(Nvector_and_kwds, Nvector=Nvector, datum=self.datum)
485 return LatLonNvectorBase.toNvector(self, **kwds)
488_Nvll = LatLon(0, 0, name=_Nv00_) # reference instance (L{LatLon})
491class Nvector(NvectorBase):
492 '''An n-vector is a position representation using a (unit) vector
493 normal to the earth ellipsoid. Unlike lat-/longitude points,
494 n-vectors have no singularities or discontinuities.
496 For many applications, n-vectors are more convenient to work
497 with than other position representations like lat-/longitude,
498 earth-centred earth-fixed (ECEF) vectors, UTM coordinates, etc.
500 Note commonality with L{sphericalNvector.Nvector}.
501 '''
502 _datum = _WGS84 # default datum (L{Datum})
504 def __init__(self, x_xyz, y=None, z=None, h=0, datum=None, ll=None, name=NN):
505 '''New n-vector normal to the earth's surface.
507 @arg x_xyz: X component of vector (C{scalar}) or (3-D) vector
508 (C{Nvector}, L{Vector3d}, L{Vector3Tuple} or
509 L{Vector4Tuple}).
510 @kwarg y: Y component of vector (C{scalar}), ignored if B{C{x_xyz}}
511 is not C{scalar}, otherwise same units as B{C{x_xyz}}.
512 @kwarg z: Z component of vector (C{scalar}), ignored if B{C{x_xyz}}
513 is not C{scalar}, otherwise same units as B{C{x_xyz}}.
514 @kwarg h: Optional height above model surface (C{meter}).
515 @kwarg datum: Optional datum this n-vector is defined in
516 (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or
517 L{a_f2Tuple}).
518 @kwarg ll: Optional, original latlon (C{LatLon}).
519 @kwarg name: Optional name (C{str}).
521 @raise TypeError: If B{C{datum}} is not a L{Datum}.
523 @example:
525 >>> from ellipsoidalNvector import Nvector
526 >>> v = Nvector(0.5, 0.5, 0.7071, 1)
527 >>> v.toLatLon() # 45.0°N, 045.0°E, +1.00m
528 '''
529 NvectorBase.__init__(self, x_xyz, y=y, z=z, h=h, ll=ll, name=name)
530 if datum not in (None, self._datum):
531 self._datum = _ellipsoidal_datum(datum, name=name)
533 @Property_RO
534 def datum(self):
535 '''Get this n-vector's datum (L{Datum}).
536 '''
537 return self._datum
539 def toCartesian(self, **Cartesian_and_kwds): # PYCHOK Cartesian=Cartesian
540 '''Convert this n-vector to C{Nvector}-based cartesian (ECEF) coordinates.
542 @kwarg Cartesian_and_kwds: Optional L{Cartesian}, B{C{h}}, B{C{datum}} and
543 other keyword arguments. Use C{B{Cartesian}=...}
544 to override this L{Cartesian} class or specify
545 C{B{Cartesian} is None}.
547 @return: The cartesian point (L{Cartesian}) or if B{C{Cartesian}} is set
548 to C{None}, an L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M,
549 datum)} with C{C} and C{M} if available.
551 @raise TypeError: Invalid B{C{Cartesian_and_kwds}}.
553 @example:
555 >>> v = Nvector(0.5, 0.5, 0.7071)
556 >>> c = v.toCartesian() # [3194434, 3194434, 4487327]
557 >>> p = c.toLatLon() # 45.0°N, 45.0°E
558 '''
559 kwds = _xkwds(Cartesian_and_kwds, h=self.h, Cartesian=Cartesian,
560 datum=self.datum)
561 return NvectorBase.toCartesian(self, **kwds) # class or .classof
563 def toLatLon(self, **LatLon_and_kwds): # PYCHOK height=None, LatLon=LatLon
564 '''Convert this n-vector to an C{Nvector}-based geodetic point.
