Coverage for pygeodesy/ellipsoidalNvector.py: 96%
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« prev ^ index » next coverage.py v7.6.1, created at 2025-04-25 13:15 -0400
2# -*- coding: utf-8 -*-
4u'''Ellipsoidal, C{N-vector}-based geodesy.
6Ellipsoidal classes geodetic L{LatLon}, geocentric (ECEF) L{Cartesian}
7and C{Nvector} and DEPRECATED L{Ned} and functions L{meanOf}, L{sumOf}
8and DEPRECATED L{toNed}.
10Pure Python implementation of n-vector-based geodetic (lat-/longitude)
11methods by I{(C) Chris Veness 2011-2024} 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) geodetic lat-/longitude points on
16the earth's surface and (b) 3-D vectors used as n-vectors representing points
17on the earth's surface or vectors normal to the plane of a great circle.
19See also I{Kenneth Gade} U{'A Non-singular Horizontal Position Representation'
20<https://www.NavLab.net/Publications/A_Nonsingular_Horizontal_Position_Representation.pdf>},
21The Journal of Navigation (2010), vol 63, nr 3, pp 395-417.
22'''
23# make sure int/int division yields float quotient, see .basics
24from __future__ import division as _; del _ # PYCHOK semicolon
26from pygeodesy.basics import _isin, issubclassof, map2, _xinstanceof, \
27 _xsubclassof
28from pygeodesy.datums import _earth_ellipsoid, _ellipsoidal_datum, _WGS84
29# from pygeodesy.dms import F_D, toDMS # _MODS
30# from pygeodesy.ecef import EcefVeness # _MODS
31from pygeodesy.ellipsoidalBase import CartesianEllipsoidalBase, \
32 _nearestOn, LatLonEllipsoidalBase, \
33 _TOL_M, _Wrap
34from pygeodesy.errors import _xkwds, _xkwds_pop2
35# from pygeodesy.fmath import fdot # from .nvectorBase
36# from pygeodesy.formy import _isequalTo # _MODS
37from pygeodesy.interns import _Nv00_, _COMMASPACE_, _pole_ # PYCHOK used!
38from pygeodesy.lazily import _ALL_LAZY, _ALL_MODS as _MODS, _ALL_OTHER
39# from pygeodesy.ltp import Ltp # _MODS
40from pygeodesy.ltpTuples import Aer as _Aer, Ned as _Ned, Ned4Tuple, \
41 sincos2d_, _xnamed
42# from pygeodesy.named import _xnamed # from .ltpTuples
43from pygeodesy.nvectorBase import LatLonNvectorBase, NorthPole, NvectorBase, \
44 sumOf as _sumOf, fabs, fdot
45from pygeodesy.props import deprecated_class, deprecated_function, \
46 deprecated_method, Property_RO, property_RO
47from pygeodesy.streprs import Fmt, fstr, _xzipairs
48from pygeodesy.units import Bearing, Distance, Height, Scalar
49# from pygeodesy.utily import sincos2d_, _Wrap # from .ltpTuples, .ellipsoidalBase
51# from math import fabs # from .nvectorBase
53__all__ = _ALL_LAZY.ellipsoidalNvector
54__version__ = '25.04.21'
57class Ned(_Ned):
58 '''DEPRECATED on 2024.02.04, use class L{pygeodesy.Ned}.'''
60 def __init__(self, north, east, down, **name):
61 deprecated_class(self.__class__)
62 _Ned.__init__(self, north, east, down, **name)
64 @deprecated_method # PYCHOK expected
65 def toRepr(self, prec=None, fmt=Fmt.SQUARE, sep=_COMMASPACE_, **unused):
66 '''DEPRECATED, use class L{pygeodesy.Ned}.
68 @kwarg prec: Number of (decimal) digits, unstripped (C{int}).
69 @kwarg fmt: Enclosing backets format (C{str}).
70 @kwarg sep: Separator between NEDs (C{str}).
72 @return: This Ned as "[L:f, B:degrees360, E:degrees90]" (C{str})
73 with length or slantrange C{L}, bearing or azimuth C{B}
74 and elevation C{E}.
