Coverage for pygeodesy/cartesianBase.py: 94%
212 statements
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« prev ^ index » next coverage.py v7.2.2, created at 2023-12-02 13:46 -0500
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 impoty 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__ = '23.11.18'
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 _MODS.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 _MODS.resections.collins5(self, pointB, pointC, alpha, beta,
139 useZ=useZ, datum=self.datum)
141 @property_doc_(''' this cartesian's datum (L{Datum}).''')
142 def datum(self):
143 '''Get this cartesian's datum (L{Datum}).
144 '''
145 return self._datum
147 @datum.setter # PYCHOK setter!
148 def datum(self, datum):
149 '''Set this cartesian's C{datum} I{without conversion}
150 (L{Datum}), ellipsoidal or spherical.
152 @raise TypeError: The B{C{datum}} is not a L{Datum}.
153 '''
154 d = _spherical_datum(datum, name=self.name)
155 if self._datum: # is not None
156 if d.isEllipsoidal and not self._datum.isEllipsoidal:
157 raise _IsnotError(_ellipsoidal_, datum=datum)
158 elif d.isSpherical and not self._datum.isSpherical:
159 raise _IsnotError(_spherical_, datum=datum)
160 if self._datum != d:
161 _update_all(self)
162 self._datum = d
164 def destinationXyz(self, delta, Cartesian=None, **Cartesian_kwds):
165 '''Calculate the destination using a I{local} delta from this cartesian.
167 @arg delta: Local delta to the destination (L{XyzLocal}, L{Enu},
168 L{Ned} or L{Local9Tuple}).
169 @kwarg Cartesian: Optional (geocentric) class to return the
170 destination or C{None}.
171 @kwarg Cartesian_kwds: Optional, additional B{C{Cartesian}} keyword
172 arguments, ignored if C{B{Cartesian} is None}.
174 @return: Destination as a C{B{Cartesian}(x, y, z, **B{Cartesian_kwds})}
175 instance or if C{B{Cartesian} is None}, an L{Ecef9Tuple}C{(x, y,
176 z, lat, lon, height, C, M, datum)} with C{M=None} always.
178 @raise TypeError: Invalid B{C{delta}}, B{C{Cartesian}} or
179 B{C{Cartesian_kwds}}.
180 '''
181 if Cartesian is None:
182 r = self._ltp._local2ecef(delta, nine=True)
183 else:
184 r = self._ltp._local2ecef(delta, nine=False)
185 r = Cartesian(*r, **_xkwds(Cartesian_kwds, datum=self.datum))
186 return r._xnamed(r) if self.name else r
188 @property_RO
189 def Ecef(self):
190 '''Get the ECEF I{class} (L{EcefKarney}), I{lazily, once}.
191 '''
192 CartesianBase.Ecef = E = _MODS.ecef.EcefKarney # overwrite property_RO
193 return E
195 @Property_RO
196 def _ecef9(self):
197 '''(INTERNAL) Helper for L{toEcef}, L{toLocal} and L{toLtp} (L{Ecef9Tuple}).
198 '''
199 return self.Ecef(self.datum, name=self.name).reverse(self, M=True)
201 @property_RO
202 def ellipsoidalCartesian(self):
203 '''Get the C{Cartesian type} iff ellipsoidal, overloaded in L{CartesianEllipsoidalBase}.
204 '''
205 return False
207 def hartzell(self, los=None, earth=None):
208 '''Compute the intersection of a Line-Of-Sight (los) from this cartesian
209 Point-Of-View (pov) with this cartesian's ellipsoid surface.
211 @kwarg los: Line-Of-Sight, I{direction} to earth (L{Los}, L{Vector3d})
212 or C{None} to point to the ellipsoid's center.
213 @kwarg earth: The earth model (L{Datum}, L{Ellipsoid}, L{Ellipsoid2},
214 L{a_f2Tuple} or C{scalar} radius in C{meter}) overriding
215 this cartesian's C{datum} ellipsoid.
217 @return: The ellipsoid intersection (C{Cartesian}) with C{.height} set
218 to the distance to this C{pov}.
