Coverage for pygeodesy/cartesianBase.py: 91%
330 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, \
20 _xdatum, _xkwds
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_, _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 _name__, _name2__, _NamedTuple, _Pass
28from pygeodesy.namedTuples import LatLon4Tuple, Vector3Tuple, Vector4Tuple, \
29 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, tienstra7
34# from pygeodesy.streprs import Fmt # from .fsums
35# from pygeodesy.triaxials import Triaxial_ # _MODS
36from pygeodesy.units import Degrees, Height, _heigHt, _isMeter, Meter, \
37 Radians, _toDegrees, _toRadians
38from pygeodesy.utily import acos1, sincos2d, sincos2_, atan2, degrees, radians
39from pygeodesy.vector3d import Vector3d, _xyzhdn3
40# from pygeodesy.vector3dBase import _xyz3 # _MODS
41# from pygeodesy import ltp, resections # _MODS
43# from math import atan2, degrees, fabs, radians, sqrt # from .fmath, .utily
45__all__ = _ALL_LAZY.cartesianBase
46__version__ = '24.05.24'
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=None, **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}), ignored if B{C{x_xyz}}
66 is not C{scalar}, otherwise same units as B{C{x_xyz}}.
67 @kwarg datum: Optional datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2}
68 or L{a_f2Tuple}).
69 @kwarg ll: Optional, original latlon (C{LatLon}).
70 @kwarg name: Optional C{B{name}=NN} (C{str}).
72 @raise TypeError: Non-scalar B{C{x_xyz}}, B{C{y}} or B{C{z}} coordinate
73 or B{C{x_xyz}} not a C{Cartesian}, L{Ecef9Tuple},
74 L{Vector3Tuple} or L{Vector4Tuple} or B{C{datum}} is
75 not a L{Datum}.
76 '''
77 h, d, n = _xyzhdn3(x_xyz, None, datum, ll, **name)
78 Vector3d.__init__(self, x_xyz, y=y, z=z, ll=ll, name=n)
79 if h is not None:
80 self._height = Height(h)
81 if d is not None:
82 self.datum = d
84# def __matmul__(self, other): # PYCHOK Python 3.5+
85# '''Return C{NotImplemented} for C{c_ = c @ datum} and C{c_ = c @ transform}.
86# '''
87# return NotImplemented if isinstance(other, (Datum, Transform)) else \
88# _NotImplemented(self, other)
90 def cassini(self, pointB, pointC, alpha, beta, useZ=False):
91 '''3-Point resection between this and 2 other points using U{Cassini
92 <https://NL.WikiPedia.org/wiki/Achterwaartse_insnijding>}'s method.
94 @arg pointB: Second point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple},
95 C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}).
96 @arg pointC: Center point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple},
97 C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}).
98 @arg alpha: Angle subtended by triangle side C{b} from B{C{pointA}} to
99 B{C{pointC}} (C{degrees}, non-negative).
100 @arg beta: Angle subtended by triangle side C{a} from B{C{pointB}} to
101 B{C{pointC}} (C{degrees}, non-negative).
102 @kwarg useZ: If C{True}, use and interpolate the Z component, otherwise
103 force C{z=INT0} (C{bool}).
105 @note: Typically, B{C{pointC}} is between this and B{C{pointB}}.
107 @return: The survey point, an instance of this (sub-)class.
109 @raise ResectionError: Near-coincident, -colinear or -concyclic points
110 or negative or invalid B{C{alpha}} or B{C{beta}}.
112 @raise TypeError: Invalid B{C{pointA}}, B{C{pointB}} or B{C{pointM}}.
114 @see: Function L{pygeodesy.cassini} for references and more details.
115 '''
116 return self._resections.cassini(self, pointB, pointC, alpha, beta,
117 useZ=useZ, datum=self.datum)
119 @deprecated_method
120 def collins(self, pointB, pointC, alpha, beta, useZ=False):
121 '''DEPRECATED, use method L{collins5}.'''
122 return self.collins5(pointB, pointC, alpha, beta, useZ=useZ)
124 def collins5(self, pointB, pointC, alpha, beta, useZ=False):
125 '''3-Point resection between this and 2 other points using U{Collins<https://Dokumen.tips/
126 documents/three-point-resection-problem-introduction-kaestner-burkhardt-method.html>}' method.
128 @arg pointB: Second point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple},
129 C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}).
130 @arg pointC: Center point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple},
131 C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}).
132 @arg alpha: Angle subtended by triangle side C{b} from B{C{pointA}} to
133 B{C{pointC}} (C{degrees}, non-negative).
134 @arg beta: Angle subtended by triangle side C{a} from B{C{pointB}} to
135 B{C{pointC}} (C{degrees}, non-negative).
136 @kwarg useZ: If C{True}, use and interpolate the Z component, otherwise
137 force C{z=INT0} (C{bool}).
139 @note: Typically, B{C{pointC}} is between this and B{C{pointB}}.
141 @return: L{Collins5Tuple}C{(pointP, pointH, a, b, c)} with survey C{pointP},
142 auxiliary C{pointH}, each an instance of this (sub-)class and
143 triangle sides C{a}, C{b} and C{c}.