75 '''
76 m = _MODS.dms
77 t = (fstr(self.slantrange, prec=prec),
78 m.toDMS(self.azimuth, form=m.F_D, prec=prec, ddd=0),
79 m.toDMS(self.elevation, form=m.F_D, prec=prec, ddd=0))
80 return _xzipairs('LBE', t, sep=sep, fmt=fmt)
83class Cartesian(CartesianEllipsoidalBase):
84 '''Extended to convert geocentric, L{Cartesian} points to
85 C{Nvector} and n-vector-based, geodetic L{LatLon}.
86 '''
87 @property_RO
88 def Ecef(self):
89 '''Get the ECEF I{class} (L{EcefVeness}), I{once}.
90 '''
91 return _Ecef()
93 def toLatLon(self, **LatLon_and_kwds): # PYCHOK LatLon=LatLon, datum=None
94 '''Convert this cartesian to an C{Nvector}-based geodetic point.
96 @kwarg LatLon_and_kwds: Optional L{LatLon}, B{C{datum}} and other
97 keyword arguments. Use C{B{LatLon}=...} to
98 override this L{LatLon} class or specify
99 C{B{LatLon} is None}.
101 @return: The geodetic point (L{LatLon}) or if C{B{LatLon} is None},
102 an L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)}
103 with C{C} and C{M} if available.
105 @raise TypeError: Invalid B{C{LatLon_and_kwds}}.
106 '''
107 kwds = _xkwds(LatLon_and_kwds, LatLon=LatLon, datum=self.datum)
108 return CartesianEllipsoidalBase.toLatLon(self, **kwds)
110 def toNvector(self, **Nvector_and_kwds): # PYCHOK Datums.WGS84
111 '''Convert this cartesian to C{Nvector} components, I{including height}.
113 @kwarg Nvector_and_kwds: Optional C{Nvector}, B{C{datum}} and other
114 keyword arguments. Use C{B{Nvector}=...} to
115 override this C{Nvector} class or specify
116 C{B{Nvector} is None}.
118 @return: The C{n-vector} components (C{Nvector}) or if C{B{Nvector}
119 is None}, a L{Vector4Tuple}C{(x, y, z, h)}.
121 @raise TypeError: Invalid B{C{Nvector_and_kwds}}.
122 '''
123 kwds = _xkwds(Nvector_and_kwds, Nvector=Nvector, datum=self.datum)
124 return CartesianEllipsoidalBase.toNvector(self, **kwds)
127class LatLon(LatLonNvectorBase, LatLonEllipsoidalBase):
128 '''An n-vector-based, ellipsoidal L{LatLon} point.
129 '''
130 _Nv = None # cached toNvector (C{Nvector})
132 def _update(self, updated, *attrs, **setters): # PYCHOK args
133 '''(INTERNAL) Zap cached attributes if updated.
134 '''
135 if updated:
136 LatLonNvectorBase._update(self, updated, _Nv=self._Nv) # special case
137 LatLonEllipsoidalBase._update(self, updated, *attrs, **setters)
139# def crossTrackDistanceTo(self, start, end, radius=R_M):
140# '''Return the (signed) distance from this point to the great
141# circle defined by a start point and an end point or bearing.
142#
143# @arg start: Start point of great circle line (L{LatLon}).
144# @arg end: End point of great circle line (L{LatLon}) or
145# initial bearing (compass C{degrees360}) at the
146# start point.
147# @kwarg radius: Mean earth radius (C{meter}).
148#
149# @return: Distance to great circle, negative if to left or
150# positive if to right of line (C{meter}, same units
151# as B{C{radius}}).
152#
153# @raise TypeError: If B{C{start}} or B{C{end}} point is not L{LatLon}.
154# '''
155# self.others(start=start)
156#
157# if _isDegrees(end): # gc from point and bearing
158# gc = start.greatCircle(end)
159# else: # gc by two points
160# gc = start.toNvector().cross(end.toNvector())
161#
162# # (signed) angle between point and gc normal vector
163# v = self.toNvector()
164# a = gc.angleTo(v, vSign=v.cross(gc))
165# a = _copysign(PI_2, a) - a
166# return a * float(radius)
168 def deltaTo(self, other, wrap=False, **Ned_and_kwds):
169 '''Calculate the local delta from this to an other point.
171 @note: This is a linear delta, I{unrelated} to a geodesic on the
172 ellipsoid.
174 @arg other: The other point (L{LatLon}).
175 @kwarg wrap: If C{True}, wrap or I{normalize} the B{C{other}}
176 point (C{bool}).
177 @kwarg Ned_and_kwds: Optional C{B{Ned}=L{Ned} class and B{name}=NN}
178 to return delta and other B{C{Ned}} keyword arguments.
