Coverage for pygeodesy/cartesianBase.py: 94%
226 statements
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2# -*- coding: utf-8 -*-
4u'''(INTERNAL) Private base classes for elliposiodal, spherical and N-/vectorial
5C{Cartesian}s.
7After I{(C) Chris Veness 2011-2015} published under the same MIT Licence**,
8see U{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, isnear0, _1_0, _N_1_0, \
15 _2_0, _4_0, _6_0
16from pygeodesy.datums import Datum, _earth_ellipsoid, _spherical_datum, \
17 _WGS84, _xinstanceof
18from pygeodesy.errors import _IsnotError, _ValueError, _xdatum, _xkwds
19from pygeodesy.fmath import cbrt, hypot_, hypot2, sqrt # hypot
20from pygeodesy.fsums import Fmt, fsumf_
21from pygeodesy.interns import NN, _COMMASPACE_, _height_, _not_
22from pygeodesy.interns import _ellipsoidal_, _spherical_ # PYCHOK used!
23from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS
24from pygeodesy.namedTuples import LatLon4Tuple, Vector4Tuple, \
25 Bearing2Tuple # PYCHOK .sphericalBase
26from pygeodesy.props import deprecated_method, Property, Property_RO, \
27 property_doc_, property_RO, _update_all
28# from pygeodesy.resections import cassini, collins5, pierlot, tienstra7
29# from pygeodesy.streprs import Fmt # from .fsums
30from pygeodesy.units import Height, _heigHt
31from pygeodesy.vector3d import Vector3d, _xyzhdn3
33# from math import sqrt # from .fmath
35__all__ = _ALL_LAZY.cartesianBase
36__version__ = '23.12.18'
39class CartesianBase(Vector3d):
40 '''(INTERNAL) Base class for ellipsoidal and spherical C{Cartesian}.
41 '''
42 _datum = None # L{Datum}, to be overriden
43 _height = None # height (L{Height}), set or approximated
45 def __init__(self, x_xyz, y=None, z=None, datum=None, ll=None, name=NN):
46 '''New C{Cartesian...}.
48 @arg x_xyz: Cartesian X coordinate (C{scalar}) or a C{Cartesian},
49 L{Ecef9Tuple}, L{Vector3Tuple} or L{Vector4Tuple}.
50 @kwarg y: Cartesian Y coordinate (C{scalar}), ignored if B{C{x_xyz}}
51 is not C{scalar}, otherwise same units as B{C{x_xyz}}.
52 @kwarg z: Cartesian Z coordinate (C{scalar}), ignored if B{C{x_xyz}}
53 is not C{scalar}, otherwise same units as B{C{x_xyz}}.
54 @kwarg datum: Optional datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2}
55 or L{a_f2Tuple}).
56 @kwarg ll: Optional, original latlon (C{LatLon}).
57 @kwarg name: Optional name (C{str}).
59 @raise TypeError: Non-scalar B{C{x_xyz}}, B{C{y}} or B{C{z}}
60 coordinate or B{C{x_xyz}} not an L{Ecef9Tuple},
61 L{Vector3Tuple} or L{Vector4Tuple}.
62 '''
63 h, d, n = _xyzhdn3(x_xyz, None, datum, ll)
64 Vector3d.__init__(self, x_xyz, y=y, z=z, ll=ll, name=name or n)
65 if h is not None:
66 self._height = Height(h)
67 if d is not None:
68 self.datum = d
70# def __matmul__(self, other): # PYCHOK Python 3.5+
71# '''Return C{NotImplemented} for C{c_ = c @ datum} and C{c_ = c @ transform}.
72# '''
73# return NotImplemented if isinstance(other, (Datum, Transform)) else \
74# _NotImplemented(self, other)
76 def cassini(self, pointB, pointC, alpha, beta, useZ=False):
77 '''3-Point resection between this and 2 other points using U{Cassini
78 <https://NL.WikiPedia.org/wiki/Achterwaartse_insnijding>}'s method.
80 @arg pointB: Second point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple},
81 C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}).
82 @arg pointC: Center point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple},
83 C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}).
84 @arg alpha: Angle subtended by triangle side C{b} from B{C{pointA}} to
85 B{C{pointC}} (C{degrees}, non-negative).
86 @arg beta: Angle subtended by triangle side C{a} from B{C{pointB}} to
87 B{C{pointC}} (C{degrees}, non-negative).
88 @kwarg useZ: If C{True}, use and interpolate the Z component, otherwise
89 force C{z=INT0} (C{bool}).
