Coverage for pygeodesy/cartesianBase.py: 91%
317 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__, _NamedLocal, _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, _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, atan2, sincos2d, sincos2_, 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 degrees, fabs, radians, sqrt # from .fmath, .utily
45__all__ = _ALL_LAZY.cartesianBase
46__version__ = '24.12.04'
48_r_ = 'r'
49_theta_ = 'theta'
52class CartesianBase(Vector3d, _NamedLocal):
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_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 C{datum} 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 datum.
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
282 C{datum} ellipsoid surface.
284 @kwarg earth: A datum, ellipsoid, triaxial ellipsoid or earth radius,
285 I{overriding} this cartesian's datum (L{Datum}, L{Ellipsoid},
286 L{Ellipsoid2}, L{a_f2Tuple} or C{meter}, conventionally).
287 @kwarg height: The height (C{meter}, conventionally), overriding this
288 cartesian's height.
289 @kwarg Cartesian_and_kwds: Optional C{B{Cartesian}=None} class to return
290 the cartesian I{at height} and additional B{C{Cartesian}}
291 keyword arguments.
293 @return: An instance of B{C{Cartesian}} or if C{B{Cartesian} is None},
294 a L{Vector3Tuple}C{(x, y, z)} with the C{x}, C{y} and C{z}
295 coordinates I{at height} in C{meter}, conventionally.
297 @note: This cartesian's coordinates are returned if B{C{earth}} and this
298 datum or B{C{height}} and/or this height are C{None} or undefined.
300 @note: Include keyword argument C{B{datum}=None} if class B{C{Cartesian}}
301 does not accept a B{C{datum}} keyword agument.
303 @raise TriaxialError: No convergence in triaxial root finding.
305 @raise TypeError: Invalid or undefined B{C{earth}} or C{datum}.
306 '''
307 n = self.height3.__name__
308 d = self.datum if earth is None else _spherical_datum(earth, name=n)
309 c, h = self, _heigHt(self, height)
310 if h and d:
311 R, r = self.Roc2(earth=d)
312 if R > EPS0:
313 R = (R + h) / R
314 r = ((r + h) / r) if r > EPS0 else _1_0
315 c = c.times_(R, R, r)
317 r = Vector3Tuple(c.x, c.y, c.z, name=n)
318 if Cartesian_and_kwds:
319 r = self._height2C(r, **_xkwds(Cartesian_and_kwds, datum=d))
320 return r
322 @Property_RO
323 def _height4(self):
324 '''(INTERNAL) Get this C{height4}-tuple.
325 '''
326 try:
327 r = self.datum.ellipsoid.height4(self, normal=True)
328 except (AttributeError, ValueError): # no datum, null cartesian,
329 r = Vector4Tuple(self.x, self.y, self.z, 0, name__=self.height4)
330 return r
332 def height4(self, earth=None, normal=True, **Cartesian_and_kwds):
333 '''Compute the projection of this point on and the height above or below
334 this datum's ellipsoid surface.
336 @kwarg earth: A datum, ellipsoid, triaxial ellipsoid or earth radius,
337 I{overriding} this datum (L{Datum}, L{Ellipsoid},
338 L{Ellipsoid2}, L{a_f2Tuple}, L{Triaxial}, L{Triaxial_},
339 L{JacobiConformal} or C{meter}, conventionally).
340 @kwarg normal: If C{True}, the projection is the nearest point on the
341 ellipsoid's surface, otherwise the intersection of the
342 radial line to the ellipsoid's center and surface C{bool}).
343 @kwarg Cartesian_and_kwds: Optional C{B{Cartesian}=None} class to return
344 the I{projection} and additional B{C{Cartesian}} keyword
345 arguments.
347 @return: An instance of B{C{Cartesian}} or if C{B{Cartesian} is None}, a
348 L{Vector4Tuple}C{(x, y, z, h)} with the I{projection} C{x}, C{y}
349 and C{z} coordinates and height C{h} in C{meter}, conventionally.
351 @note: Include keyword argument C{B{datum}=None} if class B{C{Cartesian}}
352 does not accept a B{C{datum}} keyword agument.
354 @raise TriaxialError: No convergence in triaxial root finding.
356 @raise TypeError: Invalid or undefined B{C{earth}} or C{datum}.
358 @see: Methods L{Ellipsoid.height4} and L{Triaxial_.height4} for more information.
