Coverage for pygeodesy/cartesianBase.py: 94%
211 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 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__ = '23.10.29'
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}.
191 '''
192 return _MODS.ecef.EcefKarney # default
194 @Property_RO
195 def _ecef9(self):
196 '''(INTERNAL) Helper for L{toEcef}, L{toLocal} and L{toLtp} (L{Ecef9Tuple}).
197 '''
198 return self.Ecef(self.datum, name=self.name).reverse(self, M=True)
200 @property_RO
201 def ellipsoidalCartesian(self):
202 '''Get the C{Cartesian type} iff ellipsoidal, overloaded in L{CartesianEllipsoidalBase}.
203 '''
204 return False
206 def hartzell(self, los=None, earth=None):
207 '''Compute the intersection of a Line-Of-Sight (los) from this cartesian
208 Point-Of-View (pov) with this cartesian's ellipsoid surface.
210 @kwarg los: Line-Of-Sight, I{direction} to earth (L{Los}, L{Vector3d})
211 or C{None} to point to the ellipsoid's center.
212 @kwarg earth: The earth model (L{Datum}, L{Ellipsoid}, L{Ellipsoid2},
213 L{a_f2Tuple} or C{scalar} radius in C{meter}) overriding
214 this cartesian's C{datum} ellipsoid.
216 @return: The ellipsoid intersection (C{Cartesian}) with C{.height} set
217 to the distance to this C{pov}.
219 @raise IntersectionError: Null or bad C{pov} or B{C{los}}, this C{pov}
220 is inside the ellipsoid or B{C{los}} points
221 points outside or away from the ellipsoid.
223 @raise TypeError: Invalid B{C{los}} or no B{C{datum}}.
225 @see: Function C{hartzell} for further details.
226 '''
227 return _MODS.formy._hartzell(self, los, earth)
229 @Property
230 def height(self):
231 '''Get the height (C{meter}).
232 '''
233 return self._height4.h if self._height is None else self._height
235 @height.setter # PYCHOK setter!
236 def height(self, height):
237 '''Set the height (C{meter}).
239 @raise TypeError: Invalid B{C{height}} C{type}.
241 @raise ValueError: Invalid B{C{height}}.
242 '''
243 h = Height(height)
244 if self._height != h:
245 _update_all(self)
246 self._height = h
248 @Property_RO
249 def _height4(self):
250 '''(INTERNAL) Get this C{height4}-tuple.
251 '''
252 try:
253 r = self.datum.ellipsoid.height4(self, normal=True)
254 except (AttributeError, ValueError): # no datum, null cartesian,
255 r = Vector4Tuple(self.x, self.y, self.z, 0, name=self.height4.__name__)
256 return r
258 def height4(self, earth=None, normal=True, Cartesian=None, **Cartesian_kwds):
259 '''Compute the height of this cartesian above or below and the projection
260 on this datum's ellipsoid surface.
262 @kwarg earth: A datum, ellipsoid, triaxial ellipsoid or earth radius
263 I{overriding} this datum (L{Datum}, L{Ellipsoid},
264 L{Ellipsoid2}, L{a_f2Tuple}, L{Triaxial}, L{Triaxial_},
265 L{JacobiConformal} or C{meter}, conventionally).
266 @kwarg normal: If C{True} the projection is the nearest point on the
267 ellipsoid's surface, otherwise the intersection of the
268 radial line to the center and the ellipsoid's surface.
269 @kwarg Cartesian: Optional class to return the height and projection
270 (C{Cartesian}) or C{None}.
271 @kwarg Cartesian_kwds: Optional, additional B{C{Cartesian}} keyword
272 arguments, ignored if C{B{Cartesian} is None}.
274 @note: Use keyword argument C{height=0} to override C{B{Cartesian}.height}
275 to {0} or any other C{scalar}, conventionally in C{meter}.
277 @return: An instance of B{C{Cartesian}} or if C{B{Cartesian} is None}, a
278 L{Vector4Tuple}C{(x, y, z, h)} with the I{projection} C{x}, C{y}
279 and C{z} coordinates and height C{h} in C{meter}, conventionally.
281 @raise TriaxialError: No convergence in triaxial root finding.
283 @raise TypeError: Invalid B{C{earth}}.
285 @see: L{Ellipsoid.height4} and L{Triaxial_.height4} for more information.