220 @raise IntersectionError: Null or bad C{pov} or B{C{los}}, this C{pov}
221 is inside the ellipsoid or B{C{los}} points
222 points outside or away from the ellipsoid.
224 @raise TypeError: Invalid B{C{los}} or no B{C{datum}}.
226 @see: Function C{hartzell} for further details.
227 '''
228 return _MODS.formy._hartzell(self, los, earth)
230 @Property
231 def height(self):
232 '''Get the height (C{meter}).
233 '''
234 return self._height4.h if self._height is None else self._height
236 @height.setter # PYCHOK setter!
237 def height(self, height):
238 '''Set the height (C{meter}).
240 @raise TypeError: Invalid B{C{height}} C{type}.
242 @raise ValueError: Invalid B{C{height}}.
243 '''
244 h = Height(height)
245 if self._height != h:
246 _update_all(self)
247 self._height = h
249 @Property_RO
250 def _height4(self):
251 '''(INTERNAL) Get this C{height4}-tuple.
252 '''
253 try:
254 r = self.datum.ellipsoid.height4(self, normal=True)
255 except (AttributeError, ValueError): # no datum, null cartesian,
256 r = Vector4Tuple(self.x, self.y, self.z, 0, name=self.height4.__name__)
257 return r
259 def height4(self, earth=None, normal=True, Cartesian=None, **Cartesian_kwds):
260 '''Compute the height of this cartesian above or below and the projection
261 on this datum's ellipsoid surface.
263 @kwarg earth: A datum, ellipsoid, triaxial ellipsoid or earth radius
264 I{overriding} this datum (L{Datum}, L{Ellipsoid},
265 L{Ellipsoid2}, L{a_f2Tuple}, L{Triaxial}, L{Triaxial_},
266 L{JacobiConformal} or C{meter}, conventionally).
267 @kwarg normal: If C{True} the projection is the nearest point on the
268 ellipsoid's surface, otherwise the intersection of the
269 radial line to the center and the ellipsoid's surface.
270 @kwarg Cartesian: Optional class to return the height and projection
271 (C{Cartesian}) or C{None}.
272 @kwarg Cartesian_kwds: Optional, additional B{C{Cartesian}} keyword
273 arguments, ignored if C{B{Cartesian} is None}.
275 @note: Use keyword argument C{height=0} to override C{B{Cartesian}.height}
276 to {0} or any other C{scalar}, conventionally in C{meter}.
278 @return: An instance of B{C{Cartesian}} or if C{B{Cartesian} is None}, a
279 L{Vector4Tuple}C{(x, y, z, h)} with the I{projection} C{x}, C{y}
280 and C{z} coordinates and height C{h} in C{meter}, conventionally.
282 @raise TriaxialError: No convergence in triaxial root finding.
284 @raise TypeError: Invalid B{C{earth}}.
286 @see: L{Ellipsoid.height4} and L{Triaxial_.height4} for more information.
287 '''
288 d = self.datum if earth is None else earth
289 if normal and d is self.datum:
290 r = self._height4
291 elif isinstance(d, _MODS.triaxials.Triaxial_):
292 r = d.height4(self, normal=normal)
293 else:
294 r = _earth_ellipsoid(d).height4(self, normal=normal)
295 if Cartesian is not None:
296 kwds = Cartesian_kwds.copy()
297 h = kwds.pop(_height_, None)
298 r = Cartesian(r, **kwds)
299 if h is not None:
300 r.height = Height(height=h)
301 return r
303 @Property_RO
304 def isEllipsoidal(self):
305 '''Check whether this cartesian is ellipsoidal (C{bool} or C{None} if unknown).
306 '''
307 return self.datum.isEllipsoidal if self._datum else None
309 @Property_RO
310 def isSpherical(self):
311 '''Check whether this cartesian is spherical (C{bool} or C{None} if unknown).
312 '''
313 return self.datum.isSpherical if self._datum else None
315 @Property_RO
316 def latlon(self):
317 '''Get this cartesian's (geodetic) lat- and longitude in C{degrees} (L{LatLon2Tuple}C{(lat, lon)}).
