Coverage for pygeodesy/cartesianBase.py: 92%
319 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'''
13from pygeodesy.basics import _isin, _xinstanceof, typename
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
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
24# from pygeodesy.internals import typename # from .basics
25from pygeodesy.interns import _COMMASPACE_, _datum_, _no_, _phi_
26from pygeodesy.interns import _ellipsoidal_, _spherical_ # PYCHOK used!
27from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS
28from pygeodesy.named import _name2__, _NamedLocal, _Pass
29from pygeodesy.namedTuples import LatLon4Tuple, _NamedTupleTo , Vector3Tuple, \
30 Vector4Tuple, Bearing2Tuple # PYCHOK .sphericalBase
31# from pygeodesy.nvectorBase import _N_vector # _MODS
32from pygeodesy.props import deprecated_method, Property, Property_RO, property_doc_, \
33 property_RO, _update_all
34# from pygeodesy import resections as _resections # _MODS.into
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__ = '25.04.21'
48_r_ = 'r'
49_resections = _MODS.into(resections=__name__)
50_theta_ = 'theta'
53class CartesianBase(Vector3d, _NamedLocal):
54 '''(INTERNAL) Base class for ellipsoidal and spherical C{Cartesian}.
55 '''
56 _datum = None # L{Datum}, to be overriden
57 _height = None # height (L{Height}), set or approximated
59 def __init__(self, x_xyz, y=None, z=None, datum=None, **ll_name):
60 '''New C{Cartesian...}.
62 @arg x_xyz: Cartesian X coordinate (C{scalar}) or a C{Cartesian},
63 L{Ecef9Tuple}, L{Vector3Tuple} or L{Vector4Tuple}.
64 @kwarg y: Cartesian Y coordinate (C{scalar}), ignored if B{C{x_xyz}}
65 is not C{scalar}, otherwise same units as B{C{x_xyz}}.
66 @kwarg z: Cartesian Z coordinate (C{scalar}), like B{C{y}}.
67 @kwarg datum: Optional datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2}
68 or L{a_f2Tuple}).
69 @kwarg ll_name: Optional C{B{name}=NN} (C{str}) and optional, original
70 latlon C{B{ll}=None} (C{LatLon}).
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, ll, n = _xyzhdlln4(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 _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 _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, **name_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}, L{Ned}
187 or L{Local9Tuple}).
188 @kwarg Cartesian: Optional (geocentric) class to return the destination
189 or C{None}.
190 @kwarg name_Cartesian_kwds: Optional C{B{name}=NN} (C{str}) and optionally,
191 additional B{C{Cartesian}} keyword arguments, ignored if
192 C{B{Cartesian} is None}.
194 @return: Destination as a C{B{Cartesian}(x, y, z, **B{Cartesian_kwds})}
195 instance or if C{B{Cartesian} is None}, an L{Ecef9Tuple}C{(x, y,
196 z, lat, lon, height, C, M, datum)} with C{M=None} always.
198 @raise TypeError: Invalid B{C{delta}}, B{C{Cartesian}} or B{C{Cartesian_kwds}}
199 item or C{datum} missing or incompatible.
200 '''
201 n, kwds = _name2__(name_Cartesian_kwds, _or_nameof=self)
202 if Cartesian is None:
203 r = self._Ltp._local2ecef(delta, nine=True)
204 else:
205 d = self.datum
206 if not d:
207 raise _TypeError(delta=delta, txt=_no_(_datum_))
208 t = _xkwds_get(kwds, datum=d)
209 if _xattr(t, ellipsoid=None) != d.ellipsoid:
210 raise _TypeError(datum=t, txt=str(d))
211 c = self._Ltp._local2ecef(delta, nine=False)
212 r = Cartesian(*c, **kwds)
213 return r.renamed(n) if n else r
215 @Property_RO
216 def _ecef9(self):
217 '''(INTERNAL) Helper for L{toEcef}, L{toLocal} and L{toLtp} (L{Ecef9Tuple}).
218 '''
219 return self.Ecef(self.datum, name=self.name).reverse(self, M=True)
221 @property_RO
222 def ellipsoidalCartesian(self):
223 '''Get the C{Cartesian type} iff ellipsoidal, overloaded in L{CartesianEllipsoidalBase}.
224 '''
225 return False
227 def hartzell(self, los=False, earth=None):
228 '''Compute the intersection of a Line-Of-Sight from this cartesian Point-Of-View
229 (pov) and this cartesian's C{datum} ellipsoid surface.
231 @kwarg los: Line-Of-Sight, I{direction} to the ellipsoid (L{Los}, L{Vector3d}),
232 C{True} for the I{normal, plumb} onto the surface or I{False} or
233 C{None} to point to the center of the ellipsoid.
234 @kwarg earth: The earth model (L{Datum}, L{Ellipsoid}, L{Ellipsoid2}, L{a_f2Tuple}
235 or C{scalar} radius in C{meter}), overriding this cartesian's
236 datum.
238 @return: The intersection (C{Cartesian}) with C{.height} set to the distance to
239 this C{pov}.
