Coverage for pygeodesy/cartesianBase.py: 92%
332 statements
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2# -*- coding: utf-8 -*-
4u'''(INTERNAL) Private C{CartesianBase} class for elliposiodal, spherical and N-/vectorial
5C{Cartesian}s and public functions L{rtp2xyz}, L{rtp2xyz_}, L{xyz2rtp} and L{xyz2rtp_}.
7After I{(C) Chris Veness 2011-2015} published under the same MIT Licence**, see
8U{https://www.Movable-Type.co.UK/scripts/latlong.html},
9U{https://www.Movable-Type.co.UK/scripts/latlong-vectors.html} and
10U{https://www.Movable-Type.co.UK/scripts/geodesy/docs/latlon-ellipsoidal.js.html}.
11'''
13# from pygeodesy.basics import _xinstanceof # from .datums
14from pygeodesy.constants import EPS, EPS0, INT0, PI2, _isfinite, isnear0, \
15 _0_0, _1_0, _N_1_0, _2_0, _4_0, _6_0
16from pygeodesy.datums import Datum, _earth_ellipsoid, _spherical_datum, \
17 Transform, _WGS84, _xinstanceof
18# from pygeodesy.ecef import EcefKarney # _MODS
19from pygeodesy.errors import _IsnotError, _TypeError, _ValueError, _xattr, \
20 _xdatum, _xkwds, _xkwds_get, _xkwds_pop2
21from pygeodesy.fmath import cbrt, hypot, hypot_, hypot2, fabs, sqrt # hypot
22# from pygeodesy.formy import _hartzell # _MODS
23from pygeodesy.fsums import fsumf_, Fmt
24from pygeodesy.interns import _COMMASPACE_, _datum_, _no_, _phi_
25from pygeodesy.interns import _ellipsoidal_, _spherical_ # PYCHOK used!
26from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS
27from pygeodesy.named import _name2__, _Pass
28from pygeodesy.namedTuples import LatLon4Tuple, _NamedTupleTo , Vector3Tuple, \
29 Vector4Tuple, Bearing2Tuple # PYCHOK .sphericalBase
30# from pygeodesy.nvectorBase import _N_vector # _MODS
31from pygeodesy.props import deprecated_method, Property, Property_RO, \
32 property_doc_, property_RO, _update_all
33# from pygeodesy,resections import cassini, collins5, pierlot, pierlotx, \
34# tienstra7 # _MODS
35# from pygeodesy.streprs import Fmt # from .fsums
36# from pygeodesy.triaxials import Triaxial_ # _MODS
37from pygeodesy.units import Degrees, Height, _heigHt, _isMeter, Meter, Radians
38from pygeodesy.utily import acos1, sincos2d, sincos2_, atan2, degrees, radians
39from pygeodesy.vector3d import Vector3d, _xyzhdlln4
40# from pygeodesy.vector3dBase import _xyz3 # _MODS
41# from pygeodesy import ltp # _MODS
43# from math import atan2, degrees, fabs, radians, sqrt # from .fmath, .utily
45__all__ = _ALL_LAZY.cartesianBase
46__version__ = '24.06.11'
48_r_ = 'r'
49_theta_ = 'theta'
52class CartesianBase(Vector3d):
53 '''(INTERNAL) Base class for ellipsoidal and spherical C{Cartesian}.
54 '''
55 _datum = None # L{Datum}, to be overriden
56 _height = None # height (L{Height}), set or approximated
58 def __init__(self, x_xyz, y=None, z=None, datum=None, **ll_name):
59 '''New C{Cartesian...}.
61 @arg x_xyz: Cartesian X coordinate (C{scalar}) or a C{Cartesian},
62 L{Ecef9Tuple}, L{Vector3Tuple} or L{Vector4Tuple}.
63 @kwarg y: Cartesian Y coordinate (C{scalar}), ignored if B{C{x_xyz}}
64 is not C{scalar}, otherwise same units as B{C{x_xyz}}.
65 @kwarg z: Cartesian Z coordinate (C{scalar}), like B{C{y}}.
66 @kwarg datum: Optional datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2}
67 or L{a_f2Tuple}).
68 @kwarg ll_name: Optional C{B{name}=NN} (C{str}) and optional, original
69 latlon C{B{ll}=None} (C{LatLon}).
71 @raise TypeError: Non-scalar B{C{x_xyz}}, B{C{y}} or B{C{z}} coordinate
72 or B{C{x_xyz}} not a C{Cartesian}, L{Ecef9Tuple},
73 L{Vector3Tuple} or L{Vector4Tuple} or B{C{datum}} is
74 not a L{Datum}.
75 '''
76 h, d, ll, n = _xyzhdlln4(x_xyz, None, datum, **ll_name)
77 Vector3d.__init__(self, x_xyz, y=y, z=z, ll=ll, name=n)
78 if h is not None:
79 self._height = Height(h)
80 if d is not None:
81 self.datum = d
83# def __matmul__(self, other): # PYCHOK Python 3.5+
84# '''Return C{NotImplemented} for C{c_ = c @ datum} and C{c_ = c @ transform}.
85# '''
86# return NotImplemented if isinstance(other, (Datum, Transform)) else \
87# _NotImplemented(self, other)
89 def cassini(self, pointB, pointC, alpha, beta, useZ=False):
90 '''3-Point resection between this and 2 other points using U{Cassini
91 <https://NL.WikiPedia.org/wiki/Achterwaartse_insnijding>}'s method.
93 @arg pointB: Second point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple},
94 C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}).
95 @arg pointC: Center point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple},
96 C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}).
97 @arg alpha: Angle subtended by triangle side C{b} from B{C{pointA}} to
98 B{C{pointC}} (C{degrees}, non-negative).
99 @arg beta: Angle subtended by triangle side C{a} from B{C{pointB}} to
100 B{C{pointC}} (C{degrees}, non-negative).
101 @kwarg useZ: If C{True}, use and interpolate the Z component, otherwise
102 force C{z=INT0} (C{bool}).
104 @note: Typically, B{C{pointC}} is between this and B{C{pointB}}.
106 @return: The survey point, an instance of this (sub-)class.
108 @raise ResectionError: Near-coincident, -colinear or -concyclic points
109 or negative or invalid B{C{alpha}} or B{C{beta}}.