566 @kwarg LatLon_and_kwds: Optional L{LatLon}, B{C{height}}, B{C{datum}}
567 and other keyword arguments. Use C{B{LatLon}=...}
568 to override this L{LatLon} class or specify
569 C{B{LatLon} is None}.
571 @return: The geodetic point (L{LatLon}) or if B{C{LatLon}} is set
572 to C{None}, an L{Ecef9Tuple}C{(x, y, z, lat, lon, height,
573 C, M, datum)} with C{C} and C{M} if available.
575 @raise TypeError: Invalid B{C{LatLon_and_kwds}}.
577 @example:
579 >>> v = Nvector(0.5, 0.5, 0.7071)
580 >>> p = v.toLatLon() # 45.0°N, 45.0°E
581 '''
582 kwds = _xkwds(LatLon_and_kwds, height=self.h, datum=self.datum, LatLon=LatLon)
583 return NvectorBase.toLatLon(self, **kwds) # class or .classof
585 def unit(self, ll=None):
586 '''Normalize this vector to unit length.
588 @kwarg ll: Optional, original latlon (C{LatLon}).
590 @return: Normalised vector (L{Nvector}).
591 '''
592 u = NvectorBase.unit(self, ll=ll)
593 if u.datum != self.datum:
594 u._update(False, datum=self.datum)
595 return u
598def meanOf(points, datum=_WGS84, height=None, LatLon=LatLon,
599 **LatLon_kwds):
600 '''Compute the geographic mean of several points.
602 @arg points: Points to be averaged (L{LatLon}[]).
603 @kwarg datum: Optional datum to use (L{Datum}).
604 @kwarg height: Optional height at mean point, overriding
605 the mean height (C{meter}).
606 @kwarg LatLon: Optional class to return the mean point
607 (L{LatLon}) or C{None}.
608 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}}
609 keyword arguments, ignored if
610 C{B{LatLon} is None}.
612 @return: Geographic mean point and mean height (B{C{LatLon}})
613 or if B{C{LatLon}} is C{None}, an L{Ecef9Tuple}C{(x,
614 y, z, lat, lon, height, C, M, datum)} with C{C} and
615 C{M} if available.
617 @raise ValueError: Insufficient number of B{C{points}}.
618 '''
619 Ps = _Nvll.PointsIter(points)
620 # geographic mean
621 m = sumOf(p._N_vector for p in Ps.iterate(closed=False))
622 kwds = _xkwds(LatLon_kwds, height=height, datum=datum,
623 LatLon=LatLon, name=meanOf.__name__)
624 return m.toLatLon(**kwds)
627def nearestOn(point, point1, point2, within=True, height=None, wrap=False,
628 equidistant=None, tol=_TOL_M, LatLon=LatLon, **LatLon_kwds):
629 '''Iteratively locate the closest point on the geodesic between
630 two other (ellipsoidal) points.
632 @arg point: Reference point (C{LatLon}).
633 @arg point1: Start point of the geodesic (C{LatLon}).
634 @arg point2: End point of the geodesic (C{LatLon}).
635 @kwarg within: If C{True} return the closest point I{between}
636 B{C{point1}} and B{C{point2}}, otherwise the
637 closest point elsewhere on the geodesic (C{bool}).
638 @kwarg height: Optional height for the closest point (C{meter},
639 conventionally) or C{None} or C{False} for the
640 interpolated height. If C{False}, the closest
641 takes the heights of the points into account.
642 @kwarg wrap: Wrap and unroll longitudes (C{bool}).
643 @kwarg equidistant: An azimuthal equidistant projection (I{class}
644 or function L{pygeodesy.equidistant}) or C{None}
645 for the preferred C{B{point}.Equidistant}.
646 @kwarg tol: Convergence tolerance (C{meter}).
647 @kwarg LatLon: Optional class to return the closest point
648 (L{LatLon}) or C{None}.
649 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword
650 arguments, ignored if C{B{LatLon} is None}.
652 @return: Closest point, a B{C{LatLon}} instance or if C{B{LatLon}
653 is None}, a L{LatLon4Tuple}C{(lat, lon, height, datum)}.