241 @raise IntersectionError: Null or bad C{pov} or B{C{los}}, this C{pov} is inside
242 the ellipsoid or B{C{los}} points outside or away from
243 the ellipsoid.
245 @raise TypeError: Invalid B{C{los}} or invalid or undefined B{C{earth}} or C{datum}.
247 @see: Function L{hartzell<pygeodesy.formy.hartzell>} for further details.
248 '''
249 return _MODS.formy._hartzell(self, los, earth)
251 @Property
252 def height(self):
253 '''Get the height (C{meter}).
254 '''
255 return self._height4.h if self._height is None else self._height
257 @height.setter # PYCHOK setter!
258 def height(self, height):
259 '''Set the height (C{meter}).
261 @raise TypeError: Invalid B{C{height}} C{type}.
263 @raise ValueError: Invalid B{C{height}}.
264 '''
265 h = Height(height)
266 if self._height != h:
267 _update_all(self)
268 self._height = h
270 def _height2C(self, r, Cartesian=None, datum=None, height=INT0, **kwds):
271 '''(INTERNAL) Helper for methods C{.height3} and C{.height4}.
272 '''
273 if Cartesian is not None:
274 r = Cartesian(r, **kwds)
275 if datum is not None:
276 r.datum = datum
277 if height is not None:
278 r.height = height # Height(height)
279 return r
281 def height3(self, earth=None, height=None, **Cartesian_and_kwds):
282 '''Compute the cartesian at a height above or below this certesian's
283 C{datum} ellipsoid surface.
285 @kwarg earth: A datum, ellipsoid, triaxial ellipsoid or earth radius,
286 I{overriding} this cartesian's datum (L{Datum}, L{Ellipsoid},
287 L{Ellipsoid2}, L{a_f2Tuple} or C{meter}, conventionally).
288 @kwarg height: The height (C{meter}, conventionally), overriding this
289 cartesian's height.
290 @kwarg Cartesian_and_kwds: Optional C{B{Cartesian}=None} class to return
291 the cartesian I{at height} and additional B{C{Cartesian}}
292 keyword arguments.
294 @return: An instance of B{C{Cartesian}} or if C{B{Cartesian} is None},
295 a L{Vector3Tuple}C{(x, y, z)} with the C{x}, C{y} and C{z}
296 coordinates I{at height} in C{meter}, conventionally.
298 @note: This cartesian's coordinates are returned if B{C{earth}} and this
299 datum or B{C{height}} and/or this height are C{None} or undefined.
301 @note: Include keyword argument C{B{datum}=None} if class B{C{Cartesian}}
302 does not accept a B{C{datum}} keyword agument.
304 @raise TriaxialError: No convergence in triaxial root finding.
306 @raise TypeError: Invalid or undefined B{C{earth}} or C{datum}.
307 '''
308 n = typename(self.height3)
309 d = self.datum if earth is None else _spherical_datum(earth, name=n)
310 c, h = self, _heigHt(self, height)
311 if h and d:
312 R, r = self.Roc2(earth=d)
313 if R > EPS0:
314 R = (R + h) / R
315 r = ((r + h) / r) if r > EPS0 else _1_0
316 c = c.times_(R, R, r)
318 r = Vector3Tuple(c.x, c.y, c.z, name=n)
319 if Cartesian_and_kwds:
320 r = self._height2C(r, **_xkwds(Cartesian_and_kwds, datum=d))
321 return r
323 @Property_RO
324 def _height4(self):
325 '''(INTERNAL) Get this C{height4}-tuple.
326 '''
327 try:
328 r = self.datum.ellipsoid.height4(self, normal=True)
329 except (AttributeError, ValueError): # no datum, null cartesian,
330 r = Vector4Tuple(self.x, self.y, self.z, 0, name__=self.height4)
331 return r
333 def height4(self, earth=None, normal=True, **Cartesian_and_kwds):
334 '''Compute the projection of this point on and the height above or below
335 this datum's ellipsoid surface.
337 @kwarg earth: A datum, ellipsoid, triaxial ellipsoid or earth radius,
338 I{overriding} this datum (L{Datum}, L{Ellipsoid},
339 L{Ellipsoid2}, L{a_f2Tuple}, L{Triaxial}, L{Triaxial_},
340 L{JacobiConformal} or C{meter}, conventionally).
341 @kwarg normal: If C{True}, the projection is the nearest point on the
342 ellipsoid's surface, otherwise the intersection of the
343 radial line to the ellipsoid's center and surface C{bool}).
344 @kwarg Cartesian_and_kwds: Optional C{B{Cartesian}=None} class to return
345 the I{projection} and additional B{C{Cartesian}} keyword
346 arguments.
348 @return: An instance of B{C{Cartesian}} or if C{B{Cartesian} is None}, a
349 L{Vector4Tuple}C{(x, y, z, h)} with the I{projection} C{x}, C{y}
350 and C{z} coordinates and height C{h} in C{meter}, conventionally.
352 @note: Include keyword argument C{B{datum}=None} if class B{C{Cartesian}}
353 does not accept a B{C{datum}} keyword agument.
355 @raise TriaxialError: No convergence in triaxial root finding.
357 @raise TypeError: Invalid or undefined B{C{earth}} or C{datum}.