286 '''
287 d = self.datum if earth is None else earth
288 if normal and d is self.datum:
289 r = self._height4
290 elif isinstance(d, _MODS.triaxials.Triaxial_):
291 r = d.height4(self, normal=normal)
292 else:
293 r = _earth_ellipsoid(d).height4(self, normal=normal)
294 if Cartesian is not None:
295 kwds = Cartesian_kwds.copy()
296 h = kwds.pop(_height_, None)
297 r = Cartesian(r, **kwds)
298 if h is not None:
299 r.height = Height(height=h)
300 return r
302 @Property_RO
303 def isEllipsoidal(self):
304 '''Check whether this cartesian is ellipsoidal (C{bool} or C{None} if unknown).
305 '''
306 return self.datum.isEllipsoidal if self._datum else None
308 @Property_RO
309 def isSpherical(self):
310 '''Check whether this cartesian is spherical (C{bool} or C{None} if unknown).
311 '''
312 return self.datum.isSpherical if self._datum else None
314 @Property_RO
315 def latlon(self):
316 '''Get this cartesian's (geodetic) lat- and longitude in C{degrees} (L{LatLon2Tuple}C{(lat, lon)}).
317 '''
318 return self.toEcef().latlon
320 @Property_RO
321 def latlonheight(self):
322 '''Get this cartesian's (geodetic) lat-, longitude in C{degrees} with height (L{LatLon3Tuple}C{(lat, lon, height)}).
323 '''
324 return self.toEcef().latlonheight
326 @Property_RO
327 def latlonheightdatum(self):
328 '''Get this cartesian's (geodetic) lat-, longitude in C{degrees} with height and datum (L{LatLon4Tuple}C{(lat, lon, height, datum)}).
329 '''
330 return self.toEcef().latlonheightdatum
332 @Property_RO
333 def _ltp(self):
334 '''(INTERNAL) Cache for L{toLtp}.
335 '''
336 return _MODS.ltp.Ltp(self._ecef9, ecef=self.Ecef(self.datum), name=self.name)
338 @Property_RO
339 def _N_vector(self):
340 '''(INTERNAL) Get the (C{nvectorBase._N_vector_}).
341 '''
342 x, y, z, h = self._n_xyzh4(self.datum)
343 return _MODS.nvectorBase._N_vector_(x, y, z, h=h, name=self.name)
345 def _n_xyzh4(self, datum):
346 '''(INTERNAL) Get the n-vector components as L{Vector4Tuple}.
347 '''
348 def _ErrorEPS0(x):
349 return _ValueError(origin=self, txt=Fmt.PARENTSPACED(EPS0=x))
351 _xinstanceof(Datum, datum=datum)
352 # <https://www.Movable-Type.co.UK/scripts/geodesy/docs/
353 # latlon-nvector-ellipsoidal.js.html#line309>,
354 # <https://GitHub.com/pbrod/nvector>/src/nvector/core.py>
355 # _equation23 and <https://www.NavLab.net/nvector>
356 E = datum.ellipsoid
357 x, y, z = self.xyz
359 # Kenneth Gade eqn 23
360 p = hypot2(x, y) * E.a2_
361 q = z**2 * E.e21 * E.a2_
362 r = fsumf_(p, q, -E.e4) / _6_0
363 s = (p * q * E.e4) / (_4_0 * r**3)
364 t = cbrt(fsumf_(_1_0, s, sqrt(s * (_2_0 + s))))
365 if isnear0(t):
366 raise _ErrorEPS0(t)
367 u = fsumf_(_1_0, t, _1_0 / t) * r
368 v = sqrt(u**2 + E.e4 * q)
369 t = v * _2_0
370 if t < EPS0: # isnear0
371 raise _ErrorEPS0(t)
372 w = fsumf_(u, v, -q) * E.e2 / t
373 k = sqrt(fsumf_(u, v, w**2)) - w
374 if isnear0(k):
375 raise _ErrorEPS0(k)
376 t = k + E.e2
377 if isnear0(t):
378 raise _ErrorEPS0(t)
379 e = k / t
380# d = e * hypot(x, y)
381# tmp = 1 / hypot(d, z) == 1 / hypot(e * hypot(x, y), z)
382 t = hypot_(x * e, y * e, z) # == 1 / tmp
383 if t < EPS0: # isnear0
384 raise _ErrorEPS0(t)
385 h = fsumf_(k, E.e2, _N_1_0) / k * t
386 s = e / t # == e * tmp
387 return Vector4Tuple(x * s, y * s, z / t, h, name=self.name)
389 @Property_RO
390 def philam(self):
391 '''Get this cartesian's (geodetic) lat- and longitude in C{radians} (L{PhiLam2Tuple}C{(phi, lam)}).