91 @note: Typically, B{C{pointC}} is between this and B{C{pointB}}.
93 @return: The survey point, an instance of this (sub-)class.
95 @raise ResectionError: Near-coincident, -colinear or -concyclic points
96 or negative or invalid B{C{alpha}} or B{C{beta}}.
98 @raise TypeError: Invalid B{C{pointA}}, B{C{pointB}} or B{C{pointM}}.
100 @see: Function L{pygeodesy.cassini} for references and more details.
101 '''
102 return self._resections.cassini(self, pointB, pointC, alpha, beta,
103 useZ=useZ, datum=self.datum)
105 @deprecated_method
106 def collins(self, pointB, pointC, alpha, beta, useZ=False):
107 '''DEPRECATED, use method L{collins5}.'''
108 return self.collins5(pointB, pointC, alpha, beta, useZ=useZ)
110 def collins5(self, pointB, pointC, alpha, beta, useZ=False):
111 '''3-Point resection between this and 2 other points using U{Collins<https://Dokumen.tips/
112 documents/three-point-resection-problem-introduction-kaestner-burkhardt-method.html>}' method.
114 @arg pointB: Second point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple},
115 C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}).
116 @arg pointC: Center point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple},
117 C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}).
118 @arg alpha: Angle subtended by triangle side C{b} from B{C{pointA}} to
119 B{C{pointC}} (C{degrees}, non-negative).
120 @arg beta: Angle subtended by triangle side C{a} from B{C{pointB}} to
121 B{C{pointC}} (C{degrees}, non-negative).
122 @kwarg useZ: If C{True}, use and interpolate the Z component, otherwise
123 force C{z=INT0} (C{bool}).
125 @note: Typically, B{C{pointC}} is between this and B{C{pointB}}.
127 @return: L{Collins5Tuple}C{(pointP, pointH, a, b, c)} with survey C{pointP},
128 auxiliary C{pointH}, each an instance of this (sub-)class and
129 triangle sides C{a}, C{b} and C{c}.
131 @raise ResectionError: Near-coincident, -colinear or -concyclic points
132 or negative or invalid B{C{alpha}} or B{C{beta}}.
134 @raise TypeError: Invalid B{C{pointB}} or B{C{pointM}}.
136 @see: Function L{pygeodesy.collins5} for references and more details.
137 '''
138 return self._resections.collins5(self, pointB, pointC, alpha, beta,
139 useZ=useZ, datum=self.datum)
141 @deprecated_method
142 def convertDatum(self, datum2, **datum):
143 '''DEPRECATED, use method L{toDatum}.'''
144 return self.toDatum(datum2, **datum)
146 @property_doc_(''' this cartesian's datum (L{Datum}).''')
147 def datum(self):
148 '''Get this cartesian's datum (L{Datum}).
149 '''
150 return self._datum
152 @datum.setter # PYCHOK setter!
153 def datum(self, datum):
154 '''Set this cartesian's C{datum} I{without conversion}
155 (L{Datum}), ellipsoidal or spherical.
157 @raise TypeError: The B{C{datum}} is not a L{Datum}.
158 '''
159 d = _spherical_datum(datum, name=self.name)
160 if self._datum: # is not None
161 if d.isEllipsoidal and not self._datum.isEllipsoidal:
162 raise _IsnotError(_ellipsoidal_, datum=datum)
163 elif d.isSpherical and not self._datum.isSpherical:
164 raise _IsnotError(_spherical_, datum=datum)
165 if self._datum != d:
166 _update_all(self)
167 self._datum = d
169 def destinationXyz(self, delta, Cartesian=None, **Cartesian_kwds):
170 '''Calculate the destination using a I{local} delta from this cartesian.
172 @arg delta: Local delta to the destination (L{XyzLocal}, L{Enu},
173 L{Ned} or L{Local9Tuple}).
174 @kwarg Cartesian: Optional (geocentric) class to return the
175 destination or C{None}.
176 @kwarg Cartesian_kwds: Optional, additional B{C{Cartesian}} keyword
177 arguments, ignored if C{B{Cartesian} is None}.
179 @return: Destination as a C{B{Cartesian}(x, y, z, **B{Cartesian_kwds})}
180 instance or if C{B{Cartesian} is None}, an L{Ecef9Tuple}C{(x, y,
181 z, lat, lon, height, C, M, datum)} with C{M=None} always.