359 @see: Methods L{Ellipsoid.height4} and L{Triaxial_.height4} for more information.
360 '''
361 n = typename(self.height4)
362 d = self.datum if earth is None else earth
363 if normal and d is self.datum:
364 r = self._height4
365 elif isinstance(d, _MODS.triaxials.Triaxial_):
366 r = d.height4(self, normal=normal)
367 try:
368 d = d.toEllipsoid(name=n)
369 except (TypeError, ValueError): # TriaxialError
370 d = None
371 else:
372 r = _earth_ellipsoid(d).height4(self, normal=normal)
374 if Cartesian_and_kwds:
375 if d and not isinstance(d, Datum):
376 d = _spherical_datum(d, name=n)
377 r = self._height2C(r, **_xkwds(Cartesian_and_kwds, datum=d))
378 return r
380 @Property_RO
381 def isEllipsoidal(self):
382 '''Check whether this cartesian is ellipsoidal (C{bool} or C{None} if unknown).
383 '''
384 return _xattr(self.datum, isEllipsoidal=None)
386 @Property_RO
387 def isSpherical(self):
388 '''Check whether this cartesian is spherical (C{bool} or C{None} if unknown).
389 '''
390 return _xattr(self.datum, isSpherical=None)
392 @Property_RO
393 def latlon(self):
394 '''Get this cartesian's (geodetic) lat- and longitude in C{degrees} (L{LatLon2Tuple}C{(lat, lon)}).
395 '''
396 return self.toEcef().latlon
398 @Property_RO
399 def latlonheight(self):
400 '''Get this cartesian's (geodetic) lat-, longitude in C{degrees} with height (L{LatLon3Tuple}C{(lat, lon, height)}).
401 '''
402 return self.toEcef().latlonheight
404 @Property_RO
405 def latlonheightdatum(self):
406 '''Get this cartesian's (geodetic) lat-, longitude in C{degrees} with height and datum (L{LatLon4Tuple}C{(lat, lon, height, datum)}).
407 '''
408 return self.toEcef().latlonheightdatum
410 @Property_RO
411 def _N_vector(self):
412 '''(INTERNAL) Get the (C{nvectorBase._N_vector_}).
413 '''
414 _N = _MODS.nvectorBase._N_vector_
415 x, y, z, h = self._n_xyzh4(self.datum)
416 return _N(x, y, z, h=h, name=self.name)
418 def _n_xyzh4(self, datum):
419 '''(INTERNAL) Get the n-vector components as L{Vector4Tuple}.
420 '''
421 def _ErrorEPS0(x):
422 return _ValueError(origin=self, txt=Fmt.PARENSPACED(EPS0=x))
424 _xinstanceof(Datum, datum=datum)
425 # <https://www.Movable-Type.co.UK/scripts/geodesy/docs/
426 # latlon-nvector-ellipsoidal.js.html#line309>,
427 # <https://GitHub.com/pbrod/nvector>/src/nvector/core.py>
428 # _equation23 and <https://www.NavLab.net/nvector>
429 E = datum.ellipsoid
430 x, y, z = self.xyz3
432 # Kenneth Gade eqn 23
433 p = hypot2(x, y) * E.a2_
434 q = z**2 * E.e21 * E.a2_
435 r = fsumf_(p, q, -E.e4) / _6_0
436 s = (p * q * E.e4) / (_4_0 * r**3)
437 t = cbrt(fsumf_(_1_0, s, sqrt(s * (_2_0 + s))))
438 if isnear0(t):
439 raise _ErrorEPS0(t)
440 u = fsumf_(_1_0, t, _1_0 / t) * r
441 v = sqrt(u**2 + E.e4 * q)
442 t = v * _2_0
443 if t < EPS0: # isnear0
444 raise _ErrorEPS0(t)
445 w = fsumf_(u, v, -q) * E.e2 / t
446 k = sqrt(fsumf_(u, v, w**2)) - w
447 if isnear0(k):
448 raise _ErrorEPS0(k)
449 t = k + E.e2
450 if isnear0(t):
451 raise _ErrorEPS0(t)
452 e = k / t
453# d = e * hypot(x, y)
454# tmp = 1 / hypot(d, z) == 1 / hypot(e * hypot(x, y), z)
455 t = hypot_(x * e, y * e, z) # == 1 / tmp
456 if t < EPS0: # isnear0
457 raise _ErrorEPS0(t)
458 h = fsumf_(k, E.e2, _N_1_0) / k * t
459 s = e / t # == e * tmp
460 return Vector4Tuple(x * s, y * s, z / t, h, name=self.name)
462 @Property_RO
463 def philam(self):
464 '''Get this cartesian's (geodetic) lat- and longitude in C{radians} (L{PhiLam2Tuple}C{(phi, lam)}).
465 '''
466 return self.toEcef().philam
468 @Property_RO
469 def philamheight(self):
470 '''Get this cartesian's (geodetic) lat-, longitude in C{radians} with height (L{PhiLam3Tuple}C{(phi, lam, height)}).
