Coverage for pygeodesy/ecef.py: 95%
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2# -*- coding: utf-8 -*-
4u'''I{Geocentric} Earth-Centered, Earth-Fixed (ECEF) coordinates.
6Geocentric conversions transcoded from I{Charles Karney}'s C++ class U{Geocentric
7<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Geocentric.html>}
8into pure Python class L{EcefKarney}, class L{EcefSudano} based on I{John Sudano}'s
9U{paper<https://www.ResearchGate.net/publication/
103709199_An_exact_conversion_from_an_Earth-centered_coordinate_system_to_latitude_longitude_and_altitude>},
11class L{EcefVeness} transcoded from I{Chris Veness}' JavaScript classes U{LatLonEllipsoidal,
12Cartesian<https://www.Movable-Type.co.UK/scripts/geodesy/docs/latlon-ellipsoidal.js.html>}, class L{EcefYou}
13implementing I{Rey-Jer You}'s U{transformations <https://www.ResearchGate.net/publication/240359424>} and
14classes L{EcefFarrell22} and L{EcefFarrell22} from I{Jay A. Farrell}'s U{Table 2.1 and 2.2
15<https://Books.Google.com/books?id=fW4foWASY6wC>}, page 29-30.
17Following is a copy of I{Karney}'s U{Detailed Description
18<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Geocentric.html>}.
20Convert between geodetic coordinates C{lat}-, C{lon}gitude and height C{h} (measured vertically
21from the surface of the ellipsoid) to geocentric C{x}, C{y} and C{z} coordinates, also known as
22I{Earth-Centered, Earth-Fixed} (U{ECEF<https://WikiPedia.org/wiki/ECEF>}).
24The origin of geocentric coordinates is at the center of the earth. The C{z} axis goes thru
25the North pole, C{lat} = 90°. The C{x} axis goes thru C{lat} = 0°, C{lon} = 0°.
27The I{local (cartesian) origin} is at (C{lat0}, C{lon0}, C{height0}). The I{local} C{x} axis points
28East, the I{local} C{y} axis points North and the I{local} C{z} axis is normal to the ellipsoid. The
29plane C{z = -height0} is tangent to the ellipsoid, hence the alternate name I{local tangent plane}.
31Forward conversion from geodetic to geocentric (ECEF) coordinates is straightforward.
33For the reverse transformation we use Hugues Vermeille's U{I{Direct transformation from geocentric
34coordinates to geodetic coordinates}<https://DOI.org/10.1007/s00190-002-0273-6>}, J. Geodesy
35(2002) 76, page 451-454.
37Several changes have been made to ensure that the method returns accurate results for all finite
38inputs (even if h is infinite). The changes are described in Appendix B of C. F. F. Karney
39U{I{Geodesics on an ellipsoid of revolution}<https://ArXiv.org/abs/1102.1215v1>}, Feb. 2011, 85,
40105-117 (U{preprint<https://ArXiv.org/abs/1102.1215v1>}). Vermeille similarly updated his method
41in U{I{An analytical method to transform geocentric into geodetic coordinates}
42<https://DOI.org/10.1007/s00190-010-0419-x>}, J. Geodesy (2011) 85, page 105-117. See U{Geocentric
43coordinates<https://GeographicLib.SourceForge.io/C++/doc/geocentric.html>} for more information.
45The errors in these routines are close to round-off. Specifically, for points within 5,000 Km of
46the surface of the ellipsoid (either inside or outside the ellipsoid), the error is bounded by 7
47nm (7 nanometers) for the WGS84 ellipsoid. See U{Geocentric coordinates
48<https://GeographicLib.SourceForge.io/C++/doc/geocentric.html>} for further information on the errors.
50@see: Module L{ltp} and class L{LocalCartesian}, a transcription of I{Charles Karney}'s C++ class
51U{LocalCartesian <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1LocalCartesian.html>},
52providing conversion to and from I{local} cartesian cordinates in a I{local tangent plane} as
53opposed to I{geocentric} (ECEF) ones.
54'''
56from pygeodesy.basics import copysign0, isscalar, issubclassof, neg, map1, \
57 _xinstanceof, _xsubclassof
58from pygeodesy.constants import EPS, EPS0, EPS02, EPS1, EPS2, EPS_2, PI, PI_2, \
59 _0_0, _0_0001, _0_01, _0_5, _1_0, _1_0_1T, _2_0, \
60 _3_0, _4_0, _6_0, _60_0, _90_0, _100_0, isnon0, \
61 _N_2_0 # PYCHOK used!
62from pygeodesy.datums import a_f2Tuple, _ellipsoidal_datum
63# from pygeodesy.ellipsoids import a_f2Tuple # from .datums
64from pygeodesy.errors import _IndexError, LenError, _ValueError, _TypesError, \
65 _xattr, _xdatum, _xkwds
66from pygeodesy.fmath import cbrt, fdot, hypot, hypot1, hypot2_
67from pygeodesy.fsums import Fsum, fsumf_
68from pygeodesy.interns import NN, _a_, _C_, _datum_, _ellipsoid_, _f_, _height_, \
69 _lat_, _lon_, _M_, _name_, _singular_, _SPACE_, \
70 _x_, _xyz_, _y_, _z_
71from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS
72from pygeodesy.named import _NamedBase, _NamedTuple, notOverloaded, _Pass, _xnamed
73from pygeodesy.namedTuples import LatLon2Tuple, LatLon3Tuple, \
74 PhiLam2Tuple, Vector3Tuple, Vector4Tuple
75from pygeodesy.props import deprecated_method, Property_RO, property_RO, property_doc_
76from pygeodesy.streprs import Fmt, unstr
77from pygeodesy.units import Height, Int, Lam, Lat, Lon, Meter, Phi, Scalar, Scalar_
78from pygeodesy.utily import atan2d, degrees90, degrees180, sincos2, sincos2_, \
79 sincos2d_
81from math import asin, atan2, cos, degrees, fabs, radians, sqrt
83__all__ = _ALL_LAZY.ecef
84__version__ = '23.05.15'
86_Ecef_ = 'Ecef'
87_prolate_ = 'prolate'
88_TRIPS = 17 # 8..9 sufficient, EcefSudano.reverse
89_xyz_y_z = _xyz_, _y_, _z_ # _xargs_names(_xyzn4)[:3]
92class EcefError(_ValueError):
93 '''An ECEF or C{Ecef*} related issue.
94 '''
95 pass
98def _llhn4(latlonh, lon, height, suffix=NN, Error=EcefError, name=NN): # in .ltp.LocalCartesian.forward and -.reset
99 '''(INTERNAL) Get C{lat, lon, h, name} as C{4-tuple}.