359 '''
360 n = self.height4.__name__
361 d = self.datum if earth is None else earth
362 if normal and d is self.datum:
363 r = self._height4
364 elif isinstance(d, _MODS.triaxials.Triaxial_):
365 r = d.height4(self, normal=normal)
366 try:
367 d = d.toEllipsoid(name=n)
368 except (TypeError, ValueError): # TriaxialError
369 d = None
370 else:
371 r = _earth_ellipsoid(d).height4(self, normal=normal)
373 if Cartesian_and_kwds:
374 if d and not isinstance(d, Datum):
375 d = _spherical_datum(d, name=n)
376 r = self._height2C(r, **_xkwds(Cartesian_and_kwds, datum=d))
377 return r
379 @Property_RO
380 def isEllipsoidal(self):
381 '''Check whether this cartesian is ellipsoidal (C{bool} or C{None} if unknown).
382 '''
383 return _xattr(self.datum, isEllipsoidal=None)
385 @Property_RO
386 def isSpherical(self):
387 '''Check whether this cartesian is spherical (C{bool} or C{None} if unknown).
388 '''
389 return _xattr(self.datum, isSpherical=None)
391 @Property_RO
392 def latlon(self):
393 '''Get this cartesian's (geodetic) lat- and longitude in C{degrees} (L{LatLon2Tuple}C{(lat, lon)}).
394 '''
395 return self.toEcef().latlon
397 @Property_RO
398 def latlonheight(self):
399 '''Get this cartesian's (geodetic) lat-, longitude in C{degrees} with height (L{LatLon3Tuple}C{(lat, lon, height)}).
400 '''
401 return self.toEcef().latlonheight
403 @Property_RO
404 def latlonheightdatum(self):
405 '''Get this cartesian's (geodetic) lat-, longitude in C{degrees} with height and datum (L{LatLon4Tuple}C{(lat, lon, height, datum)}).
406 '''
407 return self.toEcef().latlonheightdatum
409 @Property_RO
410 def _N_vector(self):
411 '''(INTERNAL) Get the (C{nvectorBase._N_vector_}).
412 '''
413 _N = _MODS.nvectorBase._N_vector_
414 x, y, z, h = self._n_xyzh4(self.datum)
415 return _N(x, y, z, h=h, name=self.name)
417 def _n_xyzh4(self, datum):
418 '''(INTERNAL) Get the n-vector components as L{Vector4Tuple}.
419 '''
420 def _ErrorEPS0(x):
421 return _ValueError(origin=self, txt=Fmt.PARENSPACED(EPS0=x))
423 _xinstanceof(Datum, datum=datum)
424 # <https://www.Movable-Type.co.UK/scripts/geodesy/docs/
425 # latlon-nvector-ellipsoidal.js.html#line309>,
426 # <https://GitHub.com/pbrod/nvector>/src/nvector/core.py>
427 # _equation23 and <https://www.NavLab.net/nvector>
428 E = datum.ellipsoid
429 x, y, z = self.xyz3
431 # Kenneth Gade eqn 23
432 p = hypot2(x, y) * E.a2_
433 q = z**2 * E.e21 * E.a2_
434 r = fsumf_(p, q, -E.e4) / _6_0
435 s = (p * q * E.e4) / (_4_0 * r**3)
436 t = cbrt(fsumf_(_1_0, s, sqrt(s * (_2_0 + s))))
437 if isnear0(t):
438 raise _ErrorEPS0(t)
439 u = fsumf_(_1_0, t, _1_0 / t) * r
440 v = sqrt(u**2 + E.e4 * q)
441 t = v * _2_0
442 if t < EPS0: # isnear0
443 raise _ErrorEPS0(t)
444 w = fsumf_(u, v, -q) * E.e2 / t
445 k = sqrt(fsumf_(u, v, w**2)) - w
446 if isnear0(k):
447 raise _ErrorEPS0(k)
448 t = k + E.e2
449 if isnear0(t):
450 raise _ErrorEPS0(t)
451 e = k / t
452# d = e * hypot(x, y)
453# tmp = 1 / hypot(d, z) == 1 / hypot(e * hypot(x, y), z)
454 t = hypot_(x * e, y * e, z) # == 1 / tmp
455 if t < EPS0: # isnear0
456 raise _ErrorEPS0(t)
457 h = fsumf_(k, E.e2, _N_1_0) / k * t
458 s = e / t # == e * tmp
459 return Vector4Tuple(x * s, y * s, z / t, h, name=self.name)
461 @Property_RO
462 def philam(self):
463 '''Get this cartesian's (geodetic) lat- and longitude in C{radians} (L{PhiLam2Tuple}C{(phi, lam)}).