392 '''
393 return self.toEcef().philam
395 @Property_RO
396 def philamheight(self):
397 '''Get this cartesian's (geodetic) lat-, longitude in C{radians} with height (L{PhiLam3Tuple}C{(phi, lam, height)}).
398 '''
399 return self.toEcef().philamheight
401 @Property_RO
402 def philamheightdatum(self):
403 '''Get this cartesian's (geodetic) lat-, longitude in C{radians} with height and datum (L{PhiLam4Tuple}C{(phi, lam, height, datum)}).
404 '''
405 return self.toEcef().philamheightdatum
407 def pierlot(self, point2, point3, alpha12, alpha23, useZ=False, eps=EPS):
408 '''3-Point resection between this and two other points using U{Pierlot
409 <http://www.Telecom.ULg.ac.Be/triangulation>}'s method C{ToTal} with
410 I{approximate} limits for the (pseudo-)singularities.
412 @arg point2: Second point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple},
413 C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}).
414 @arg point3: Third point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple},
415 C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}).
416 @arg alpha12: Angle subtended from this point to B{C{point2}} or
417 B{C{alpha2 - alpha}} (C{degrees}).
418 @arg alpha23: Angle subtended from B{C{point2}} to B{C{point3}} or
419 B{C{alpha3 - alpha2}} (C{degrees}).
420 @kwarg useZ: If C{True}, interpolate the Z component, otherwise use C{z=INT0}
421 (C{bool}).
422 @kwarg eps: Tolerance for C{cot} (pseudo-)singularities (C{float}).
424 @note: This point, B{C{point2}} and B{C{point3}} are ordered counter-clockwise.
426 @return: The survey (or robot) point, an instance of this (sub-)class.
428 @raise ResectionError: Near-coincident, -colinear or -concyclic points
429 or invalid B{C{alpha12}} or B{C{alpha23}}.
431 @raise TypeError: Invalid B{C{point2}} or B{C{point3}}.
433 @see: Function L{pygeodesy.pierlot} for references and more details.
434 '''
435 return _MODS.resections.pierlot(self, point2, point3, alpha12, alpha23,
436 useZ=useZ, eps=eps, datum=self.datum)
438 def pierlotx(self, point2, point3, alpha1, alpha2, alpha3, useZ=False):
439 '''3-Point resection between this and two other points using U{Pierlot
440 <http://www.Telecom.ULg.ac.Be/publi/publications/pierlot/Pierlot2014ANewThree>}'s
441 method C{ToTal} with I{exact} limits for the (pseudo-)singularities.
443 @arg point2: Second point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple},
444 C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}).
445 @arg point3: Third point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple},
446 C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}).
447 @arg alpha1: Angle at B{C{point1}} (C{degrees}).
448 @arg alpha2: Angle at B{C{point2}} (C{degrees}).
449 @arg alpha3: Angle at B{C{point3}} (C{degrees}).
450 @kwarg useZ: If C{True}, interpolate the survey point's Z component,
451 otherwise use C{z=INT0} (C{bool}).
453 @return: The survey (or robot) point, an instance of this (sub-)class.
455 @raise ResectionError: Near-coincident, -colinear or -concyclic points or
456 invalid B{C{alpha1}}, B{C{alpha2}} or B{C{alpha3}}.
458 @raise TypeError: Invalid B{C{point2}} or B{C{point3}}.
460 @see: Function L{pygeodesy.pierlotx} for references and more details.
461 '''
462 return _MODS.resections.pierlotx(self, point2, point3, alpha1, alpha2, alpha3,
463 useZ=useZ, datum=self.datum)
465 @property_RO
466 def sphericalCartesian(self):
467 '''Get the C{Cartesian type} iff spherical, overloaded in L{CartesianSphericalBase}.