100 '''
101 try:
102 lat, lon = latlonh.lat, latlonh.lon
103 h = _xattr(latlonh, height=_xattr(latlonh, h=height))
104 n = _xattr(latlonh, name=NN)
105 except AttributeError:
106 lat, h, n = latlonh, height, NN
108 try:
109 llhn = Lat(lat), Lon(lon), Height(h), (name or n)
110 except (TypeError, ValueError) as x:
111 t = _lat_, _lon_, _height_
112 if suffix:
113 t = (_ + suffix for _ in t)
114 d = dict(zip(t, (lat, lon, h)))
115 raise Error(cause=x, **d)
116 return llhn
119def _xyzn4(xyz, y, z, Types, Error=EcefError, name=NN, # in .ltp
120 _xyz_y_z_names=_xyz_y_z):
121 '''(INTERNAL) Get an C{(x, y, z, name)} 4-tuple.
122 '''
123 try:
124 try:
125 t = xyz.x, xyz.y, xyz.z, _xattr(xyz, name=name)
126 if not isinstance(xyz, Types):
127 raise _TypesError(_xyz_y_z_names[0], xyz, *Types)
128 except AttributeError:
129 t = map1(float, xyz, y, z) + (name,)
131 except (TypeError, ValueError) as x:
132 d = dict(zip(_xyz_y_z_names, (xyz, y, z)))
133 raise Error(cause=x, **d)
134 return t
136# assert _xyz_y_z == _xargs_names(_xyzn4)[:3]
139class _EcefBase(_NamedBase):
140 '''(INTERNAL) Base class for L{EcefFarrell21}, L{EcefFarrell22}, L{EcefKarney},
141 L{EcefSudano}, L{EcefVeness} and L{EcefYou}.
142 '''
143 _datum = None
144 _E = None
146 def __init__(self, a_ellipsoid, f=None, name=NN):
147 '''New C{Ecef*} converter.
149 @arg a_ellipsoid: A (non-prolate) ellipsoid (L{Ellipsoid}, L{Ellipsoid2},
150 L{Datum} or L{a_f2Tuple}) or C{scalar} ellipsoid's
151 equatorial radius (C{meter}).
152 @kwarg f: C{None} or the ellipsoid flattening (C{scalar}), required
153 for C{scalar} B{C{a_ellipsoid}}, C{B{f}=0} represents a
154 sphere, negative B{C{f}} a prolate ellipsoid.
155 @kwarg name: Optional name (C{str}).
157 @raise EcefError: If B{C{a_ellipsoid}} not L{Ellipsoid}, L{Ellipsoid2},
158 L{Datum} or L{a_f2Tuple} or C{scalar} or B{C{f}} not
159 C{scalar} or if C{scalar} B{C{a_ellipsoid}} not positive
160 or B{C{f}} not less than 1.0.
161 '''
162 if name:
163 self.name = name
164 try:
165 E = a_ellipsoid
166 if f is None:
167 pass
168 elif isscalar(E) and isscalar(f):
169 E = a_f2Tuple(E, f)
170 else:
171 raise ValueError # _invalid_
173 d = _ellipsoidal_datum(E, name=name)
174 E = d.ellipsoid
175 if E.a < EPS or E.f > EPS1:
176 raise ValueError # _invalid_
178 except (TypeError, ValueError) as x:
179 t = unstr(self.classname, a=a_ellipsoid, f=f)
180 raise EcefError(_SPACE_(t, _ellipsoid_), cause=x)
182 self._datum = d
183 self._E = E
185 def __eq__(self, other):
186 '''Compare this and an other Ecef.
188 @arg other: The other ecef (C{Ecef*}).
190 @return: C{True} if equal, C{False} otherwise.
191 '''
192 return other is self or (isinstance(other, self.__class__) and
193 other.ellipsoid == self.ellipsoid)
195 @Property_RO
196 def equatoradius(self):
197 '''Get the I{equatorial} radius, semi-axis (C{meter}).
198 '''
199 return self.ellipsoid.a
201 a = equatorialRadius = equatoradius # Karney property
203 @Property_RO
204 def datum(self):
205 '''Get the datum (L{Datum}).
206 '''
207 return self._datum
209 @Property_RO
210 def ellipsoid(self):
211 '''Get the ellipsoid (L{Ellipsoid} or L{Ellipsoid2}).
212 '''
213 return self._E
215 @Property_RO
216 def flattening(self): # Karney property
217 '''Get the I{flattening} (C{float}), M{(a - b) / a}, positive for
218 I{oblate}, negative for I{prolate} or C{0} for I{near-spherical}.
219 '''
220 return self.ellipsoid.f
222 f = flattening
224 def _forward(self, lat, lon, h, name, M=False, _philam=False): # in .ltp.LocalCartesian.forward and -.reset
225 '''(INTERNAL) Common for all C{Ecef*}.
226 '''
227 E = self.ellipsoid
229 if _philam:
230 sa, ca, sb, cb = sincos2_(lat, lon)
231 lat = Lat(degrees90( lat))
232 lon = Lon(degrees180(lon))
233 else:
234 sa, ca, sb, cb = sincos2d_(lat, lon)
236 n = E.roc1_(sa, ca) if self._isYou else E.roc1_(sa)
237 z = (h + n * E.e21) * sa
238 x = (h + n) * ca
240 m = self._Matrix(sa, ca, sb, cb) if M else None
241 return Ecef9Tuple(x * cb, x * sb, z, lat, lon, h,
242 0, m, self.datum,
243 name=name or self.name)
245 def forward(self, latlonh, lon=None, height=0, M=False, name=NN):
246 '''Convert from geodetic C{(lat, lon, height)} to geocentric C{(x, y, z)}.
248 @arg latlonh: Either a C{LatLon}, an L{Ecef9Tuple} or C{scalar}
249 latitude (C{degrees}).
250 @kwarg lon: Optional C{scalar} longitude for C{scalar} B{C{latlonh}}
251 (C{degrees}).
252 @kwarg height: Optional height (C{meter}), vertically above (or below)
253 the surface of the ellipsoid.
254 @kwarg M: Optionally, return the rotation L{EcefMatrix} (C{bool}).
255 @kwarg name: Optional name (C{str}).
257 @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with
258 geocentric C{(x, y, z)} coordinates for the given geodetic ones
259 C{(lat, lon, height)}, case C{C} 0, optional C{M} (L{EcefMatrix})
260 and C{datum} if available.
262 @raise EcefError: If B{C{latlonh}} not C{LatLon}, L{Ecef9Tuple} or
263 C{scalar} or B{C{lon}} not C{scalar} for C{scalar}
264 B{C{latlonh}} or C{abs(lat)} exceeds 90°.
266 @note: Use method C{.forward_} to specify C{lat} and C{lon} in C{radians}
267 and avoid double angle conversions.