180 @return: Delta from this to the other point (B{C{Ned}}).
182 @raise TypeError: The B{C{other}} point is not L{LatLon} or B{C{Ned}}
183 is not an L{Ned4Tuple<pygeodesy.Ned4Tuple>} nor an
184 L{Ned<pygeodesy.Ned>} nor a DEPRECATED L{Ned}.
186 @raise ValueError: If ellipsoids are incompatible.
187 '''
188 self.ellipsoids(other) # throws TypeError and ValueError
190 p = self.others(other)
191 if wrap:
192 p = _Wrap.point(p)
193 # get delta in cartesian frame
194 dc = p.toCartesian().minus(self.toCartesian())
195 # rotate dc to get delta in n-vector reference
196 # frame using the rotation matrix row vectors
197 ned_ = map2(dc.dot, self._rotation3)
199 N, kwds = _xkwds_pop2(Ned_and_kwds, Ned=Ned)
200 if issubclassof(N, Ned4Tuple):
201 ned_ += _MODS.ltp.Ltp(self, ecef=self.Ecef(self.datum)),
202 else:
203 _xsubclassof(_Ned, Ned4Tuple, Ned=N)
204 return N(*ned_, **_xkwds(kwds, name=self.name))
206# def destination(self, distance, bearing, radius=R_M, height=None):
207# '''Return the destination point after traveling from this
208# point the given distance on the given initial bearing.
209#
210# @arg distance: Distance traveled (C{meter}, same units as
211# given earth B{C{radius}}).
212# @arg bearing: Initial bearing (compass C{degrees360}).
213# @kwarg radius: Mean earth radius (C{meter}).
214# @kwarg height: Optional height at destination point,
215# overriding default (C{meter}, same units
216# as B{C{radius}}).
217#
218# @return: Destination point (L{LatLon}).
219# '''
220# r = _m2radians(distance, radius) # angular distance in radians
221# # great circle by starting from this point on given bearing
222# gc = self.greatCircle(bearing)
223#
224# v1 = self.toNvector()
225# x = v1.times(cos(r)) # component of v2 parallel to v1
226# y = gc.cross(v1).times(sin(r)) # component of v2 perpendicular to v1
227#
228# v2 = x.plus(y).unit()
229# return v2.toLatLon(height=self._heigHt(height))
231 def destinationNed(self, delta):
232 '''Calculate the destination point using the supplied NED delta
233 from this point.
235 @arg delta: Delta from this to the other point in the local
236 tangent plane (LTP) of this point (L{Ned}).
238 @return: Destination point (L{LatLon}).
240 @raise TypeError: If B{C{delta}} is not an L{Ned<pygeodesy.Ned>}
241 or a DEPRECATED L{Ned}.
242 '''
243 _xinstanceof(_Ned, delta=delta)
245 nv, ev, dv = self._rotation3
246 # convert NED delta to standard coordinate frame of n-vector
247 dn = delta.ned[:3] # XXX Ned4Tuple.to3Tuple
248 # rotate dn to get delta in cartesian (ECEF) coordinate
249 # reference frame using the rotation matrix column vectors
250 dc = Cartesian(fdot(dn, nv.x, ev.x, dv.x),
251 fdot(dn, nv.y, ev.y, dv.y),
252 fdot(dn, nv.z, ev.z, dv.z))
254 # apply (cartesian) delta to this Cartesian to obtain destination as cartesian
255 v = self.toCartesian().plus(dc)
256 return v.toLatLon(datum=self.datum, LatLon=self.classof) # Cartesian(v.x, v.y, v.z).toLatLon(...)
258 def distanceTo(self, other, radius=None, wrap=False):
259 '''I{Approximate} the distance from this to an other point.
261 @arg other: The other point (L{LatLon}).
262 @kwarg radius: Mean earth radius, ellipsoid or datum (C{meter},
263 L{Ellipsoid}, L{Ellipsoid2}, L{Datum} or
264 L{a_f2Tuple}), overriding the mean radius C{R1}
265 of this point's datum..
266 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the
267 B{C{other}} and angular distance (C{bool}).
269 @return: Distance (C{meter}, same units as B{C{radius}}).
271 @raise TypeError: The B{C{other}} point is not L{LatLon}.
273 @raise ValueError: Invalid B{C{radius}}.