464 '''
465 return self.toEcef().philam
467 @Property_RO
468 def philamheight(self):
469 '''Get this cartesian's (geodetic) lat-, longitude in C{radians} with height (L{PhiLam3Tuple}C{(phi, lam, height)}).
470 '''
471 return self.toEcef().philamheight
473 @Property_RO
474 def philamheightdatum(self):
475 '''Get this cartesian's (geodetic) lat-, longitude in C{radians} with height and datum (L{PhiLam4Tuple}C{(phi, lam, height, datum)}).
476 '''
477 return self.toEcef().philamheightdatum
479 def pierlot(self, point2, point3, alpha12, alpha23, useZ=False, eps=EPS):
480 '''3-Point resection between this and two other points using U{Pierlot
481 <http://www.Telecom.ULg.ac.Be/triangulation>}'s method C{ToTal} with
482 I{approximate} limits for the (pseudo-)singularities.
484 @arg point2: Second point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple},
485 C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}).
486 @arg point3: Third point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple},
487 C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}).
488 @arg alpha12: Angle subtended from this point to B{C{point2}} or
489 B{C{alpha2 - alpha}} (C{degrees}).
490 @arg alpha23: Angle subtended from B{C{point2}} to B{C{point3}} or
491 B{C{alpha3 - alpha2}} (C{degrees}).
492 @kwarg useZ: If C{True}, interpolate the Z component, otherwise use C{z=INT0}
493 (C{bool}).
494 @kwarg eps: Tolerance for C{cot} (pseudo-)singularities (C{float}).
496 @note: This point, B{C{point2}} and B{C{point3}} are ordered counter-clockwise.
498 @return: The survey (or robot) point, an instance of this (sub-)class.
500 @raise ResectionError: Near-coincident, -colinear or -concyclic points
501 or invalid B{C{alpha12}} or B{C{alpha23}}.
503 @raise TypeError: Invalid B{C{point2}} or B{C{point3}}.
505 @see: Function L{pygeodesy.pierlot} for references and more details.
506 '''
507 return _MODS.resections.pierlot(self, point2, point3, alpha12, alpha23,
508 useZ=useZ, eps=eps, datum=self.datum)
510 def pierlotx(self, point2, point3, alpha1, alpha2, alpha3, useZ=False):
511 '''3-Point resection between this and two other points using U{Pierlot
512 <http://www.Telecom.ULg.ac.Be/publi/publications/pierlot/Pierlot2014ANewThree>}'s
513 method C{ToTal} with I{exact} limits for the (pseudo-)singularities.
515 @arg point2: Second point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple},
516 C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}).
517 @arg point3: Third point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple},
518 C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}).
519 @arg alpha1: Angle at B{C{point1}} (C{degrees}).
520 @arg alpha2: Angle at B{C{point2}} (C{degrees}).
521 @arg alpha3: Angle at B{C{point3}} (C{degrees}).
522 @kwarg useZ: If C{True}, interpolate the survey point's Z component,
523 otherwise use C{z=INT0} (C{bool}).
525 @return: The survey (or robot) point, an instance of this (sub-)class.
527 @raise ResectionError: Near-coincident, -colinear or -concyclic points or
528 invalid B{C{alpha1}}, B{C{alpha2}} or B{C{alpha3}}.
530 @raise TypeError: Invalid B{C{point2}} or B{C{point3}}.
532 @see: Function L{pygeodesy.pierlotx} for references and more details.
533 '''
534 return _MODS.resections.pierlotx(self, point2, point3, alpha1, alpha2, alpha3,
535 useZ=useZ, datum=self.datum)
537 def Roc2(self, earth=None):
538 '''Compute this cartesian's I{normal} and I{pseudo, z-based} radius of curvature.
540 @kwarg earth: A datum, ellipsoid, triaxial ellipsoid or earth radius,
541 I{overriding} this cartesian's datum (L{Datum}, L{Ellipsoid},
542 L{Ellipsoid2}, L{a_f2Tuple} or C{meter}, conventionally).
544 @return: 2-Tuple C{(R, r)} with the I{normal} and I{pseudo, z-based} radius of
545 curvature C{R} respectively C{r}, both in C{meter} conventionally.
