Coverage for pygeodesy/cartesianBase.py: 91%
327 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 2011-2024} 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, property_doc_, \
32 property_RO, property_ROnce, _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__ = '24.11.06'
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 optionally,
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_ROnce
215 def Ecef(self):
216 '''Get the ECEF I{class} (L{EcefKarney}), I{once}.
217 '''
218 return _MODS.ecef.EcefKarney
220 @Property_RO
221 def _ecef9(self):
222 '''(INTERNAL) Helper for L{toEcef}, L{toLocal} and L{toLtp} (L{Ecef9Tuple}).
223 '''
224 return self.Ecef(self.datum, name=self.name).reverse(self, M=True)
226 @property_RO
227 def ellipsoidalCartesian(self):
228 '''Get the C{Cartesian type} iff ellipsoidal, overloaded in L{CartesianEllipsoidalBase}.
229 '''
230 return False
232 def hartzell(self, los=False, earth=None):
233 '''Compute the intersection of a Line-Of-Sight from this cartesian Point-Of-View
234 (pov) and this cartesian's ellipsoid surface.
236 @kwarg los: Line-Of-Sight, I{direction} to the ellipsoid (L{Los}, L{Vector3d}),
237 C{True} for the I{normal, plumb} onto the surface or I{False} or
238 C{None} to point to the center of the ellipsoid.
239 @kwarg earth: The earth model (L{Datum}, L{Ellipsoid}, L{Ellipsoid2}, L{a_f2Tuple}
240 or C{scalar} radius in C{meter}), overriding this cartesian's
241 C{datum} ellipsoid.
243 @return: The intersection (C{Cartesian}) with C{.height} set to the distance to
244 this C{pov}.
246 @raise IntersectionError: Null or bad C{pov} or B{C{los}}, this C{pov} is inside
247 the ellipsoid or B{C{los}} points outside or away from
248 the ellipsoid.
250 @raise TypeError: Invalid B{C{los}} or invalid or undefined B{C{earth}} or C{datum}.
252 @see: Function L{hartzell<pygeodesy.formy.hartzell>} for further details.
253 '''
254 return _MODS.formy._hartzell(self, los, earth)
256 @Property
257 def height(self):
258 '''Get the height (C{meter}).
259 '''
260 return self._height4.h if self._height is None else self._height
262 @height.setter # PYCHOK setter!
263 def height(self, height):
264 '''Set the height (C{meter}).
266 @raise TypeError: Invalid B{C{height}} C{type}.
268 @raise ValueError: Invalid B{C{height}}.
269 '''
270 h = Height(height)
271 if self._height != h:
272 _update_all(self)
273 self._height = h
275 def _height2C(self, r, Cartesian=None, datum=None, height=INT0, **kwds):
276 '''(INTERNAL) Helper for methods C{.height3} and C{.height4}.
277 '''
278 if Cartesian is not None:
279 r = Cartesian(r, **kwds)
280 if datum is not None:
281 r.datum = datum
282 if height is not None:
283 r.height = height # Height(height)
284 return r
286 def height3(self, earth=None, height=None, **Cartesian_and_kwds):
287 '''Compute the cartesian at a height above or below this certesian's ellipsoid.
289 @kwarg earth: A datum, ellipsoid, triaxial ellipsoid or earth radius,
290 I{overriding} this cartesian's datum (L{Datum}, L{Ellipsoid},
291 L{Ellipsoid2}, L{a_f2Tuple} or C{meter}, conventionally).
292 @kwarg height: The height (C{meter}, conventionally), overriding this
293 cartesian's height.
294 @kwarg Cartesian_and_kwds: Optional C{B{Cartesian}=None} class to return
295 the cartesian I{at height} and additional B{C{Cartesian}}
296 keyword arguments.
298 @return: An instance of B{C{Cartesian}} or if C{B{Cartesian} is None},
299 a L{Vector3Tuple}C{(x, y, z)} with the C{x}, C{y} and C{z}
300 coordinates I{at height} in C{meter}, conventionally.
302 @note: This cartesian's coordinates are returned if B{C{earth}} and this
303 datum or B{C{height}} and/or this height are C{None} or undefined.
305 @note: Include keyword argument C{B{datum}=None} if class B{C{Cartesian}}
306 does not accept a B{C{datum}} keyword agument.
308 @raise TriaxialError: No convergence in triaxial root finding.
310 @raise TypeError: Invalid or undefined B{C{earth}} or C{datum}.
311 '''
312 n = self.height3.__name__
313 d = self.datum if earth is None else _spherical_datum(earth, name=n)
314 c, h = self, _heigHt(self, height)
315 if h and d:
316 R, r = self.Roc2(earth=d)
317 if R > EPS0:
318 R = (R + h) / R
319 r = ((r + h) / r) if r > EPS0 else _1_0
320 c = c.times_(R, R, r)
322 r = Vector3Tuple(c.x, c.y, c.z, name=n)
323 if Cartesian_and_kwds:
324 r = self._height2C(r, **_xkwds(Cartesian_and_kwds, datum=d))
325 return r
327 @Property_RO
328 def _height4(self):
329 '''(INTERNAL) Get this C{height4}-tuple.