183 @raise TypeError: Invalid B{C{delta}}, B{C{Cartesian}} or
184 B{C{Cartesian_kwds}}.
185 '''
186 if Cartesian is None:
187 r = self._Ltp._local2ecef(delta, nine=True)
188 else:
189 r = self._Ltp._local2ecef(delta, nine=False)
190 r = Cartesian(*r, **_xkwds(Cartesian_kwds, datum=self.datum))
191 return r._xnamed(r) if self.name else r
193 @property_RO
194 def Ecef(self):
195 '''Get the ECEF I{class} (L{EcefKarney}), I{once}.
196 '''
197 CartesianBase.Ecef = E = _MODS.ecef.EcefKarney # overwrite property_RO
198 return E
200 @Property_RO
201 def _ecef9(self):
202 '''(INTERNAL) Helper for L{toEcef}, L{toLocal} and L{toLtp} (L{Ecef9Tuple}).
203 '''
204 return self.Ecef(self.datum, name=self.name).reverse(self, M=True)
206 @property_RO
207 def ellipsoidalCartesian(self):
208 '''Get the C{Cartesian type} iff ellipsoidal, overloaded in L{CartesianEllipsoidalBase}.
209 '''
210 return False
212 def hartzell(self, los=None, earth=None):
213 '''Compute the intersection of a Line-Of-Sight (los) from this cartesian
214 Point-Of-View (pov) with this cartesian's ellipsoid surface.
216 @kwarg los: Line-Of-Sight, I{direction} to earth (L{Los}, L{Vector3d})
217 or C{None} to point to the ellipsoid's center.
218 @kwarg earth: The earth model (L{Datum}, L{Ellipsoid}, L{Ellipsoid2},
219 L{a_f2Tuple} or C{scalar} radius in C{meter}) overriding
220 this cartesian's C{datum} ellipsoid.
222 @return: The ellipsoid intersection (C{Cartesian}) with C{.height} set
223 to the distance to this C{pov}.
225 @raise IntersectionError: Null or bad C{pov} or B{C{los}}, this C{pov}
226 is inside the ellipsoid or B{C{los}} points
227 outside or away from the ellipsoid.
229 @raise TypeError: Invalid B{C{los}} or no B{C{datum}}.
231 @see: Function C{hartzell} for further details.
232 '''
233 return _MODS.formy._hartzell(self, los, earth)
235 @Property
236 def height(self):
237 '''Get the height (C{meter}).
238 '''
239 return self._height4.h if self._height is None else self._height
241 @height.setter # PYCHOK setter!
242 def height(self, height):
243 '''Set the height (C{meter}).
245 @raise TypeError: Invalid B{C{height}} C{type}.
247 @raise ValueError: Invalid B{C{height}}.
248 '''
249 h = Height(height)
250 if self._height != h:
251 _update_all(self)
252 self._height = h
254 @Property_RO
255 def _height4(self):
256 '''(INTERNAL) Get this C{height4}-tuple.
257 '''
258 try:
259 r = self.datum.ellipsoid.height4(self, normal=True)
260 except (AttributeError, ValueError): # no datum, null cartesian,
261 r = Vector4Tuple(self.x, self.y, self.z, 0, name=self.height4.__name__)
262 return r
264 def height4(self, earth=None, normal=True, Cartesian=None, **Cartesian_kwds):
265 '''Compute the height of this cartesian above or below and the projection
266 on this datum's ellipsoid surface.
268 @kwarg earth: A datum, ellipsoid, triaxial ellipsoid or earth radius
269 I{overriding} this datum (L{Datum}, L{Ellipsoid},
270 L{Ellipsoid2}, L{a_f2Tuple}, L{Triaxial}, L{Triaxial_},
271 L{JacobiConformal} or C{meter}, conventionally).
272 @kwarg normal: If C{True} the projection is the nearest point on the
273 ellipsoid's surface, otherwise the intersection of the
274 radial line to the center and the ellipsoid's surface.
275 @kwarg Cartesian: Optional class to return the height and projection
276 (C{Cartesian}) or C{None}.
277 @kwarg Cartesian_kwds: Optional, additional B{C{Cartesian}} keyword
278 arguments, ignored if C{B{Cartesian} is None}.
280 @note: Use keyword argument C{height=0} to override C{B{Cartesian}.height}
281 to {0} or any other C{scalar}, conventionally in C{meter}.