471 '''
472 return self.toEcef().philamheight
474 @Property_RO
475 def philamheightdatum(self):
476 '''Get this cartesian's (geodetic) lat-, longitude in C{radians} with height and datum (L{PhiLam4Tuple}C{(phi, lam, height, datum)}).
477 '''
478 return self.toEcef().philamheightdatum
480 def pierlot(self, point2, point3, alpha12, alpha23, useZ=False, eps=EPS):
481 '''3-Point resection between this and two other points using U{Pierlot
482 <http://www.Telecom.ULg.ac.Be/triangulation>}'s method C{ToTal} with
483 I{approximate} limits for the (pseudo-)singularities.
485 @arg point2: Second point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple},
486 C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}).
487 @arg point3: Third point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple},
488 C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}).
489 @arg alpha12: Angle subtended from this point to B{C{point2}} or
490 B{C{alpha2 - alpha}} (C{degrees}).
491 @arg alpha23: Angle subtended from B{C{point2}} to B{C{point3}} or
492 B{C{alpha3 - alpha2}} (C{degrees}).
493 @kwarg useZ: If C{True}, interpolate the Z component, otherwise use C{z=INT0}
494 (C{bool}).
495 @kwarg eps: Tolerance for C{cot} (pseudo-)singularities (C{float}).
497 @note: This point, B{C{point2}} and B{C{point3}} are ordered counter-clockwise.
499 @return: The survey (or robot) point, an instance of this (sub-)class.
501 @raise ResectionError: Near-coincident, -colinear or -concyclic points
502 or invalid B{C{alpha12}} or B{C{alpha23}}.
504 @raise TypeError: Invalid B{C{point2}} or B{C{point3}}.
506 @see: Function L{pygeodesy.pierlot} for references and more details.
507 '''
508 return _resections.pierlot(self, point2, point3, alpha12, alpha23,
509 useZ=useZ, eps=eps, datum=self.datum)
511 def pierlotx(self, point2, point3, alpha1, alpha2, alpha3, useZ=False):
512 '''3-Point resection between this and two other points using U{Pierlot
513 <http://www.Telecom.ULg.ac.Be/publi/publications/pierlot/Pierlot2014ANewThree>}'s
514 method C{ToTal} with I{exact} limits for the (pseudo-)singularities.
516 @arg point2: Second point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple},
517 C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}).
518 @arg point3: Third point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple},
519 C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}).
520 @arg alpha1: Angle at B{C{point1}} (C{degrees}).
521 @arg alpha2: Angle at B{C{point2}} (C{degrees}).
522 @arg alpha3: Angle at B{C{point3}} (C{degrees}).
523 @kwarg useZ: If C{True}, interpolate the survey point's Z component,
524 otherwise use C{z=INT0} (C{bool}).
526 @return: The survey (or robot) point, an instance of this (sub-)class.
528 @raise ResectionError: Near-coincident, -colinear or -concyclic points or
529 invalid B{C{alpha1}}, B{C{alpha2}} or B{C{alpha3}}.
531 @raise TypeError: Invalid B{C{point2}} or B{C{point3}}.
533 @see: Function L{pygeodesy.pierlotx} for references and more details.
534 '''
535 return _resections.pierlotx(self, point2, point3, alpha1, alpha2, alpha3,
536 useZ=useZ, datum=self.datum)
538 def Roc2(self, earth=None):
539 '''Compute this cartesian's I{normal} and I{pseudo, z-based} radius of curvature.
541 @kwarg earth: A datum, ellipsoid, triaxial ellipsoid or earth radius,
542 I{overriding} this cartesian's datum (L{Datum}, L{Ellipsoid},
543 L{Ellipsoid2}, L{a_f2Tuple} or C{meter}, conventionally).
545 @return: 2-Tuple C{(R, r)} with the I{normal} and I{pseudo, z-based} radius of
546 curvature C{R} respectively C{r}, both in C{meter} conventionally.
548 @raise TypeError: Invalid or undefined B{C{earth}} or C{datum}.
549 '''
550 r = z = fabs( self.z)
551 R, _0 = hypot(self.x, self.y), EPS0
552 if R < _0: # polar
553 R = z
554 elif z > _0: # non-equatorial
555 d = self.datum if earth is None else _spherical_datum(earth)
556 e = self.toLatLon(datum=d, height=0, LatLon=None) # Ecef9Tuple
557 M = e.M # EcefMatrix
558 sa, ca = map(fabs, (M._2_2_, M._2_1_) if M else sincos2d(e.lat))
559 if ca < _0: # polar
560 R = z
561 else: # prime-vertical, normal roc R
562 R = R / ca # /= chokes PyChecker
563 r = R if sa < _0 else (r / sa) # non-/equatorial
564 return R, r
566 @property_RO
567 def sphericalCartesian(self):
568 '''Get the C{Cartesian type} iff spherical, overloaded in L{CartesianSphericalBase}.
569 '''
570 return False
572 @deprecated_method
573 def tienstra(self, pointB, pointC, alpha, beta=None, gamma=None, useZ=False):
574 '''DEPRECATED, use method L{tienstra7}.'''