111 @raise TypeError: Invalid B{C{pointA}}, B{C{pointB}} or B{C{pointM}}.
113 @see: Function L{pygeodesy.cassini} for references and more details.
114 '''
115 return _MODS.resections.cassini(self, pointB, pointC, alpha, beta,
116 useZ=useZ, datum=self.datum)
118 @deprecated_method
119 def collins(self, pointB, pointC, alpha, beta, useZ=False):
120 '''DEPRECATED, use method L{collins5}.'''
121 return self.collins5(pointB, pointC, alpha, beta, useZ=useZ)
123 def collins5(self, pointB, pointC, alpha, beta, useZ=False):
124 '''3-Point resection between this and 2 other points using U{Collins<https://Dokumen.tips/
125 documents/three-point-resection-problem-introduction-kaestner-burkhardt-method.html>}' method.
127 @arg pointB: Second point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple},
128 C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}).
129 @arg pointC: Center point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple},
130 C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}).
131 @arg alpha: Angle subtended by triangle side C{b} from B{C{pointA}} to
132 B{C{pointC}} (C{degrees}, non-negative).
133 @arg beta: Angle subtended by triangle side C{a} from B{C{pointB}} to
134 B{C{pointC}} (C{degrees}, non-negative).
135 @kwarg useZ: If C{True}, use and interpolate the Z component, otherwise
136 force C{z=INT0} (C{bool}).
138 @note: Typically, B{C{pointC}} is between this and B{C{pointB}}.
140 @return: L{Collins5Tuple}C{(pointP, pointH, a, b, c)} with survey C{pointP},
141 auxiliary C{pointH}, each an instance of this (sub-)class and
142 triangle sides C{a}, C{b} and C{c}.
144 @raise ResectionError: Near-coincident, -colinear or -concyclic points
145 or negative or invalid B{C{alpha}} or B{C{beta}}.
147 @raise TypeError: Invalid B{C{pointB}} or B{C{pointM}}.
149 @see: Function L{pygeodesy.collins5} for references and more details.
150 '''
151 return _MODS.resections.collins5(self, pointB, pointC, alpha, beta,
152 useZ=useZ, datum=self.datum)
154 @deprecated_method
155 def convertDatum(self, datum2, **datum):
156 '''DEPRECATED, use method L{toDatum}.'''
157 return self.toDatum(datum2, **datum)
159 @property_doc_(''' this cartesian's datum (L{Datum}).''')
160 def datum(self):
161 '''Get this cartesian's datum (L{Datum}).
162 '''
163 return self._datum
165 @datum.setter # PYCHOK setter!
166 def datum(self, datum):
167 '''Set this cartesian's C{datum} I{without conversion}
168 (L{Datum}), ellipsoidal or spherical.
170 @raise TypeError: The B{C{datum}} is not a L{Datum}.
171 '''
172 d = _spherical_datum(datum, name=self.name)
173 if self._datum: # is not None
174 if d.isEllipsoidal and not self._datum.isEllipsoidal:
175 raise _IsnotError(_ellipsoidal_, datum=datum)
176 elif d.isSpherical and not self._datum.isSpherical:
177 raise _IsnotError(_spherical_, datum=datum)
178 if self._datum != d:
179 _update_all(self)
180 self._datum = d
182 def destinationXyz(self, delta, Cartesian=None, **name_Cartesian_kwds):
183 '''Calculate the destination using a I{local} delta from this cartesian.
185 @arg delta: Local delta to the destination (L{XyzLocal}, L{Enu}, L{Ned}
186 or L{Local9Tuple}).
187 @kwarg Cartesian: Optional (geocentric) class to return the destination
188 or C{None}.
189 @kwarg name_Cartesian_kwds: Optional C{B{name}=NN} (C{str}) and optional,
190 additional B{C{Cartesian}} keyword arguments, ignored if
191 C{B{Cartesian} is None}.
193 @return: Destination as a C{B{Cartesian}(x, y, z, **B{Cartesian_kwds})}
194 instance or if C{B{Cartesian} is None}, an L{Ecef9Tuple}C{(x, y,
195 z, lat, lon, height, C, M, datum)} with C{M=None} always.
197 @raise TypeError: Invalid B{C{delta}}, B{C{Cartesian}} or B{C{Cartesian_kwds}}
198 item or C{datum} missing or incompatible.
199 '''
200 n, kwds = _name2__(name_Cartesian_kwds, _or_nameof=self)
201 if Cartesian is None:
202 r = self._Ltp._local2ecef(delta, nine=True)
203 else:
204 d = self.datum
205 if not d:
206 raise _TypeError(delta=delta, txt=_no_(_datum_))
207 t = _xkwds_get(kwds, datum=d)
208 if _xattr(t, ellipsoid=None) != d.ellipsoid:
209 raise _TypeError(datum=t, txt=str(d))
210 c = self._Ltp._local2ecef(delta, nine=False)
211 r = Cartesian(*c, **kwds)
212 return r.renamed(n) if n else r
214 @property_RO
215 def Ecef(self):
216 '''Get the ECEF I{class} (L{EcefKarney}), I{once}.
217 '''
218 CartesianBase.Ecef = E = _MODS.ecef.EcefKarney # overwrite property_RO
219 return E
221 @Property_RO
222 def _ecef9(self):
223 '''(INTERNAL) Helper for L{toEcef}, L{toLocal} and L{toLtp} (L{Ecef9Tuple}).
224 '''
225 return self.Ecef(self.datum, name=self.name).reverse(self, M=True)
227 @property_RO
228 def ellipsoidalCartesian(self):
229 '''Get the C{Cartesian type} iff ellipsoidal, overloaded in L{CartesianEllipsoidalBase}.
230 '''
231 return False
233 def hartzell(self, los=False, earth=None):
234 '''Compute the intersection of a Line-Of-Sight from this cartesian Point-Of-View
235 (pov) and this cartesian's ellipsoid surface.
237 @kwarg los: Line-Of-Sight, I{direction} to the ellipsoid (L{Los}, L{Vector3d}),
238 C{True} for the I{normal, plumb} onto the surface or I{False} or
239 C{None} to point to the center of the ellipsoid.
240 @kwarg earth: The earth model (L{Datum}, L{Ellipsoid}, L{Ellipsoid2}, L{a_f2Tuple}
241 or C{scalar} radius in C{meter}), overriding this cartesian's
242 C{datum} ellipsoid.
244 @return: The intersection (C{Cartesian}) with C{.height} set to the distance to
245 this C{pov}.