268 '''
269 llhn = _llhn4(latlonh, lon, height, name=name)
270 return _EcefBase._forward(self, *llhn, M=M)
272 def forward_(self, phi, lam, height=0, M=False, name=NN):
273 '''Like method C{.forward} except with geodetic lat- and longitude given
274 in I{radians}.
276 @arg phi: Latitude in I{radians} (C{scalar}).
277 @arg lam: Longitude in I{radians} (C{scalar}).
278 @kwarg height: Optional height (C{meter}), vertically above (or below)
279 the surface of the ellipsoid.
280 @kwarg M: Optionally, return the rotation L{EcefMatrix} (C{bool}).
281 @kwarg name: Optional name (C{str}).
283 @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)}
284 with C{lat} set to C{degrees90(B{phi})} and C{lon} to
285 C{degrees180(B{lam})}.
287 @raise EcefError: If B{C{phi}} or B{C{lam}} invalid or not C{scalar}.
288 '''
289 try: # like function C{_llhn4} above
290 plhn = Phi(phi), Lam(lam), Height(height), name
291 except (TypeError, ValueError) as x:
292 raise EcefError(phi=phi, lam=lam, height=height, cause=x)
293 return self._forward(*plhn, M=M, _philam=True)
295 @property_RO
296 def _Geocentrics(self):
297 '''(INTERNAL) Valid geocentric classes.
298 '''
299 t = Ecef9Tuple, _MODS.cartesianBase.CartesianBase
300 _EcefBase._Geocentrics = t # overwrite the property
301 return t
303 @Property_RO
304 def _isYou(self):
305 '''(INTERNAL) Is this an C{EcefYou}?.
306 '''
307 return isinstance(self, EcefYou)
309 def _Matrix(self, sa, ca, sb, cb):
310 '''Creation a rotation matrix.
312 @arg sa: C{sin(phi)} (C{float}).
313 @arg ca: C{cos(phi)} (C{float}).
314 @arg sb: C{sin(lambda)} (C{float}).
315 @arg cb: C{cos(lambda)} (C{float}).
317 @return: An L{EcefMatrix}.
318 '''
319 return self._xnamed(EcefMatrix(sa, ca, sb, cb))
321 def reverse(self, xyz, y=None, z=None, M=False, name=NN): # PYCHOK no cover
322 '''(INTERNAL) I{Must be overloaded}, see function C{notOverloaded}.
323 '''
324 notOverloaded(self, xyz, y=y, z=z, M=M, name=name)
326 def toStr(self, prec=9, **unused): # PYCHOK signature
327 '''Return this C{Ecef*} as a string.
329 @kwarg prec: Precision, number of decimal digits (0..9).
331 @return: This C{Ecef*} (C{str}).
332 '''
333 return self.attrs(_a_, _f_, _datum_, _name_, prec=prec) # _ellipsoid_
336class EcefFarrell21(_EcefBase):
337 '''Conversion between geodetic and geocentric, I{Earth-Centered, Earth-Fixed} (ECEF)
338 coordinates based on I{Jay A. Farrell}'s U{Table 2.1<https://Books.Google.com/
339 books?id=fW4foWASY6wC>}, page 29.
340 '''
342 def reverse(self, xyz, y=None, z=None, M=None, name=NN): # PYCHOK unused M
343 '''Convert from geocentric C{(x, y, z)} to geodetic C{(lat, lon, height)} using
344 I{Farrell}'s U{Table 2.1<https://Books.Google.com/books?id=fW4foWASY6wC>},
345 page 29.
347 @arg xyz: A geocentric (C{Cartesian}, L{Ecef9Tuple}) or C{scalar} ECEF C{x}
348 coordinate (C{meter}).
349 @kwarg y: ECEF C{y} coordinate for C{scalar} B{C{xyz}} and B{C{z}} (C{meter}).
350 @kwarg z: ECEF C{z} coordinate for C{scalar} B{C{xyz}} and B{C{y}} (C{meter}).
351 @kwarg M: I{Ignored}, rotation matrix C{M} not available.
352 @kwarg name: Optional name (C{str}).
354 @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with
355 geodetic coordinates C{(lat, lon, height)} for the given geocentric
356 ones C{(x, y, z)}, case C{C=1}, C{M=None} always and C{datum}
357 if available.
359 @raise EcefError: Invalid B{C{xyz}} or C{scalar} C{x} or B{C{y}} and/or B{C{z}}
360 not C{scalar} for C{scalar} B{C{xyz}} or C{sqrt} domain or
361 zero division error.
363 @see: L{EcefFarrell22} and L{EcefVeness}.
364 '''
365 x, y, z, name = _xyzn4(xyz, y, z, self._Geocentrics, name=name)
367 E = self.ellipsoid
368 a = E.a
369 a2 = E.a2
370 b2 = E.b2
371 e2 = E.e2
372 e2_ = E.e2abs * E.a2_b2 # (E.e * E.a_b)**2 = 0.0820944... WGS84
373 e4 = E.e4
375 try: # names as page 29
376 z2 = z**2
377 ez = (_1_0 - e2) * z2 # E.e2s2(z)
379 p = hypot(x, y)
380 p2 = p**2
381 G = p2 + ez - e2 * (a2 - b2) # p2 + ez - e4 * a2
382 F = b2 * z2 * 54
383 c = e4 * p2 * F / G**3
384 s = cbrt(_1_0 + c + sqrt(c**2 + c * 2))
385 P = F / (_3_0 * (fsumf_(_1_0, s, _1_0 / s) * G)**2)
386 Q = sqrt(_1_0 + _2_0 * e4 * P)
387 Q1 = Q + _1_0
388 r0 = P * e2 * p / Q1 - sqrt(fsumf_(a2 * (Q1 / Q) * _0_5,
389 -P * ez / (Q * Q1),
390 -P * p2 * _0_5))
391 r = p + e2 * r0
392 v = b2 / (a * sqrt(r**2 + ez))
394 h = hypot(r, z) * (_1_0 - v)
395 t = atan2((e2_ * v + _1_0) * z, p)
396 # note, phi and lam are swapped on page 29
398 except (ValueError, ZeroDivisionError) as e:
399 raise EcefError(x=x, y=y, z=z, cause=e)
401 return Ecef9Tuple(x, y, z, degrees90(t), atan2d(y, x), h,
402 1, None, self.datum,
403 name=name or self.name)
406class EcefFarrell22(_EcefBase):
407 '''Conversion between geodetic and geocentric, I{Earth-Centered, Earth-Fixed} (ECEF)
408 coordinates based on I{Jay A. Farrell}'s U{Table 2.2<https://Books.Google.com/
409 books?id=fW4foWASY6wC>}, page 30.