145 @raise ResectionError: Near-coincident, -colinear or -concyclic points
146 or negative or invalid B{C{alpha}} or B{C{beta}}.
148 @raise TypeError: Invalid B{C{pointB}} or B{C{pointM}}.
150 @see: Function L{pygeodesy.collins5} for references and more details.
151 '''
152 return self._resections.collins5(self, pointB, pointC, alpha, beta,
153 useZ=useZ, datum=self.datum)
155 @deprecated_method
156 def convertDatum(self, datum2, **datum):
157 '''DEPRECATED, use method L{toDatum}.'''
158 return self.toDatum(datum2, **datum)
160 @property_doc_(''' this cartesian's datum (L{Datum}).''')
161 def datum(self):
162 '''Get this cartesian's datum (L{Datum}).
163 '''
164 return self._datum
166 @datum.setter # PYCHOK setter!
167 def datum(self, datum):
168 '''Set this cartesian's C{datum} I{without conversion}
169 (L{Datum}), ellipsoidal or spherical.
171 @raise TypeError: The B{C{datum}} is not a L{Datum}.
172 '''
173 d = _spherical_datum(datum, name=self.name)
174 if self._datum: # is not None
175 if d.isEllipsoidal and not self._datum.isEllipsoidal:
176 raise _IsnotError(_ellipsoidal_, datum=datum)
177 elif d.isSpherical and not self._datum.isSpherical:
178 raise _IsnotError(_spherical_, datum=datum)
179 if self._datum != d:
180 _update_all(self)
181 self._datum = d
183 def destinationXyz(self, delta, Cartesian=None, **Cartesian_kwds):
184 '''Calculate the destination using a I{local} delta from this cartesian.
186 @arg delta: Local delta to the destination (L{XyzLocal}, L{Enu},
187 L{Ned} or L{Local9Tuple}).
188 @kwarg Cartesian: Optional (geocentric) class to return the
189 destination or C{None}.
190 @kwarg Cartesian_kwds: Optional, additional B{C{Cartesian}} keyword
191 arguments, ignored if 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
198 B{C{Cartesian_kwds}}.
199 '''
200 if Cartesian is None:
201 r = self._Ltp._local2ecef(delta, nine=True)
202 else:
203 r = self._Ltp._local2ecef(delta, nine=False)
204 r = Cartesian(*r, **_xkwds(Cartesian_kwds, datum=self.datum))
205 return r._xnamed(r) if self.name else r
207 @property_RO
208 def Ecef(self):
209 '''Get the ECEF I{class} (L{EcefKarney}), I{once}.
210 '''
211 CartesianBase.Ecef = E = _MODS.ecef.EcefKarney # overwrite property_RO
212 return E
214 @Property_RO
215 def _ecef9(self):
216 '''(INTERNAL) Helper for L{toEcef}, L{toLocal} and L{toLtp} (L{Ecef9Tuple}).
217 '''
218 return self.Ecef(self.datum, name=self.name).reverse(self, M=True)
220 @property_RO
221 def ellipsoidalCartesian(self):
222 '''Get the C{Cartesian type} iff ellipsoidal, overloaded in L{CartesianEllipsoidalBase}.
223 '''
224 return False
226 def hartzell(self, los=False, earth=None):
227 '''Compute the intersection of a Line-Of-Sight from this cartesian Point-Of-View
228 (pov) and this cartesian's ellipsoid surface.
230 @kwarg los: Line-Of-Sight, I{direction} to the ellipsoid (L{Los}, L{Vector3d}),
231 C{True} for the I{normal, plumb} onto the surface or I{False} or
232 C{None} to point to the center of the ellipsoid.
233 @kwarg earth: The earth model (L{Datum}, L{Ellipsoid}, L{Ellipsoid2}, L{a_f2Tuple}
234 or C{scalar} radius in C{meter}), overriding this cartesian's
235 C{datum} ellipsoid.
237 @return: The intersection (C{Cartesian}) with C{.height} set to the distance to
238 this C{pov}.
240 @raise IntersectionError: Null or bad C{pov} or B{C{los}}, this C{pov} is inside
241 the ellipsoid or B{C{los}} points outside or away from
242 the ellipsoid.
244 @raise TypeError: Invalid B{C{los}} or invalid or undefined B{C{earth}} or C{datum}.
246 @see: Function L{hartzell<pygeodesy.formy.hartzell>} for further details.
247 '''
248 return _MODS.formy._hartzell(self, los, earth)
250 @Property
251 def height(self):
252 '''Get the height (C{meter}).
253 '''
254 return self._height4.h if self._height is None else self._height
256 @height.setter # PYCHOK setter!
257 def height(self, height):
258 '''Set the height (C{meter}).
260 @raise TypeError: Invalid B{C{height}} C{type}.
262 @raise ValueError: Invalid B{C{height}}.
263 '''
264 h = Height(height)
265 if self._height != h:
266 _update_all(self)
267 self._height = h
269 def _height2C(self, r, Cartesian=None, datum=None, height=INT0, **kwds):
270 '''(INTERNAL) Helper for methods C{.height3} and C{.height4}.