468 '''
469 return False
471 @deprecated_method
472 def tienstra(self, pointB, pointC, alpha, beta=None, gamma=None, useZ=False):
473 '''DEPRECATED, use method L{tienstra7}.'''
474 return self.tienstra7(pointB, pointC, alpha, beta=beta, gamma=gamma, useZ=useZ)
476 def tienstra7(self, pointB, pointC, alpha, beta=None, gamma=None, useZ=False):
477 '''3-Point resection between this and two other points using U{Tienstra
478 <https://WikiPedia.org/wiki/Tienstra_formula>}'s formula.
480 @arg pointB: Second point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple}, C{Vector4Tuple} or
481 C{Vector2Tuple} if C{B{useZ}=False}).
482 @arg pointC: Third point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple}, C{Vector4Tuple} or
483 C{Vector2Tuple} if C{B{useZ}=False}).
484 @arg alpha: Angle subtended by triangle side C{a} from B{C{pointB}} to B{C{pointC}} (C{degrees},
485 non-negative).
486 @kwarg beta: Angle subtended by triangle side C{b} from this to B{C{pointC}} (C{degrees},
487 non-negative) or C{None} if C{B{gamma} is not None}.
488 @kwarg gamma: Angle subtended by triangle side C{c} from this to B{C{pointB}} (C{degrees},
489 non-negative) or C{None} if C{B{beta} is not None}.
490 @kwarg useZ: If C{True}, use and interpolate the Z component, otherwise force C{z=INT0}
491 (C{bool}).
493 @note: This point, B{C{pointB}} and B{C{pointC}} are ordered clockwise.
495 @return: L{Tienstra7Tuple}C{(pointP, A, B, C, a, b, c)} with survey C{pointP},
496 an instance of this (sub-)class and triangle angle C{A} at this point,
497 C{B} at B{C{pointB}} and C{C} at B{C{pointC}} in C{degrees} and
498 triangle sides C{a}, C{b} and C{c}.
500 @raise ResectionError: Near-coincident, -colinear or -concyclic points or sum of
501 B{C{alpha}}, B{C{beta}} and B{C{gamma}} not C{360} or
502 negative B{C{alpha}}, B{C{beta}} or B{C{gamma}}.
504 @raise TypeError: Invalid B{C{pointB}} or B{C{pointC}}.
506 @see: Function L{pygeodesy.tienstra7} for references and more details.
507 '''
508 return _MODS.resections.tienstra7(self, pointB, pointC, alpha, beta, gamma,
509 useZ=useZ, datum=self.datum)
511 @deprecated_method
512 def to2ab(self): # PYCHOK no cover
513 '''DEPRECATED, use property C{philam}.
515 @return: A L{PhiLam2Tuple}C{(phi, lam)}.
516 '''
517 return self.philam
519 @deprecated_method
520 def to2ll(self): # PYCHOK no cover
521 '''DEPRECATED, use property C{latlon}.
523 @return: A L{LatLon2Tuple}C{(lat, lon)}.
524 '''
525 return self.latlon
527 @deprecated_method
528 def to3llh(self, datum=None): # PYCHOK no cover
529 '''DEPRECATED, use property L{latlonheightdatum} or L{latlonheight}.
531 @return: A L{LatLon4Tuple}C{(lat, lon, height, datum)}.
533 @note: This method returns a B{C{-4Tuple}} I{and not a} C{-3Tuple}
534 as its name may suggest.
535 '''
536 t = self.toLatLon(datum=datum, LatLon=None)
537 return LatLon4Tuple(t.lat, t.lon, t.height, t.datum, name=self.name)
539# def _to3LLh(self, datum, LL, **pairs): # OBSOLETE
540# '''(INTERNAL) Helper for C{subclass.toLatLon} and C{.to3llh}.
541# '''
542# r = self.to3llh(datum) # LatLon3Tuple
543# if LL is not None:
544# r = LL(r.lat, r.lon, height=r.height, datum=datum, name=self.name)
545# for n, v in pairs.items():
546# setattr(r, n, v)
547# return r
549 def toDatum(self, datum2, datum=None):
550 '''Convert this cartesian from one datum to an other.
552 @arg datum2: Datum to convert I{to} (L{Datum}).
553 @kwarg datum: Datum to convert I{from} (L{Datum}).
555 @return: The converted point (C{Cartesian}).