575 return self.tienstra7(pointB, pointC, alpha, beta=beta, gamma=gamma, useZ=useZ)
577 def tienstra7(self, pointB, pointC, alpha, beta=None, gamma=None, useZ=False):
578 '''3-Point resection between this and two other points using U{Tienstra
579 <https://WikiPedia.org/wiki/Tienstra_formula>}'s formula.
581 @arg pointB: Second point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple}, C{Vector4Tuple} or
582 C{Vector2Tuple} if C{B{useZ}=False}).
583 @arg pointC: Third point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple}, C{Vector4Tuple} or
584 C{Vector2Tuple} if C{B{useZ}=False}).
585 @arg alpha: Angle subtended by triangle side C{a} from B{C{pointB}} to B{C{pointC}} (C{degrees},
586 non-negative).
587 @kwarg beta: Angle subtended by triangle side C{b} from this to B{C{pointC}} (C{degrees},
588 non-negative) or C{None} if C{B{gamma} is not None}.
589 @kwarg gamma: Angle subtended by triangle side C{c} from this to B{C{pointB}} (C{degrees},
590 non-negative) or C{None} if C{B{beta} is not None}.
591 @kwarg useZ: If C{True}, use and interpolate the Z component, otherwise force C{z=INT0}
592 (C{bool}).
594 @note: This point, B{C{pointB}} and B{C{pointC}} are ordered clockwise.
596 @return: L{Tienstra7Tuple}C{(pointP, A, B, C, a, b, c)} with survey C{pointP},
597 an instance of this (sub-)class and triangle angle C{A} at this point,
598 C{B} at B{C{pointB}} and C{C} at B{C{pointC}} in C{degrees} and
599 triangle sides C{a}, C{b} and C{c}.
601 @raise ResectionError: Near-coincident, -colinear or -concyclic points or sum of
602 B{C{alpha}}, B{C{beta}} and B{C{gamma}} not C{360} or
603 negative B{C{alpha}}, B{C{beta}} or B{C{gamma}}.
605 @raise TypeError: Invalid B{C{pointB}} or B{C{pointC}}.
607 @see: Function L{pygeodesy.tienstra7} for references and more details.
608 '''
609 return _resections.tienstra7(self, pointB, pointC, alpha, beta, gamma,
610 useZ=useZ, datum=self.datum)
612 @deprecated_method
613 def to2ab(self): # PYCHOK no cover
614 '''DEPRECATED, use property C{philam}.
616 @return: A L{PhiLam2Tuple}C{(phi, lam)}.
617 '''
618 return self.philam
620 @deprecated_method
621 def to2ll(self): # PYCHOK no cover
622 '''DEPRECATED, use property C{latlon}.
624 @return: A L{LatLon2Tuple}C{(lat, lon)}.
625 '''
626 return self.latlon
628 @deprecated_method
629 def to3llh(self, datum=None): # PYCHOK no cover
630 '''DEPRECATED, use property L{latlonheight} or L{latlonheightdatum}.
632 @return: A L{LatLon4Tuple}C{(lat, lon, height, datum)}.
634 @note: This method returns a B{C{-4Tuple}} I{and not a} C{-3Tuple}
635 as its name may suggest.
636 '''
637 t = self.toLatLon(datum=datum, LatLon=None)
638 return LatLon4Tuple(t.lat, t.lon, t.height, t.datum, name=self.name)
640# def _to3LLh(self, datum, LL, **pairs): # OBSOLETE
641# '''(INTERNAL) Helper for C{subclass.toLatLon} and C{.to3llh}.
642# '''
643# r = self.to3llh(datum) # LatLon3Tuple
644# if LL is not None:
645# r = LL(r.lat, r.lon, height=r.height, datum=datum, name=self.name)
646# for n, v in pairs.items():
647# setattr(r, n, v)
648# return r
650 def toDatum(self, datum2, datum=None):
651 '''Convert this cartesian from one datum to an other.
653 @arg datum2: Datum to convert I{to} (L{Datum}).
654 @kwarg datum: Datum to convert I{from} (L{Datum}).
656 @return: The converted point (C{Cartesian}).
658 @raise TypeError: B{C{datum2}} or B{C{datum}}
659 invalid.
660 '''
661 _xinstanceof(Datum, datum2=datum2)
663 c = self if _isin(datum, None, self.datum) else \
664 self.toDatum(datum)
666 i, d = False, c.datum
667 if d == datum2:
668 return c.copy() if c is self else c
670 elif d is None or (d.transform.isunity and
671 datum2.transform.isunity):
672 return c.dup(datum=datum2)
674 elif d == _WGS84:
675 d = datum2 # convert from WGS84 to datum2
677 elif datum2 == _WGS84:
678 i = True # convert to WGS84 by inverse transformation
680 else: # neither datum2 nor c.datum is WGS84, invert to WGS84 first
681 c = c.toTransform(d.transform, inverse=True, datum=_WGS84)
682 d = datum2
684 return c.toTransform(d.transform, inverse=i, datum=datum2)
686 def toEcef(self):
687 '''Convert this cartesian to I{geodetic} (lat-/longitude) coordinates.
689 @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)}
690 with C{C} and C{M} if available.
692 @raise EcefError: A C{.datum} or an ECEF issue.