410 '''
412 def reverse(self, xyz, y=None, z=None, M=None, name=NN): # PYCHOK unused M
413 '''Convert from geocentric C{(x, y, z)} to geodetic C{(lat, lon, height)} using
414 I{Farrell}'s U{Table 2.2<https://Books.Google.com/books?id=fW4foWASY6wC>},
415 page 30.
417 @arg xyz: A geocentric (C{Cartesian}, L{Ecef9Tuple}) or C{scalar} ECEF C{x}
418 coordinate (C{meter}).
419 @kwarg y: ECEF C{y} coordinate for C{scalar} B{C{xyz}} and B{C{z}} (C{meter}).
420 @kwarg z: ECEF C{z} coordinate for C{scalar} B{C{xyz}} and B{C{y}} (C{meter}).
421 @kwarg M: I{Ignored}, rotation matrix C{M} not available.
422 @kwarg name: Optional name (C{str}).
424 @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with
425 geodetic coordinates C{(lat, lon, height)} for the given geocentric
426 ones C{(x, y, z)}, case C{C=1}, C{M=None} always and C{datum}
427 if available.
429 @raise EcefError: Invalid B{C{xyz}} or C{scalar} C{x} or B{C{y}} and/or B{C{z}}
430 not C{scalar} for C{scalar} B{C{xyz}} or C{sqrt} domain or
431 zero division error.
433 @see: L{EcefFarrell21} and L{EcefVeness}.
434 '''
435 x, y, z, name = _xyzn4(xyz, y, z, self._Geocentrics, name=name)
437 E = self.ellipsoid
438 a = E.a
439 b = E.b
441 try: # see EcefVeness.reverse
442 p = hypot(x, y)
443 s, c = sincos2(atan2(z * a, p * b))
445 t = atan2(z + E.e22 * b * s**3,
446 p - E.e2 * a * c**3)
447 s, c = sincos2(t)
448 if c: # E.roc1_(s) = E.a / sqrt(1 - E.e2 * s**2)
449 h = p / c - (E.roc1_(s) if s else a)
450 else: # polar
451 h = fabs(z) - b
452 # note, phi and lam are swapped on page 30
454 except (ValueError, ZeroDivisionError) as e:
455 raise EcefError(x=x, y=y, z=z, cause=e)
457 return Ecef9Tuple(x, y, z, degrees90(t), atan2d(y, x), h,
458 1, None, self.datum,
459 name=name or self.name)
462class EcefKarney(_EcefBase):
463 '''Conversion between geodetic and geocentric, I{Earth-Centered, Earth-Fixed} (ECEF)
464 coordinates transcoded from I{Karney}'s C++ U{Geocentric<https://GeographicLib.SourceForge.io/
465 C++/doc/classGeographicLib_1_1Geocentric.html>} methods.
467 @note: On methods C{.forward} and C{.forwar_}, let C{v} be a unit vector located
468 at C{(lat, lon, h)}. We can express C{v} as column vectors in one of two
469 ways, C{v1} in east, north, up coordinates (where the components are
470 relative to a local coordinate system at C{C(lat0, lon0, h0)}) or as C{v0}
471 in geocentric C{x, y, z} coordinates. Then, M{v0 = M ⋅ v1} where C{M} is
472 the rotation matrix.
473 '''
475 @Property_RO
476 def hmax(self):
477 '''Get the distance or height limit (C{meter}, conventionally).
478 '''
479 return self.equatoradius / EPS_2 # self.equatoradius * _2_EPS, 12M lighyears
481 def reverse(self, xyz, y=None, z=None, M=False, name=NN):
482 '''Convert from geocentric C{(x, y, z)} to geodetic C{(lat, lon, height)}.
484 @arg xyz: A geocentric (C{Cartesian}, L{Ecef9Tuple}) or C{scalar} ECEF C{x}
485 coordinate (C{meter}).
486 @kwarg y: ECEF C{y} coordinate for C{scalar} B{C{xyz}} and B{C{z}} (C{meter}).
487 @kwarg z: ECEF C{z} coordinate for C{scalar} B{C{xyz}} and B{C{y}} (C{meter}).
488 @kwarg M: Optionally, return the rotation L{EcefMatrix} (C{bool}).
489 @kwarg name: Optional name (C{str}).
491 @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with
492 geodetic coordinates C{(lat, lon, height)} for the given geocentric
493 ones C{(x, y, z)}, case C{C}, optional C{M} (L{EcefMatrix}) and
494 C{datum} if available.
496 @raise EcefError: Invalid B{C{xyz}} or C{scalar} C{x} or B{C{y}} and/or B{C{z}}
497 not C{scalar} for C{scalar} B{C{xyz}}.
499 @note: In general, there are multiple solutions and the result which minimizes
500 C{height} is returned, i.e., C{(lat, lon)} corresponds to the closest
501 point on the ellipsoid. If there are still multiple solutions with
502 different latitudes (applies only if C{z} = 0), then the solution with
503 C{lat} > 0 is returned. If there are still multiple solutions with
504 different longitudes (applies only if C{x} = C{y} = 0) then C{lon} = 0
505 is returned. The returned C{height} value is not below M{−E.a * (1 −
506 E.e2) / sqrt(1 − E.e2 * sin(lat)**2)}. The returned C{lon} is in the
507 range [−180°, 180°]. Like C{forward} above, M{v1 = Transpose(M) ⋅ v0}.
508 '''
509 def norm3(y, x):
510 h = hypot(y, x) # EPS0, EPS_2
511 return (y / h, x / h, h) if h > 0 else (_0_0, _1_0, h)
513 x, y, z, name = _xyzn4(xyz, y, z, self._Geocentrics, name=name)
515 E = self.ellipsoid
517 sb, cb, R = norm3(y, x)
518 h = hypot(R, z) # distance to earth center
519 if h > self.hmax: # PYCHOK no cover
520 # We are really far away (> 12M light years). Treat the earth
521 # as a point and h, above as an acceptable approximation to the
522 # height. This avoids overflow, e.g., in the computation of disc
523 # below. It's possible that h has overflowed to INF, that's OK.
524 # Treat finite x, y, but R overflows to +INF by scaling by 2.
525 sb, cb, R = norm3(y * _0_5, x * _0_5)
526 sa, ca, _ = norm3(z * _0_5, R)
527 C = 1
529 elif E.e4: # E.isEllipsoidal
530 # Treat prolate spheroids by swapping R and Z here and by
531 # switching the arguments to phi = atan2(...) at the end.
532 p = (R / E.a)**2
533 q = E.e21 * (z / E.a)**2
534 if E.isProlate:
535 p, q = q, p
536 r = p + q - E.e4
537 e = E.e4 * q
538 if e or r > 0:
539 # Avoid possible division by zero when r = 0 by multiplying
540 # equations for s and t by r^3 and r, respectively.