247 @raise IntersectionError: Null or bad C{pov} or B{C{los}}, this C{pov} is inside
248 the ellipsoid or B{C{los}} points outside or away from
249 the ellipsoid.
251 @raise TypeError: Invalid B{C{los}} or invalid or undefined B{C{earth}} or C{datum}.
253 @see: Function L{hartzell<pygeodesy.formy.hartzell>} for further details.
254 '''
255 return _MODS.formy._hartzell(self, los, earth)
257 @Property
258 def height(self):
259 '''Get the height (C{meter}).
260 '''
261 return self._height4.h if self._height is None else self._height
263 @height.setter # PYCHOK setter!
264 def height(self, height):
265 '''Set the height (C{meter}).
267 @raise TypeError: Invalid B{C{height}} C{type}.
269 @raise ValueError: Invalid B{C{height}}.
270 '''
271 h = Height(height)
272 if self._height != h:
273 _update_all(self)
274 self._height = h
276 def _height2C(self, r, Cartesian=None, datum=None, height=INT0, **kwds):
277 '''(INTERNAL) Helper for methods C{.height3} and C{.height4}.
278 '''
279 if Cartesian is not None:
280 r = Cartesian(r, **kwds)
281 if datum is not None:
282 r.datum = datum
283 if height is not None:
284 r.height = height # Height(height)
285 return r
287 def height3(self, earth=None, height=None, **Cartesian_and_kwds):
288 '''Compute the cartesian at a height above or below this certesian's ellipsoid.
290 @kwarg earth: A datum, ellipsoid, triaxial ellipsoid or earth radius,
291 I{overriding} this cartesian's datum (L{Datum}, L{Ellipsoid},
292 L{Ellipsoid2}, L{a_f2Tuple} or C{meter}, conventionally).
293 @kwarg height: The height (C{meter}, conventionally), overriding this
294 cartesian's height.
295 @kwarg Cartesian_and_kwds: Optional C{B{Cartesian}=None} class to return
296 the cartesian I{at height} and additional B{C{Cartesian}}
297 keyword arguments.
299 @return: An instance of B{C{Cartesian}} or if C{B{Cartesian} is None},
300 a L{Vector3Tuple}C{(x, y, z)} with the C{x}, C{y} and C{z}
301 coordinates I{at height} in C{meter}, conventionally.
303 @note: This cartesian's coordinates are returned if B{C{earth}} and this
304 datum or B{C{heigth}} and/or this height are C{None} or undefined.
306 @note: Include keyword argument C{B{datum}=None} if class B{C{Cartesian}}
307 does not accept a B{C{datum}} keyword agument.
309 @raise TriaxialError: No convergence in triaxial root finding.
311 @raise TypeError: Invalid or undefined B{C{earth}} or C{datum}.
312 '''
313 n = self.height3.__name__
314 d = self.datum if earth is None else _spherical_datum(earth, name=n)
315 c, h = self, _heigHt(self, height)
316 if h and d:
317 R, r = self.Roc2(earth=d)
318 if R > EPS0:
319 R = (R + h) / R
320 r = ((r + h) / r) if r > EPS0 else _1_0
321 c = c.times_(R, R, r)
323 r = Vector3Tuple(c.x, c.y, c.z, name=n)
324 if Cartesian_and_kwds:
325 r = self._height2C(r, **_xkwds(Cartesian_and_kwds, datum=d))
326 return r
328 @Property_RO
329 def _height4(self):
330 '''(INTERNAL) Get this C{height4}-tuple.
331 '''
332 try:
333 r = self.datum.ellipsoid.height4(self, normal=True)
334 except (AttributeError, ValueError): # no datum, null cartesian,
335 r = Vector4Tuple(self.x, self.y, self.z, 0, name__=self.height4)
336 return r
338 def height4(self, earth=None, normal=True, **Cartesian_and_kwds):
339 '''Compute the projection of this point on and the height above or below
340 this datum's ellipsoid surface.
342 @kwarg earth: A datum, ellipsoid, triaxial ellipsoid or earth radius,
343 I{overriding} this datum (L{Datum}, L{Ellipsoid},
344 L{Ellipsoid2}, L{a_f2Tuple}, L{Triaxial}, L{Triaxial_},
345 L{JacobiConformal} or C{meter}, conventionally).
346 @kwarg normal: If C{True} the projection is the nearest point on the
347 ellipsoid's surface, otherwise the intersection of the
348 radial line to the ellipsoid's center and the surface.
349 @kwarg Cartesian_and_kwds: Optional C{B{Cartesian}=None} class to return
350 the I{projection} and additional B{C{Cartesian}} keyword
351 arguments.
353 @return: An instance of B{C{Cartesian}} or if C{B{Cartesian} is None}, a
354 L{Vector4Tuple}C{(x, y, z, h)} with the I{projection} C{x}, C{y}
355 and C{z} coordinates and height C{h} in C{meter}, conventionally.
357 @note: Include keyword argument C{B{datum}=None} if class B{C{Cartesian}}
358 does not accept a B{C{datum}} keyword agument.
360 @raise TriaxialError: No convergence in triaxial root finding.
362 @raise TypeError: Invalid or undefined B{C{earth}} or C{datum}.
364 @see: Methods L{Ellipsoid.height4} and L{Triaxial_.height4} for more information.
365 '''
366 n = self.height4.__name__
367 d = self.datum if earth is None else earth
368 if normal and d is self.datum:
369 r = self._height4
370 elif isinstance(d, _MODS.triaxials.Triaxial_):
371 r = d.height4(self, normal=normal)
372 try:
373 d = d.toEllipsoid(name=n)
374 except (TypeError, ValueError): # TriaxialError
375 d = None
376 else:
377 r = _earth_ellipsoid(d).height4(self, normal=normal)
379 if Cartesian_and_kwds:
380 if d and not isinstance(d, Datum):
381 d = _spherical_datum(d, name=n)
382 r = self._height2C(r, **_xkwds(Cartesian_and_kwds, datum=d))
383 return r
385 @Property_RO
386 def isEllipsoidal(self):
387 '''Check whether this cartesian is ellipsoidal (C{bool} or C{None} if unknown).