693 '''
694 return self._ecef9
696 def toLatLon(self, datum=None, height=None, LatLon=None, **LatLon_kwds): # see .ecef.Ecef9Tuple.toDatum
697 '''Convert this cartesian to a I{geodetic} (lat-/longitude) point.
699 @kwarg datum: Optional datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}).
700 @kwarg height: Optional height, overriding the converted height (C{meter}), only if
701 C{B{LatLon} is not None}.
702 @kwarg LatLon: Optional class to return the geodetic point (C{LatLon}) or C{None}.
703 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments, ignored if
704 C{B{LatLon} is None}.
706 @return: The geodetic point (B{C{LatLon}}) or if C{B{LatLon}is None}, an
707 L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with C{C}
708 and C{M} if available.
710 @raise TypeError: Invalid B{C{datum}} or B{C{LatLon_kwds}}.
711 '''
712 d = _spherical_datum(datum or self.datum, name=self.name)
713 if d == self.datum:
714 r = self.toEcef()
715 else:
716 c = self.toDatum(d)
717 r = c.Ecef(d, name=self.name).reverse(c, M=LatLon is None)
719 if LatLon: # class or .classof
720 h = _heigHt(r, height)
721 r = LatLon(r.lat, r.lon, datum=r.datum, height=h,
722 **_xkwds(LatLon_kwds, name=r.name))
723 _xdatum(r.datum, d)
724 return r
726 def toNvector(self, Nvector=None, datum=None, **name_Nvector_kwds):
727 '''Convert this cartesian to C{n-vector} components, I{including height}.
729 @kwarg Nvector: Optional class to return the C{n-vector} components
730 (C{Nvector}) or C{None}.
731 @kwarg datum: Optional datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2}
732 or L{a_f2Tuple}) overriding this cartesian's datum.
733 @kwarg name_Nvector_kwds: Optional C{B{name}=NN} (C{str}) and optionally,
734 additional B{C{Nvector}} keyword arguments, ignored if
735 C{B{Nvector} is None}.
737 @return: An B{C{Nvector}} or a L{Vector4Tuple}C{(x, y, z, h)} if
738 C{B{Nvector} is None}.
740 @raise TypeError: Invalid B{C{Nvector}}, B{C{datum}} or
741 B{C{name_Nvector_kwds}} item.
743 @raise ValueError: B{C{Cartesian}} at origin.
744 '''
745 r, d = self._N_vector.xyzh, self.datum
746 if datum is not None:
747 d = _spherical_datum(datum, name=self.name)
748 if d != self.datum:
749 r = self._n_xyzh4(d)
751 if Nvector is None:
752 n, _ = _name2__(name_Nvector_kwds, _or_nameof=self)
753 if n:
754 r = r.dup(name=n)
755 else:
756 kwds = _xkwds(name_Nvector_kwds, h=r.h, datum=d)
757 r = Nvector(r.x, r.y, r.z, **self._name1__(kwds))
758 return r
760 def toRtp(self):
761 '''Convert this cartesian to I{spherical, polar} coordinates.
763 @return: L{RadiusThetaPhi3Tuple}C{(r, theta, phi)} with C{theta}
764 and C{phi}, both in L{Degrees}.
766 @see: Function L{xyz2rtp_} and class L{RadiusThetaPhi3Tuple}.
767 '''
768 return _rtp3(self.toRtp, Degrees, self, name=self.name)
770 def toStr(self, prec=3, fmt=Fmt.SQUARE, sep=_COMMASPACE_): # PYCHOK expected
771 '''Return the string representation of this cartesian.
773 @kwarg prec: Number of (decimal) digits, unstripped (C{int}).
774 @kwarg fmt: Enclosing backets format (C{letter}).
775 @kwarg sep: Separator to join (C{str}).
777 @return: Cartesian represented as "[x, y, z]" (C{str}).
778 '''
779 return Vector3d.toStr(self, prec=prec, fmt=fmt, sep=sep)
781 def toTransform(self, transform, inverse=False, datum=None):
782 '''Apply a Helmert transform to this cartesian.
784 @arg transform: Transform to apply (L{Transform} or L{TransformXform}).
785 @kwarg inverse: Apply the inverse of the C{B{transform}} (C{bool}).
786 @kwarg datum: Datum for the transformed cartesian (L{Datum}), overriding
787 this cartesian's datum but I{not} taken it into account.
789 @return: A transformed cartesian (C{Cartesian}) or a copy of this
790 cartesian if C{B{transform}.isunity}.
792 @raise TypeError: Invalid B{C{transform}}.
793 '''
794 _xinstanceof(Transform, transform=transform)
795 if transform.isunity:
796 c = self.dup(datum=datum or self.datum)
797 else:
798 # if inverse and d != _WGS84:
799 # raise _ValueError(inverse=inverse, datum=d,
800 # txt_not_=_WGS84.name)
801 xyz = transform.transform(*self.xyz3, inverse=inverse)
802 c = self.dup(xyz=xyz, datum=datum or self.datum)
803 return c
805 def toVector(self, Vector=None, **Vector_kwds):
806 '''Return this cartesian's I{geocentric} components as vector.