557 @raise TypeError: B{C{datum2}} or B{C{datum}}
558 invalid.
559 '''
560 _xinstanceof(Datum, datum2=datum2)
562 c = self if datum in (None, self.datum) else \
563 self.toDatum(datum)
565 i, d = False, c.datum
566 if d == datum2:
567 return c.copy() if c is self else c
569 elif d == _WGS84:
570 d = datum2 # convert from WGS84 to datum2
572 elif datum2 == _WGS84:
573 i = True # convert to WGS84 by inverse transformation
575 else: # neither datum2 nor c.datum is WGS84, invert to WGS84 first
576 c = c.toTransform(d.transform, inverse=True, datum=_WGS84)
577 d = datum2
579 return c.toTransform(d.transform, inverse=i, datum=datum2)
581 convertDatum = toDatum # for backward compatibility
583 def toEcef(self):
584 '''Convert this cartesian to I{geodetic} (lat-/longitude) coordinates.
586 @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height,
587 C, M, datum)} with C{C} and C{M} if available.
589 @raise EcefError: A C{.datum} or an ECEF issue.
590 '''
591 return self._ecef9
593 def toLatLon(self, datum=None, height=None, LatLon=None, **LatLon_kwds): # see .ecef.Ecef9Tuple.toDatum
594 '''Convert this cartesian to a geodetic (lat-/longitude) point.
596 @kwarg datum: Optional datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2}
597 or L{a_f2Tuple}).
598 @kwarg height: Optional height, overriding the converted height
599 (C{meter}), iff B{C{LatLon}} is not C{None}.
600 @kwarg LatLon: Optional class to return the geodetic point
601 (C{LatLon}) or C{None}.
602 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword
603 arguments, ignored if C{B{LatLon} is None}.
605 @return: The geodetic point (B{C{LatLon}}) or if B{C{LatLon}}
606 is C{None}, an L{Ecef9Tuple}C{(x, y, z, lat, lon,
607 height, C, M, datum)} with C{C} and C{M} if available.
609 @raise TypeError: Invalid B{C{datum}} or B{C{LatLon_kwds}}.
610 '''
611 d = _spherical_datum(datum or self.datum, name=self.name)
612 if d == self.datum:
613 r = self.toEcef()
614 else:
615 c = self.toDatum(d)
616 r = c.Ecef(d, name=self.name).reverse(c, M=LatLon is None)
618 if LatLon: # class or .classof
619 h = _heigHt(r, height)
620 r = LatLon(r.lat, r.lon, datum=r.datum, height=h,
621 **_xkwds(LatLon_kwds, name=r.name))
622 _xdatum(r.datum, d)
623 return r
625 def toLocal(self, Xyz=None, ltp=None, **Xyz_kwds):
626 '''Convert this I{geocentric} cartesian to I{local} C{X}, C{Y} and C{Z}.
628 @kwarg Xyz: Optional class to return C{X}, C{Y} and C{Z}
629 (L{XyzLocal}, L{Enu}, L{Ned}) or C{None}.
630 @kwarg ltp: The I{local tangent plane} (LTP) to use,
631 overriding this cartesian's LTP (L{Ltp}).
632 @kwarg Xyz_kwds: Optional, additional B{C{Xyz}} keyword
633 arguments, ignored if C{B{Xyz} is None}.
635 @return: An B{C{Xyz}} instance or if C{B{Xyz} is None},
636 a L{Local9Tuple}C{(x, y, z, lat, lon, height,
637 ltp, ecef, M)} with C{M=None} always.
639 @raise TypeError: Invalid B{C{ltp}}.
640 '''
641 p = _MODS.ltp._xLtp(ltp, self._ltp)
642 return p._ecef2local(self._ecef9, Xyz, Xyz_kwds)
644 def toLtp(self, Ecef=None):
645 '''Return the I{local tangent plane} (LTP) for this cartesian.
647 @kwarg Ecef: Optional ECEF I{class} (L{EcefKarney}, ...
648 L{EcefYou}), overriding this cartesian's C{Ecef}.
649 '''
650 return self._ltp if Ecef in (None, self.Ecef) else _MODS.ltp.Ltp(
651 self._ecef9, ecef=Ecef(self.datum), name=self.name)
653 def toNvector(self, Nvector=None, datum=None, **Nvector_kwds):
654 '''Convert this cartesian to C{n-vector} components.