547 @raise TypeError: Invalid or undefined B{C{earth}} or C{datum}.
548 '''
549 r = z = fabs( self.z)
550 R, _0 = hypot(self.x, self.y), EPS0
551 if R < _0: # polar
552 R = z
553 elif z > _0: # non-equatorial
554 d = self.datum if earth is None else _spherical_datum(earth)
555 e = self.toLatLon(datum=d, height=0, LatLon=None) # Ecef9Tuple
556 M = e.M # EcefMatrix
557 sa, ca = map(fabs, (M._2_2_, M._2_1_) if M else sincos2d(e.lat))
558 if ca < _0: # polar
559 R = z
560 else: # prime-vertical, normal roc R
561 R = R / ca # /= chokes PyChecker
562 r = R if sa < _0 else (r / sa) # non-/equatorial
563 return R, r
565 @property_RO
566 def sphericalCartesian(self):
567 '''Get the C{Cartesian type} iff spherical, overloaded in L{CartesianSphericalBase}.
568 '''
569 return False
571 @deprecated_method
572 def tienstra(self, pointB, pointC, alpha, beta=None, gamma=None, useZ=False):
573 '''DEPRECATED, use method L{tienstra7}.'''
574 return self.tienstra7(pointB, pointC, alpha, beta=beta, gamma=gamma, useZ=useZ)
576 def tienstra7(self, pointB, pointC, alpha, beta=None, gamma=None, useZ=False):
577 '''3-Point resection between this and two other points using U{Tienstra
578 <https://WikiPedia.org/wiki/Tienstra_formula>}'s formula.
580 @arg pointB: Second point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple}, C{Vector4Tuple} or
581 C{Vector2Tuple} if C{B{useZ}=False}).
582 @arg pointC: Third point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple}, C{Vector4Tuple} or
583 C{Vector2Tuple} if C{B{useZ}=False}).
584 @arg alpha: Angle subtended by triangle side C{a} from B{C{pointB}} to B{C{pointC}} (C{degrees},
585 non-negative).
586 @kwarg beta: Angle subtended by triangle side C{b} from this to B{C{pointC}} (C{degrees},
587 non-negative) or C{None} if C{B{gamma} is not None}.
588 @kwarg gamma: Angle subtended by triangle side C{c} from this to B{C{pointB}} (C{degrees},
589 non-negative) or C{None} if C{B{beta} is not None}.
590 @kwarg useZ: If C{True}, use and interpolate the Z component, otherwise force C{z=INT0}
591 (C{bool}).
593 @note: This point, B{C{pointB}} and B{C{pointC}} are ordered clockwise.
595 @return: L{Tienstra7Tuple}C{(pointP, A, B, C, a, b, c)} with survey C{pointP},
596 an instance of this (sub-)class and triangle angle C{A} at this point,
597 C{B} at B{C{pointB}} and C{C} at B{C{pointC}} in C{degrees} and
598 triangle sides C{a}, C{b} and C{c}.
600 @raise ResectionError: Near-coincident, -colinear or -concyclic points or sum of
601 B{C{alpha}}, B{C{beta}} and B{C{gamma}} not C{360} or
602 negative B{C{alpha}}, B{C{beta}} or B{C{gamma}}.
604 @raise TypeError: Invalid B{C{pointB}} or B{C{pointC}}.
606 @see: Function L{pygeodesy.tienstra7} for references and more details.
607 '''
608 return _MODS.resections.tienstra7(self, pointB, pointC, alpha, beta, gamma,
609 useZ=useZ, datum=self.datum)
611 @deprecated_method
612 def to2ab(self): # PYCHOK no cover
613 '''DEPRECATED, use property C{philam}.
615 @return: A L{PhiLam2Tuple}C{(phi, lam)}.
616 '''
617 return self.philam
619 @deprecated_method
620 def to2ll(self): # PYCHOK no cover
621 '''DEPRECATED, use property C{latlon}.
623 @return: A L{LatLon2Tuple}C{(lat, lon)}.
624 '''
625 return self.latlon
627 @deprecated_method
628 def to3llh(self, datum=None): # PYCHOK no cover
629 '''DEPRECATED, use property L{latlonheight} or L{latlonheightdatum}.
631 @return: A L{LatLon4Tuple}C{(lat, lon, height, datum)}.