271 '''
272 if Cartesian is not None:
273 r = Cartesian(r, **kwds)
274 if datum is not None:
275 r.datum = datum
276 if height is not None:
277 r.height = height # Height(height)
278 return r
280 def height3(self, earth=None, height=None, **Cartesian_and_kwds):
281 '''Compute the cartesian at a height above or below this certesian's ellipsoid.
283 @kwarg earth: A datum, ellipsoid, triaxial ellipsoid or earth radius,
284 I{overriding} this cartesian's datum (L{Datum}, L{Ellipsoid},
285 L{Ellipsoid2}, L{a_f2Tuple} or C{meter}, conventionally).
286 @kwarg height: The height (C{meter}, conventionally), overriding this
287 cartesian's height.
288 @kwarg Cartesian_and_kwds: Optional C{B{Cartesian}=None} class to return
289 the cartesian I{at height} and additional B{C{Cartesian}}
290 keyword arguments.
292 @return: An instance of B{C{Cartesian}} or if C{B{Cartesian} is None},
293 a L{Vector3Tuple}C{(x, y, z)} with the C{x}, C{y} and C{z}
294 coordinates I{at height} in C{meter}, conventionally.
296 @note: This cartesian's coordinates are returned if B{C{earth}} and this
297 datum or B{C{heigth}} and/or this height are C{None} or undefined.
299 @note: Include keyword argument C{B{datum}=None} if class B{C{Cartesian}}
300 does not accept a B{C{datum}} keyword agument.
302 @raise TriaxialError: No convergence in triaxial root finding.
304 @raise TypeError: Invalid or undefined B{C{earth}} or C{datum}.
305 '''
306 n = self.height3.__name__
307 d = self.datum if earth is None else _spherical_datum(earth, name=n)
308 c, h = self, _heigHt(self, height)
309 if h and d:
310 R, r = self.Roc2(earth=d)
311 if R > EPS0:
312 R = (R + h) / R
313 r = ((r + h) / r) if r > EPS0 else _1_0
314 c = c.times_(R, R, r)
316 r = Vector3Tuple(c.x, c.y, c.z, name=n)
317 if Cartesian_and_kwds:
318 r = self._height2C(r, **_xkwds(Cartesian_and_kwds, datum=d))
319 return r
321 @Property_RO
322 def _height4(self):
323 '''(INTERNAL) Get this C{height4}-tuple.
324 '''
325 try:
326 r = self.datum.ellipsoid.height4(self, normal=True)
327 except (AttributeError, ValueError): # no datum, null cartesian,
328 r = Vector4Tuple(self.x, self.y, self.z, 0, name__=self.height4)
329 return r
331 def height4(self, earth=None, normal=True, **Cartesian_and_kwds):
332 '''Compute the projection of this point on and the height above or below
333 this datum's ellipsoid surface.
335 @kwarg earth: A datum, ellipsoid, triaxial ellipsoid or earth radius,
336 I{overriding} this datum (L{Datum}, L{Ellipsoid},
337 L{Ellipsoid2}, L{a_f2Tuple}, L{Triaxial}, L{Triaxial_},
338 L{JacobiConformal} or C{meter}, conventionally).
339 @kwarg normal: If C{True} the projection is the nearest point on the
340 ellipsoid's surface, otherwise the intersection of the
341 radial line to the ellipsoid's center and the surface.
342 @kwarg Cartesian_and_kwds: Optional C{B{Cartesian}=None} class to return
343 the I{projection} and additional B{C{Cartesian}} keyword
344 arguments.
346 @return: An instance of B{C{Cartesian}} or if C{B{Cartesian} is None}, a
347 L{Vector4Tuple}C{(x, y, z, h)} with the I{projection} C{x}, C{y}
348 and C{z} coordinates and height C{h} in C{meter}, conventionally.
350 @note: Include keyword argument C{B{datum}=None} if class B{C{Cartesian}}
351 does not accept a B{C{datum}} keyword agument.
353 @raise TriaxialError: No convergence in triaxial root finding.
355 @raise TypeError: Invalid or undefined B{C{earth}} or C{datum}.
357 @see: Methods L{Ellipsoid.height4} and L{Triaxial_.height4} for more information.
358 '''
359 n = self.height4.__name__
360 d = self.datum if earth is None else earth
361 if normal and d is self.datum:
362 r = self._height4
363 elif isinstance(d, _MODS.triaxials.Triaxial_):
364 r = d.height4(self, normal=normal)
365 try:
366 d = d.toEllipsoid(name=n)
367 except (TypeError, ValueError): # TriaxialError
368 d = None
369 else:
370 r = _earth_ellipsoid(d).height4(self, normal=normal)
372 if Cartesian_and_kwds:
373 if d and not isinstance(d, Datum):
374 d = _spherical_datum(d, name=n)
375 r = self._height2C(r, **_xkwds(Cartesian_and_kwds, datum=d))
376 return r
378 @Property_RO
379 def isEllipsoidal(self):
380 '''Check whether this cartesian is ellipsoidal (C{bool} or C{None} if unknown).
381 '''
382 return self.datum.isEllipsoidal if self._datum else None
384 @Property_RO
385 def isSpherical(self):
386 '''Check whether this cartesian is spherical (C{bool} or C{None} if unknown).