274 '''
275 p = self.others(other)
276 if wrap:
277 p = _Wrap.point(p)
278 a = self._N_vector.angleTo(p._N_vector, wrap=wrap)
279 E = self.datum.ellipsoid if radius is None else _earth_ellipsoid(radius)
280 return fabs(a) * E.R1 # see .utily.radians2m
282 @property_RO
283 def Ecef(self):
284 '''Get the ECEF I{class} (L{EcefVeness}), I{once}.
285 '''
286 return _Ecef()
288 @deprecated_method
289 def equals(self, other, eps=None): # PYCHOK no cover
290 '''DEPRECATED, use method L{isequalTo}.
291 '''
292 return self.isequalTo(other, eps=eps)
294 def isequalTo(self, other, eps=None):
295 '''Compare this point with an other point.
297 @arg other: The other point (L{LatLon}).
298 @kwarg eps: Optional margin (C{float}).
300 @return: C{True} if points are identical, including
301 datum, I{ignoring height}, C{False} otherwise.
303 @raise TypeError: The B{C{other}} point is not L{LatLon}.
305 @raise ValueError: Invalid B{C{eps}}.
307 @see: Method C{isequalTo3} to include I{height}.
308 '''
309 return self.datum == self.others(other).datum and \
310 _MODS.formy._isequalTo(self, other, eps=eps)
312# def greatCircle(self, bearing):
313# '''Return the great circle heading on the given bearing
314# from this point.
315#
316# Direction of vector is such that initial bearing vector
317# b = c × p, where p is representing this point.
318#
319# @arg bearing: Bearing from this point (compass C{degrees360}).
320#
321# @return: N-vector representing great circle (C{Nvector}).
322# '''
323# a, b, _ = self.philamheight
324# t = radians(bearing)
325#
326# sa, ca, sb, cb, st, ct = sincos2_(a, b, t)
327# return self._xnamed(Nvector(sb * ct - sa * cb * st,
328# -cb * ct - sa * sb * st,
329# ca * st)
331# def initialBearingTo(self, other, wrap=False):
332# '''Return the initial bearing (forward azimuth) from
333# this to an other point.
334#
335# @arg other: The other point (L{LatLon}).
336# @kwarg wrap: If C{True}, wrap or I{normalize}
337# and unroll the B{C{other}} (C{bool}).
338#
339# @return: Initial bearing (compass C{degrees360}).
340#
341# @raise TypeError: The B{C{other}} point is not L{LatLon}.
342# '''
343# p = self.others(other)
344# if wrap:
345# p = _Wrap.point(p)
346# v1 = self.toNvector()
347#
348# gc1 = v1.cross(p.toNvector()) # gc through v1 & v2
349# gc2 = v1.cross(_NP3) # gc through v1 & North pole
350#
351# # bearing is (signed) angle between gc1 & gc2
352# return degrees360(gc1.angleTo(gc2, vSign=v1))
354 def intermediateTo(self, other, fraction, height=None, wrap=False):
355 '''Return the point at given fraction between this and
356 an other point.
358 @arg other: The other point (L{LatLon}).
359 @arg fraction: Fraction between both points (C{scalar},
360 0.0 at this to 1.0 at the other point.
361 @kwarg height: Optional height, overriding the fractional
362 height (C{meter}).
363 @kwarg wrap: If C{True}, wrap or I{normalize} the
364 B{C{other}} point (C{bool}).
366 @return: Intermediate point (L{LatLon}).
368 @raise TypeError: The B{C{other}} point is not L{LatLon}.
369 '''
370 p = self.others(other)
371 if wrap:
372 p = _Wrap.point(p)
373 f = Scalar(fraction=fraction)
374 h = self._havg(other, f=f, h=height)
375 i = self.toNvector().intermediateTo(p.toNvector(), f)
376 return i.toLatLon(height=h, LatLon=self.classof) # Nvector(i.x, i.y, i.z).toLatLon(...)
378 @Property_RO
379 def _rotation3(self):
380 '''(INTERNAL) Get the rotation matrix from n-vector coordinate frame axes.
381 '''
382 nv = self.toNvector() # local (n-vector) coordinate frame
384 dv = nv.negate() # down, opposite to n-vector
385 ev = NorthPole.cross(nv, raiser=_pole_).unit() # east, pointing perpendicular to the plane
386 nv = ev.cross(dv) # north, by right hand rule
387 return nv, ev, dv # matrix rows
389 def toCartesian(self, **Cartesian_and_kwds): # PYCHOK Cartesian=Cartesian, datum=None
390 '''Convert this point to an C{Nvector}-based geodetic point.