633 @note: This method returns a B{C{-4Tuple}} I{and not a} C{-3Tuple}
634 as its name may suggest.
635 '''
636 t = self.toLatLon(datum=datum, LatLon=None)
637 return LatLon4Tuple(t.lat, t.lon, t.height, t.datum, name=self.name)
639# def _to3LLh(self, datum, LL, **pairs): # OBSOLETE
640# '''(INTERNAL) Helper for C{subclass.toLatLon} and C{.to3llh}.
641# '''
642# r = self.to3llh(datum) # LatLon3Tuple
643# if LL is not None:
644# r = LL(r.lat, r.lon, height=r.height, datum=datum, name=self.name)
645# for n, v in pairs.items():
646# setattr(r, n, v)
647# return r
649 def toDatum(self, datum2, datum=None):
650 '''Convert this cartesian from one datum to an other.
652 @arg datum2: Datum to convert I{to} (L{Datum}).
653 @kwarg datum: Datum to convert I{from} (L{Datum}).
655 @return: The converted point (C{Cartesian}).
657 @raise TypeError: B{C{datum2}} or B{C{datum}}
658 invalid.
659 '''
660 _xinstanceof(Datum, datum2=datum2)
662 c = self if datum in (None, self.datum) else \
663 self.toDatum(datum)
665 i, d = False, c.datum
666 if d == datum2:
667 return c.copy() if c is self else c
669 elif d is None or (d.transform.isunity and
670 datum2.transform.isunity):
671 return c.dup(datum=datum2)
673 elif d == _WGS84:
674 d = datum2 # convert from WGS84 to datum2
676 elif datum2 == _WGS84:
677 i = True # convert to WGS84 by inverse transformation
679 else: # neither datum2 nor c.datum is WGS84, invert to WGS84 first
680 c = c.toTransform(d.transform, inverse=True, datum=_WGS84)
681 d = datum2
683 return c.toTransform(d.transform, inverse=i, datum=datum2)
685 def toEcef(self):
686 '''Convert this cartesian to I{geodetic} (lat-/longitude) coordinates.
688 @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)}
689 with C{C} and C{M} if available.
691 @raise EcefError: A C{.datum} or an ECEF issue.
692 '''
693 return self._ecef9
695 def toLatLon(self, datum=None, height=None, LatLon=None, **LatLon_kwds): # see .ecef.Ecef9Tuple.toDatum
696 '''Convert this cartesian to a I{geodetic} (lat-/longitude) point.
698 @kwarg datum: Optional datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}).
699 @kwarg height: Optional height, overriding the converted height (C{meter}), only if
700 C{B{LatLon} is not None}.
701 @kwarg LatLon: Optional class to return the geodetic point (C{LatLon}) or C{None}.
702 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments, ignored if
703 C{B{LatLon} is None}.
705 @return: The geodetic point (B{C{LatLon}}) or if C{B{LatLon}is None}, an
706 L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with C{C}
707 and C{M} if available.
709 @raise TypeError: Invalid B{C{datum}} or B{C{LatLon_kwds}}.
710 '''
711 d = _spherical_datum(datum or self.datum, name=self.name)
712 if d == self.datum:
713 r = self.toEcef()
714 else:
715 c = self.toDatum(d)
716 r = c.Ecef(d, name=self.name).reverse(c, M=LatLon is None)
718 if LatLon: # class or .classof
719 h = _heigHt(r, height)
720 r = LatLon(r.lat, r.lon, datum=r.datum, height=h,
721 **_xkwds(LatLon_kwds, name=r.name))
722 _xdatum(r.datum, d)
723 return r
725 def toNvector(self, Nvector=None, datum=None, **name_Nvector_kwds):
726 '''Convert this cartesian to C{n-vector} components, I{including height}.
728 @kwarg Nvector: Optional class to return the C{n-vector} components
729 (C{Nvector}) or C{None}.
730 @kwarg datum: Optional datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2}
731 or L{a_f2Tuple}) overriding this cartesian's datum.
732 @kwarg name_Nvector_kwds: Optional C{B{name}=NN} (C{str}) and optionally,
733 additional B{C{Nvector}} keyword arguments, ignored if
734 C{B{Nvector} is None}.
736 @return: An B{C{Nvector}} or a L{Vector4Tuple}C{(x, y, z, h)} if
737 C{B{Nvector} is None}.
739 @raise TypeError: Invalid B{C{Nvector}}, B{C{datum}} or
740 B{C{name_Nvector_kwds}} item.
742 @raise ValueError: B{C{Cartesian}} at origin.