655 @raise ImportError: Package U{geographiclib
656 <https://PyPI.org/project/geographiclib>}
657 not installed or not found.
659 @raise TypeError: Invalid or non-ellipsoidal B{C{point}}, B{C{point1}}
660 or B{C{point2}} or invalid B{C{equidistant}}.
662 @raise ValueError: No convergence for the B{C{tol}}.
664 @see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/
665 calculating-intersection-of-two-circles>} and U{Karney's paper
666 <https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{14. MARITIME
667 BOUNDARIES} for more details about the iteration algorithm.
668 '''
669 return _nearestOn(point, point1, point2, within=within, height=height, wrap=wrap,
670 equidistant=equidistant, tol=tol, LatLon=LatLon, **LatLon_kwds)
673def sumOf(nvectors, Vector=Nvector, h=None, **Vector_kwds):
674 '''Return the vectorial sum of two or more n-vectors.
676 @arg nvectors: Vectors to be added (L{Nvector}[]).
677 @kwarg Vector: Optional class for the vectorial sum (L{Nvector}).
678 @kwarg h: Optional height, overriding the mean height (C{meter}).
679 @kwarg Vector_kwds: Optional, additional B{C{Vector}} keyword
680 arguments, ignored if C{B{Vector} is None}.
682 @return: Vectorial sum (B{C{Vector}}).
684 @raise VectorError: No B{C{nvectors}}.
685 '''
686 return _sumOf(nvectors, Vector=Vector, h=h, **Vector_kwds)
689@deprecated_function
690def toNed(distance, bearing, elevation, Ned=Ned, name=NN):
691 '''DEPRECATED, use L{pygeodesy.Aer}C{(bearing, elevation,
692 distance).xyzLocal.toNed(B{Ned}, name=B{name})} or
693 L{XyzLocal}C{(pygeodesy.Aer(bearing, elevation,
694 distance)).toNed(B{Ned}, name=B{name})}.
696 Create an NED vector from distance, bearing and elevation
697 (in local coordinate system).
699 @arg distance: NED vector length (C{meter}).
700 @arg bearing: NED vector bearing (compass C{degrees360}).
701 @arg elevation: NED vector elevation from local coordinate
702 frame horizontal (C{degrees}).
703 @kwarg Ned: Optional class to return the NED (C{Ned}) or
704 C{None}.
705 @kwarg name: Optional name (C{str}).
707 @return: An NED vector equivalent to this B{C{distance}},
708 B{C{bearing}} and B{C{elevation}} (DEPRECATED L{Ned})
709 or a DEPRECATED L{Ned3Tuple}C{(north, east, down)}
710 if C{B{Ned} is None}.
712 @raise ValueError: Invalid B{C{distance}}, B{C{bearing}}
713 or B{C{elevation}}.
714 '''
715 if True: # use new Aer class
716 n, e, d, _ = _Aer(bearing, elevation, distance).xyz4
717 else: # DEPRECATED
718 d = Distance(distance)
720 sb, cb, se, ce = sincos2d_(Bearing(bearing),
721 Height(elevation=elevation))
722 n = cb * d * ce
723 e = sb * d * ce
724 d *= se
726 r = _MODS.deprecated.Ned3Tuple(n, e, -d) if Ned is None else \
727 Ned(n, e, -d)
728 return _xnamed(r, name)
731__all__ += _ALL_OTHER(Cartesian, LatLon, Ned, Nvector, # classes
732 meanOf, sumOf, toNed)
734# **) MIT License
735#
736# Copyright (C) 2016-2023 -- mrJean1 at Gmail -- All Rights Reserved.
737#
738# Permission is hereby granted, free of charge, to any person obtaining a
739# copy of this software and associated documentation files (the "Software"),
740# to deal in the Software without restriction, including without limitation
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743# Software is furnished to do so, subject to the following conditions:
744#
745# The above copyright notice and this permission notice shall be included
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