387 '''
388 return self.datum.isSpherical if self._datum else None
390 @Property_RO
391 def latlon(self):
392 '''Get this cartesian's (geodetic) lat- and longitude in C{degrees} (L{LatLon2Tuple}C{(lat, lon)}).
393 '''
394 return self.toEcef().latlon
396 @Property_RO
397 def latlonheight(self):
398 '''Get this cartesian's (geodetic) lat-, longitude in C{degrees} with height (L{LatLon3Tuple}C{(lat, lon, height)}).
399 '''
400 return self.toEcef().latlonheight
402 @Property_RO
403 def latlonheightdatum(self):
404 '''Get this cartesian's (geodetic) lat-, longitude in C{degrees} with height and datum (L{LatLon4Tuple}C{(lat, lon, height, datum)}).
405 '''
406 return self.toEcef().latlonheightdatum
408 @property_RO
409 def _ltp(self):
410 '''(INTERNAL) Get module C{.ltp}, I{once}.
411 '''
412 CartesianBase._ltp = m = _MODS.ltp # overwrite property_RO
413 return m
415 @Property_RO
416 def _Ltp(self):
417 '''(INTERNAL) Cache for L{toLtp}.
418 '''
419 return self._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 m = _MODS.nvectorBase
426 x, y, z, h = self._n_xyzh4(self.datum)
427 return m._N_vector_(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 self._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 self._resections.pierlotx(self, point2, point3, alpha1, alpha2, alpha3,
547 useZ=useZ, datum=self.datum)
549 @property_RO
550 def _resections(self):
551 '''(INTERNAL) Import the C{.resections} module, I{once}.
552 '''
553 CartesianBase._resections = m = _MODS.resections # overwrite property_RO
554 return m
556 def Roc2(self, earth=None):
557 '''Compute this cartesian's I{normal} and I{pseudo, z-based} radius of curvature.
559 @kwarg earth: A datum, ellipsoid, triaxial ellipsoid or earth radius,
560 I{overriding} this cartesian's datum (L{Datum}, L{Ellipsoid},
561 L{Ellipsoid2}, L{a_f2Tuple} or C{meter}, conventionally).
563 @return: 2-Tuple C{(R, r)} with the I{normal} and I{pseudo, z-based} radius of
564 curvature C{R} respectively C{r}, both in C{meter} conventionally.
566 @raise TypeError: Invalid or undefined B{C{earth}} or C{datum}.
567 '''
568 r = z = fabs( self.z)
569 R, _0 = hypot(self.x, self.y), EPS0
570 if R < _0: # polar
571 R = z
572 elif z > _0: # non-equatorial
573 d = self.datum if earth is None else _spherical_datum(earth)
574 e = self.toLatLon(datum=d, height=0, LatLon=None) # Ecef9Tuple
575 M = e.M # EcefMatrix
576 sa, ca = map(fabs, (M._2_2_, M._2_1_) if M else sincos2d(e.lat))
577 if ca < _0: # polar
578 R = z
579 else: # prime-vertical, normal roc R
580 R = R / ca # /= chokes PyChecker
581 r = R if sa < _0 else (r / sa) # non-/equatorial
582 return R, r
584 @property_RO
585 def sphericalCartesian(self):
586 '''Get the C{Cartesian type} iff spherical, overloaded in L{CartesianSphericalBase}.
587 '''
588 return False
590 @deprecated_method
591 def tienstra(self, pointB, pointC, alpha, beta=None, gamma=None, useZ=False):
592 '''DEPRECATED, use method L{tienstra7}.'''
593 return self.tienstra7(pointB, pointC, alpha, beta=beta, gamma=gamma, useZ=useZ)
595 def tienstra7(self, pointB, pointC, alpha, beta=None, gamma=None, useZ=False):
596 '''3-Point resection between this and two other points using U{Tienstra
597 <https://WikiPedia.org/wiki/Tienstra_formula>}'s formula.
599 @arg pointB: Second point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple}, C{Vector4Tuple} or
600 C{Vector2Tuple} if C{B{useZ}=False}).
601 @arg pointC: Third point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple}, C{Vector4Tuple} or
602 C{Vector2Tuple} if C{B{useZ}=False}).
603 @arg alpha: Angle subtended by triangle side C{a} from B{C{pointB}} to B{C{pointC}} (C{degrees},
604 non-negative).
605 @kwarg beta: Angle subtended by triangle side C{b} from this to B{C{pointC}} (C{degrees},
606 non-negative) or C{None} if C{B{gamma} is not None}.
607 @kwarg gamma: Angle subtended by triangle side C{c} from this to B{C{pointB}} (C{degrees},
608 non-negative) or C{None} if C{B{beta} is not None}.
609 @kwarg useZ: If C{True}, use and interpolate the Z component, otherwise force C{z=INT0}
610 (C{bool}).
612 @note: This point, B{C{pointB}} and B{C{pointC}} are ordered clockwise.
614 @return: L{Tienstra7Tuple}C{(pointP, A, B, C, a, b, c)} with survey C{pointP},
615 an instance of this (sub-)class and triangle angle C{A} at this point,
616 C{B} at B{C{pointB}} and C{C} at B{C{pointC}} in C{degrees} and
617 triangle sides C{a}, C{b} and C{c}.