743 '''
744 r, d = self._N_vector.xyzh, self.datum
745 if datum is not None:
746 d = _spherical_datum(datum, name=self.name)
747 if d != self.datum:
748 r = self._n_xyzh4(d)
750 if Nvector is None:
751 n, _ = _name2__(name_Nvector_kwds, _or_nameof=self)
752 if n:
753 r = r.dup(name=n)
754 else:
755 kwds = _xkwds(name_Nvector_kwds, h=r.h, datum=d)
756 r = Nvector(r.x, r.y, r.z, **self._name1__(kwds))
757 return r
759 def toRtp(self):
760 '''Convert this cartesian to I{spherical, polar} coordinates.
762 @return: L{RadiusThetaPhi3Tuple}C{(r, theta, phi)} with C{theta}
763 and C{phi}, both in L{Degrees}.
765 @see: Function L{xyz2rtp_} and class L{RadiusThetaPhi3Tuple}.
766 '''
767 return _rtp3(self.toRtp, Degrees, self, name=self.name)
769 def toStr(self, prec=3, fmt=Fmt.SQUARE, sep=_COMMASPACE_): # PYCHOK expected
770 '''Return the string representation of this cartesian.
772 @kwarg prec: Number of (decimal) digits, unstripped (C{int}).
773 @kwarg fmt: Enclosing backets format (C{letter}).
774 @kwarg sep: Separator to join (C{str}).
776 @return: Cartesian represented as "[x, y, z]" (C{str}).
777 '''
778 return Vector3d.toStr(self, prec=prec, fmt=fmt, sep=sep)
780 def toTransform(self, transform, inverse=False, datum=None):
781 '''Apply a Helmert transform to this cartesian.
783 @arg transform: Transform to apply (L{Transform} or L{TransformXform}).
784 @kwarg inverse: Apply the inverse of the C{B{transform}} (C{bool}).
785 @kwarg datum: Datum for the transformed cartesian (L{Datum}), overriding
786 this cartesian's datum but I{not} taken it into account.
788 @return: A transformed cartesian (C{Cartesian}) or a copy of this
789 cartesian if C{B{transform}.isunity}.
791 @raise TypeError: Invalid B{C{transform}}.
792 '''
793 _xinstanceof(Transform, transform=transform)
794 if transform.isunity:
795 c = self.dup(datum=datum or self.datum)
796 else:
797 # if inverse and d != _WGS84:
798 # raise _ValueError(inverse=inverse, datum=d,
799 # txt_not_=_WGS84.name)
800 xyz = transform.transform(*self.xyz3, inverse=inverse)
801 c = self.dup(xyz=xyz, datum=datum or self.datum)
802 return c
804 def toVector(self, Vector=None, **Vector_kwds):
805 '''Return this cartesian's I{geocentric} components as vector.
807 @kwarg Vector: Optional class to return the I{geocentric}
808 components (L{Vector3d}) or C{None}.
809 @kwarg Vector_kwds: Optional, additional B{C{Vector}} keyword
810 arguments, ignored if C{B{Vector} is None}.
812 @return: A B{C{Vector}} or a L{Vector3Tuple}C{(x, y, z)} if
813 C{B{Vector} is None}.
815 @raise TypeError: Invalid B{C{Vector}} or B{C{Vector_kwds}}.
816 '''
817 return self.xyz if Vector is None else Vector(
818 self.x, self.y, self.z, **self._name1__(Vector_kwds))
821class RadiusThetaPhi3Tuple(_NamedTupleTo):
822 '''3-Tuple C{(r, theta, phi)} with radial distance C{r} in C{meter}, inclination
823 C{theta} (with respect to the positive z-axis) and azimuthal angle C{phi} in
824 L{Degrees} I{or} L{Radians} representing a U{spherical, polar position
825 <https://WikiPedia.org/wiki/Spherical_coordinate_system>}.
826 '''
827 _Names_ = (_r_, _theta_, _phi_)
828 _Units_ = ( Meter, _Pass, _Pass)
830 def toCartesian(self, **name_Cartesian_and_kwds):
831 '''Convert this L{RadiusThetaPhi3Tuple} to a cartesian C{(x, y, z)} vector.