330 '''
331 try:
332 r = self.datum.ellipsoid.height4(self, normal=True)
333 except (AttributeError, ValueError): # no datum, null cartesian,
334 r = Vector4Tuple(self.x, self.y, self.z, 0, name__=self.height4)
335 return r
337 def height4(self, earth=None, normal=True, **Cartesian_and_kwds):
338 '''Compute the projection of this point on and the height above or below
339 this datum's ellipsoid surface.
341 @kwarg earth: A datum, ellipsoid, triaxial ellipsoid or earth radius,
342 I{overriding} this datum (L{Datum}, L{Ellipsoid},
343 L{Ellipsoid2}, L{a_f2Tuple}, L{Triaxial}, L{Triaxial_},
344 L{JacobiConformal} or C{meter}, conventionally).
345 @kwarg normal: If C{True}, the projection is the nearest point on the
346 ellipsoid's surface, otherwise the intersection of the
347 radial line to the ellipsoid's center and surface C{bool}).
348 @kwarg Cartesian_and_kwds: Optional C{B{Cartesian}=None} class to return
349 the I{projection} and additional B{C{Cartesian}} keyword
350 arguments.
352 @return: An instance of B{C{Cartesian}} or if C{B{Cartesian} is None}, a
353 L{Vector4Tuple}C{(x, y, z, h)} with the I{projection} C{x}, C{y}
354 and C{z} coordinates and height C{h} in C{meter}, conventionally.
356 @note: Include keyword argument C{B{datum}=None} if class B{C{Cartesian}}
357 does not accept a B{C{datum}} keyword agument.
359 @raise TriaxialError: No convergence in triaxial root finding.
361 @raise TypeError: Invalid or undefined B{C{earth}} or C{datum}.
363 @see: Methods L{Ellipsoid.height4} and L{Triaxial_.height4} for more information.
364 '''
365 n = self.height4.__name__
366 d = self.datum if earth is None else earth
367 if normal and d is self.datum:
368 r = self._height4
369 elif isinstance(d, _MODS.triaxials.Triaxial_):
370 r = d.height4(self, normal=normal)
371 try:
372 d = d.toEllipsoid(name=n)
373 except (TypeError, ValueError): # TriaxialError
374 d = None
375 else:
376 r = _earth_ellipsoid(d).height4(self, normal=normal)
378 if Cartesian_and_kwds:
379 if d and not isinstance(d, Datum):
380 d = _spherical_datum(d, name=n)
381 r = self._height2C(r, **_xkwds(Cartesian_and_kwds, datum=d))
382 return r
384 @Property_RO
385 def isEllipsoidal(self):
386 '''Check whether this cartesian is ellipsoidal (C{bool} or C{None} if unknown).
387 '''
388 return _xattr(self.datum, isEllipsoidal=None)
390 @Property_RO
391 def isSpherical(self):
392 '''Check whether this cartesian is spherical (C{bool} or C{None} if unknown).
393 '''
394 return _xattr(self.datum, isSpherical=None)
396 @Property_RO
397 def latlon(self):
398 '''Get this cartesian's (geodetic) lat- and longitude in C{degrees} (L{LatLon2Tuple}C{(lat, lon)}).
399 '''
400 return self.toEcef().latlon
402 @Property_RO
403 def latlonheight(self):
404 '''Get this cartesian's (geodetic) lat-, longitude in C{degrees} with height (L{LatLon3Tuple}C{(lat, lon, height)}).
405 '''
406 return self.toEcef().latlonheight
408 @Property_RO
409 def latlonheightdatum(self):
410 '''Get this cartesian's (geodetic) lat-, longitude in C{degrees} with height and datum (L{LatLon4Tuple}C{(lat, lon, height, datum)}).
411 '''
412 return self.toEcef().latlonheightdatum
414 @Property_RO
415 def _Ltp(self):
416 '''(INTERNAL) Cache for L{toLtp}.
417 '''
418 return _MODS.ltp.Ltp(self._ecef9, ecef=self.Ecef(self.datum), name=self.name)
420 @Property_RO
421 def _N_vector(self):
422 '''(INTERNAL) Get the (C{nvectorBase._N_vector_}).
423 '''
424 _N = _MODS.nvectorBase._N_vector_
425 x, y, z, h = self._n_xyzh4(self.datum)
426 return _N(x, y, z, h=h, name=self.name)
428 def _n_xyzh4(self, datum):
429 '''(INTERNAL) Get the n-vector components as L{Vector4Tuple}.