388 '''
389 return _xattr(self.datum, isEllipsoidal=None)
391 @Property_RO
392 def isSpherical(self):
393 '''Check whether this cartesian is spherical (C{bool} or C{None} if unknown).
394 '''
395 return _xattr(self.datum, isSpherical=None)
397 @Property_RO
398 def latlon(self):
399 '''Get this cartesian's (geodetic) lat- and longitude in C{degrees} (L{LatLon2Tuple}C{(lat, lon)}).
400 '''
401 return self.toEcef().latlon
403 @Property_RO
404 def latlonheight(self):
405 '''Get this cartesian's (geodetic) lat-, longitude in C{degrees} with height (L{LatLon3Tuple}C{(lat, lon, height)}).
406 '''
407 return self.toEcef().latlonheight
409 @Property_RO
410 def latlonheightdatum(self):
411 '''Get this cartesian's (geodetic) lat-, longitude in C{degrees} with height and datum (L{LatLon4Tuple}C{(lat, lon, height, datum)}).
412 '''
413 return self.toEcef().latlonheightdatum
415 @Property_RO
416 def _Ltp(self):
417 '''(INTERNAL) Cache for L{toLtp}.
418 '''
419 return _MODS.ltp.Ltp(self._ecef9, ecef=self.Ecef(self.datum), name=self.name)
421 @Property_RO
422 def _N_vector(self):
423 '''(INTERNAL) Get the (C{nvectorBase._N_vector_}).
424 '''
425 _N = _MODS.nvectorBase._N_vector_
426 x, y, z, h = self._n_xyzh4(self.datum)
427 return _N(x, y, z, h=h, name=self.name)
429 def _n_xyzh4(self, datum):
430 '''(INTERNAL) Get the n-vector components as L{Vector4Tuple}.
431 '''
432 def _ErrorEPS0(x):
433 return _ValueError(origin=self, txt=Fmt.PARENSPACED(EPS0=x))
435 _xinstanceof(Datum, datum=datum)
436 # <https://www.Movable-Type.co.UK/scripts/geodesy/docs/
437 # latlon-nvector-ellipsoidal.js.html#line309>,
438 # <https://GitHub.com/pbrod/nvector>/src/nvector/core.py>
439 # _equation23 and <https://www.NavLab.net/nvector>
440 E = datum.ellipsoid
441 x, y, z = self.xyz
443 # Kenneth Gade eqn 23
444 p = hypot2(x, y) * E.a2_
445 q = z**2 * E.e21 * E.a2_
446 r = fsumf_(p, q, -E.e4) / _6_0
447 s = (p * q * E.e4) / (_4_0 * r**3)
448 t = cbrt(fsumf_(_1_0, s, sqrt(s * (_2_0 + s))))
449 if isnear0(t):
450 raise _ErrorEPS0(t)
451 u = fsumf_(_1_0, t, _1_0 / t) * r
452 v = sqrt(u**2 + E.e4 * q)
453 t = v * _2_0
454 if t < EPS0: # isnear0
455 raise _ErrorEPS0(t)
456 w = fsumf_(u, v, -q) * E.e2 / t
457 k = sqrt(fsumf_(u, v, w**2)) - w
458 if isnear0(k):
459 raise _ErrorEPS0(k)
460 t = k + E.e2
461 if isnear0(t):
462 raise _ErrorEPS0(t)
463 e = k / t
464# d = e * hypot(x, y)
465# tmp = 1 / hypot(d, z) == 1 / hypot(e * hypot(x, y), z)
466 t = hypot_(x * e, y * e, z) # == 1 / tmp
467 if t < EPS0: # isnear0
468 raise _ErrorEPS0(t)
469 h = fsumf_(k, E.e2, _N_1_0) / k * t
470 s = e / t # == e * tmp
471 return Vector4Tuple(x * s, y * s, z / t, h, name=self.name)
473 @Property_RO
474 def philam(self):
475 '''Get this cartesian's (geodetic) lat- and longitude in C{radians} (L{PhiLam2Tuple}C{(phi, lam)}).
476 '''
477 return self.toEcef().philam
479 @Property_RO
480 def philamheight(self):
481 '''Get this cartesian's (geodetic) lat-, longitude in C{radians} with height (L{PhiLam3Tuple}C{(phi, lam, height)}).
482 '''
483 return self.toEcef().philamheight
485 @Property_RO
486 def philamheightdatum(self):
487 '''Get this cartesian's (geodetic) lat-, longitude in C{radians} with height and datum (L{PhiLam4Tuple}C{(phi, lam, height, datum)}).
488 '''
489 return self.toEcef().philamheightdatum
491 def pierlot(self, point2, point3, alpha12, alpha23, useZ=False, eps=EPS):
492 '''3-Point resection between this and two other points using U{Pierlot
493 <http://www.Telecom.ULg.ac.Be/triangulation>}'s method C{ToTal} with
494 I{approximate} limits for the (pseudo-)singularities.
496 @arg point2: Second point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple},
497 C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}).
498 @arg point3: Third point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple},
499 C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}).
500 @arg alpha12: Angle subtended from this point to B{C{point2}} or
501 B{C{alpha2 - alpha}} (C{degrees}).
502 @arg alpha23: Angle subtended from B{C{point2}} to B{C{point3}} or
503 B{C{alpha3 - alpha2}} (C{degrees}).
504 @kwarg useZ: If C{True}, interpolate the Z component, otherwise use C{z=INT0}
505 (C{bool}).
506 @kwarg eps: Tolerance for C{cot} (pseudo-)singularities (C{float}).
508 @note: This point, B{C{point2}} and B{C{point3}} are ordered counter-clockwise.
510 @return: The survey (or robot) point, an instance of this (sub-)class.
512 @raise ResectionError: Near-coincident, -colinear or -concyclic points
513 or invalid B{C{alpha12}} or B{C{alpha23}}.
515 @raise TypeError: Invalid B{C{point2}} or B{C{point3}}.
517 @see: Function L{pygeodesy.pierlot} for references and more details.