833 @kwarg name_Cartesian_and_kwds: Optional C{B{name}=NN}, overriding this
834 name and optional class C{B{Cartesian}=None} and additional
835 C{B{Cartesian}} keyword arguments.
837 @return: A C{B{Cartesian}(x, y, z)} instance or if no C{B{Cartesian}} keyword
838 argument is given, a L{Vector3Tuple}C{(x, y, z)} with C{x}, C{y}
839 and C{z} in the same units as radius C{r}, C{meter} conventionally.
841 @see: Function L{rtp2xyz_}.
842 '''
843 r, t, p = self
844 t, p, _ = _NamedTupleTo._Radians3(self, t, p)
845 return rtp2xyz_(r, t, p, **name_Cartesian_and_kwds)
847 def toDegrees(self, **name):
848 '''Convert this L{RadiusThetaPhi3Tuple}'s angles to L{Degrees}.
850 @kwarg name: Optional C{B{name}=NN} (C{str}), overriding this name.
852 @return: L{RadiusThetaPhi3Tuple}C{(r, theta, phi)} with C{theta}
853 and C{phi} both in L{Degrees}.
854 '''
855 return self._toX3U(_NamedTupleTo._Degrees3, Degrees, name)
857 def toRadians(self, **name):
858 '''Convert this L{RadiusThetaPhi3Tuple}'s angles to L{Radians}.
860 @kwarg name: Optional C{B{name}=NN} (C{str}), overriding this name.
862 @return: L{RadiusThetaPhi3Tuple}C{(r, theta, phi)} with C{theta}
863 and C{phi} both in L{Radians}.
864 '''
865 return self._toX3U(_NamedTupleTo._Radians3, Radians, name)
867 def _toU(self, U):
868 M = RadiusThetaPhi3Tuple._Units_[0] # Meter
869 return self.reUnit(M, U, U).toUnits()
871 def _toX3U(self, _X3, U, name):
872 r, t, p = self
873 t, p, s = _X3(self, t, p)
874 if s is None or name:
875 n = self._name__(name)
876 s = self.classof(r, t, p, name=n)._toU(U)
877 return s
880def rtp2xyz(r_rtp, theta=0, phi=0, **name_Cartesian_and_kwds):
881 '''Convert I{spherical, polar} C{(r, theta, phi)} to cartesian C{(x, y, z)} coordinates.
883 @arg theta: Inclination B{C{theta}} (C{degrees} with respect to the positive z-axis),
884 required if C{B{r_rtp}} is C{scalar}, ignored otherwise.
885 @arg phi: Azimuthal angle B{C{phi}} (C{degrees}), like B{C{theta}}.
887 @see: Function L{rtp2xyz_} for further details.
888 '''
889 if isinstance(r_rtp, RadiusThetaPhi3Tuple):
890 c = r_rtp.toCartesian(**name_Cartesian_and_kwds)
891 else:
892 c = rtp2xyz_(r_rtp, radians(theta), radians(phi), **name_Cartesian_and_kwds)
893 return c
896def rtp2xyz_(r_rtp, theta=0, phi=0, **name_Cartesian_and_kwds):
897 '''Convert I{spherical, polar} C{(r, theta, phi)} to cartesian C{(x, y, z)} coordinates.
899 @arg r_rtp: Radial distance (C{scalar}, conventially C{meter}) or a previous
900 L{RadiusThetaPhi3Tuple} instance.
901 @arg theta: Inclination B{C{theta}} (C{radians} with respect to the positive z-axis),
902 required if C{B{r_rtp}} is C{scalar}, ignored otherwise.
903 @arg phi: Azimuthal angle B{C{phi}} (C{radians}), like B{C{theta}}.
904 @kwarg name_Cartesian_and_kwds: Optional C{B{name}=NN} (C{str}), C{B{Cartesian}=None}
905 class to return the coordinates and optionally, additional C{B{Cartesian}}
906 keyword arguments.
908 @return: A C{B{Cartesian}(x, y, z)} instance or if no C{B{Cartesian}} keyword argument
909 is given a L{Vector3Tuple}C{(x, y, z)}, with C{x}, C{y} and C{z} in the same
910 units as radius C{r}, C{meter} conventionally.
912 @raise TypeError: Invalid B{C{r_rtp}}, B{C{theta}}, B{C{phi}} or
913 B{C{name_Cartesian_and_kwds}} item.
915 @see: U{Physics convention<https://WikiPedia.org/wiki/Spherical_coordinate_system>}
916 (ISO 80000-2:2019), class L{RadiusThetaPhi3Tuple} and functions L{rtp2xyz}
917 and L{xyz2rtp}.