392 @kwarg Cartesian_and_kwds: Optional L{Cartesian}, B{C{datum}} and other
393 keyword arguments. Use C{B{Cartesian}=...}
394 to override this L{Cartesian} class or specify
395 C{B{Cartesian}=None}.
397 @return: The geodetic point (L{Cartesian}) or if C{B{Cartesian} is None},
398 an L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with
399 C{C} and C{M} if available.
401 @raise TypeError: Invalid B{C{Cartesian}} or other B{C{Cartesian_and_kwds}}.
402 '''
403 kwds = _xkwds(Cartesian_and_kwds, Cartesian=Cartesian, datum=self.datum)
404 return LatLonEllipsoidalBase.toCartesian(self, **kwds)
406 def toNvector(self, **Nvector_and_kwds): # PYCHOK signature
407 '''Convert this point to C{Nvector} components, I{including height}.
409 @kwarg Nvector_and_kwds: Optional C{Nvector}, B{C{datum}} and other
410 keyword arguments. Use C{B{Nvector}=...}
411 to override this C{Nvector} class or specify
412 C{B{Nvector}=None}.
414 @return: The C{n-vector} components (C{Nvector}) or if B{C{Nvector}}
415 is set to C{None}, a L{Vector4Tuple}C{(x, y, z, h)}.
417 @raise TypeError: Invalid B{C{Nvector}} or other B{C{Nvector_and_kwds}}.
418 '''
419 kwds = _xkwds(Nvector_and_kwds, Nvector=Nvector, datum=self.datum)
420 return LatLonNvectorBase.toNvector(self, **kwds)
423_Nv00 = LatLon(0, 0, name=_Nv00_) # reference instance (L{LatLon})
426class Nvector(NvectorBase):
427 '''An n-vector is a position representation using a (unit) vector
428 normal to the earth ellipsoid. Unlike lat-/longitude points,
429 n-vectors have no singularities or discontinuities.
431 For many applications, n-vectors are more convenient to work
432 with than other position representations like lat-/longitude,
433 earth-centred earth-fixed (ECEF) vectors, UTM coordinates, etc.
435 Note commonality with L{pygeodesy.sphericalNvector.Nvector}.
436 '''
437 _datum = _WGS84 # default datum (L{Datum})
439 def __init__(self, x_xyz, y=None, z=None, h=0, datum=None, ll=None, **name):
440 '''New n-vector normal to the earth's surface.
442 @arg x_xyz: X component of vector (C{scalar}) or (3-D) vector
443 (C{Nvector}, L{Vector3d}, L{Vector3Tuple} or
444 L{Vector4Tuple}).
445 @kwarg y: Y component of vector (C{scalar}), ignored if B{C{x_xyz}}
446 is not C{scalar}, otherwise same units as B{C{x_xyz}}.
447 @kwarg z: Z component of vector (C{scalar}), ignored if B{C{x_xyz}}
448 is not C{scalar}, otherwise same units as B{C{x_xyz}}.
449 @kwarg h: Optional height above model surface (C{meter}).
450 @kwarg datum: Optional datum this n-vector is defined in
451 (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or
452 L{a_f2Tuple}).
453 @kwarg ll: Optional, original latlon (C{LatLon}).
454 @kwarg name: Optional C{B{name}=NN} (C{str}).
456 @raise TypeError: If B{C{datum}} is not a L{Datum}.
457 '''
458 NvectorBase.__init__(self, x_xyz, y=y, z=z, h=h, ll=ll, **name)
459 if not _isin(datum, None, self._datum):
460 self._datum = _ellipsoidal_datum(datum, **name)
462 @Property_RO
463 def datum(self):
464 '''Get this n-vector's datum (L{Datum}).
465 '''
466 return self._datum
468 @property_RO
469 def ellipsoidalNvector(self):
470 '''Get this C{Nvector}'s ellipsoidal class.
471 '''
472 return type(self)
474 def toCartesian(self, **Cartesian_and_kwds): # PYCHOK Cartesian=Cartesian
475 '''Convert this n-vector to C{Nvector}-based cartesian (ECEF) coordinates.