430 '''
431 def _ErrorEPS0(x):
432 return _ValueError(origin=self, txt=Fmt.PARENSPACED(EPS0=x))
434 _xinstanceof(Datum, datum=datum)
435 # <https://www.Movable-Type.co.UK/scripts/geodesy/docs/
436 # latlon-nvector-ellipsoidal.js.html#line309>,
437 # <https://GitHub.com/pbrod/nvector>/src/nvector/core.py>
438 # _equation23 and <https://www.NavLab.net/nvector>
439 E = datum.ellipsoid
440 x, y, z = self.xyz3
442 # Kenneth Gade eqn 23
443 p = hypot2(x, y) * E.a2_
444 q = z**2 * E.e21 * E.a2_
445 r = fsumf_(p, q, -E.e4) / _6_0
446 s = (p * q * E.e4) / (_4_0 * r**3)
447 t = cbrt(fsumf_(_1_0, s, sqrt(s * (_2_0 + s))))
448 if isnear0(t):
449 raise _ErrorEPS0(t)
450 u = fsumf_(_1_0, t, _1_0 / t) * r
451 v = sqrt(u**2 + E.e4 * q)
452 t = v * _2_0
453 if t < EPS0: # isnear0
454 raise _ErrorEPS0(t)
455 w = fsumf_(u, v, -q) * E.e2 / t
456 k = sqrt(fsumf_(u, v, w**2)) - w
457 if isnear0(k):
458 raise _ErrorEPS0(k)
459 t = k + E.e2
460 if isnear0(t):
461 raise _ErrorEPS0(t)
462 e = k / t
463# d = e * hypot(x, y)
464# tmp = 1 / hypot(d, z) == 1 / hypot(e * hypot(x, y), z)
465 t = hypot_(x * e, y * e, z) # == 1 / tmp
466 if t < EPS0: # isnear0
467 raise _ErrorEPS0(t)
468 h = fsumf_(k, E.e2, _N_1_0) / k * t
469 s = e / t # == e * tmp
470 return Vector4Tuple(x * s, y * s, z / t, h, name=self.name)
472 @Property_RO
473 def philam(self):
474 '''Get this cartesian's (geodetic) lat- and longitude in C{radians} (L{PhiLam2Tuple}C{(phi, lam)}).
475 '''
476 return self.toEcef().philam
478 @Property_RO
479 def philamheight(self):
480 '''Get this cartesian's (geodetic) lat-, longitude in C{radians} with height (L{PhiLam3Tuple}C{(phi, lam, height)}).
481 '''
482 return self.toEcef().philamheight
484 @Property_RO
485 def philamheightdatum(self):
486 '''Get this cartesian's (geodetic) lat-, longitude in C{radians} with height and datum (L{PhiLam4Tuple}C{(phi, lam, height, datum)}).
487 '''
488 return self.toEcef().philamheightdatum
490 def pierlot(self, point2, point3, alpha12, alpha23, useZ=False, eps=EPS):
491 '''3-Point resection between this and two other points using U{Pierlot
492 <http://www.Telecom.ULg.ac.Be/triangulation>}'s method C{ToTal} with
493 I{approximate} limits for the (pseudo-)singularities.
495 @arg point2: Second point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple},
496 C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}).
497 @arg point3: Third point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple},
498 C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}).
499 @arg alpha12: Angle subtended from this point to B{C{point2}} or
500 B{C{alpha2 - alpha}} (C{degrees}).
501 @arg alpha23: Angle subtended from B{C{point2}} to B{C{point3}} or
502 B{C{alpha3 - alpha2}} (C{degrees}).
503 @kwarg useZ: If C{True}, interpolate the Z component, otherwise use C{z=INT0}
504 (C{bool}).
505 @kwarg eps: Tolerance for C{cot} (pseudo-)singularities (C{float}).
507 @note: This point, B{C{point2}} and B{C{point3}} are ordered counter-clockwise.
509 @return: The survey (or robot) point, an instance of this (sub-)class.
511 @raise ResectionError: Near-coincident, -colinear or -concyclic points
512 or invalid B{C{alpha12}} or B{C{alpha23}}.
514 @raise TypeError: Invalid B{C{point2}} or B{C{point3}}.
516 @see: Function L{pygeodesy.pierlot} for references and more details.
517 '''
518 return _MODS.resections.pierlot(self, point2, point3, alpha12, alpha23,
519 useZ=useZ, eps=eps, datum=self.datum)
521 def pierlotx(self, point2, point3, alpha1, alpha2, alpha3, useZ=False):
522 '''3-Point resection between this and two other points using U{Pierlot
523 <http://www.Telecom.ULg.ac.Be/publi/publications/pierlot/Pierlot2014ANewThree>}'s
524 method C{ToTal} with I{exact} limits for the (pseudo-)singularities.
526 @arg point2: Second point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple},
527 C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}).
528 @arg point3: Third point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple},
529 C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}).
530 @arg alpha1: Angle at B{C{point1}} (C{degrees}).
531 @arg alpha2: Angle at B{C{point2}} (C{degrees}).
532 @arg alpha3: Angle at B{C{point3}} (C{degrees}).