619 @raise ResectionError: Near-coincident, -colinear or -concyclic points or sum of
620 B{C{alpha}}, B{C{beta}} and B{C{gamma}} not C{360} or
621 negative B{C{alpha}}, B{C{beta}} or B{C{gamma}}.
623 @raise TypeError: Invalid B{C{pointB}} or B{C{pointC}}.
625 @see: Function L{pygeodesy.tienstra7} for references and more details.
626 '''
627 return self._resections.tienstra7(self, pointB, pointC, alpha, beta, gamma,
628 useZ=useZ, datum=self.datum)
630 @deprecated_method
631 def to2ab(self): # PYCHOK no cover
632 '''DEPRECATED, use property C{philam}.
634 @return: A L{PhiLam2Tuple}C{(phi, lam)}.
635 '''
636 return self.philam
638 @deprecated_method
639 def to2ll(self): # PYCHOK no cover
640 '''DEPRECATED, use property C{latlon}.
642 @return: A L{LatLon2Tuple}C{(lat, lon)}.
643 '''
644 return self.latlon
646 @deprecated_method
647 def to3llh(self, datum=None): # PYCHOK no cover
648 '''DEPRECATED, use property L{latlonheight} or L{latlonheightdatum}.
650 @return: A L{LatLon4Tuple}C{(lat, lon, height, datum)}.
652 @note: This method returns a B{C{-4Tuple}} I{and not a} C{-3Tuple}
653 as its name may suggest.
654 '''
655 t = self.toLatLon(datum=datum, LatLon=None)
656 return LatLon4Tuple(t.lat, t.lon, t.height, t.datum, name=self.name)
658# def _to3LLh(self, datum, LL, **pairs): # OBSOLETE
659# '''(INTERNAL) Helper for C{subclass.toLatLon} and C{.to3llh}.
660# '''
661# r = self.to3llh(datum) # LatLon3Tuple
662# if LL is not None:
663# r = LL(r.lat, r.lon, height=r.height, datum=datum, name=self.name)
664# for n, v in pairs.items():
665# setattr(r, n, v)
666# return r
668 def toDatum(self, datum2, datum=None):
669 '''Convert this cartesian from one datum to an other.
671 @arg datum2: Datum to convert I{to} (L{Datum}).
672 @kwarg datum: Datum to convert I{from} (L{Datum}).
674 @return: The converted point (C{Cartesian}).
676 @raise TypeError: B{C{datum2}} or B{C{datum}}
677 invalid.
678 '''
679 _xinstanceof(Datum, datum2=datum2)
681 c = self if datum in (None, self.datum) else \
682 self.toDatum(datum)
684 i, d = False, c.datum
685 if d == datum2:
686 return c.copy() if c is self else c
688 elif datum2.transform.isunity and \
689 d.transform.isunity:
690 return c.dup(datum=datum2)
692 elif d == _WGS84:
693 d = datum2 # convert from WGS84 to datum2
695 elif datum2 == _WGS84:
696 i = True # convert to WGS84 by inverse transformation
698 else: # neither datum2 nor c.datum is WGS84, invert to WGS84 first
699 c = c.toTransform(d.transform, inverse=True, datum=_WGS84)
700 d = datum2
702 return c.toTransform(d.transform, inverse=i, datum=datum2)
704 def toEcef(self):
705 '''Convert this cartesian to I{geodetic} (lat-/longitude) coordinates.
707 @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height,
708 C, M, datum)} with C{C} and C{M} if available.
710 @raise EcefError: A C{.datum} or an ECEF issue.
711 '''
712 return self._ecef9
714 def toLatLon(self, datum=None, height=None, LatLon=None, **LatLon_kwds): # see .ecef.Ecef9Tuple.toDatum
715 '''Convert this cartesian to a I{geodetic} (lat-/longitude) point.
717 @kwarg datum: Optional datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2}
718 or L{a_f2Tuple}).
719 @kwarg height: Optional height, overriding the converted height
720 (C{meter}), iff B{C{LatLon}} is not C{None}.
721 @kwarg LatLon: Optional class to return the geodetic point
722 (C{LatLon}) or C{None}.
723 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword
724 arguments, ignored if C{B{LatLon} is None}.
726 @return: The geodetic point (B{C{LatLon}}) or if B{C{LatLon}}
727 is C{None}, an L{Ecef9Tuple}C{(x, y, z, lat, lon,
728 height, C, M, datum)} with C{C} and C{M} if available.
730 @raise TypeError: Invalid B{C{datum}} or B{C{LatLon_kwds}}.
731 '''
732 d = _spherical_datum(datum or self.datum, name=self.name)
733 if d == self.datum:
734 r = self.toEcef()
735 else:
736 c = self.toDatum(d)
737 r = c.Ecef(d, name=self.name).reverse(c, M=LatLon is None)
739 if LatLon: # class or .classof
740 h = _heigHt(r, height)
741 r = LatLon(r.lat, r.lon, datum=r.datum, height=h,
742 **_xkwds(LatLon_kwds, name=r.name))
743 _xdatum(r.datum, d)
744 return r
746 def toLocal(self, Xyz=None, ltp=None, **Xyz_kwds):
747 '''Convert this I{geocentric} cartesian to I{local} C{X}, C{Y} and C{Z}.