477 @kwarg Cartesian_and_kwds: Optional L{Cartesian}, B{C{h}}, B{C{datum}} and
478 other keyword arguments. Use C{B{Cartesian}=...}
479 to override this L{Cartesian} class or specify
480 C{B{Cartesian} is None}.
482 @return: The cartesian point (L{Cartesian}) or if C{B{Cartesian} is None},
483 an L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with
484 C{C} and C{M} if available.
486 @raise TypeError: Invalid B{C{Cartesian_and_kwds}}.
487 '''
488 kwds = _xkwds(Cartesian_and_kwds, h=self.h, Cartesian=Cartesian,
489 datum=self.datum)
490 return NvectorBase.toCartesian(self, **kwds) # class or .classof
492 def toLatLon(self, **LatLon_and_kwds): # PYCHOK height=None, LatLon=LatLon
493 '''Convert this n-vector to an C{Nvector}-based geodetic point.
495 @kwarg LatLon_and_kwds: Optional L{LatLon}, B{C{height}}, B{C{datum}}
496 and other keyword arguments. Use C{B{LatLon}=...}
497 to override this L{LatLon} class or specify
498 C{B{LatLon} is None}.
500 @return: The geodetic point (L{LatLon}) or if C{B{LatLon} is None},
501 an L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)}
502 with C{C} and C{M} if available.
504 @raise TypeError: Invalid B{C{LatLon_and_kwds}}.
505 '''
506 kwds = _xkwds(LatLon_and_kwds, height=self.h, datum=self.datum, LatLon=LatLon)
507 return NvectorBase.toLatLon(self, **kwds) # class or .classof
509 def unit(self, ll=None):
510 '''Normalize this vector to unit length.
512 @kwarg ll: Optional, original latlon (C{LatLon}).
514 @return: Normalised vector (C{Nvector}).
515 '''
516 u = NvectorBase.unit(self, ll=ll)
517 if u.datum != self.datum:
518 u._update(False, datum=self.datum)
519 return u
522def _Ecef():
523 # return the Ecef class and overwrite property_RO
524 Cartesian.Ecef = LatLon.Ecef = E = _MODS.ecef.EcefVeness
525 return E
528def meanOf(points, datum=_WGS84, height=None, wrap=False,
529 **LatLon_and_kwds):
530 '''Compute the geographic mean of several points.
532 @arg points: Points to be averaged (L{LatLon}[]).
533 @kwarg datum: Optional datum to use (L{Datum}).
534 @kwarg height: Optional height at mean point, overriding the mean
535 height (C{meter}).
536 @kwarg wrap: If C{True}, wrap or I{normalize} B{C{points}} (C{bool}).
537 @kwarg LatLon_and_kwds: Optional B{C{LatLon}} class to return the mean
538 points (or C{None}) and additional B{C{LatLon}} keyword
539 arguments, ignored if C{B{LatLon} is None}.
541 @return: Geographic mean point and height (B{C{LatLon}}) or if C{B{LatLon}
542 is None}, an L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M,
543 datum)} with C{C} and C{M} if available.
545 @raise ValueError: Insufficient number of B{C{points}}.
546 '''
547 Ps = _Nv00.PointsIter(points, wrap=wrap)
548 n = sumOf(p._N_vector for p in Ps.iterate(closed=False))
549 return n.toLatLon(**_xkwds(LatLon_and_kwds, height=height, datum=datum,
550 LatLon=LatLon, name__=meanOf))
553def nearestOn(point, point1, point2, within=True, height=None, wrap=False,
554 equidistant=None, tol=_TOL_M, LatLon=LatLon, **LatLon_kwds):
555 '''I{Iteratively} locate the closest point on the geodesic between
556 two other (ellipsoidal) points.
558 @arg point: Reference point (C{LatLon}).
559 @arg point1: Start point of the geodesic (C{LatLon}).
560 @arg point2: End point of the geodesic (C{LatLon}).
561 @kwarg within: If C{True}, return the closest point I{between}
562 B{C{point1}} and B{C{point2}}, otherwise the
563 closest point elsewhere on the geodesic (C{bool}).
564 @kwarg height: Optional height for the closest point (C{meter},
565 conventionally) or C{None} or C{False} for the
566 interpolated height. If C{False}, the closest
567 takes the heights of the points into account.
568 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll I{only}
569 B{C{point1}} and B{C{point2}} (C{bool}).
570 @kwarg equidistant: An azimuthal equidistant projection (I{class}
571 or function L{pygeodesy.equidistant}) or C{None}
572 for the preferred C{B{point}.Equidistant}.
573 @kwarg tol: Convergence tolerance (C{meter}).