318 '''
319 return self.toEcef().latlon
321 @Property_RO
322 def latlonheight(self):
323 '''Get this cartesian's (geodetic) lat-, longitude in C{degrees} with height (L{LatLon3Tuple}C{(lat, lon, height)}).
324 '''
325 return self.toEcef().latlonheight
327 @Property_RO
328 def latlonheightdatum(self):
329 '''Get this cartesian's (geodetic) lat-, longitude in C{degrees} with height and datum (L{LatLon4Tuple}C{(lat, lon, height, datum)}).
330 '''
331 return self.toEcef().latlonheightdatum
333 @Property_RO
334 def _ltp(self):
335 '''(INTERNAL) Cache for L{toLtp}.
336 '''
337 return _MODS.ltp.Ltp(self._ecef9, ecef=self.Ecef(self.datum), name=self.name)
339 @Property_RO
340 def _N_vector(self):
341 '''(INTERNAL) Get the (C{nvectorBase._N_vector_}).
342 '''
343 x, y, z, h = self._n_xyzh4(self.datum)
344 return _MODS.nvectorBase._N_vector_(x, y, z, h=h, name=self.name)
346 def _n_xyzh4(self, datum):
347 '''(INTERNAL) Get the n-vector components as L{Vector4Tuple}.
348 '''
349 def _ErrorEPS0(x):
350 return _ValueError(origin=self, txt=Fmt.PARENSPACED(EPS0=x))
352 _xinstanceof(Datum, datum=datum)
353 # <https://www.Movable-Type.co.UK/scripts/geodesy/docs/
354 # latlon-nvector-ellipsoidal.js.html#line309>,
355 # <https://GitHub.com/pbrod/nvector>/src/nvector/core.py>
356 # _equation23 and <https://www.NavLab.net/nvector>
357 E = datum.ellipsoid
358 x, y, z = self.xyz
360 # Kenneth Gade eqn 23
361 p = hypot2(x, y) * E.a2_
362 q = z**2 * E.e21 * E.a2_
363 r = fsumf_(p, q, -E.e4) / _6_0
364 s = (p * q * E.e4) / (_4_0 * r**3)
365 t = cbrt(fsumf_(_1_0, s, sqrt(s * (_2_0 + s))))
366 if isnear0(t):
367 raise _ErrorEPS0(t)
368 u = fsumf_(_1_0, t, _1_0 / t) * r
369 v = sqrt(u**2 + E.e4 * q)
370 t = v * _2_0
371 if t < EPS0: # isnear0
372 raise _ErrorEPS0(t)
373 w = fsumf_(u, v, -q) * E.e2 / t
374 k = sqrt(fsumf_(u, v, w**2)) - w
375 if isnear0(k):
376 raise _ErrorEPS0(k)
377 t = k + E.e2
378 if isnear0(t):
379 raise _ErrorEPS0(t)
380 e = k / t
381# d = e * hypot(x, y)
382# tmp = 1 / hypot(d, z) == 1 / hypot(e * hypot(x, y), z)
383 t = hypot_(x * e, y * e, z) # == 1 / tmp
384 if t < EPS0: # isnear0
385 raise _ErrorEPS0(t)
386 h = fsumf_(k, E.e2, _N_1_0) / k * t
387 s = e / t # == e * tmp
388 return Vector4Tuple(x * s, y * s, z / t, h, name=self.name)
390 @Property_RO
391 def philam(self):
392 '''Get this cartesian's (geodetic) lat- and longitude in C{radians} (L{PhiLam2Tuple}C{(phi, lam)}).
393 '''
394 return self.toEcef().philam
396 @Property_RO
397 def philamheight(self):
398 '''Get this cartesian's (geodetic) lat-, longitude in C{radians} with height (L{PhiLam3Tuple}C{(phi, lam, height)}).
399 '''
400 return self.toEcef().philamheight
402 @Property_RO
403 def philamheightdatum(self):
404 '''Get this cartesian's (geodetic) lat-, longitude in C{radians} with height and datum (L{PhiLam4Tuple}C{(phi, lam, height, datum)}).