749 @kwarg Xyz: Optional class to return C{X}, C{Y} and C{Z}
750 (L{XyzLocal}, L{Enu}, L{Ned}) or C{None}.
751 @kwarg ltp: The I{local tangent plane} (LTP) to use,
752 overriding this cartesian's LTP (L{Ltp}).
753 @kwarg Xyz_kwds: Optional, additional B{C{Xyz}} keyword
754 arguments, ignored if C{B{Xyz} is None}.
756 @return: An B{C{Xyz}} instance or if C{B{Xyz} is None},
757 a L{Local9Tuple}C{(x, y, z, lat, lon, height,
758 ltp, ecef, M)} with C{M=None} always.
760 @raise TypeError: Invalid B{C{ltp}}.
761 '''
762 p = self._ltp._xLtp(ltp, self._Ltp)
763 return p._ecef2local(self._ecef9, Xyz, Xyz_kwds)
765 def toLtp(self, Ecef=None):
766 '''Return the I{local tangent plane} (LTP) for this cartesian.
768 @kwarg Ecef: Optional ECEF I{class} (L{EcefKarney}, ...
769 L{EcefYou}), overriding this cartesian's C{Ecef}.
770 '''
771 return self._Ltp if Ecef in (None, self.Ecef) else self._ltp.Ltp(
772 self._ecef9, ecef=Ecef(self.datum), name=self.name)
774 def toNvector(self, Nvector=None, datum=None, **Nvector_kwds):
775 '''Convert this cartesian to C{n-vector} components, I{including height}.
777 @kwarg Nvector: Optional class to return the C{n-vector} components
778 (C{Nvector}) or C{None}.
779 @kwarg datum: Optional datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2}
780 or L{a_f2Tuple}) overriding this cartesian's datum.
781 @kwarg Nvector_kwds: Optional, additional B{C{Nvector}} keyword
782 arguments, ignored if C{B{Nvector} is None}.
784 @return: An B{C{Nvector}} or a L{Vector4Tuple}C{(x, y, z, h)} if
785 B{C{Nvector}} is C{None}.
787 @raise TypeError: Invalid B{C{Nvector}}, B{C{Nvector_kwds}} or
788 B{C{datum}}.
790 @raise ValueError: B{C{Cartesian}} at origin.
791 '''
792 r, d = self._N_vector.xyzh, self.datum
793 if datum is not None:
794 d = _spherical_datum(datum, name=self.name)
795 if d != self.datum:
796 r = self._n_xyzh4(d)
798 if Nvector is not None:
799 kwds = _xkwds(Nvector_kwds, h=r.h, datum=d)
800 r = self._xnamed(Nvector(r.x, r.y, r.z, **kwds))
801 return r
803 def toRtp(self):
804 '''Convert this cartesian to I{spherical, polar} coordinates.
806 @return: L{RadiusThetaPhi3Tuple}C{(r, theta, phi)} with C{theta}
807 and C{phi}, both in L{Degrees}.
809 @see: Function L{xyz2rtp_} and class L{RadiusThetaPhi3Tuple}.
810 '''
811 return _rtp3(self.toRtp, Degrees, self, name=self.name)
813 def toStr(self, prec=3, fmt=Fmt.SQUARE, sep=_COMMASPACE_): # PYCHOK expected
814 '''Return the string representation of this cartesian.
816 @kwarg prec: Number of (decimal) digits, unstripped (C{int}).
817 @kwarg fmt: Enclosing backets format (C{letter}).
818 @kwarg sep: Separator to join (C{str}).
820 @return: Cartesian represented as "[x, y, z]" (C{str}).
821 '''
822 return Vector3d.toStr(self, prec=prec, fmt=fmt, sep=sep)
824 def toTransform(self, transform, inverse=False, datum=None):
825 '''Apply a Helmert transform to this cartesian.
827 @arg transform: Transform to apply (L{Transform} or L{TransformXform}).
828 @kwarg inverse: Apply the inverse of the C{B{transform}} (C{bool}).
829 @kwarg datum: Datum for the transformed cartesian (L{Datum}), overriding
830 this cartesian's datum but I{not} taken it into account.
832 @return: A transformed cartesian (C{Cartesian}) or a copy of this
833 cartesian if C{B{transform}.isunity}.
835 @raise TypeError: Invalid B{C{transform}}.
836 '''
837 _xinstanceof(Transform, transform=transform)
838 if transform.isunity:
839 c = self.dup(datum=datum or self.datum)
840 else:
841 # if inverse and d != _WGS84:
842 # raise _ValueError(inverse=inverse, datum=d,
843 # txt_not_=_WGS84.name)
844 xyz = transform.transform(*self.xyz, inverse=inverse)
845 c = self.dup(xyz=xyz, datum=datum or self.datum)
846 return c
848 def toVector(self, Vector=None, **Vector_kwds):
849 '''Return this cartesian's I{geocentric} components as vector.
851 @kwarg Vector: Optional class to return the I{geocentric}
852 components (L{Vector3d}) or C{None}.