283 @return: An instance of B{C{Cartesian}} or if C{B{Cartesian} is None}, a
284 L{Vector4Tuple}C{(x, y, z, h)} with the I{projection} C{x}, C{y}
285 and C{z} coordinates and height C{h} in C{meter}, conventionally.
287 @raise TriaxialError: No convergence in triaxial root finding.
289 @raise TypeError: Invalid B{C{earth}}.
291 @see: L{Ellipsoid.height4} and L{Triaxial_.height4} for more information.
292 '''
293 d = self.datum if earth is None else earth
294 if normal and d is self.datum:
295 r = self._height4
296 elif isinstance(d, _MODS.triaxials.Triaxial_):
297 r = d.height4(self, normal=normal)
298 else:
299 r = _earth_ellipsoid(d).height4(self, normal=normal)
300 if Cartesian is not None:
301 kwds = Cartesian_kwds.copy()
302 h = kwds.pop(_height_, None)
303 r = Cartesian(r, **kwds)
304 if h is not None:
305 r.height = Height(height=h)
306 return r
308 @Property_RO
309 def isEllipsoidal(self):
310 '''Check whether this cartesian is ellipsoidal (C{bool} or C{None} if unknown).
311 '''
312 return self.datum.isEllipsoidal if self._datum else None
314 @Property_RO
315 def isSpherical(self):
316 '''Check whether this cartesian is spherical (C{bool} or C{None} if unknown).
317 '''
318 return self.datum.isSpherical if self._datum else None
320 @Property_RO
321 def latlon(self):
322 '''Get this cartesian's (geodetic) lat- and longitude in C{degrees} (L{LatLon2Tuple}C{(lat, lon)}).
323 '''
324 return self.toEcef().latlon
326 @Property_RO
327 def latlonheight(self):
328 '''Get this cartesian's (geodetic) lat-, longitude in C{degrees} with height (L{LatLon3Tuple}C{(lat, lon, height)}).
329 '''
330 return self.toEcef().latlonheight
332 @Property_RO
333 def latlonheightdatum(self):
334 '''Get this cartesian's (geodetic) lat-, longitude in C{degrees} with height and datum (L{LatLon4Tuple}C{(lat, lon, height, datum)}).
335 '''
336 return self.toEcef().latlonheightdatum
338 @property_RO
339 def _ltp(self):
340 '''(INTERNAL) Get module C{.ltp}, I{once}.
341 '''
342 CartesianBase._ltp = m = _MODS.ltp # overwrite property_RO
343 return m
345 @Property_RO
346 def _Ltp(self):
347 '''(INTERNAL) Cache for L{toLtp}.
348 '''
349 return self._ltp.Ltp(self._ecef9, ecef=self.Ecef(self.datum), name=self.name)
351 @Property_RO
352 def _N_vector(self):
353 '''(INTERNAL) Get the (C{nvectorBase._N_vector_}).
354 '''
355 m = _MODS.nvectorBase
356 x, y, z, h = self._n_xyzh4(self.datum)
357 return m._N_vector_(x, y, z, h=h, name=self.name)
359 def _n_xyzh4(self, datum):
360 '''(INTERNAL) Get the n-vector components as L{Vector4Tuple}.
361 '''
362 def _ErrorEPS0(x):
363 return _ValueError(origin=self, txt=Fmt.PARENSPACED(EPS0=x))
365 _xinstanceof(Datum, datum=datum)
366 # <https://www.Movable-Type.co.UK/scripts/geodesy/docs/
367 # latlon-nvector-ellipsoidal.js.html#line309>,
368 # <https://GitHub.com/pbrod/nvector>/src/nvector/core.py>
369 # _equation23 and <https://www.NavLab.net/nvector>
370 E = datum.ellipsoid
371 x, y, z = self.xyz
373 # Kenneth Gade eqn 23
374 p = hypot2(x, y) * E.a2_
375 q = z**2 * E.e21 * E.a2_
376 r = fsumf_(p, q, -E.e4) / _6_0
377 s = (p * q * E.e4) / (_4_0 * r**3)
378 t = cbrt(fsumf_(_1_0, s, sqrt(s * (_2_0 + s))))
379 if isnear0(t):
380 raise _ErrorEPS0(t)
381 u = fsumf_(_1_0, t, _1_0 / t) * r
382 v = sqrt(u**2 + E.e4 * q)
383 t = v * _2_0
384 if t < EPS0: # isnear0
385 raise _ErrorEPS0(t)
386 w = fsumf_(u, v, -q) * E.e2 / t
387 k = sqrt(fsumf_(u, v, w**2)) - w
388 if isnear0(k):
389 raise _ErrorEPS0(k)
390 t = k + E.e2
391 if isnear0(t):
392 raise _ErrorEPS0(t)
393 e = k / t
394# d = e * hypot(x, y)
395# tmp = 1 / hypot(d, z) == 1 / hypot(e * hypot(x, y), z)
396 t = hypot_(x * e, y * e, z) # == 1 / tmp
397 if t < EPS0: # isnear0
398 raise _ErrorEPS0(t)
399 h = fsumf_(k, E.e2, _N_1_0) / k * t
400 s = e / t # == e * tmp
401 return Vector4Tuple(x * s, y * s, z / t, h, name=self.name)
403 @Property_RO
404 def philam(self):
405 '''Get this cartesian's (geodetic) lat- and longitude in C{radians} (L{PhiLam2Tuple}C{(phi, lam)}).