533 @kwarg useZ: If C{True}, interpolate the survey point's Z component,
534 otherwise use C{z=INT0} (C{bool}).
536 @return: The survey (or robot) point, an instance of this (sub-)class.
538 @raise ResectionError: Near-coincident, -colinear or -concyclic points or
539 invalid B{C{alpha1}}, B{C{alpha2}} or B{C{alpha3}}.
541 @raise TypeError: Invalid B{C{point2}} or B{C{point3}}.
543 @see: Function L{pygeodesy.pierlotx} for references and more details.
544 '''
545 return _MODS.resections.pierlotx(self, point2, point3, alpha1, alpha2, alpha3,
546 useZ=useZ, datum=self.datum)
548 def Roc2(self, earth=None):
549 '''Compute this cartesian's I{normal} and I{pseudo, z-based} radius of curvature.
551 @kwarg earth: A datum, ellipsoid, triaxial ellipsoid or earth radius,
552 I{overriding} this cartesian's datum (L{Datum}, L{Ellipsoid},
553 L{Ellipsoid2}, L{a_f2Tuple} or C{meter}, conventionally).
555 @return: 2-Tuple C{(R, r)} with the I{normal} and I{pseudo, z-based} radius of
556 curvature C{R} respectively C{r}, both in C{meter} conventionally.
558 @raise TypeError: Invalid or undefined B{C{earth}} or C{datum}.
559 '''
560 r = z = fabs( self.z)
561 R, _0 = hypot(self.x, self.y), EPS0
562 if R < _0: # polar
563 R = z
564 elif z > _0: # non-equatorial
565 d = self.datum if earth is None else _spherical_datum(earth)
566 e = self.toLatLon(datum=d, height=0, LatLon=None) # Ecef9Tuple
567 M = e.M # EcefMatrix
568 sa, ca = map(fabs, (M._2_2_, M._2_1_) if M else sincos2d(e.lat))
569 if ca < _0: # polar
570 R = z
571 else: # prime-vertical, normal roc R
572 R = R / ca # /= chokes PyChecker
573 r = R if sa < _0 else (r / sa) # non-/equatorial
574 return R, r
576 @property_RO
577 def sphericalCartesian(self):
578 '''Get the C{Cartesian type} iff spherical, overloaded in L{CartesianSphericalBase}.
579 '''
580 return False
582 @deprecated_method
583 def tienstra(self, pointB, pointC, alpha, beta=None, gamma=None, useZ=False):
584 '''DEPRECATED, use method L{tienstra7}.'''
585 return self.tienstra7(pointB, pointC, alpha, beta=beta, gamma=gamma, useZ=useZ)
587 def tienstra7(self, pointB, pointC, alpha, beta=None, gamma=None, useZ=False):
588 '''3-Point resection between this and two other points using U{Tienstra
589 <https://WikiPedia.org/wiki/Tienstra_formula>}'s formula.
591 @arg pointB: Second point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple}, C{Vector4Tuple} or
592 C{Vector2Tuple} if C{B{useZ}=False}).
593 @arg pointC: Third point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple}, C{Vector4Tuple} or
594 C{Vector2Tuple} if C{B{useZ}=False}).
595 @arg alpha: Angle subtended by triangle side C{a} from B{C{pointB}} to B{C{pointC}} (C{degrees},
596 non-negative).
597 @kwarg beta: Angle subtended by triangle side C{b} from this to B{C{pointC}} (C{degrees},
598 non-negative) or C{None} if C{B{gamma} is not None}.
599 @kwarg gamma: Angle subtended by triangle side C{c} from this to B{C{pointB}} (C{degrees},
600 non-negative) or C{None} if C{B{beta} is not None}.
601 @kwarg useZ: If C{True}, use and interpolate the Z component, otherwise force C{z=INT0}
602 (C{bool}).
604 @note: This point, B{C{pointB}} and B{C{pointC}} are ordered clockwise.
606 @return: L{Tienstra7Tuple}C{(pointP, A, B, C, a, b, c)} with survey C{pointP},
607 an instance of this (sub-)class and triangle angle C{A} at this point,
608 C{B} at B{C{pointB}} and C{C} at B{C{pointC}} in C{degrees} and
609 triangle sides C{a}, C{b} and C{c}.
611 @raise ResectionError: Near-coincident, -colinear or -concyclic points or sum of
612 B{C{alpha}}, B{C{beta}} and B{C{gamma}} not C{360} or
613 negative B{C{alpha}}, B{C{beta}} or B{C{gamma}}.
615 @raise TypeError: Invalid B{C{pointB}} or B{C{pointC}}.
617 @see: Function L{pygeodesy.tienstra7} for references and more details.
618 '''
619 return _MODS.resections.tienstra7(self, pointB, pointC, alpha, beta, gamma,
620 useZ=useZ, datum=self.datum)
622 @deprecated_method
623 def to2ab(self): # PYCHOK no cover
624 '''DEPRECATED, use property C{philam}.