918 '''
919 if isinstance(r_rtp, RadiusThetaPhi3Tuple):
920 c = r_rtp.toCartesian(**name_Cartesian_and_kwds)
921 elif _isMeter(r_rtp):
922 r = r_rtp
923 if r and _isfinite(r):
924 s, z, y, x = sincos2_(theta, phi)
925 s *= r
926 z *= r
927 y *= s
928 x *= s
929 else:
930 x = y = z = r
932 n, kwds = _name2__(**name_Cartesian_and_kwds)
933 C, kwds = _xkwds_pop2(kwds, Cartesian=None)
934 c = Vector3Tuple(x, y, z, name=n) if C is None else \
935 C(x, y, z, name=n, **kwds)
936 else:
937 raise _TypeError(r_rtp=r_rtp, theta=theta, phi=phi)
938 return c
941def _rtp3(where, U, *x_y_z, **name):
942 '''(INTERNAL) Helper for C{.toRtp}, C{xyz2rtp} and C{xyz2rtp_}.
943 '''
944 x, y, z = _MODS.vector3dBase._xyz3(where, *x_y_z)
945 r = hypot_(x, y, z)
946 if r > 0:
947 t = acos1(z / r)
948 p = atan2(y, x)
949 while p < 0:
950 p += PI2
951 if U is Degrees:
952 t = degrees(t)
953 p = degrees(p)
954 else:
955 t = p = _0_0
956 return RadiusThetaPhi3Tuple(r, t, p, **name)._toU(U)
959def xyz2rtp(x_xyz, y=0, z=0, **name):
960 '''Convert cartesian C{(x, y, z)} to I{spherical, polar} C{(r, theta, phi)} coordinates.
962 @return: L{RadiusThetaPhi3Tuple}C{(r, theta, phi)} with C{theta} and C{phi}, both
963 in L{Degrees}.
965 @see: Function L{xyz2rtp_} for further details.
966 '''
967 return _rtp3(xyz2rtp, Degrees, x_xyz, y, z, **name)
970def xyz2rtp_(x_xyz, y=0, z=0, **name):
971 '''Convert cartesian C{(x, y, z)} to I{spherical, polar} C{(r, theta, phi)} coordinates.
973 @arg x_xyz: X component (C{scalar}) or a cartesian (C{Cartesian}, L{Ecef9Tuple},
974 C{Nvector}, L{Vector3d}, L{Vector3Tuple}, L{Vector4Tuple} or a C{tuple} or
975 C{list} of 3+ C{scalar} items) if no C{y_z} specified.
976 @arg y: Y component (C{scalar}), required if C{B{x_xyz}} is C{scalar}, ignored otherwise.
977 @arg z: Z component (C{scalar}), like B{C{y}}.
978 @kwarg name: Optional C{B{name}=NN} (C{str}).
980 @return: L{RadiusThetaPhi3Tuple}C{(r, theta, phi)} with radial distance C{r} (C{meter},
981 same units as C{x}, C{y} and C{z}), inclination C{theta} (with respect to the
982 positive z-axis) and azimuthal angle C{phi}, both in L{Radians}.
984 @see: U{Physics convention<https://WikiPedia.org/wiki/Spherical_coordinate_system>}
985 (ISO 80000-2:2019), class L{RadiusThetaPhi3Tuple} and function L{xyz2rtp}.
986 '''
987 return _rtp3(xyz2rtp_, Radians, x_xyz, y, z, **name)
990__all__ += _ALL_DOCS(CartesianBase)
992# **) MIT License
993#
994# Copyright (C) 2016-2025 -- mrJean1 at Gmail -- All Rights Reserved.
995#
996# Permission is hereby granted, free of charge, to any person obtaining a
997# copy of this software and associated documentation files (the "Software"),
998# to deal in the Software without restriction, including without limitation
999# the rights to use, copy, modify, merge, publish, distribute, sublicense,
1000# and/or sell copies of the Software, and to permit persons to whom the
1001# Software is furnished to do so, subject to the following conditions:
1002#
1003# The above copyright notice and this permission notice shall be included
1004# in all copies or substantial portions of the Software.
1005#
1006# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
1007# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
1008# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
1009# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
1010# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
1011# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
1012# OTHER DEALINGS IN THE SOFTWARE.