406 '''
407 return self.toEcef().philam
409 @Property_RO
410 def philamheight(self):
411 '''Get this cartesian's (geodetic) lat-, longitude in C{radians} with height (L{PhiLam3Tuple}C{(phi, lam, height)}).
412 '''
413 return self.toEcef().philamheight
415 @Property_RO
416 def philamheightdatum(self):
417 '''Get this cartesian's (geodetic) lat-, longitude in C{radians} with height and datum (L{PhiLam4Tuple}C{(phi, lam, height, datum)}).
418 '''
419 return self.toEcef().philamheightdatum
421 def pierlot(self, point2, point3, alpha12, alpha23, useZ=False, eps=EPS):
422 '''3-Point resection between this and two other points using U{Pierlot
423 <http://www.Telecom.ULg.ac.Be/triangulation>}'s method C{ToTal} with
424 I{approximate} limits for the (pseudo-)singularities.
426 @arg point2: Second point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple},
427 C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}).
428 @arg point3: Third point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple},
429 C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}).
430 @arg alpha12: Angle subtended from this point to B{C{point2}} or
431 B{C{alpha2 - alpha}} (C{degrees}).
432 @arg alpha23: Angle subtended from B{C{point2}} to B{C{point3}} or
433 B{C{alpha3 - alpha2}} (C{degrees}).
434 @kwarg useZ: If C{True}, interpolate the Z component, otherwise use C{z=INT0}
435 (C{bool}).
436 @kwarg eps: Tolerance for C{cot} (pseudo-)singularities (C{float}).
438 @note: This point, B{C{point2}} and B{C{point3}} are ordered counter-clockwise.
440 @return: The survey (or robot) point, an instance of this (sub-)class.
442 @raise ResectionError: Near-coincident, -colinear or -concyclic points
443 or invalid B{C{alpha12}} or B{C{alpha23}}.
445 @raise TypeError: Invalid B{C{point2}} or B{C{point3}}.
447 @see: Function L{pygeodesy.pierlot} for references and more details.
448 '''
449 return self._resections.pierlot(self, point2, point3, alpha12, alpha23,
450 useZ=useZ, eps=eps, datum=self.datum)
452 def pierlotx(self, point2, point3, alpha1, alpha2, alpha3, useZ=False):
453 '''3-Point resection between this and two other points using U{Pierlot
454 <http://www.Telecom.ULg.ac.Be/publi/publications/pierlot/Pierlot2014ANewThree>}'s
455 method C{ToTal} with I{exact} limits for the (pseudo-)singularities.
457 @arg point2: Second point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple},
458 C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}).
459 @arg point3: Third point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple},
460 C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}).
461 @arg alpha1: Angle at B{C{point1}} (C{degrees}).
462 @arg alpha2: Angle at B{C{point2}} (C{degrees}).
463 @arg alpha3: Angle at B{C{point3}} (C{degrees}).
464 @kwarg useZ: If C{True}, interpolate the survey point's Z component,
465 otherwise use C{z=INT0} (C{bool}).
467 @return: The survey (or robot) point, an instance of this (sub-)class.
469 @raise ResectionError: Near-coincident, -colinear or -concyclic points or
470 invalid B{C{alpha1}}, B{C{alpha2}} or B{C{alpha3}}.
472 @raise TypeError: Invalid B{C{point2}} or B{C{point3}}.
474 @see: Function L{pygeodesy.pierlotx} for references and more details.