626 @return: A L{PhiLam2Tuple}C{(phi, lam)}.
627 '''
628 return self.philam
630 @deprecated_method
631 def to2ll(self): # PYCHOK no cover
632 '''DEPRECATED, use property C{latlon}.
634 @return: A L{LatLon2Tuple}C{(lat, lon)}.
635 '''
636 return self.latlon
638 @deprecated_method
639 def to3llh(self, datum=None): # PYCHOK no cover
640 '''DEPRECATED, use property L{latlonheight} or L{latlonheightdatum}.
642 @return: A L{LatLon4Tuple}C{(lat, lon, height, datum)}.
644 @note: This method returns a B{C{-4Tuple}} I{and not a} C{-3Tuple}
645 as its name may suggest.
646 '''
647 t = self.toLatLon(datum=datum, LatLon=None)
648 return LatLon4Tuple(t.lat, t.lon, t.height, t.datum, name=self.name)
650# def _to3LLh(self, datum, LL, **pairs): # OBSOLETE
651# '''(INTERNAL) Helper for C{subclass.toLatLon} and C{.to3llh}.
652# '''
653# r = self.to3llh(datum) # LatLon3Tuple
654# if LL is not None:
655# r = LL(r.lat, r.lon, height=r.height, datum=datum, name=self.name)
656# for n, v in pairs.items():
657# setattr(r, n, v)
658# return r
660 def toDatum(self, datum2, datum=None):
661 '''Convert this cartesian from one datum to an other.
663 @arg datum2: Datum to convert I{to} (L{Datum}).
664 @kwarg datum: Datum to convert I{from} (L{Datum}).
666 @return: The converted point (C{Cartesian}).
668 @raise TypeError: B{C{datum2}} or B{C{datum}}
669 invalid.
670 '''
671 _xinstanceof(Datum, datum2=datum2)
673 c = self if datum in (None, self.datum) else \
674 self.toDatum(datum)
676 i, d = False, c.datum
677 if d == datum2:
678 return c.copy() if c is self else c
680 elif d is None or (d.transform.isunity and
681 datum2.transform.isunity):
682 return c.dup(datum=datum2)
684 elif d == _WGS84:
685 d = datum2 # convert from WGS84 to datum2
687 elif datum2 == _WGS84:
688 i = True # convert to WGS84 by inverse transformation
690 else: # neither datum2 nor c.datum is WGS84, invert to WGS84 first
691 c = c.toTransform(d.transform, inverse=True, datum=_WGS84)
692 d = datum2
694 return c.toTransform(d.transform, inverse=i, datum=datum2)
696 def toEcef(self):
697 '''Convert this cartesian to I{geodetic} (lat-/longitude) coordinates.
699 @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height,
700 C, M, datum)} with C{C} and C{M} if available.
702 @raise EcefError: A C{.datum} or an ECEF issue.
703 '''
704 return self._ecef9
706 def toLatLon(self, datum=None, height=None, LatLon=None, **LatLon_kwds): # see .ecef.Ecef9Tuple.toDatum
707 '''Convert this cartesian to a I{geodetic} (lat-/longitude) point.
709 @kwarg datum: Optional datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2}
710 or L{a_f2Tuple}).
711 @kwarg height: Optional height, overriding the converted height
712 (C{meter}), only if C{B{LatLon} is not None}.
713 @kwarg LatLon: Optional class to return the geodetic point
714 (C{LatLon}) or C{None}.
715 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword
716 arguments, ignored if C{B{LatLon} is None}.
718 @return: The geodetic point (B{C{LatLon}}) or if C{B{LatLon}
719 is None}, an L{Ecef9Tuple}C{(x, y, z, lat, lon, height,
720 C, M, datum)} with C{C} and C{M} if available.
722 @raise TypeError: Invalid B{C{datum}} or B{C{LatLon_kwds}}.
723 '''
724 d = _spherical_datum(datum or self.datum, name=self.name)
725 if d == self.datum:
726 r = self.toEcef()
727 else:
728 c = self.toDatum(d)
729 r = c.Ecef(d, name=self.name).reverse(c, M=LatLon is None)
731 if LatLon: # class or .classof
732 h = _heigHt(r, height)
733 r = LatLon(r.lat, r.lon, datum=r.datum, height=h,
734 **_xkwds(LatLon_kwds, name=r.name))
735 _xdatum(r.datum, d)
736 return r
738 def toLocal(self, Xyz=None, ltp=None, **Xyz_kwds):
739 '''Convert this I{geocentric} cartesian to I{local} C{X}, C{Y} and C{Z}.
741 @kwarg Xyz: Optional class to return C{X}, C{Y} and C{Z} (L{XyzLocal},
742 L{Enu}, L{Ned}) or C{None}.
743 @kwarg ltp: The I{local tangent plane} (LTP) to use, overriding this
744 cartesian's LTP (L{Ltp}).