405 '''
406 return self.toEcef().philamheightdatum
408 def pierlot(self, point2, point3, alpha12, alpha23, useZ=False, eps=EPS):
409 '''3-Point resection between this and two other points using U{Pierlot
410 <http://www.Telecom.ULg.ac.Be/triangulation>}'s method C{ToTal} with
411 I{approximate} limits for the (pseudo-)singularities.
413 @arg point2: Second point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple},
414 C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}).
415 @arg point3: Third point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple},
416 C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}).
417 @arg alpha12: Angle subtended from this point to B{C{point2}} or
418 B{C{alpha2 - alpha}} (C{degrees}).
419 @arg alpha23: Angle subtended from B{C{point2}} to B{C{point3}} or
420 B{C{alpha3 - alpha2}} (C{degrees}).
421 @kwarg useZ: If C{True}, interpolate the Z component, otherwise use C{z=INT0}
422 (C{bool}).
423 @kwarg eps: Tolerance for C{cot} (pseudo-)singularities (C{float}).
425 @note: This point, B{C{point2}} and B{C{point3}} are ordered counter-clockwise.
427 @return: The survey (or robot) point, an instance of this (sub-)class.
429 @raise ResectionError: Near-coincident, -colinear or -concyclic points
430 or invalid B{C{alpha12}} or B{C{alpha23}}.
432 @raise TypeError: Invalid B{C{point2}} or B{C{point3}}.
434 @see: Function L{pygeodesy.pierlot} for references and more details.
435 '''
436 return _MODS.resections.pierlot(self, point2, point3, alpha12, alpha23,
437 useZ=useZ, eps=eps, datum=self.datum)
439 def pierlotx(self, point2, point3, alpha1, alpha2, alpha3, useZ=False):
440 '''3-Point resection between this and two other points using U{Pierlot
441 <http://www.Telecom.ULg.ac.Be/publi/publications/pierlot/Pierlot2014ANewThree>}'s
442 method C{ToTal} with I{exact} limits for the (pseudo-)singularities.
444 @arg point2: Second point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple},
445 C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}).
446 @arg point3: Third point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple},
447 C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}).
448 @arg alpha1: Angle at B{C{point1}} (C{degrees}).
449 @arg alpha2: Angle at B{C{point2}} (C{degrees}).
450 @arg alpha3: Angle at B{C{point3}} (C{degrees}).
451 @kwarg useZ: If C{True}, interpolate the survey point's Z component,
452 otherwise use C{z=INT0} (C{bool}).
454 @return: The survey (or robot) point, an instance of this (sub-)class.
456 @raise ResectionError: Near-coincident, -colinear or -concyclic points or
457 invalid B{C{alpha1}}, B{C{alpha2}} or B{C{alpha3}}.
459 @raise TypeError: Invalid B{C{point2}} or B{C{point3}}.
461 @see: Function L{pygeodesy.pierlotx} for references and more details.
462 '''
463 return _MODS.resections.pierlotx(self, point2, point3, alpha1, alpha2, alpha3,
464 useZ=useZ, datum=self.datum)
466 @property_RO
467 def sphericalCartesian(self):
468 '''Get the C{Cartesian type} iff spherical, overloaded in L{CartesianSphericalBase}.
469 '''
470 return False
472 @deprecated_method
473 def tienstra(self, pointB, pointC, alpha, beta=None, gamma=None, useZ=False):
474 '''DEPRECATED, use method L{tienstra7}.'''
475 return self.tienstra7(pointB, pointC, alpha, beta=beta, gamma=gamma, useZ=useZ)
477 def tienstra7(self, pointB, pointC, alpha, beta=None, gamma=None, useZ=False):
478 '''3-Point resection between this and two other points using U{Tienstra
479 <https://WikiPedia.org/wiki/Tienstra_formula>}'s formula.