475 '''
476 return self._resections.pierlotx(self, point2, point3, alpha1, alpha2, alpha3,
477 useZ=useZ, datum=self.datum)
479 @property_RO
480 def _resections(self):
481 '''(INTERNAL) Import the C{.resections} module, I{once}.
482 '''
483 CartesianBase._resections = m = _MODS.resections # overwrite property_RO
484 return m
486 @property_RO
487 def sphericalCartesian(self):
488 '''Get the C{Cartesian type} iff spherical, overloaded in L{CartesianSphericalBase}.
489 '''
490 return False
492 @deprecated_method
493 def tienstra(self, pointB, pointC, alpha, beta=None, gamma=None, useZ=False):
494 '''DEPRECATED, use method L{tienstra7}.'''
495 return self.tienstra7(pointB, pointC, alpha, beta=beta, gamma=gamma, useZ=useZ)
497 def tienstra7(self, pointB, pointC, alpha, beta=None, gamma=None, useZ=False):
498 '''3-Point resection between this and two other points using U{Tienstra
499 <https://WikiPedia.org/wiki/Tienstra_formula>}'s formula.
501 @arg pointB: Second point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple}, C{Vector4Tuple} or
502 C{Vector2Tuple} if C{B{useZ}=False}).
503 @arg pointC: Third point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple}, C{Vector4Tuple} or
504 C{Vector2Tuple} if C{B{useZ}=False}).
505 @arg alpha: Angle subtended by triangle side C{a} from B{C{pointB}} to B{C{pointC}} (C{degrees},
506 non-negative).
507 @kwarg beta: Angle subtended by triangle side C{b} from this to B{C{pointC}} (C{degrees},
508 non-negative) or C{None} if C{B{gamma} is not None}.
509 @kwarg gamma: Angle subtended by triangle side C{c} from this to B{C{pointB}} (C{degrees},
510 non-negative) or C{None} if C{B{beta} is not None}.
511 @kwarg useZ: If C{True}, use and interpolate the Z component, otherwise force C{z=INT0}
512 (C{bool}).
514 @note: This point, B{C{pointB}} and B{C{pointC}} are ordered clockwise.
516 @return: L{Tienstra7Tuple}C{(pointP, A, B, C, a, b, c)} with survey C{pointP},
517 an instance of this (sub-)class and triangle angle C{A} at this point,
518 C{B} at B{C{pointB}} and C{C} at B{C{pointC}} in C{degrees} and
519 triangle sides C{a}, C{b} and C{c}.
521 @raise ResectionError: Near-coincident, -colinear or -concyclic points or sum of
522 B{C{alpha}}, B{C{beta}} and B{C{gamma}} not C{360} or
523 negative B{C{alpha}}, B{C{beta}} or B{C{gamma}}.
525 @raise TypeError: Invalid B{C{pointB}} or B{C{pointC}}.
527 @see: Function L{pygeodesy.tienstra7} for references and more details.
528 '''
529 return self._resections.tienstra7(self, pointB, pointC, alpha, beta, gamma,
530 useZ=useZ, datum=self.datum)
532 @deprecated_method
533 def to2ab(self): # PYCHOK no cover
534 '''DEPRECATED, use property C{philam}.
536 @return: A L{PhiLam2Tuple}C{(phi, lam)}.
537 '''
538 return self.philam
540 @deprecated_method
541 def to2ll(self): # PYCHOK no cover
542 '''DEPRECATED, use property C{latlon}.
544 @return: A L{LatLon2Tuple}C{(lat, lon)}.
545 '''
546 return self.latlon
548 @deprecated_method
549 def to3llh(self, datum=None): # PYCHOK no cover
550 '''DEPRECATED, use property L{latlonheight} or L{latlonheightdatum}.
552 @return: A L{LatLon4Tuple}C{(lat, lon, height, datum)}.
554 @note: This method returns a B{C{-4Tuple}} I{and not a} C{-3Tuple}
555 as its name may suggest.
556 '''
557 t = self.toLatLon(datum=datum, LatLon=None)
558 return LatLon4Tuple(t.lat, t.lon, t.height, t.datum, name=self.name)
560# def _to3LLh(self, datum, LL, **pairs): # OBSOLETE
561# '''(INTERNAL) Helper for C{subclass.toLatLon} and C{.to3llh}.