745 @kwarg Xyz_kwds: Optional, additional B{C{Xyz}} keyword arguments,
746 ignored if C{B{Xyz} is None}.
748 @return: An B{C{Xyz}} instance or a L{Local9Tuple}C{(x, y, z, lat, lon,
749 height, ltp, ecef, M)} if C{B{Xyz} is None} (with C{M=None}).
751 @raise TypeError: Invalid B{C{ltp}}.
752 '''
753 return _MODS.ltp._toLocal(self, ltp, Xyz, Xyz_kwds) # self._ecef9
755 def toLtp(self, Ecef=None, **name):
756 '''Return the I{local tangent plane} (LTP) for this cartesian.
758 @kwarg Ecef: Optional ECEF I{class} (L{EcefKarney}, ...
759 L{EcefYou}), overriding this cartesian's C{Ecef}.
760 @kwarg name: Optional C{B{name}=NN} (C{str}).
761 '''
762 return _MODS.ltp._toLtp(self, Ecef, self._ecef9, name) # self._Ltp
764 def toNvector(self, Nvector=None, datum=None, **name_Nvector_kwds):
765 '''Convert this cartesian to C{n-vector} components, I{including height}.
767 @kwarg Nvector: Optional class to return the C{n-vector} components
768 (C{Nvector}) or C{None}.
769 @kwarg datum: Optional datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2}
770 or L{a_f2Tuple}) overriding this cartesian's datum.
771 @kwarg name_Nvector_kwds: Optional C{B{name}=NN} (C{str}) and optionally,
772 additional B{C{Nvector}} keyword arguments, ignored if
773 C{B{Nvector} is None}.
775 @return: An B{C{Nvector}} or a L{Vector4Tuple}C{(x, y, z, h)} if
776 C{B{Nvector} is None}.
778 @raise TypeError: Invalid B{C{Nvector}}, B{C{datum}} or
779 B{C{name_Nvector_kwds}} item.
781 @raise ValueError: B{C{Cartesian}} at origin.
782 '''
783 r, d = self._N_vector.xyzh, self.datum
784 if datum is not None:
785 d = _spherical_datum(datum, name=self.name)
786 if d != self.datum:
787 r = self._n_xyzh4(d)
789 if Nvector is None:
790 n, _ = _name2__(name_Nvector_kwds, _or_nameof=self)
791 if n:
792 r = r.dup(name=n)
793 else:
794 kwds = _xkwds(name_Nvector_kwds, h=r.h, datum=d)
795 r = Nvector(r.x, r.y, r.z, **self._name1__(kwds))
796 return r
798 def toRtp(self):
799 '''Convert this cartesian to I{spherical, polar} coordinates.
801 @return: L{RadiusThetaPhi3Tuple}C{(r, theta, phi)} with C{theta}
802 and C{phi}, both in L{Degrees}.
804 @see: Function L{xyz2rtp_} and class L{RadiusThetaPhi3Tuple}.
805 '''
806 return _rtp3(self.toRtp, Degrees, self, name=self.name)
808 def toStr(self, prec=3, fmt=Fmt.SQUARE, sep=_COMMASPACE_): # PYCHOK expected
809 '''Return the string representation of this cartesian.
811 @kwarg prec: Number of (decimal) digits, unstripped (C{int}).
812 @kwarg fmt: Enclosing backets format (C{letter}).
813 @kwarg sep: Separator to join (C{str}).
815 @return: Cartesian represented as "[x, y, z]" (C{str}).
816 '''
817 return Vector3d.toStr(self, prec=prec, fmt=fmt, sep=sep)
819 def toTransform(self, transform, inverse=False, datum=None):
820 '''Apply a Helmert transform to this cartesian.
822 @arg transform: Transform to apply (L{Transform} or L{TransformXform}).
823 @kwarg inverse: Apply the inverse of the C{B{transform}} (C{bool}).
824 @kwarg datum: Datum for the transformed cartesian (L{Datum}), overriding
825 this cartesian's datum but I{not} taken it into account.
827 @return: A transformed cartesian (C{Cartesian}) or a copy of this
828 cartesian if C{B{transform}.isunity}.
830 @raise TypeError: Invalid B{C{transform}}.
831 '''
832 _xinstanceof(Transform, transform=transform)
833 if transform.isunity:
834 c = self.dup(datum=datum or self.datum)
835 else:
836 # if inverse and d != _WGS84:
837 # raise _ValueError(inverse=inverse, datum=d,
838 # txt_not_=_WGS84.name)
839 xyz = transform.transform(*self.xyz3, inverse=inverse)
840 c = self.dup(xyz=xyz, datum=datum or self.datum)
841 return c
843 def toVector(self, Vector=None, **Vector_kwds):
844 '''Return this cartesian's I{geocentric} components as vector.
846 @kwarg Vector: Optional class to return the I{geocentric}
847 components (L{Vector3d}) or C{None}.
848 @kwarg Vector_kwds: Optional, additional B{C{Vector}} keyword
849 arguments, ignored if C{B{Vector} is None}.