481 @arg pointB: Second point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple}, C{Vector4Tuple} or
482 C{Vector2Tuple} if C{B{useZ}=False}).
483 @arg pointC: Third point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple}, C{Vector4Tuple} or
484 C{Vector2Tuple} if C{B{useZ}=False}).
485 @arg alpha: Angle subtended by triangle side C{a} from B{C{pointB}} to B{C{pointC}} (C{degrees},
486 non-negative).
487 @kwarg beta: Angle subtended by triangle side C{b} from this to B{C{pointC}} (C{degrees},
488 non-negative) or C{None} if C{B{gamma} is not None}.
489 @kwarg gamma: Angle subtended by triangle side C{c} from this to B{C{pointB}} (C{degrees},
490 non-negative) or C{None} if C{B{beta} is not None}.
491 @kwarg useZ: If C{True}, use and interpolate the Z component, otherwise force C{z=INT0}
492 (C{bool}).
494 @note: This point, B{C{pointB}} and B{C{pointC}} are ordered clockwise.
496 @return: L{Tienstra7Tuple}C{(pointP, A, B, C, a, b, c)} with survey C{pointP},
497 an instance of this (sub-)class and triangle angle C{A} at this point,
498 C{B} at B{C{pointB}} and C{C} at B{C{pointC}} in C{degrees} and
499 triangle sides C{a}, C{b} and C{c}.
501 @raise ResectionError: Near-coincident, -colinear or -concyclic points or sum of
502 B{C{alpha}}, B{C{beta}} and B{C{gamma}} not C{360} or
503 negative B{C{alpha}}, B{C{beta}} or B{C{gamma}}.
505 @raise TypeError: Invalid B{C{pointB}} or B{C{pointC}}.
507 @see: Function L{pygeodesy.tienstra7} for references and more details.
508 '''
509 return _MODS.resections.tienstra7(self, pointB, pointC, alpha, beta, gamma,
510 useZ=useZ, datum=self.datum)
512 @deprecated_method
513 def to2ab(self): # PYCHOK no cover
514 '''DEPRECATED, use property C{philam}.
516 @return: A L{PhiLam2Tuple}C{(phi, lam)}.
517 '''
518 return self.philam
520 @deprecated_method
521 def to2ll(self): # PYCHOK no cover
522 '''DEPRECATED, use property C{latlon}.
524 @return: A L{LatLon2Tuple}C{(lat, lon)}.
525 '''
526 return self.latlon
528 @deprecated_method
529 def to3llh(self, datum=None): # PYCHOK no cover
530 '''DEPRECATED, use property L{latlonheightdatum} or L{latlonheight}.
532 @return: A L{LatLon4Tuple}C{(lat, lon, height, datum)}.
534 @note: This method returns a B{C{-4Tuple}} I{and not a} C{-3Tuple}
535 as its name may suggest.
536 '''
537 t = self.toLatLon(datum=datum, LatLon=None)
538 return LatLon4Tuple(t.lat, t.lon, t.height, t.datum, name=self.name)
540# def _to3LLh(self, datum, LL, **pairs): # OBSOLETE
541# '''(INTERNAL) Helper for C{subclass.toLatLon} and C{.to3llh}.
542# '''
543# r = self.to3llh(datum) # LatLon3Tuple
544# if LL is not None:
545# r = LL(r.lat, r.lon, height=r.height, datum=datum, name=self.name)
546# for n, v in pairs.items():
547# setattr(r, n, v)
548# return r
550 def toDatum(self, datum2, datum=None):
551 '''Convert this cartesian from one datum to an other.
553 @arg datum2: Datum to convert I{to} (L{Datum}).
554 @kwarg datum: Datum to convert I{from} (L{Datum}).
556 @return: The converted point (C{Cartesian}).
558 @raise TypeError: B{C{datum2}} or B{C{datum}}
559 invalid.