518 '''
519 return _MODS.resections.pierlot(self, point2, point3, alpha12, alpha23,
520 useZ=useZ, eps=eps, datum=self.datum)
522 def pierlotx(self, point2, point3, alpha1, alpha2, alpha3, useZ=False):
523 '''3-Point resection between this and two other points using U{Pierlot
524 <http://www.Telecom.ULg.ac.Be/publi/publications/pierlot/Pierlot2014ANewThree>}'s
525 method C{ToTal} with I{exact} limits for the (pseudo-)singularities.
527 @arg point2: Second point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple},
528 C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}).
529 @arg point3: Third point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple},
530 C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}).
531 @arg alpha1: Angle at B{C{point1}} (C{degrees}).
532 @arg alpha2: Angle at B{C{point2}} (C{degrees}).
533 @arg alpha3: Angle at B{C{point3}} (C{degrees}).
534 @kwarg useZ: If C{True}, interpolate the survey point's Z component,
535 otherwise use C{z=INT0} (C{bool}).
537 @return: The survey (or robot) point, an instance of this (sub-)class.
539 @raise ResectionError: Near-coincident, -colinear or -concyclic points or
540 invalid B{C{alpha1}}, B{C{alpha2}} or B{C{alpha3}}.
542 @raise TypeError: Invalid B{C{point2}} or B{C{point3}}.
544 @see: Function L{pygeodesy.pierlotx} for references and more details.
545 '''
546 return _MODS.resections.pierlotx(self, point2, point3, alpha1, alpha2, alpha3,
547 useZ=useZ, datum=self.datum)
549 def Roc2(self, earth=None):
550 '''Compute this cartesian's I{normal} and I{pseudo, z-based} radius of curvature.
552 @kwarg earth: A datum, ellipsoid, triaxial ellipsoid or earth radius,
553 I{overriding} this cartesian's datum (L{Datum}, L{Ellipsoid},
554 L{Ellipsoid2}, L{a_f2Tuple} or C{meter}, conventionally).
556 @return: 2-Tuple C{(R, r)} with the I{normal} and I{pseudo, z-based} radius of
557 curvature C{R} respectively C{r}, both in C{meter} conventionally.
559 @raise TypeError: Invalid or undefined B{C{earth}} or C{datum}.
560 '''
561 r = z = fabs( self.z)
562 R, _0 = hypot(self.x, self.y), EPS0
563 if R < _0: # polar
564 R = z
565 elif z > _0: # non-equatorial
566 d = self.datum if earth is None else _spherical_datum(earth)
567 e = self.toLatLon(datum=d, height=0, LatLon=None) # Ecef9Tuple
568 M = e.M # EcefMatrix
569 sa, ca = map(fabs, (M._2_2_, M._2_1_) if M else sincos2d(e.lat))
570 if ca < _0: # polar
571 R = z
572 else: # prime-vertical, normal roc R
573 R = R / ca # /= chokes PyChecker
574 r = R if sa < _0 else (r / sa) # non-/equatorial
575 return R, r
577 @property_RO
578 def sphericalCartesian(self):
579 '''Get the C{Cartesian type} iff spherical, overloaded in L{CartesianSphericalBase}.
580 '''
581 return False
583 @deprecated_method
584 def tienstra(self, pointB, pointC, alpha, beta=None, gamma=None, useZ=False):
585 '''DEPRECATED, use method L{tienstra7}.'''
586 return self.tienstra7(pointB, pointC, alpha, beta=beta, gamma=gamma, useZ=useZ)
588 def tienstra7(self, pointB, pointC, alpha, beta=None, gamma=None, useZ=False):
589 '''3-Point resection between this and two other points using U{Tienstra
590 <https://WikiPedia.org/wiki/Tienstra_formula>}'s formula.
592 @arg pointB: Second point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple}, C{Vector4Tuple} or
593 C{Vector2Tuple} if C{B{useZ}=False}).
594 @arg pointC: Third point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple}, C{Vector4Tuple} or
595 C{Vector2Tuple} if C{B{useZ}=False}).
596 @arg alpha: Angle subtended by triangle side C{a} from B{C{pointB}} to B{C{pointC}} (C{degrees},
597 non-negative).
598 @kwarg beta: Angle subtended by triangle side C{b} from this to B{C{pointC}} (C{degrees},
599 non-negative) or C{None} if C{B{gamma} is not None}.
600 @kwarg gamma: Angle subtended by triangle side C{c} from this to B{C{pointB}} (C{degrees},
601 non-negative) or C{None} if C{B{beta} is not None}.
602 @kwarg useZ: If C{True}, use and interpolate the Z component, otherwise force C{z=INT0}
603 (C{bool}).
605 @note: This point, B{C{pointB}} and B{C{pointC}} are ordered clockwise.
607 @return: L{Tienstra7Tuple}C{(pointP, A, B, C, a, b, c)} with survey C{pointP},
608 an instance of this (sub-)class and triangle angle C{A} at this point,
609 C{B} at B{C{pointB}} and C{C} at B{C{pointC}} in C{degrees} and
610 triangle sides C{a}, C{b} and C{c}.
612 @raise ResectionError: Near-coincident, -colinear or -concyclic points or sum of
613 B{C{alpha}}, B{C{beta}} and B{C{gamma}} not C{360} or
614 negative B{C{alpha}}, B{C{beta}} or B{C{gamma}}.
616 @raise TypeError: Invalid B{C{pointB}} or B{C{pointC}}.
618 @see: Function L{pygeodesy.tienstra7} for references and more details.
619 '''
620 return _MODS.resections.tienstra7(self, pointB, pointC, alpha, beta, gamma,
621 useZ=useZ, datum=self.datum)
623 @deprecated_method
624 def to2ab(self): # PYCHOK no cover
625 '''DEPRECATED, use property C{philam}.
627 @return: A L{PhiLam2Tuple}C{(phi, lam)}.
628 '''
629 return self.philam
631 @deprecated_method
632 def to2ll(self): # PYCHOK no cover
633 '''DEPRECATED, use property C{latlon}.
635 @return: A L{LatLon2Tuple}C{(lat, lon)}.
636 '''
637 return self.latlon
639 @deprecated_method
640 def to3llh(self, datum=None): # PYCHOK no cover
641 '''DEPRECATED, use property L{latlonheight} or L{latlonheightdatum}.
643 @return: A L{LatLon4Tuple}C{(lat, lon, height, datum)}.
645 @note: This method returns a B{C{-4Tuple}} I{and not a} C{-3Tuple}
646 as its name may suggest.