808 @kwarg Vector: Optional class to return the I{geocentric}
809 components (L{Vector3d}) or C{None}.
810 @kwarg Vector_kwds: Optional, additional B{C{Vector}} keyword
811 arguments, ignored if C{B{Vector} is None}.
813 @return: A B{C{Vector}} or a L{Vector3Tuple}C{(x, y, z)} if
814 C{B{Vector} is None}.
816 @raise TypeError: Invalid B{C{Vector}} or B{C{Vector_kwds}}.
817 '''
818 return self.xyz if Vector is None else Vector(
819 self.x, self.y, self.z, **self._name1__(Vector_kwds))
822class RadiusThetaPhi3Tuple(_NamedTupleTo):
823 '''3-Tuple C{(r, theta, phi)} with radial distance C{r} in C{meter}, inclination
824 C{theta} (with respect to the positive z-axis) and azimuthal angle C{phi} in
825 L{Degrees} I{or} L{Radians} representing a U{spherical, polar position
826 <https://WikiPedia.org/wiki/Spherical_coordinate_system>}.
827 '''
828 _Names_ = (_r_, _theta_, _phi_)
829 _Units_ = ( Meter, _Pass, _Pass)
831 def toCartesian(self, **name_Cartesian_and_kwds):
832 '''Convert this L{RadiusThetaPhi3Tuple} to a cartesian C{(x, y, z)} vector.
834 @kwarg name_Cartesian_and_kwds: Optional C{B{name}=NN}, overriding this
835 name and optional class C{B{Cartesian}=None} and additional
836 C{B{Cartesian}} keyword arguments.
838 @return: A C{B{Cartesian}(x, y, z)} instance or if no C{B{Cartesian}} keyword
839 argument is given, a L{Vector3Tuple}C{(x, y, z)} with C{x}, C{y}
840 and C{z} in the same units as radius C{r}, C{meter} conventionally.
842 @see: Function L{rtp2xyz_}.
843 '''
844 r, t, p = self
845 t, p, _ = _NamedTupleTo._Radians3(self, t, p)
846 return rtp2xyz_(r, t, p, **name_Cartesian_and_kwds)
848 def toDegrees(self, **name):
849 '''Convert this L{RadiusThetaPhi3Tuple}'s angles to L{Degrees}.
851 @kwarg name: Optional C{B{name}=NN} (C{str}), overriding this name.
853 @return: L{RadiusThetaPhi3Tuple}C{(r, theta, phi)} with C{theta}
854 and C{phi} both in L{Degrees}.
855 '''
856 return self._toX3U(_NamedTupleTo._Degrees3, Degrees, name)
858 def toRadians(self, **name):
859 '''Convert this L{RadiusThetaPhi3Tuple}'s angles to L{Radians}.
861 @kwarg name: Optional C{B{name}=NN} (C{str}), overriding this name.
863 @return: L{RadiusThetaPhi3Tuple}C{(r, theta, phi)} with C{theta}
864 and C{phi} both in L{Radians}.
865 '''
866 return self._toX3U(_NamedTupleTo._Radians3, Radians, name)
868 def _toU(self, U):
869 M = RadiusThetaPhi3Tuple._Units_[0] # Meter
870 return self.reUnit(M, U, U).toUnits()
872 def _toX3U(self, _X3, U, name):
873 r, t, p = self
874 t, p, s = _X3(self, t, p)
875 if s is None or name:
876 n = self._name__(name)
877 s = self.classof(r, t, p, name=n)._toU(U)
878 return s
881def rtp2xyz(r_rtp, theta=0, phi=0, **name_Cartesian_and_kwds):
882 '''Convert I{spherical, polar} C{(r, theta, phi)} to cartesian C{(x, y, z)} coordinates.
884 @arg theta: Inclination B{C{theta}} (C{degrees} with respect to the positive z-axis),
885 required if C{B{r_rtp}} is C{scalar}, ignored otherwise.
886 @arg phi: Azimuthal angle B{C{phi}} (C{degrees}), like B{C{theta}}.
888 @see: Function L{rtp2xyz_} for further details.
889 '''
890 if isinstance(r_rtp, RadiusThetaPhi3Tuple):
891 c = r_rtp.toCartesian(**name_Cartesian_and_kwds)
892 else:
893 c = rtp2xyz_(r_rtp, radians(theta), radians(phi), **name_Cartesian_and_kwds)
894 return c
897def rtp2xyz_(r_rtp, theta=0, phi=0, **name_Cartesian_and_kwds):
898 '''Convert I{spherical, polar} C{(r, theta, phi)} to cartesian C{(x, y, z)} coordinates.
900 @arg r_rtp: Radial distance (C{scalar}, conventially C{meter}) or a previous
901 L{RadiusThetaPhi3Tuple} instance.
902 @arg theta: Inclination B{C{theta}} (C{radians} with respect to the positive z-axis),
903 required if C{B{r_rtp}} is C{scalar}, ignored otherwise.
904 @arg phi: Azimuthal angle B{C{phi}} (C{radians}), like B{C{theta}}.