560 '''
561 _xinstanceof(Datum, datum2=datum2)
563 c = self if datum in (None, self.datum) else \
564 self.toDatum(datum)
566 i, d = False, c.datum
567 if d == datum2:
568 return c.copy() if c is self else c
570 elif d == _WGS84:
571 d = datum2 # convert from WGS84 to datum2
573 elif datum2 == _WGS84:
574 i = True # convert to WGS84 by inverse transformation
576 else: # neither datum2 nor c.datum is WGS84, invert to WGS84 first
577 c = c.toTransform(d.transform, inverse=True, datum=_WGS84)
578 d = datum2
580 return c.toTransform(d.transform, inverse=i, datum=datum2)
582 convertDatum = toDatum # for backward compatibility
584 def toEcef(self):
585 '''Convert this cartesian to I{geodetic} (lat-/longitude) coordinates.
587 @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height,
588 C, M, datum)} with C{C} and C{M} if available.
590 @raise EcefError: A C{.datum} or an ECEF issue.
591 '''
592 return self._ecef9
594 def toLatLon(self, datum=None, height=None, LatLon=None, **LatLon_kwds): # see .ecef.Ecef9Tuple.toDatum
595 '''Convert this cartesian to a geodetic (lat-/longitude) point.
597 @kwarg datum: Optional datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2}
598 or L{a_f2Tuple}).
599 @kwarg height: Optional height, overriding the converted height
600 (C{meter}), iff B{C{LatLon}} is not C{None}.
601 @kwarg LatLon: Optional class to return the geodetic point
602 (C{LatLon}) or C{None}.
603 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword
604 arguments, ignored if C{B{LatLon} is None}.
606 @return: The geodetic point (B{C{LatLon}}) or if B{C{LatLon}}
607 is C{None}, an L{Ecef9Tuple}C{(x, y, z, lat, lon,
608 height, C, M, datum)} with C{C} and C{M} if available.
610 @raise TypeError: Invalid B{C{datum}} or B{C{LatLon_kwds}}.
611 '''
612 d = _spherical_datum(datum or self.datum, name=self.name)
613 if d == self.datum:
614 r = self.toEcef()
615 else:
616 c = self.toDatum(d)
617 r = c.Ecef(d, name=self.name).reverse(c, M=LatLon is None)
619 if LatLon: # class or .classof
620 h = _heigHt(r, height)
621 r = LatLon(r.lat, r.lon, datum=r.datum, height=h,
622 **_xkwds(LatLon_kwds, name=r.name))
623 _xdatum(r.datum, d)
624 return r
626 def toLocal(self, Xyz=None, ltp=None, **Xyz_kwds):
627 '''Convert this I{geocentric} cartesian to I{local} C{X}, C{Y} and C{Z}.
629 @kwarg Xyz: Optional class to return C{X}, C{Y} and C{Z}
630 (L{XyzLocal}, L{Enu}, L{Ned}) or C{None}.
631 @kwarg ltp: The I{local tangent plane} (LTP) to use,
632 overriding this cartesian's LTP (L{Ltp}).
633 @kwarg Xyz_kwds: Optional, additional B{C{Xyz}} keyword
634 arguments, ignored if C{B{Xyz} is None}.
636 @return: An B{C{Xyz}} instance or if C{B{Xyz} is None},
637 a L{Local9Tuple}C{(x, y, z, lat, lon, height,
638 ltp, ecef, M)} with C{M=None} always.
640 @raise TypeError: Invalid B{C{ltp}}.
641 '''
642 p = _MODS.ltp._xLtp(ltp, self._ltp)
643 return p._ecef2local(self._ecef9, Xyz, Xyz_kwds)
645 def toLtp(self, Ecef=None):
646 '''Return the I{local tangent plane} (LTP) for this cartesian.
648 @kwarg Ecef: Optional ECEF I{class} (L{EcefKarney}, ...
649 L{EcefYou}), overriding this cartesian's C{Ecef}.
650 '''
651 return self._ltp if Ecef in (None, self.Ecef) else _MODS.ltp.Ltp(
652 self._ecef9, ecef=Ecef(self.datum), name=self.name)
654 def toNvector(self, Nvector=None, datum=None, **Nvector_kwds):
655 '''Convert this cartesian to C{n-vector} components.
657 @kwarg Nvector: Optional class to return the C{n-vector}
658 components (C{Nvector}) or C{None}.
659 @kwarg datum: Optional datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2}
660 or L{a_f2Tuple}) overriding this cartesian's datum.