647 '''
648 t = self.toLatLon(datum=datum, LatLon=None)
649 return LatLon4Tuple(t.lat, t.lon, t.height, t.datum, name=self.name)
651# def _to3LLh(self, datum, LL, **pairs): # OBSOLETE
652# '''(INTERNAL) Helper for C{subclass.toLatLon} and C{.to3llh}.
653# '''
654# r = self.to3llh(datum) # LatLon3Tuple
655# if LL is not None:
656# r = LL(r.lat, r.lon, height=r.height, datum=datum, name=self.name)
657# for n, v in pairs.items():
658# setattr(r, n, v)
659# return r
661 def toDatum(self, datum2, datum=None):
662 '''Convert this cartesian from one datum to an other.
664 @arg datum2: Datum to convert I{to} (L{Datum}).
665 @kwarg datum: Datum to convert I{from} (L{Datum}).
667 @return: The converted point (C{Cartesian}).
669 @raise TypeError: B{C{datum2}} or B{C{datum}}
670 invalid.
671 '''
672 _xinstanceof(Datum, datum2=datum2)
674 c = self if datum in (None, self.datum) else \
675 self.toDatum(datum)
677 i, d = False, c.datum
678 if d == datum2:
679 return c.copy() if c is self else c
681 elif d is None or (d.transform.isunity and
682 datum2.transform.isunity):
683 return c.dup(datum=datum2)
685 elif d == _WGS84:
686 d = datum2 # convert from WGS84 to datum2
688 elif datum2 == _WGS84:
689 i = True # convert to WGS84 by inverse transformation
691 else: # neither datum2 nor c.datum is WGS84, invert to WGS84 first
692 c = c.toTransform(d.transform, inverse=True, datum=_WGS84)
693 d = datum2
695 return c.toTransform(d.transform, inverse=i, datum=datum2)
697 def toEcef(self):
698 '''Convert this cartesian to I{geodetic} (lat-/longitude) coordinates.
700 @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height,
701 C, M, datum)} with C{C} and C{M} if available.
703 @raise EcefError: A C{.datum} or an ECEF issue.
704 '''
705 return self._ecef9
707 def toLatLon(self, datum=None, height=None, LatLon=None, **LatLon_kwds): # see .ecef.Ecef9Tuple.toDatum
708 '''Convert this cartesian to a I{geodetic} (lat-/longitude) point.
710 @kwarg datum: Optional datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2}
711 or L{a_f2Tuple}).
712 @kwarg height: Optional height, overriding the converted height
713 (C{meter}), only if C{B{LatLon} is not None}.
714 @kwarg LatLon: Optional class to return the geodetic point
715 (C{LatLon}) or C{None}.
716 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword
717 arguments, ignored if C{B{LatLon} is None}.
719 @return: The geodetic point (B{C{LatLon}}) or if C{B{LatLon}
720 is None}, an L{Ecef9Tuple}C{(x, y, z, lat, lon, height,
721 C, M, datum)} with C{C} and C{M} if available.
723 @raise TypeError: Invalid B{C{datum}} or B{C{LatLon_kwds}}.
724 '''
725 d = _spherical_datum(datum or self.datum, name=self.name)
726 if d == self.datum:
727 r = self.toEcef()
728 else:
729 c = self.toDatum(d)
730 r = c.Ecef(d, name=self.name).reverse(c, M=LatLon is None)
732 if LatLon: # class or .classof
733 h = _heigHt(r, height)
734 r = LatLon(r.lat, r.lon, datum=r.datum, height=h,
735 **_xkwds(LatLon_kwds, name=r.name))
736 _xdatum(r.datum, d)
737 return r
739 def toLocal(self, Xyz=None, ltp=None, **Xyz_kwds):
740 '''Convert this I{geocentric} cartesian to I{local} C{X}, C{Y} and C{Z}.
742 @kwarg Xyz: Optional class to return C{X}, C{Y} and C{Z} (L{XyzLocal},
743 L{Enu}, L{Ned}) or C{None}.
744 @kwarg ltp: The I{local tangent plane} (LTP) to use, overriding this
745 cartesian's LTP (L{Ltp}).
746 @kwarg Xyz_kwds: Optional, additional B{C{Xyz}} keyword arguments,
747 ignored if C{B{Xyz} is None}.
749 @return: An B{C{Xyz}} instance or a L{Local9Tuple}C{(x, y, z, lat, lon,
750 height, ltp, ecef, M)} if C{B{Xyz} is None} (with C{M=None}).
752 @raise TypeError: Invalid B{C{ltp}}.
753 '''
754 return _MODS.ltp._toLocal(self, ltp, Xyz, Xyz_kwds) # self._ecef9
756 def toLtp(self, Ecef=None, **name):
757 '''Return the I{local tangent plane} (LTP) for this cartesian.
759 @kwarg Ecef: Optional ECEF I{class} (L{EcefKarney}, ...
760 L{EcefYou}), overriding this cartesian's C{Ecef}.
761 @kwarg name: Optional C{B{name}=NN} (C{str}).
762 '''
763 return _MODS.ltp._toLtp(self, Ecef, self._ecef9, name) # self._Ltp
765 def toNvector(self, Nvector=None, datum=None, **name_Nvector_kwds):
766 '''Convert this cartesian to C{n-vector} components, I{including height}.
768 @kwarg Nvector: Optional class to return the C{n-vector} components
769 (C{Nvector}) or C{None}.
770 @kwarg datum: Optional datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2}
771 or L{a_f2Tuple}) overriding this cartesian's datum.
772 @kwarg name_Nvector_kwds: Optional C{B{name}=NN} (C{str}) and optional,
773 additional B{C{Nvector}} keyword arguments, ignored if
774 C{B{Nvector} is None}.
776 @return: An B{C{Nvector}} or a L{Vector4Tuple}C{(x, y, z, h)} if
777 C{B{Nvector} is None}.
779 @raise TypeError: Invalid B{C{Nvector}}, B{C{datum}} or
780 B{C{name_Nvector_kwds}} item.
782 @raise ValueError: B{C{Cartesian}} at origin.