851 @return: A B{C{Vector}} or a L{Vector3Tuple}C{(x, y, z)} if
852 C{B{Vector} is None}.
854 @raise TypeError: Invalid B{C{Vector}} or B{C{Vector_kwds}}.
855 '''
856 return self.xyz if Vector is None else Vector(
857 self.x, self.y, self.z, **self._name1__(Vector_kwds))
860class RadiusThetaPhi3Tuple(_NamedTupleTo):
861 '''3-Tuple C{(r, theta, phi)} with radial distance C{r} in C{meter}, inclination
862 C{theta} (with respect to the positive z-axis) and azimuthal angle C{phi} in
863 L{Degrees} I{or} L{Radians} representing a U{spherical, polar position
864 <https://WikiPedia.org/wiki/Spherical_coordinate_system>}.
865 '''
866 _Names_ = (_r_, _theta_, _phi_)
867 _Units_ = ( Meter, _Pass, _Pass)
869 def toCartesian(self, **name_Cartesian_and_kwds):
870 '''Convert this L{RadiusThetaPhi3Tuple} to a cartesian C{(x, y, z)} vector.
872 @kwarg name_Cartesian_and_kwds: Optional C{B{name}=NN}, overriding this
873 name and optional class C{B{Cartesian}=None} and additional
874 C{B{Cartesian}} keyword arguments.
876 @return: A C{B{Cartesian}(x, y, z)} instance or if no C{B{Cartesian}} keyword
877 argument is given, a L{Vector3Tuple}C{(x, y, z)} with C{x}, C{y}
878 and C{z} in the same units as radius C{r}, C{meter} conventionally.
880 @see: Function L{rtp2xyz_}.
881 '''
882 r, t, p = self
883 t, p, _ = _NamedTupleTo._Radians3(self, t, p)
884 return rtp2xyz_(r, t, p, **name_Cartesian_and_kwds)
886 def toDegrees(self, **name):
887 '''Convert this L{RadiusThetaPhi3Tuple}'s angles to L{Degrees}.
889 @kwarg name: Optional C{B{name}=NN} (C{str}), overriding this name.
891 @return: L{RadiusThetaPhi3Tuple}C{(r, theta, phi)} with C{theta}
892 and C{phi} both in L{Degrees}.
893 '''
894 return self._toX3U(_NamedTupleTo._Degrees3, Degrees, name)
896 def toRadians(self, **name):
897 '''Convert this L{RadiusThetaPhi3Tuple}'s angles to L{Radians}.
899 @kwarg name: Optional C{B{name}=NN} (C{str}), overriding this name.
901 @return: L{RadiusThetaPhi3Tuple}C{(r, theta, phi)} with C{theta}
902 and C{phi} both in L{Radians}.
903 '''
904 return self._toX3U(_NamedTupleTo._Radians3, Radians, name)
906 def _toU(self, U):
907 M = RadiusThetaPhi3Tuple._Units_[0] # Meter
908 return self.reUnit(M, U, U).toUnits()
910 def _toX3U(self, _X3, U, name):
911 r, t, p = self
912 t, p, s = _X3(self, t, p)
913 if s is None or name:
914 n = self._name__(name)
915 s = self.classof(r, t, p, name=n)._toU(U)
916 return s
919def rtp2xyz(r_rtp, theta=0, phi=0, **name_Cartesian_and_kwds):
920 '''Convert I{spherical, polar} C{(r, theta, phi)} to cartesian C{(x, y, z)} coordinates.
922 @arg theta: Inclination B{C{theta}} (C{degrees} with respect to the positive z-axis),
923 required if C{B{r_rtp}} is C{scalar}, ignored otherwise.
924 @arg phi: Azimuthal angle B{C{phi}} (C{degrees}), like B{C{theta}}.
926 @see: Function L{rtp2xyz_} for further details.
927 '''
928 if isinstance(r_rtp, RadiusThetaPhi3Tuple):
929 c = r_rtp.toCartesian(**name_Cartesian_and_kwds)
930 else:
931 c = rtp2xyz_(r_rtp, radians(theta), radians(phi), **name_Cartesian_and_kwds)
932 return c
935def rtp2xyz_(r_rtp, theta=0, phi=0, **name_Cartesian_and_kwds):
936 '''Convert I{spherical, polar} C{(r, theta, phi)} to cartesian C{(x, y, z)} coordinates.
938 @arg r_rtp: Radial distance (C{scalar}, conventially C{meter}) or a previous
939 L{RadiusThetaPhi3Tuple} instance.
940 @arg theta: Inclination B{C{theta}} (C{radians} with respect to the positive z-axis),
941 required if C{B{r_rtp}} is C{scalar}, ignored otherwise.
942 @arg phi: Azimuthal angle B{C{phi}} (C{radians}), like B{C{theta}}.