661 @kwarg Nvector_kwds: Optional, additional B{C{Nvector}} keyword
662 arguments, ignored if C{B{Nvector} is None}.
664 @return: The C{unit, n-vector} components (B{C{Nvector}}) or a
665 L{Vector4Tuple}C{(x, y, z, h)} if B{C{Nvector}} is C{None}.
667 @raise TypeError: Invalid B{C{datum}}.
669 @raise ValueError: The B{C{Cartesian}} at origin.
671 @example:
673 >>> c = Cartesian(3980581, 97, 4966825)
674 >>> n = c.toNvector() # (x=0.622818, y=0.00002, z=0.782367, h=0.242887)
675 '''
676 d = _spherical_datum(datum or self.datum, name=self.name)
677 r = self._N_vector.xyzh if self.datum == d else self._n_xyzh4(d)
679 if Nvector is not None:
680 kwds = _xkwds(Nvector_kwds, h=r.h, datum=d)
681 r = self._xnamed(Nvector(r.x, r.y, r.z, **kwds))
682 return r
684 def toStr(self, prec=3, fmt=Fmt.SQUARE, sep=_COMMASPACE_): # PYCHOK expected
685 '''Return the string representation of this cartesian.
687 @kwarg prec: Number of (decimal) digits, unstripped (C{int}).
688 @kwarg fmt: Enclosing backets format (string).
689 @kwarg sep: Separator to join (string).
691 @return: Cartesian represented as "[x, y, z]" (string).
692 '''
693 return Vector3d.toStr(self, prec=prec, fmt=fmt, sep=sep)
695 def toTransform(self, transform, inverse=False, datum=None):
696 '''Return a new cartesian by applying a Helmert transform
697 to this cartesian.
699 @arg transform: Transform to apply (L{Transform}).
700 @kwarg inverse: Apply the inverse of the Helmert
701 transform (C{bool}).
702 @kwarg datum: Datum for the transformed cartesian (L{Datum}),
703 overriding this cartesian's datum.
705 @return: The transformed cartesian (C{Cartesian}).
707 @raise Valuerror: If C{B{inverse}=True} and B{C{datum}}
708 is not L{Datums}C{.WGS84}.
709 '''
710 d = datum or self.datum
711 if inverse and d != _WGS84:
712 raise _ValueError(inverse=inverse, datum=d,
713 txt=_not_(_WGS84.name))
715 xyz = transform.transform(*self.xyz, inverse=inverse)
716 return self.classof(xyz, datum=d)
718 def toVector(self, Vector=None, **Vector_kwds):
719 '''Return this cartesian's components as vector.
721 @kwarg Vector: Optional class to return the C{n-vector}
722 components (L{Vector3d}) or C{None}.
723 @kwarg Vector_kwds: Optional, additional B{C{Vector}} keyword
724 arguments, ignored if C{B{Vector} is None}.
726 @return: A B{C{Vector}} or a L{Vector3Tuple}C{(x, y, z)} if
727 B{C{Vector}} is C{None}.
729 @raise TypeError: Invalid B{C{Vector}} or B{C{Vector_kwds}}.
730 '''
731 return self.xyz if Vector is None else self._xnamed(
732 Vector(self.x, self.y, self.z, **Vector_kwds))
735__all__ += _ALL_DOCS(CartesianBase)
737# **) MIT License
738#
739# Copyright (C) 2016-2023 -- mrJean1 at Gmail -- All Rights Reserved.
740#
741# Permission is hereby granted, free of charge, to any person obtaining a
742# copy of this software and associated documentation files (the "Software"),
743# to deal in the Software without restriction, including without limitation
744# the rights to use, copy, modify, merge, publish, distribute, sublicense,
745# and/or sell copies of the Software, and to permit persons to whom the
746# Software is furnished to do so, subject to the following conditions:
747#
748# The above copyright notice and this permission notice shall be included
749# in all copies or substantial portions of the Software.
750#
751# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
752# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
753# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
754# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
755# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
756# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
757# OTHER DEALINGS IN THE SOFTWARE.