783 '''
784 r, d = self._N_vector.xyzh, self.datum
785 if datum is not None:
786 d = _spherical_datum(datum, name=self.name)
787 if d != self.datum:
788 r = self._n_xyzh4(d)
790 if Nvector is None:
791 n, _ = _name2__(name_Nvector_kwds, _or_nameof=self)
792 if n:
793 r = r.dup(name=n)
794 else:
795 kwds = _xkwds(name_Nvector_kwds, h=r.h, datum=d)
796 r = Nvector(r.x, r.y, r.z, **self._name1__(kwds))
797 return r
799 def toRtp(self):
800 '''Convert this cartesian to I{spherical, polar} coordinates.
802 @return: L{RadiusThetaPhi3Tuple}C{(r, theta, phi)} with C{theta}
803 and C{phi}, both in L{Degrees}.
805 @see: Function L{xyz2rtp_} and class L{RadiusThetaPhi3Tuple}.
806 '''
807 return _rtp3(self.toRtp, Degrees, self, name=self.name)
809 def toStr(self, prec=3, fmt=Fmt.SQUARE, sep=_COMMASPACE_): # PYCHOK expected
810 '''Return the string representation of this cartesian.
812 @kwarg prec: Number of (decimal) digits, unstripped (C{int}).
813 @kwarg fmt: Enclosing backets format (C{letter}).
814 @kwarg sep: Separator to join (C{str}).
816 @return: Cartesian represented as "[x, y, z]" (C{str}).
817 '''
818 return Vector3d.toStr(self, prec=prec, fmt=fmt, sep=sep)
820 def toTransform(self, transform, inverse=False, datum=None):
821 '''Apply a Helmert transform to this cartesian.
823 @arg transform: Transform to apply (L{Transform} or L{TransformXform}).
824 @kwarg inverse: Apply the inverse of the C{B{transform}} (C{bool}).
825 @kwarg datum: Datum for the transformed cartesian (L{Datum}), overriding
826 this cartesian's datum but I{not} taken it into account.
828 @return: A transformed cartesian (C{Cartesian}) or a copy of this
829 cartesian if C{B{transform}.isunity}.
831 @raise TypeError: Invalid B{C{transform}}.
832 '''
833 _xinstanceof(Transform, transform=transform)
834 if transform.isunity:
835 c = self.dup(datum=datum or self.datum)
836 else:
837 # if inverse and d != _WGS84:
838 # raise _ValueError(inverse=inverse, datum=d,
839 # txt_not_=_WGS84.name)
840 xyz = transform.transform(*self.xyz, inverse=inverse)
841 c = self.dup(xyz=xyz, datum=datum or self.datum)
842 return c
844 def toVector(self, Vector=None, **Vector_kwds):
845 '''Return this cartesian's I{geocentric} components as vector.
847 @kwarg Vector: Optional class to return the I{geocentric}
848 components (L{Vector3d}) or C{None}.
849 @kwarg Vector_kwds: Optional, additional B{C{Vector}} keyword
850 arguments, ignored if C{B{Vector} is None}.
852 @return: A B{C{Vector}} or a L{Vector3Tuple}C{(x, y, z)} if
853 C{B{Vector} is None}.
855 @raise TypeError: Invalid B{C{Vector}} or B{C{Vector_kwds}}.
856 '''
857 return self.xyz if Vector is None else Vector(
858 self.x, self.y, self.z, **self._name1__(Vector_kwds))
861class RadiusThetaPhi3Tuple(_NamedTupleTo):
862 '''3-Tuple C{(r, theta, phi)} with radial distance C{r} in C{meter}, inclination
863 C{theta} (with respect to the positive z-axis) and azimuthal angle C{phi} in
864 L{Degrees} I{or} L{Radians} representing a U{spherical, polar position
865 <https://WikiPedia.org/wiki/Spherical_coordinate_system>}.
866 '''
867 _Names_ = (_r_, _theta_, _phi_)
868 _Units_ = ( Meter, _Pass, _Pass)
870 def toCartesian(self, **name_Cartesian_and_kwds):
871 '''Convert this L{RadiusThetaPhi3Tuple} to a cartesian C{(x, y, z)} vector.
873 @kwarg name_Cartesian_and_kwds: Optional C{B{name}=NN}, overriding this
874 name and optional class C{B{Cartesian}=None} and additional
875 C{B{Cartesian}} keyword arguments.
877 @return: A C{B{Cartesian}(x, y, z)} instance or if no C{B{Cartesian}} keyword
878 argument is given, a L{Vector3Tuple}C{(x, y, z)} with C{x}, C{y}
879 and C{z} in the same units as radius C{r}, C{meter} conventionally.
881 @see: Function L{rtp2xyz_}.
882 '''
883 r, t, p = self
884 t, p, _ = _NamedTupleTo._Radians3(self, t, p)
885 return rtp2xyz_(r, t, p, **name_Cartesian_and_kwds)
887 def toDegrees(self, **name):
888 '''Convert this L{RadiusThetaPhi3Tuple}'s angles to L{Degrees}.
890 @kwarg name: Optional C{B{name}=NN} (C{str}), overriding this name.
892 @return: L{RadiusThetaPhi3Tuple}C{(r, theta, phi)} with C{theta}
893 and C{phi} both in L{Degrees}.
894 '''
895 return self._toX3U(_NamedTupleTo._Degrees3, Degrees, name)
897 def toRadians(self, **name):
898 '''Convert this L{RadiusThetaPhi3Tuple}'s angles to L{Radians}.
900 @kwarg name: Optional C{B{name}=NN} (C{str}), overriding this name.
902 @return: L{RadiusThetaPhi3Tuple}C{(r, theta, phi)} with C{theta}
903 and C{phi} both in L{Radians}.
904 '''
905 return self._toX3U(_NamedTupleTo._Radians3, Radians, name)
907 def _toU(self, U):
908 M = RadiusThetaPhi3Tuple._Units_[0] # Meter
909 return self.reUnit(M, U, U).toUnits()
911 def _toX3U(self, _X3, U, name):
912 r, t, p = self
913 t, p, s = _X3(self, t, p)
914 if s is None or name:
915 n = self._name__(name)
916 s = self.classof(r, t, p, name=n)._toU(U)
917 return s
920def rtp2xyz(r_rtp, theta=0, phi=0, **name_Cartesian_and_kwds):
921 '''Convert I{spherical, polar} C{(r, theta, phi)} to cartesian C{(x, y, z)} coordinates.