541 s = e * p / _4_0 # s = r^3 * s
542 u = r = r / _6_0
543 r2 = r**2
544 r3 = r * r2
545 t3 = s + r3
546 disc = s * (r3 + t3)
547 if disc < 0:
548 # t is complex, but the way u is defined, the result is real.
549 # There are three possible cube roots. We choose the root
550 # which avoids cancellation. Note, disc < 0 implies r < 0.
551 u += _2_0 * r * cos(atan2(sqrt(-disc), -t3) / _3_0)
552 else:
553 # Pick the sign on the sqrt to maximize abs(T3). This
554 # minimizes loss of precision due to cancellation. The
555 # result is unchanged because of the way the t is used
556 # in definition of u.
557 if disc > 0:
558 t3 += copysign0(sqrt(disc), t3) # t3 = (r * t)^3
559 # N.B. cbrt always returns the real root, cbrt(-8) = -2.
560 t = cbrt(t3) # t = r * t
561 # t can be zero; but then r2 / t -> 0.
562 if t:
563 u = fsumf_(u, t, r2 / t)
564 v = sqrt(e + u**2) # guaranteed positive
565 # Avoid loss of accuracy when u < 0. Underflow doesn't occur in
566 # E.e4 * q / (v - u) because u ~ e^4 when q is small and u < 0.
567 uv = (e / (v - u)) if u < 0 else (u + v) # u+v, guaranteed positive
568 # Need to guard against w going negative due to roundoff in uv - q.
569 w = max(_0_0, E.e2abs * (uv - q) / (_2_0 * v))
570 # Rearrange expression for k to avoid loss of accuracy due to
571 # subtraction. Division by 0 not possible because uv > 0, w >= 0.
572 k1 = k2 = uv / (sqrt(uv + w**2) + w)
573 if E.isProlate:
574 k1 -= E.e2
575 else:
576 k2 += E.e2
577 sa, ca, h = norm3(z / k1, R / k2)
578 h *= k1 - E.e21
579 C = 2
581 else: # e = E.e4 * q == 0 and r <= 0
582 # This leads to k = 0 (oblate, equatorial plane) and k + E.e^2 = 0
583 # (prolate, rotation axis) and the generation of 0/0 in the general
584 # formulas for phi and h, using the general formula and division
585 # by 0 in formula for h. Handle this case by taking the limits:
586 # f > 0: z -> 0, k -> E.e2 * sqrt(q) / sqrt(E.e4 - p)
587 # f < 0: r -> 0, k + E.e2 -> -E.e2 * sqrt(q) / sqrt(E.e4 - p)
588 q = E.e4 - p
589 if E.isProlate:
590 p, q = q, p
591 e = E.a
592 else:
593 e = E.b2_a
594 sa, ca, h = norm3(sqrt(q * E._1_e21), sqrt(p))
595 if z < 0:
596 sa = neg(sa) # for tiny negative z, not for prolate
597 h *= neg(e / E.e2abs)
598 C = 3
600 else: # E.e4 == 0, spherical case
601 # Dealing with underflow in the general case with E.e2 = 0 is
602 # difficult. Origin maps to North pole, same as with ellipsoid.
603 sa, ca, _ = norm3((z if h else _1_0), R)
604 h -= E.a
605 C = 4
607 m = self._Matrix(sa, ca, sb, cb) if M else None
608 return Ecef9Tuple(x, y, z, atan2d(sa, ca),
609 atan2d(sb, cb), h,
610 C, m, self.datum,
611 name=name or self.name)
614class EcefSudano(_EcefBase):
615 '''Conversion between geodetic and geocentric, I{Earth-Centered, Earth-Fixed} (ECEF) coordinates
616 based on I{John J. Sudano}'s U{paper<https://www.ResearchGate.net/publication/
617 3709199_An_exact_conversion_from_an_Earth-centered_coordinate_system_to_latitude_longitude_and_altitude>}.
618 '''
619 _tol = EPS2
621 def reverse(self, xyz, y=None, z=None, M=None, name=NN): # PYCHOK unused M
622 '''Convert from geocentric C{(x, y, z)} to geodetic C{(lat, lon, height)} using
623 I{Sudano}'s U{iterative method<https://www.ResearchGate.net/publication/
624 3709199_An_exact_conversion_from_an_Earth-centered_coordinate_system_to_latitude_longitude_and_altitude>}.
626 @arg xyz: A geocentric (C{Cartesian}, L{Ecef9Tuple}) or C{scalar} ECEF C{x}
627 coordinate (C{meter}).
628 @kwarg y: ECEF C{y} coordinate for C{scalar} B{C{xyz}} and B{C{z}} (C{meter}).
629 @kwarg z: ECEF C{z} coordinate for C{scalar} B{C{xyz}} and B{C{y}} (C{meter}).
630 @kwarg M: I{Ignored}, rotation matrix C{M} not available.
631 @kwarg name: Optional name (C{str}).
633 @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with geodetic
634 coordinates C{(lat, lon, height)} for the given geocentric ones C{(x, y, z)},
635 iteration C{C}, C{M=None} always and C{datum} if available.
637 @raise EcefError: Invalid B{C{xyz}} or C{scalar} C{x} or B{C{y}} and/or B{C{z}}
638 not C{scalar} for C{scalar} B{C{xyz}} or no convergence.
639 '''
640 x, y, z, name = _xyzn4(xyz, y, z, self._Geocentrics, name=name)
642 E = self.ellipsoid
643 e = E.e2 * E.a
644 h = hypot(x, y) # Rh
645 d = e - h
647 a = atan2(z, h * E.e21)
648 sa, ca = sincos2(fabs(a))
649 # Sudano's Eq (A-6) and (A-7) refactored/reduced,
650 # replacing Rn from Eq (A-4) with n = E.a / ca:
651 # N = ca**2 * ((z + E.e2 * n * sa) * ca - h * sa)
652 # = ca**2 * (z * ca + E.e2 * E.a * sa - h * sa)
653 # = ca**2 * (z * ca + (E.e2 * E.a - h) * sa)
654 # D = ca**3 * (E.e2 * n / E.e2s2(sa)) - h
655 # = ca**2 * (E.e2 * E.a / E.e2s2(sa) - h / ca**2)
656 # N / D = (z * ca + (E.e2 * E.a - h) * sa) /
657 # (E.e2 * E.a / E.e2s2(sa) - h / ca**2)
658 tol = self.tolerance
659 _S2_ = Fsum(sa).fsum2_
660 for C in range(1, _TRIPS):
661 ca2 = _1_0 - sa**2
662 if ca2 < EPS_2: # PYCHOK no cover
663 ca = _0_0
664 break
665 ca = sqrt(ca2)
666 r = e / E.e2s2(sa) - h / ca2
667 if fabs(r) < EPS_2:
668 break
669 a = None
670 sa, r = _S2_(-z * ca / r, -d * sa / r)
671 if fabs(r) < tol:
672 break
673 else:
674 t = unstr(self.reverse, x=x, y=y, z=z)
675 raise EcefError(Fmt.no_convergence(r, tol), txt=t)
677 if a is None:
678 a = copysign0(asin(sa), z)
679 h = fsumf_(h * ca, fabs(z * sa), -E.a * E.e2s(sa)) # use Veness',
680 # since Sudano's Eq (7) doesn't provide the correct height
681 # h = (fabs(z) + h - E.a * cos(a + E.e21) * sa / ca) / (ca + sa)
683 r = Ecef9Tuple(x, y, z, degrees90(a), atan2d(y, x), h,
684 C, None, self.datum,
685 name=name or self.name)
686 r._iteration = C
687 return r
689 @property_doc_(''' the convergence tolerance (C{float}).''')