853 @kwarg Vector_kwds: Optional, additional B{C{Vector}} keyword
854 arguments, ignored if C{B{Vector} is None}.
856 @return: A B{C{Vector}} or a L{Vector3Tuple}C{(x, y, z)} if
857 B{C{Vector}} is C{None}.
859 @raise TypeError: Invalid B{C{Vector}} or B{C{Vector_kwds}}.
860 '''
861 return self.xyz if Vector is None else self._xnamed(
862 Vector(self.x, self.y, self.z, **Vector_kwds))
865class RadiusThetaPhi3Tuple(_NamedTuple):
866 '''3-Tuple C{(r, theta, phi)} with radial distance C{r} in C{meter}, inclination
867 C{theta} (with respect to the positive z-axis) and azimuthal angle C{phi} in
868 L{Degrees} I{or} L{Radians} representing a U{spherical, polar position
869 <https://WikiPedia.org/wiki/Spherical_coordinate_system>}.
870 '''
871 _Names_ = (_r_, _theta_, _phi_)
872 _Units_ = ( Meter, _Pass, _Pass)
874 def toCartesian(self, **name_Cartesian_and_kwds):
875 '''Convert this L{RadiusThetaPhi3Tuple} to a cartesian C{(x, y, z)} vector.
877 @kwarg name_Cartesian_and_kwds: Optional C{B{name}=NN}, overriding this
878 name and optional class C{B{Cartesian}=None} and additional
879 C{B{Cartesian}} keyword arguments.
881 @return: A C{B{Cartesian}(x, y, z)} instance or if no C{B{Cartesian}} keyword
882 argument is given, a L{Vector3Tuple}C{(x, y, z)} with C{x}, C{y}
883 and C{z} in the same units as radius C{r}, C{meter} conventionally.
885 @see: Function L{rtp2xyz_}.
886 '''
887 r, t, p = self
888 t, p, _ = _toRadians(self, t, p)
889 n, kwds = _name2__(name_Cartesian_and_kwds, _or_nameof=self)
890 return rtp2xyz_(r, t, p, name=n, **kwds)
892 def toDegrees(self, **name):
893 '''Convert this L{RadiusThetaPhi3Tuple}'s angles to L{Degrees}.
895 @kwarg name: Optional name (C{str}), overriding this name.
897 @return: L{RadiusThetaPhi3Tuple}C{(r, theta, phi)} with C{theta}
898 and C{phi} both in L{Degrees}.
899 '''
900 r, t, p = self
901 t, p, _ = _toDegrees(self, t, p)
902 return _ or self.classof(r, Degrees(theta=t), Degrees(phi=p),
903 name=_name__(name, _or_nameof=self))
905 def toRadians(self, **name):
906 '''Convert this L{RadiusThetaPhi3Tuple}'s angles to L{Radians}.
908 @kwarg name: Optional, overriding C{B{name}=NN} (C{str}).
910 @return: L{RadiusThetaPhi3Tuple}C{(r, theta, phi)} with
911 C{theta} and C{phi} both in L{Radians}.
912 '''
913 r, t, p = self
914 t, p, _ = _toRadians(self, t, p)
915 return _ or self.classof(r, Radians(theta=t), Radians(phi=p),
916 name=_name__(name, _or_nameof=self))
919def rtp2xyz(r_rtp, *theta_phi, **name_Cartesian_and_kwds):
920 '''Convert I{spherical, polar} C{(r, theta, phi)} to cartesian C{(x, y, z)} coordinates.
922 @arg r_rtp: Radial distance (C{scalar}, conventially C{meter}) or a previous
923 L{RadiusThetaPhi3Tuple} instance.
924 @arg theta_phi: Inclination B{C{theta}} (C{degrees} with respect to the positive z-axis)
925 and azimuthal angle B{C{phi}} (C{degrees}), ignored if C{B{r_rtp}} is a
926 L{RadiusThetaPhi3Tuple}.
927 @kwarg name_Cartesian_and_kwds: Optional C{B{name}=NN} (C{str}), a C{B{Cartesian}=None}
928 class to return the coordinates and additional C{B{Cartesian}}
929 keyword arguments.
931 @return: A C{B{Cartesian}(x, y, z)} instance or if no C{B{Cartesian}} keyword argument
932 is given a L{Vector3Tuple}C{(x, y, z)}, with C{x}, C{y} and C{z} in the same
933 units as radius C{r}, C{meter} conventionally.
935 @raise TypeError: Invalid B{C{r_rtp}}.
937 @see: Functions L{rtp2xyz_} and L{xyz2rtp}.
938 '''
939 if isinstance(r_rtp, RadiusThetaPhi3Tuple):
940 c = r_rtp.toCartesian(**name_Cartesian_and_kwds)
941 else:
942 c = rtp2xyz_(r_rtp, *map(radians, theta_phi), **name_Cartesian_and_kwds)
943 return c
946def rtp2xyz_(r_rtp, *theta_phi, **name_Cartesian_and_kwds):
947 '''Convert I{spherical, polar} C{(r, theta, phi)} to cartesian C{(x, y, z)} coordinates.