562# '''
563# r = self.to3llh(datum) # LatLon3Tuple
564# if LL is not None:
565# r = LL(r.lat, r.lon, height=r.height, datum=datum, name=self.name)
566# for n, v in pairs.items():
567# setattr(r, n, v)
568# return r
570 def toDatum(self, datum2, datum=None):
571 '''Convert this cartesian from one datum to an other.
573 @arg datum2: Datum to convert I{to} (L{Datum}).
574 @kwarg datum: Datum to convert I{from} (L{Datum}).
576 @return: The converted point (C{Cartesian}).
578 @raise TypeError: B{C{datum2}} or B{C{datum}}
579 invalid.
580 '''
581 _xinstanceof(Datum, datum2=datum2)
583 c = self if datum in (None, self.datum) else \
584 self.toDatum(datum)
586 i, d = False, c.datum
587 if d == datum2:
588 return c.copy() if c is self else c
590 elif d == _WGS84:
591 d = datum2 # convert from WGS84 to datum2
593 elif datum2 == _WGS84:
594 i = True # convert to WGS84 by inverse transformation
596 else: # neither datum2 nor c.datum is WGS84, invert to WGS84 first
597 c = c.toTransform(d.transform, inverse=True, datum=_WGS84)
598 d = datum2
600 return c.toTransform(d.transform, inverse=i, datum=datum2)
602 def toEcef(self):
603 '''Convert this cartesian to I{geodetic} (lat-/longitude) coordinates.
605 @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height,
606 C, M, datum)} with C{C} and C{M} if available.
608 @raise EcefError: A C{.datum} or an ECEF issue.
609 '''
610 return self._ecef9
612 def toLatLon(self, datum=None, height=None, LatLon=None, **LatLon_kwds): # see .ecef.Ecef9Tuple.toDatum
613 '''Convert this cartesian to a I{geodetic} (lat-/longitude) point.
615 @kwarg datum: Optional datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2}
616 or L{a_f2Tuple}).
617 @kwarg height: Optional height, overriding the converted height
618 (C{meter}), iff B{C{LatLon}} is not C{None}.
619 @kwarg LatLon: Optional class to return the geodetic point
620 (C{LatLon}) or C{None}.
621 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword
622 arguments, ignored if C{B{LatLon} is None}.
624 @return: The geodetic point (B{C{LatLon}}) or if B{C{LatLon}}
625 is C{None}, an L{Ecef9Tuple}C{(x, y, z, lat, lon,
626 height, C, M, datum)} with C{C} and C{M} if available.
628 @raise TypeError: Invalid B{C{datum}} or B{C{LatLon_kwds}}.
629 '''
630 d = _spherical_datum(datum or self.datum, name=self.name)
631 if d == self.datum:
632 r = self.toEcef()
633 else:
634 c = self.toDatum(d)
635 r = c.Ecef(d, name=self.name).reverse(c, M=LatLon is None)
637 if LatLon: # class or .classof
638 h = _heigHt(r, height)
639 r = LatLon(r.lat, r.lon, datum=r.datum, height=h,
640 **_xkwds(LatLon_kwds, name=r.name))
641 _xdatum(r.datum, d)
642 return r
644 def toLocal(self, Xyz=None, ltp=None, **Xyz_kwds):
645 '''Convert this I{geocentric} cartesian to I{local} C{X}, C{Y} and C{Z}.
647 @kwarg Xyz: Optional class to return C{X}, C{Y} and C{Z}
648 (L{XyzLocal}, L{Enu}, L{Ned}) or C{None}.
649 @kwarg ltp: The I{local tangent plane} (LTP) to use,
650 overriding this cartesian's LTP (L{Ltp}).
651 @kwarg Xyz_kwds: Optional, additional B{C{Xyz}} keyword
652 arguments, ignored if C{B{Xyz} is None}.
654 @return: An B{C{Xyz}} instance or if C{B{Xyz} is None},
655 a L{Local9Tuple}C{(x, y, z, lat, lon, height,
656 ltp, ecef, M)} with C{M=None} always.
658 @raise TypeError: Invalid B{C{ltp}}.
659 '''
660 p = self._ltp._xLtp(ltp, self._Ltp)
661 return p._ecef2local(self._ecef9, Xyz, Xyz_kwds)
663 def toLtp(self, Ecef=None):
664 '''Return the I{local tangent plane} (LTP) for this cartesian.
666 @kwarg Ecef: Optional ECEF I{class} (L{EcefKarney}, ...