943 @kwarg name_Cartesian_and_kwds: Optional C{B{name}=NN} (C{str}), C{B{Cartesian}=None}
944 class to return the coordinates and optionally, additional C{B{Cartesian}}
945 keyword arguments.
947 @return: A C{B{Cartesian}(x, y, z)} instance or if no C{B{Cartesian}} keyword argument
948 is given a L{Vector3Tuple}C{(x, y, z)}, with C{x}, C{y} and C{z} in the same
949 units as radius C{r}, C{meter} conventionally.
951 @raise TypeError: Invalid B{C{r_rtp}}, B{C{theta}}, B{C{phi}} or
952 B{C{name_Cartesian_and_kwds}} item.
954 @see: U{Physics convention<https://WikiPedia.org/wiki/Spherical_coordinate_system>}
955 (ISO 80000-2:2019), class L{RadiusThetaPhi3Tuple} and functions L{rtp2xyz}
956 and L{xyz2rtp}.
957 '''
958 if isinstance(r_rtp, RadiusThetaPhi3Tuple):
959 c = r_rtp.toCartesian(**name_Cartesian_and_kwds)
960 elif _isMeter(r_rtp):
961 r = r_rtp
962 if r and _isfinite(r):
963 s, z, y, x = sincos2_(theta, phi)
964 s *= r
965 z *= r
966 y *= s
967 x *= s
968 else:
969 x = y = z = r
971 n, kwds = _name2__(**name_Cartesian_and_kwds)
972 C, kwds = _xkwds_pop2(kwds, Cartesian=None)
973 c = Vector3Tuple(x, y, z, name=n) if C is None else \
974 C(x, y, z, name=n, **kwds)
975 else:
976 raise _TypeError(r_rtp=r_rtp, theta=theta, phi=phi)
977 return c
980def _rtp3(where, U, *x_y_z, **name):
981 '''(INTERNAL) Helper for C{.toRtp}, C{xyz2rtp} and C{xyz2rtp_}.
982 '''
983 x, y, z = _MODS.vector3dBase._xyz3(where, *x_y_z)
984 r = hypot_(x, y, z)
985 if r > 0:
986 t = acos1(z / r)
987 p = atan2(y, x)
988 while p < 0:
989 p += PI2
990 if U is Degrees:
991 t = degrees(t)
992 p = degrees(p)
993 else:
994 t = p = _0_0
995 return RadiusThetaPhi3Tuple(r, t, p, **name)._toU(U)
998def xyz2rtp(x_xyz, y=0, z=0, **name):
999 '''Convert cartesian C{(x, y, z)} to I{spherical, polar} C{(r, theta, phi)} coordinates.
1001 @return: L{RadiusThetaPhi3Tuple}C{(r, theta, phi)} with C{theta} and C{phi}, both
1002 in L{Degrees}.
1004 @see: Function L{xyz2rtp_} for further details.
1005 '''
1006 return _rtp3(xyz2rtp, Degrees, x_xyz, y, z, **name)
1009def xyz2rtp_(x_xyz, y=0, z=0, **name):
1010 '''Convert cartesian C{(x, y, z)} to I{spherical, polar} C{(r, theta, phi)} coordinates.
1012 @arg x_xyz: X component (C{scalar}) or a cartesian (C{Cartesian}, L{Ecef9Tuple},
1013 C{Nvector}, L{Vector3d}, L{Vector3Tuple}, L{Vector4Tuple} or a C{tuple} or
1014 C{list} of 3+ C{scalar} items) if no C{y_z} specified.
1015 @arg y: Y component (C{scalar}), required if C{B{x_xyz}} is C{scalar}, ignored otherwise.
1016 @arg z: Z component (C{scalar}), like B{C{y}}.
1017 @kwarg name: Optional C{B{name}=NN} (C{str}).
1019 @return: L{RadiusThetaPhi3Tuple}C{(r, theta, phi)} with radial distance C{r} (C{meter},
1020 same units as C{x}, C{y} and C{z}), inclination C{theta} (with respect to the
1021 positive z-axis) and azimuthal angle C{phi}, both in L{Radians}.
1023 @see: U{Physics convention<https://WikiPedia.org/wiki/Spherical_coordinate_system>}
1024 (ISO 80000-2:2019), class L{RadiusThetaPhi3Tuple} and function L{xyz2rtp}.
1025 '''
1026 return _rtp3(xyz2rtp_, Radians, x_xyz, y, z, **name)
1029__all__ += _ALL_DOCS(CartesianBase)
1031# **) MIT License
1032#
1033# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.
1034#
1035# Permission is hereby granted, free of charge, to any person obtaining a
1036# copy of this software and associated documentation files (the "Software"),
1037# to deal in the Software without restriction, including without limitation
1038# the rights to use, copy, modify, merge, publish, distribute, sublicense,
1039# and/or sell copies of the Software, and to permit persons to whom the
1040# Software is furnished to do so, subject to the following conditions:
1041#
1042# The above copyright notice and this permission notice shall be included
1043# in all copies or substantial portions of the Software.
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