949 @arg r_rtp: Radial distance (C{scalar}, conventially C{meter}) or a previous
950 L{RadiusThetaPhi3Tuple} instance.
951 @arg theta_phi: Inclination B{C{theta}} (C{radians} with respect to the positive z-axis)
952 and azimuthal angle B{C{phi}} (C{degrees}), ignored is C{B{r_rtp}} is a
953 L{RadiusThetaPhi3Tuple}.
954 @kwarg name_Cartesian_and_kwds: Optional C{B{name}=NN} (C{str}), a C{B{Cartesian}=None}
955 class to return the coordinates and additional C{B{Cartesian}}
956 keyword arguments.
958 @return: A C{B{Cartesian}(x, y, z)} instance or if no C{B{Cartesian}} keyword argument
959 is given a L{Vector3Tuple}C{(x, y, z)}, with C{x}, C{y} and C{z} in the same
960 units as radius C{r}, C{meter} conventionally.
962 @raise TypeError: Invalid B{C{r_rtp}} or B{C{theta_phi}}.
964 @see: U{Physics convention<https://WikiPedia.org/wiki/Spherical_coordinate_system>}
965 (ISO 80000-2:2019).
966 '''
967 if _isMeter(r_rtp) and len(theta_phi) == 2:
968 r = r_rtp
969 if r and _isfinite(r):
970 s, z, y, x = sincos2_(*theta_phi)
971 s *= r
972 z *= r
973 y *= s
974 x *= s
975 else:
976 x = y = z = r
978 def _n_C_kwds3(Cartesian=None, **name_kwds):
979 n, kwds = _name2__(**name_kwds)
980 return n, Cartesian, kwds
982 n, C, kwds = _n_C_kwds3(**name_Cartesian_and_kwds)
983 c = Vector3Tuple(x, y, z, name=n) if C is None else \
984 C(x, y, z, name=n, **kwds)
986 elif isinstance(r_rtp, RadiusThetaPhi3Tuple):
987 c = r_rtp.toCartesian(**name_Cartesian_and_kwds)
988 else:
989 raise _TypeError(r_rtp=r_rtp, theta_phi=theta_phi)
990 return c
993def _rtp3(where, Unit, *x_y_z, **name):
994 '''(INTERNAL) Helper for C{.toRtp}, C{xyz2rtp} and C{xyz2rtp_}.
995 '''
996 x, y, z = _MODS.vector3dBase._xyz3(where, *x_y_z)
997 r = hypot_(x, y, z)
998 if r > 0:
999 t = acos1(z / r)
1000 p = atan2(y, x)
1001 while p < 0:
1002 p += PI2
1003 if Unit is Degrees:
1004 t = degrees(t)
1005 p = degrees(p)
1006 else:
1007 t = p = _0_0
1008 return RadiusThetaPhi3Tuple(r, Unit(theta=t), Unit(phi=p), **name)
1011def xyz2rtp(x_xyz, *y_z, **name):
1012 '''Convert cartesian C{(x, y, z)} to I{spherical, polar} C{(r, theta, phi)} coordinates.
1014 @return: L{RadiusThetaPhi3Tuple}C{(r, theta, phi)} with C{theta} and C{phi},
1015 both in L{Degrees}.
1017 @see: Function L{xyz2rtp_} and class L{RadiusThetaPhi3Tuple}.
1018 '''
1019 return _rtp3(xyz2rtp, Degrees, x_xyz, *y_z, **name)
1022def xyz2rtp_(x_xyz, *y_z, **name):
1023 '''Convert cartesian C{(x, y, z)} to I{spherical, polar} C{(r, theta, phi)} coordinates.
1025 @arg x_xyz: X component (C{scalar}) or a cartesian (C{Cartesian}, L{Ecef9Tuple},
1026 C{Nvector}, L{Vector3d}, L{Vector3Tuple}, L{Vector4Tuple} or a
1027 C{tuple} or C{list} of 3+ C{scalar} items) if no C{y_z} specified.
1028 @arg y_z: Y and Z component (C{scalar}s), ignored if C{x_xyz} is not a C{scalar}.
1029 @kwarg name: Optional C{B{name}=NN} (C{str}).
1031 @return: L{RadiusThetaPhi3Tuple}C{(r, theta, phi)} with radial distance C{r}
1032 (C{meter}, same units as C{x}, C{y} and C{z}), inclination C{theta}
1033 (with respect to the positive z-axis) and azimuthal angle C{phi},
1034 both in L{Radians}.
1036 @see: U{Physics convention<https://WikiPedia.org/wiki/Spherical_coordinate_system>}
1037 (ISO 80000-2:2019).
1038 '''
1039 return _rtp3(xyz2rtp_, Radians, x_xyz, *y_z, **name)
1042__all__ += _ALL_DOCS(CartesianBase)
1044# **) MIT License
1045#
1046# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.
1047#
1048# Permission is hereby granted, free of charge, to any person obtaining a
1049# copy of this software and associated documentation files (the "Software"),
1050# to deal in the Software without restriction, including without limitation
1051# the rights to use, copy, modify, merge, publish, distribute, sublicense,
1052# and/or sell copies of the Software, and to permit persons to whom the
1053# Software is furnished to do so, subject to the following conditions:
1054#
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