690 def tolerance(self):
691 '''Get the convergence tolerance (C{scalar}).
692 '''
693 return self._tol
695 @tolerance.setter # PYCHOK setter!
696 def tolerance(self, tol):
697 '''Set the convergence tolerance (C{scalar}).
699 @raise EcefError: Non-scalar or invalid B{C{tol}}.
700 '''
701 self._tol = Scalar_(tolerance=tol, low=EPS, Error=EcefError)
704class EcefVeness(_EcefBase):
705 '''Conversion between geodetic and geocentric, I{Earth-Centered, Earth-Fixed} (ECEF) coordinates
706 transcoded from I{Chris Veness}' JavaScript classes U{LatLonEllipsoidal, Cartesian<https://
707 www.Movable-Type.co.UK/scripts/geodesy/docs/latlon-ellipsoidal.js.html>}.
709 @see: U{I{A Guide to Coordinate Systems in Great Britain}<https://
710 www.OrdnanceSurvey.co.UK/documents/resources/guide-coordinate-systems-great-britain.pdf>},
711 section I{B) Converting between 3D Cartesian and ellipsoidal
712 latitude, longitude and height coordinates}.
713 '''
715 def reverse(self, xyz, y=None, z=None, M=None, name=NN): # PYCHOK unused M
716 '''Convert from geocentric C{(x, y, z)} to geodetic C{(lat, lon, height)}
717 transcoded from I{Chris Veness}' U{JavaScript<https://www.Movable-Type.co.UK/
718 scripts/geodesy/docs/latlon-ellipsoidal.js.html>}.
720 Uses B. R. Bowring’s formulation for μm precision in concise form U{I{The accuracy
721 of geodetic latitude and height equations}<https://www.ResearchGate.net/publication/
722 233668213_The_Accuracy_of_Geodetic_Latitude_and_Height_Equations>}, Survey Review,
723 Vol 28, 218, Oct 1985.
725 @arg xyz: A geocentric (C{Cartesian}, L{Ecef9Tuple}) or C{scalar} ECEF C{x}
726 coordinate (C{meter}).
727 @kwarg y: ECEF C{y} coordinate for C{scalar} B{C{xyz}} and B{C{z}} (C{meter}).
728 @kwarg z: ECEF C{z} coordinate for C{scalar} B{C{xyz}} and B{C{y}} (C{meter}).
729 @kwarg M: I{Ignored}, rotation matrix C{M} not available.
730 @kwarg name: Optional name (C{str}).
732 @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with
733 geodetic coordinates C{(lat, lon, height)} for the given geocentric
734 ones C{(x, y, z)}, case C{C}, C{M=None} always and C{datum} if available.
736 @raise EcefError: Invalid B{C{xyz}} or C{scalar} C{x} or B{C{y}} and/or B{C{z}}
737 not C{scalar} for C{scalar} B{C{xyz}}.
739 @see: Toms, Ralph M. U{I{An Efficient Algorithm for Geocentric to Geodetic
740 Coordinate Conversion}<https://www.OSTI.gov/scitech/biblio/110235>},
741 Sept 1995 and U{I{An Improved Algorithm for Geocentric to Geodetic
742 Coordinate Conversion}<https://www.OSTI.gov/scitech/servlets/purl/231228>},
743 Apr 1996, both from Lawrence Livermore National Laboratory (LLNL) and
744 Sudano, John J, U{I{An exact conversion from an Earth-centered coordinate
745 system to latitude longitude and altitude}<https://www.ResearchGate.net/
746 publication/3709199_An_exact_conversion_from_an_Earth-centered_coordinate_system_to_latitude_longitude_and_altitude>}.
747 '''
748 x, y, z, name = _xyzn4(xyz, y, z, self._Geocentrics, name=name)
750 E = self.ellipsoid
752 p = hypot(x, y) # distance from minor axis
753 r = hypot(p, z) # polar radius
754 if min(p, r) > EPS0:
755 b = E.b * E.e22
756 # parametric latitude (Bowring eqn 17, replaced)
757 t = (E.b * z) / (E.a * p) * (_1_0 + b / r)
758 c = _1_0 / hypot1(t)
759 s = t * c
761 # geodetic latitude (Bowring eqn 18)
762 a = atan2(z + b * s**3,
763 p - E.e2 * E.a * c**3)
765 # height above ellipsoid (Bowring eqn 7)
766 sa, ca = sincos2(a)
767# r = E.a / E.e2s(sa) # length of normal terminated by minor axis
768# h = p * ca + z * sa - (E.a * E.a / r)
769 h = fsumf_(p * ca, z * sa, -E.a * E.e2s(sa))
771 C, lat, lon = 1, degrees90(a), atan2d(y, x)
773 # see <https://GIS.StackExchange.com/questions/28446>
774 elif p > EPS: # lat arbitrarily zero
775 C, lat, lon, h = 2, _0_0, atan2d(y, x), p - E.a
777 else: # polar lat, lon arbitrarily zero
778 C, lat, lon, h = 3, copysign0(_90_0, z), _0_0, fabs(z) - E.b
780 return Ecef9Tuple(x, y, z, lat, lon, h,
781 C, None, # M=None
782 self.datum, name=name or self.name)
785class EcefYou(_EcefBase):
786 '''Conversion between geodetic and geocentric, I{Earth-Centered, Earth-Fixed} (ECEF) coordinates
787 using I{Rey-Jer You}'s U{transformation<https://www.ResearchGate.net/publication/240359424>}.