574 @kwarg LatLon: Optional class to return the closest point
575 (L{LatLon}) or C{None}.
576 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword
577 arguments, ignored if C{B{LatLon} is None}.
579 @return: Closest point, a B{C{LatLon}} instance or if C{B{LatLon}
580 is None}, a L{LatLon4Tuple}C{(lat, lon, height, datum)}.
582 @raise ImportError: Package U{geographiclib
583 <https://PyPI.org/project/geographiclib>}
584 not installed or not found.
586 @raise TypeError: Invalid or non-ellipsoidal B{C{point}}, B{C{point1}}
587 or B{C{point2}} or invalid B{C{equidistant}}.
589 @raise ValueError: No convergence for the B{C{tol}}.
591 @see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/
592 calculating-intersection-of-two-circles>} and U{Karney's paper
593 <https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{14. MARITIME
594 BOUNDARIES} for more details about the iteration algorithm.
595 '''
596 return _nearestOn(point, point1, point2, within=within, height=height, wrap=wrap,
597 equidistant=equidistant, tol=tol, LatLon=LatLon, **LatLon_kwds)
600def sumOf(nvectors, Vector=Nvector, h=None, **Vector_kwds):
601 '''Return the vectorial sum of two or more n-vectors.
603 @arg nvectors: Vectors to be added (C{Nvector}[]).
604 @kwarg Vector: Optional class for the vectorial sum (C{Nvector}).
605 @kwarg h: Optional height, overriding the mean height (C{meter}).
606 @kwarg Vector_kwds: Optional, additional B{C{Vector}} keyword
607 arguments, ignored if C{B{Vector} is None}.
609 @return: Vectorial sum (B{C{Vector}}).
611 @raise VectorError: No B{C{nvectors}}.
612 '''
613 return _sumOf(nvectors, Vector=Vector, h=h, **Vector_kwds)
616@deprecated_function
617def toNed(distance, bearing, elevation, Ned=Ned, **name):
618 '''DEPRECATED, use L{pygeodesy.Aer}C{(bearing, elevation,
619 distance).xyzLocal.toNed(B{Ned}, name=B{name})} or
620 L{XyzLocal}C{(pygeodesy.Aer(bearing, elevation,
621 distance)).toNed(B{Ned}, name=B{name})}.
623 Create an NED vector from distance, bearing and elevation
624 (in local coordinate system).
626 @arg distance: NED vector length (C{meter}).
627 @arg bearing: NED vector bearing (compass C{degrees360}).
628 @arg elevation: NED vector elevation from local coordinate
629 frame horizontal (C{degrees}).
630 @kwarg Ned: Optional class to return the NED (C{Ned}) or
631 C{None}.
632 @kwarg name: Optional C{B{name}=NN} (C{str}).
634 @return: An NED vector equivalent to this B{C{distance}},
635 B{C{bearing}} and B{C{elevation}} (DEPRECATED L{Ned})
636 or a DEPRECATED L{Ned3Tuple}C{(north, east, down)}
637 if C{B{Ned} is None}.
639 @raise ValueError: Invalid B{C{distance}}, B{C{bearing}}
640 or B{C{elevation}}.
641 '''
642 if True: # use new Aer class
643 n, e, d, _ = _Aer(bearing, elevation, distance).xyz4
644 else: # DEPRECATED
645 d = Distance(distance)
647 sb, cb, se, ce = sincos2d_(Bearing(bearing),
648 Height(elevation=elevation))
649 n = cb * d * ce
650 e = sb * d * ce
651 d *= se
653 r = _MODS.deprecated.classes.Ned3Tuple(n, e, -d) if Ned is None else \
654 Ned(n, e, -d)
655 return _xnamed(r, name)
658__all__ += _ALL_OTHER(Cartesian, LatLon, Ned, Nvector, # classes
659 meanOf, sumOf, toNed)
661# **) MIT License
662#
663# Copyright (C) 2016-2025 -- mrJean1 at Gmail -- All Rights Reserved.
664#
665# Permission is hereby granted, free of charge, to any person obtaining a
666# copy of this software and associated documentation files (the "Software"),
667# to deal in the Software without restriction, including without limitation
668# the rights to use, copy, modify, merge, publish, distribute, sublicense,
669# and/or sell copies of the Software, and to permit persons to whom the
670# Software is furnished to do so, subject to the following conditions:
671#
672# The above copyright notice and this permission notice shall be included
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