905 @kwarg name_Cartesian_and_kwds: Optional C{B{name}=NN} (C{str}), C{B{Cartesian}=None}
906 class to return the coordinates and optionally, additional C{B{Cartesian}}
907 keyword arguments.
909 @return: A C{B{Cartesian}(x, y, z)} instance or if no C{B{Cartesian}} keyword argument
910 is given a L{Vector3Tuple}C{(x, y, z)}, with C{x}, C{y} and C{z} in the same
911 units as radius C{r}, C{meter} conventionally.
913 @raise TypeError: Invalid B{C{r_rtp}}, B{C{theta}}, B{C{phi}} or
914 B{C{name_Cartesian_and_kwds}} item.
916 @see: U{Physics convention<https://WikiPedia.org/wiki/Spherical_coordinate_system>}
917 (ISO 80000-2:2019), class L{RadiusThetaPhi3Tuple} and functions L{rtp2xyz}
918 and L{xyz2rtp}.
919 '''
920 if isinstance(r_rtp, RadiusThetaPhi3Tuple):
921 c = r_rtp.toCartesian(**name_Cartesian_and_kwds)
922 elif _isMeter(r_rtp):
923 r = r_rtp
924 if r and _isfinite(r):
925 s, z, y, x = sincos2_(theta, phi)
926 s *= r
927 z *= r
928 y *= s
929 x *= s
930 else:
931 x = y = z = r
933 n, kwds = _name2__(**name_Cartesian_and_kwds)
934 C, kwds = _xkwds_pop2(kwds, Cartesian=None)
935 c = Vector3Tuple(x, y, z, name=n) if C is None else \
936 C(x, y, z, name=n, **kwds)
937 else:
938 raise _TypeError(r_rtp=r_rtp, theta=theta, phi=phi)
939 return c
942def _rtp3(where, U, *x_y_z, **name):
943 '''(INTERNAL) Helper for C{.toRtp}, C{xyz2rtp} and C{xyz2rtp_}.
944 '''
945 x, y, z = _MODS.vector3dBase._xyz3(where, *x_y_z)
946 r = hypot_(x, y, z)
947 if r > 0:
948 t = acos1(z / r)
949 p = atan2(y, x)
950 while p < 0:
951 p += PI2
952 if U is Degrees:
953 t = degrees(t)
954 p = degrees(p)
955 else:
956 t = p = _0_0
957 return RadiusThetaPhi3Tuple(r, t, p, **name)._toU(U)
960def xyz2rtp(x_xyz, y=0, z=0, **name):
961 '''Convert cartesian C{(x, y, z)} to I{spherical, polar} C{(r, theta, phi)} coordinates.
963 @return: L{RadiusThetaPhi3Tuple}C{(r, theta, phi)} with C{theta} and C{phi}, both
964 in L{Degrees}.
966 @see: Function L{xyz2rtp_} for further details.
967 '''
968 return _rtp3(xyz2rtp, Degrees, x_xyz, y, z, **name)
971def xyz2rtp_(x_xyz, y=0, z=0, **name):
972 '''Convert cartesian C{(x, y, z)} to I{spherical, polar} C{(r, theta, phi)} coordinates.
974 @arg x_xyz: X component (C{scalar}) or a cartesian (C{Cartesian}, L{Ecef9Tuple},
975 C{Nvector}, L{Vector3d}, L{Vector3Tuple}, L{Vector4Tuple} or a C{tuple} or
976 C{list} of 3+ C{scalar} items) if no C{y_z} specified.
977 @arg y: Y component (C{scalar}), required if C{B{x_xyz}} is C{scalar}, ignored otherwise.
978 @arg z: Z component (C{scalar}), like B{C{y}}.
979 @kwarg name: Optional C{B{name}=NN} (C{str}).
981 @return: L{RadiusThetaPhi3Tuple}C{(r, theta, phi)} with radial distance C{r} (C{meter},
982 same units as C{x}, C{y} and C{z}), inclination C{theta} (with respect to the
983 positive z-axis) and azimuthal angle C{phi}, both in L{Radians}.
985 @see: U{Physics convention<https://WikiPedia.org/wiki/Spherical_coordinate_system>}
986 (ISO 80000-2:2019), class L{RadiusThetaPhi3Tuple} and function L{xyz2rtp}.
987 '''
988 return _rtp3(xyz2rtp_, Radians, x_xyz, y, z, **name)
991__all__ += _ALL_DOCS(CartesianBase)
993# **) MIT License
994#
995# Copyright (C) 2016-2025 -- mrJean1 at Gmail -- All Rights Reserved.
996#
997# Permission is hereby granted, free of charge, to any person obtaining a
998# copy of this software and associated documentation files (the "Software"),
999# to deal in the Software without restriction, including without limitation
1000# the rights to use, copy, modify, merge, publish, distribute, sublicense,
1001# and/or sell copies of the Software, and to permit persons to whom the
1002# Software is furnished to do so, subject to the following conditions:
1003#
1004# The above copyright notice and this permission notice shall be included
1005# in all copies or substantial portions of the Software.
1006#
1007# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
1008# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
1009# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
1010# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
1011# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
1012# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
1013# OTHER DEALINGS IN THE SOFTWARE.