789 @see: Featherstone, W.E., Claessens, S.J. U{I{Closed-form transformation between geodetic and
790 ellipsoidal coordinates}<https://Espace.Curtin.edu.AU/bitstream/handle/20.500.11937/
791 11589/115114_9021_geod2ellip_final.pdf>} Studia Geophysica et Geodaetica, 2008, 52,
792 pages 1-18 and U{PyMap3D <https://PyPI.org/project/pymap3d>}.
793 '''
795 def __init__(self, a_ellipsoid, f=None, name=NN):
796 _EcefBase.__init__(self, a_ellipsoid, f=f, name=name) # inherited documentation
797 E = self.ellipsoid
798 if E.isProlate or (E.a2 - E.b2) < 0:
799 raise EcefError(ellipsoid=E, txt=_prolate_)
801 def reverse(self, xyz, y=None, z=None, M=None, name=NN): # PYCHOK unused M
802 '''Convert geocentric C{(x, y, z)} to geodetic C{(lat, lon, height)}
803 using I{Rey-Jer You}'s transformation.
805 @arg xyz: A geocentric (C{Cartesian}, L{Ecef9Tuple}) or C{scalar} ECEF C{x}
806 coordinate (C{meter}).
807 @kwarg y: ECEF C{y} coordinate for C{scalar} B{C{xyz}} and B{C{z}} (C{meter}).
808 @kwarg z: ECEF C{z} coordinate for C{scalar} B{C{xyz}} and B{C{y}} (C{meter}).
809 @kwarg M: I{Ignored}, rotation matrix C{M} not available.
810 @kwarg name: Optional name (C{str}).
812 @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with
813 geodetic coordinates C{(lat, lon, height)} for the given geocentric
814 ones C{(x, y, z)}, case C{C=1}, C{M=None} always and C{datum} if
815 available.
817 @raise EcefError: Invalid B{C{xyz}} or C{scalar} C{x} or B{C{y}} and/or
818 B{C{z}} not C{scalar} for C{scalar} B{C{xyz}}.
819 '''
820 x, y, z, name = _xyzn4(xyz, y, z, self._Geocentrics, name=name)
822 r2 = hypot2_(x, y, z)
824 E = self.ellipsoid
825 e2 = E.a2 - E.b2 # == E.e2 * E.a2
826 if e2 < 0:
827 raise EcefError(ellipsoid=E, txt=_prolate_)
828 e = sqrt(e2) # XXX sqrt0(e2)?
830 q = hypot(x, y)
831 u = fsumf_(r2, -e2, hypot(r2 - e2, 2 * e * z)) * _0_5
832 if u > EPS02:
833 u = sqrt(u)
834 p = hypot(u, e)
835 B = atan2(p * z, u * q) # beta0 = atan(p / u * z / q)
836 sB, cB = sincos2(B)
837 if cB and sB:
838 p *= E.a
839 d = (p / cB - e2 * cB) / sB
840 if isnon0(d):
841 B += fsumf_(u * E.b, -p, e2) / d
842 sB, cB = sincos2(B)
843 elif u < 0:
844 raise EcefError(x=x, y=y, z=z, txt=_singular_)
845 else:
846 sB, cB = copysign0(_1_0, z), _0_0
848 h = hypot(z - E.b * sB, q - E.a * cB)
849 if hypot2_(x, y, z * E.a_b) < E.a2:
850 h = neg(h) # inside ellipsoid
852 return Ecef9Tuple(x, y, z, atan2d(E.a * sB, E.b * cB), # atan(E.a_b * tan(B))
853 atan2d(y, x), h,
854 1, None, # C=1, M=None
855 self.datum, name=name or self.name)
858class EcefMatrix(_NamedTuple):
859 '''A rotation matrix.
860 '''
861 _Names_ = ('_0_0_', '_0_1_', '_0_2_', # row-order
862 '_1_0_', '_1_1_', '_1_2_',
863 '_2_0_', '_2_1_', '_2_2_')
864 _Units_ = (Scalar,) * len(_Names_)
866 def _validate(self, **_OK): # PYCHOK unused
867 '''(INTERNAL) Allow C{_Names_} with leading underscore.
868 '''
869 _NamedTuple._validate(self, _OK=True)
871 def __new__(cls, sa, ca, sb, cb, *_more):
872 '''New L{EcefMatrix} matrix.
874 @arg sa: C{sin(phi)} (C{float}).
875 @arg ca: C{cos(phi)} (C{float}).
876 @arg sb: C{sin(lambda)} (C{float}).
877 @arg cb: C{cos(lambda)} (C{float}).
878 @arg _more: (INTERNAL) from C{.multiply}.
880 @raise EcefError: If B{C{sa}}, B{C{ca}}, B{C{sb}} or
881 B{C{cb}} outside M{[-1.0, +1.0]}.
882 '''
883 t = sa, ca, sb, cb
884 if _more: # all 9 matrix elements ...
885 t += _more # ... from .multiply
887 elif max(map(fabs, t)) > _1_0:
888 raise EcefError(unstr(EcefMatrix.__name__, *t))
890 else: # build matrix from the following quaternion operations
891 # qrot(lam, [0,0,1]) * qrot(phi, [0,-1,0]) * [1,1,1,1]/2
892 # or
893 # qrot(pi/2 + lam, [0,0,1]) * qrot(-pi/2 + phi, [-1,0,0])
894 # where
895 # qrot(t,v) = [cos(t/2), sin(t/2)*v[1], sin(t/2)*v[2], sin(t/2)*v[3]]
897 # Local X axis (east) in geocentric coords
898 # M[0] = -slam; M[3] = clam; M[6] = 0;
899 # Local Y axis (north) in geocentric coords
900 # M[1] = -clam * sphi; M[4] = -slam * sphi; M[7] = cphi;
901 # Local Z axis (up) in geocentric coords
902 # M[2] = clam * cphi; M[5] = slam * cphi; M[8] = sphi;
903 t = (-sb, -cb * sa, cb * ca,
904 cb, -sb * sa, sb * ca,
905 _0_0, ca, sa)
907 return _NamedTuple.__new__(cls, *t)
909 def column(self, column):
910 '''Get matrix B{C{column}} as 3-tuple.
911 '''
912 if 0 <= column < 3:
913 return self[column::3]
914 raise _IndexError(column=column)
916 @Property_RO
917 def _column_0(self):
918 return self.column(0)
920 @Property_RO
921 def _column_1(self):
922 return self.column(1)
924 @Property_RO
925 def _column_2(self):
926 return self.column(2)
928 def copy(self, **unused): # PYCHOK signature
929 '''Make a shallow or deep copy of this instance.
931 @return: The copy (C{This class} or subclass thereof).