667 L{EcefYou}), overriding this cartesian's C{Ecef}.
668 '''
669 return self._Ltp if Ecef in (None, self.Ecef) else self._ltp.Ltp(
670 self._ecef9, ecef=Ecef(self.datum), name=self.name)
672 def toNvector(self, Nvector=None, datum=None, **Nvector_kwds):
673 '''Convert this cartesian to C{n-vector} components, I{including height}.
675 @kwarg Nvector: Optional class to return the C{n-vector} components
676 (C{Nvector}) or C{None}.
677 @kwarg datum: Optional datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2}
678 or L{a_f2Tuple}) overriding this cartesian's datum.
679 @kwarg Nvector_kwds: Optional, additional B{C{Nvector}} keyword
680 arguments, ignored if C{B{Nvector} is None}.
682 @return: An B{C{Nvector}} or a L{Vector4Tuple}C{(x, y, z, h)} if
683 B{C{Nvector}} is C{None}.
685 @raise TypeError: Invalid B{C{Nvector}}, B{C{Nvector_kwds}} or
686 B{C{datum}}.
688 @raise ValueError: B{C{Cartesian}} at origin.
689 '''
690 r, d = self._N_vector.xyzh, self.datum
691 if datum is not None:
692 d = _spherical_datum(datum, name=self.name)
693 if d != self.datum:
694 r = self._n_xyzh4(d)
696 if Nvector is not None:
697 kwds = _xkwds(Nvector_kwds, h=r.h, datum=d)
698 r = self._xnamed(Nvector(r.x, r.y, r.z, **kwds))
699 return r
701 def toStr(self, prec=3, fmt=Fmt.SQUARE, sep=_COMMASPACE_): # PYCHOK expected
702 '''Return the string representation of this cartesian.
704 @kwarg prec: Number of (decimal) digits, unstripped (C{int}).
705 @kwarg fmt: Enclosing backets format (C{str}).
706 @kwarg sep: Separator to join (C{str}).
708 @return: Cartesian represented as "[x, y, z]" (C{str}).
709 '''
710 return Vector3d.toStr(self, prec=prec, fmt=fmt, sep=sep)
712 def toTransform(self, transform, inverse=False, datum=None):
713 '''Return a new cartesian by applying a Helmert transform
714 to this cartesian.
716 @arg transform: Transform to apply (L{Transform}).
717 @kwarg inverse: Apply the inverse of the Helmert
718 transform (C{bool}).
719 @kwarg datum: Datum for the transformed cartesian (L{Datum}),
720 overriding this cartesian's datum.
722 @return: The transformed cartesian (C{Cartesian}).
724 @raise Valuerror: If C{B{inverse}=True} and B{C{datum}}
725 is not L{Datums}C{.WGS84}.
726 '''
727 d = datum or self.datum
728 if inverse and d != _WGS84:
729 raise _ValueError(inverse=inverse, datum=d,
730 txt=_not_(_WGS84.name))
732 xyz = transform.transform(*self.xyz, inverse=inverse)
733 return self.classof(xyz, datum=d)
735 def toVector(self, Vector=None, **Vector_kwds):
736 '''Return this cartesian's I{geocentric} components as vector.
738 @kwarg Vector: Optional class to return the I{geocentric}
739 components (L{Vector3d}) or C{None}.
740 @kwarg Vector_kwds: Optional, additional B{C{Vector}} keyword
741 arguments, ignored if C{B{Vector} is None}.
743 @return: A B{C{Vector}} or a L{Vector3Tuple}C{(x, y, z)} if
744 B{C{Vector}} is C{None}.
746 @raise TypeError: Invalid B{C{Vector}} or B{C{Vector_kwds}}.
747 '''
748 return self.xyz if Vector is None else self._xnamed(
749 Vector(self.x, self.y, self.z, **Vector_kwds))
752__all__ += _ALL_DOCS(CartesianBase)
754# **) MIT License
755#
756# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.
757#
758# Permission is hereby granted, free of charge, to any person obtaining a
759# copy of this software and associated documentation files (the "Software"),
760# to deal in the Software without restriction, including without limitation
761# the rights to use, copy, modify, merge, publish, distribute, sublicense,
762# and/or sell copies of the Software, and to permit persons to whom the
763# Software is furnished to do so, subject to the following conditions:
764#
765# The above copyright notice and this permission notice shall be included
766# in all copies or substantial portions of the Software.
767#
768# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
769# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
770# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
771# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
772# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
773# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
774# OTHER DEALINGS IN THE SOFTWARE.