656 @kwarg Nvector: Optional class to return the C{n-vector}
657 components (C{Nvector}) or C{None}.
658 @kwarg datum: Optional datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2}
659 or L{a_f2Tuple}) overriding this cartesian's datum.
660 @kwarg Nvector_kwds: Optional, additional B{C{Nvector}} keyword
661 arguments, ignored if C{B{Nvector} is None}.
663 @return: The C{unit, n-vector} components (B{C{Nvector}}) or a
664 L{Vector4Tuple}C{(x, y, z, h)} if B{C{Nvector}} is C{None}.
666 @raise TypeError: Invalid B{C{datum}}.
668 @raise ValueError: The B{C{Cartesian}} at origin.
670 @example:
672 >>> c = Cartesian(3980581, 97, 4966825)
673 >>> n = c.toNvector() # (x=0.622818, y=0.00002, z=0.782367, h=0.242887)
674 '''
675 d = _spherical_datum(datum or self.datum, name=self.name)
676 r = self._N_vector.xyzh if self.datum == d else self._n_xyzh4(d)
678 if Nvector is not None:
679 kwds = _xkwds(Nvector_kwds, h=r.h, datum=d)
680 r = self._xnamed(Nvector(r.x, r.y, r.z, **kwds))
681 return r
683 def toStr(self, prec=3, fmt=Fmt.SQUARE, sep=_COMMASPACE_): # PYCHOK expected
684 '''Return the string representation of this cartesian.
686 @kwarg prec: Number of (decimal) digits, unstripped (C{int}).
687 @kwarg fmt: Enclosing backets format (string).
688 @kwarg sep: Separator to join (string).
690 @return: Cartesian represented as "[x, y, z]" (string).
691 '''
692 return Vector3d.toStr(self, prec=prec, fmt=fmt, sep=sep)
694 def toTransform(self, transform, inverse=False, datum=None):
695 '''Return a new cartesian by applying a Helmert transform
696 to this cartesian.
698 @arg transform: Transform to apply (L{Transform}).
699 @kwarg inverse: Apply the inverse of the Helmert
700 transform (C{bool}).
701 @kwarg datum: Datum for the transformed cartesian (L{Datum}),
702 overriding this cartesian's datum.
704 @return: The transformed cartesian (C{Cartesian}).
706 @raise Valuerror: If C{B{inverse}=True} and B{C{datum}}
707 is not L{Datums}C{.WGS84}.
708 '''
709 d = datum or self.datum
710 if inverse and d != _WGS84:
711 raise _ValueError(inverse=inverse, datum=d,
712 txt=_not_(_WGS84.name))
714 xyz = transform.transform(*self.xyz, inverse=inverse)
715 return self.classof(xyz, datum=d)
717 def toVector(self, Vector=None, **Vector_kwds):
718 '''Return this cartesian's components as vector.
720 @kwarg Vector: Optional class to return the C{n-vector}
721 components (L{Vector3d}) or C{None}.
722 @kwarg Vector_kwds: Optional, additional B{C{Vector}} keyword
723 arguments, ignored if C{B{Vector} is None}.
725 @return: A B{C{Vector}} or a L{Vector3Tuple}C{(x, y, z)} if
726 B{C{Vector}} is C{None}.
728 @raise TypeError: Invalid B{C{Vector}} or B{C{Vector_kwds}}.
729 '''
730 return self.xyz if Vector is None else self._xnamed(
731 Vector(self.x, self.y, self.z, **Vector_kwds))
734__all__ += _ALL_DOCS(CartesianBase)
736# **) MIT License
737#
738# Copyright (C) 2016-2023 -- mrJean1 at Gmail -- All Rights Reserved.
739#
740# Permission is hereby granted, free of charge, to any person obtaining a
741# copy of this software and associated documentation files (the "Software"),
742# to deal in the Software without restriction, including without limitation
743# the rights to use, copy, modify, merge, publish, distribute, sublicense,
744# and/or sell copies of the Software, and to permit persons to whom the
745# Software is furnished to do so, subject to the following conditions:
746#
747# The above copyright notice and this permission notice shall be included
748# in all copies or substantial portions of the Software.
749#
750# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
751# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
752# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
753# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
754# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
755# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
756# OTHER DEALINGS IN THE SOFTWARE.