923 @arg theta: Inclination B{C{theta}} (C{degrees} with respect to the positive z-axis),
924 required if C{B{r_rtp}} is C{scalar}, ignored otherwise.
925 @arg phi: Azimuthal angle B{C{phi}} (C{degrees}), like B{C{theta}}.
927 @see: Function L{rtp2xyz_} for further details.
928 '''
929 if isinstance(r_rtp, RadiusThetaPhi3Tuple):
930 c = r_rtp.toCartesian(**name_Cartesian_and_kwds)
931 else:
932 c = rtp2xyz_(r_rtp, radians(theta), radians(phi), **name_Cartesian_and_kwds)
933 return c
936def rtp2xyz_(r_rtp, theta=0, phi=0, **name_Cartesian_and_kwds):
937 '''Convert I{spherical, polar} C{(r, theta, phi)} to cartesian C{(x, y, z)} coordinates.
939 @arg r_rtp: Radial distance (C{scalar}, conventially C{meter}) or a previous
940 L{RadiusThetaPhi3Tuple} instance.
941 @arg theta: Inclination B{C{theta}} (C{radians} with respect to the positive z-axis),
942 required if C{B{r_rtp}} is C{scalar}, ignored otherwise.
943 @arg phi: Azimuthal angle B{C{phi}} (C{radians}), like B{C{theta}}.
944 @kwarg name_Cartesian_and_kwds: Optional C{B{name}=NN} (C{str}), a C{B{Cartesian}=None}
945 class to return the coordinates and optional, additional C{B{Cartesian}}
946 keyword arguments.
948 @return: A C{B{Cartesian}(x, y, z)} instance or if no C{B{Cartesian}} keyword argument
949 is given a L{Vector3Tuple}C{(x, y, z)}, with C{x}, C{y} and C{z} in the same
950 units as radius C{r}, C{meter} conventionally.
952 @raise TypeError: Invalid B{C{r_rtp}}, B{C{theta}}, B{C{phi}} or
953 B{C{name_Cartesian_and_kwds}} item.
955 @see: U{Physics convention<https://WikiPedia.org/wiki/Spherical_coordinate_system>}
956 (ISO 80000-2:2019), class L{RadiusThetaPhi3Tuple} and functions L{rtp2xyz}
957 and L{xyz2rtp}.
958 '''
959 if isinstance(r_rtp, RadiusThetaPhi3Tuple):
960 c = r_rtp.toCartesian(**name_Cartesian_and_kwds)
961 elif _isMeter(r_rtp):
962 r = r_rtp
963 if r and _isfinite(r):
964 s, z, y, x = sincos2_(theta, phi)
965 s *= r
966 z *= r
967 y *= s
968 x *= s
969 else:
970 x = y = z = r
972 n, kwds = _name2__(**name_Cartesian_and_kwds)
973 C, kwds = _xkwds_pop2(kwds, Cartesian=None)
974 c = Vector3Tuple(x, y, z, name=n) if C is None else \
975 C(x, y, z, name=n, **kwds)
976 else:
977 raise _TypeError(r_rtp=r_rtp, theta=theta, phi=phi)
978 return c
981def _rtp3(where, U, *x_y_z, **name):
982 '''(INTERNAL) Helper for C{.toRtp}, C{xyz2rtp} and C{xyz2rtp_}.
983 '''
984 x, y, z = _MODS.vector3dBase._xyz3(where, *x_y_z)
985 r = hypot_(x, y, z)
986 if r > 0:
987 t = acos1(z / r)
988 p = atan2(y, x)
989 while p < 0:
990 p += PI2
991 if U is Degrees:
992 t = degrees(t)
993 p = degrees(p)
994 else:
995 t = p = _0_0
996 return RadiusThetaPhi3Tuple(r, t, p, **name)._toU(U)
999def xyz2rtp(x_xyz, y=0, z=0, **name):
1000 '''Convert cartesian C{(x, y, z)} to I{spherical, polar} C{(r, theta, phi)} coordinates.
1002 @return: L{RadiusThetaPhi3Tuple}C{(r, theta, phi)} with C{theta} and C{phi}, both
1003 in L{Degrees}.
1005 @see: Function L{xyz2rtp_} for further details.
1006 '''
1007 return _rtp3(xyz2rtp, Degrees, x_xyz, y, z, **name)
1010def xyz2rtp_(x_xyz, y=0, z=0, **name):
1011 '''Convert cartesian C{(x, y, z)} to I{spherical, polar} C{(r, theta, phi)} coordinates.
1013 @arg x_xyz: X component (C{scalar}) or a cartesian (C{Cartesian}, L{Ecef9Tuple},
1014 C{Nvector}, L{Vector3d}, L{Vector3Tuple}, L{Vector4Tuple} or a C{tuple} or
1015 C{list} of 3+ C{scalar} items) if no C{y_z} specified.
1016 @arg y: Y component (C{scalar}), required if C{B{x_xyz}} is C{scalar}, ignored otherwise.
1017 @arg z: Z component (C{scalar}), like B{C{y}}.
1018 @kwarg name: Optional C{B{name}=NN} (C{str}).
1020 @return: L{RadiusThetaPhi3Tuple}C{(r, theta, phi)} with radial distance C{r} (C{meter},
1021 same units as C{x}, C{y} and C{z}), inclination C{theta} (with respect to the
1022 positive z-axis) and azimuthal angle C{phi}, both in L{Radians}.
1024 @see: U{Physics convention<https://WikiPedia.org/wiki/Spherical_coordinate_system>}
1025 (ISO 80000-2:2019), class L{RadiusThetaPhi3Tuple} and function L{xyz2rtp}.
1026 '''
1027 return _rtp3(xyz2rtp_, Radians, x_xyz, y, z, **name)
1030__all__ += _ALL_DOCS(CartesianBase)
1032# **) MIT License
1033#
1034# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.
1035#
1036# Permission is hereby granted, free of charge, to any person obtaining a
1037# copy of this software and associated documentation files (the "Software"),
1038# to deal in the Software without restriction, including without limitation
1039# the rights to use, copy, modify, merge, publish, distribute, sublicense,
1040# and/or sell copies of the Software, and to permit persons to whom the
1041# Software is furnished to do so, subject to the following conditions:
1042#
1043# The above copyright notice and this permission notice shall be included
1044# in all copies or substantial portions of the Software.
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