932 '''
933 return self.classof(*self)
935 __copy__ = __deepcopy__ = copy
937 def multiply(self, other):
938 '''Matrix multiply M{M0' ⋅ M} this matrix transposed with
939 an other matrix.
941 @arg other: The other matrix (L{EcefMatrix}).
943 @return: The matrix product (L{EcefMatrix}).
945 @raise TypeError: If B{C{other}} is not L{EcefMatrix}.
946 '''
947 _xinstanceof(EcefMatrix, other=other)
949 # like LocalCartesian.MatrixMultiply, transposed(self) X other
950 # <https://GeographicLib.SourceForge.io/C++/doc/LocalCartesian_8cpp_source.html>
951 M = (fdot(self[r::3], *other[c::3]) for r in range(3) for c in range(3))
952 return _xnamed(EcefMatrix(*M), EcefMatrix.multiply.__name__)
954 def rotate(self, xyz, *xyz0):
955 '''Forward rotation M{M0' ⋅ ([x, y, z] - [x0, y0, z0])'}.
957 @arg xyz: Local C{(x, y, z)} coordinates (C{3-tuple}).
958 @arg xyz0: Optional, local C{(x0, y0, z0)} origin (C{3-tuple}).
960 @return: Rotated C{(x, y, z)} location (C{3-tuple}).
962 @raise LenError: Unequal C{len(B{xyz})} and C{len(B{xyz0})}.
963 '''
964 if xyz0:
965 if len(xyz0) != len(xyz):
966 raise LenError(self.rotate, xyz0=len(xyz0), xyz=len(xyz))
968 xyz = tuple(c - c0 for c, c0 in zip(xyz, xyz0))
970 # x' = M[0] * x + M[3] * y + M[6] * z
971 # y' = M[1] * x + M[4] * y + M[7] * z
972 # z' = M[2] * x + M[5] * y + M[8] * z
973 return (fdot(xyz, *self._column_0),
974 fdot(xyz, *self._column_1),
975 fdot(xyz, *self._column_2))
977 def row(self, row):
978 '''Get matrix B{C{row}} as 3-tuple.
979 '''
980 if 0 <= row < 3:
981 r = row * 3
982 return self[r:r+3]
983 raise _IndexError(row=row)
985 @Property_RO
986 def _row_0(self):
987 return self.row(0)
989 @Property_RO
990 def _row_1(self):
991 return self.row(1)
993 @Property_RO
994 def _row_2(self):
995 return self.row(2)
997 def unrotate(self, xyz, *xyz0):
998 '''Inverse rotation M{[x0, y0, z0] + M0 ⋅ [x,y,z]'}.
1000 @arg xyz: Local C{(x, y, z)} coordinates (C{3-tuple}).
1001 @arg xyz0: Optional, local C{(x0, y0, z0)} origin (C{3-tuple}).
1003 @return: Unrotated C{(x, y, z)} location (C{3-tuple}).
1005 @raise LenError: Unequal C{len(B{xyz})} and C{len(B{xyz0})}.
1006 '''
1007 if xyz0:
1008 if len(xyz0) != len(xyz):
1009 raise LenError(self.unrotate, xyz0=len(xyz0), xyz=len(xyz))
1011 _xyz = _1_0_1T + xyz
1012 # x' = x0 + M[0] * x + M[1] * y + M[2] * z
1013 # y' = y0 + M[3] * x + M[4] * y + M[5] * z
1014 # z' = z0 + M[6] * x + M[7] * y + M[8] * z
1015 xyz_ = (fdot(_xyz, xyz0[0], *self._row_0),
1016 fdot(_xyz, xyz0[1], *self._row_1),
1017 fdot(_xyz, xyz0[2], *self._row_2))
1018 else:
1019 # x' = M[0] * x + M[1] * y + M[2] * z
1020 # y' = M[3] * x + M[4] * y + M[5] * z
1021 # z' = M[6] * x + M[7] * y + M[8] * z
1022 xyz_ = (fdot(xyz, *self._row_0),
1023 fdot(xyz, *self._row_1),
1024 fdot(xyz, *self._row_2))
1025 return xyz_
1028class Ecef9Tuple(_NamedTuple):
1029 '''9-Tuple C{(x, y, z, lat, lon, height, C, M, datum)} with I{geocentric}
1030 C{x}, C{y} and C{z} plus I{geodetic} C{lat}, C{lon} and C{height}, case
1031 C{C} (see the C{Ecef*.reverse} methods) and optionally, the rotation
1032 matrix C{M} (L{EcefMatrix}) and C{datum}, with C{lat} and C{lon} in
1033 C{degrees} and C{x}, C{y}, C{z} and C{height} in C{meter}, conventionally.
1034 '''
1035 _Names_ = (_x_, _y_, _z_, _lat_, _lon_, _height_, _C_, _M_, _datum_)
1036 _Units_ = ( Meter, Meter, Meter, Lat, Lon, Height, Int, _Pass, _Pass)
1038 _IndexM = _Names_.index(_M_) # for ._M_x_M
1040 @property_RO
1041 def _CartesianBase(self):
1042 '''(INTERNAL) Get/cache class C{CartesianBase}.
1043 '''
1044 Ecef9Tuple._CartesianBase = C = _MODS.cartesianBase.CartesianBase # overwrite property
1045 return C
1047 @deprecated_method
1048 def convertDatum(self, datum2): # for backward compatibility
1049 '''DEPRECATED, use method L{toDatum}.'''
1050 return self.toDatum(datum2)
1052 @Property_RO
1053 def lam(self):
1054 '''Get the longitude in C{radians} (C{float}).
1055 '''
1056 return self.philam.lam
1058 @Property_RO
1059 def lamVermeille(self):
1060 '''Get the longitude in C{radians [-PI*3/2..+PI*3/2]} after U{Vermeille
1061 <https://Search.ProQuest.com/docview/639493848>} (2004), page 95.
1063 @see: U{Karney<https://GeographicLib.SourceForge.io/C++/doc/geocentric.html>},
1064 U{Vermeille<https://Search.ProQuest.com/docview/847292978>} 2011, pp 112-113, 116
1065 and U{Featherstone, et.al.<https://Search.ProQuest.com/docview/872827242>}, page 7.
1066 '''
1067 x, y = self.x, self.y
1068 if y > EPS0:
1069 r = _N_2_0 * atan2(x, hypot(y, x) + y) + PI_2
1070 elif y < -EPS0:
1071 r = _2_0 * atan2(x, hypot(y, x) - y) - PI_2
1072 else: # y == 0
1073 r = PI if x < 0 else _0_0
1074 return Lam(Vermeille=r)
1076 @Property_RO
1077 def latlon(self):
1078 '''Get the lat-, longitude in C{degrees} (L{LatLon2Tuple}C{(lat, lon)}).
1079 '''
1080 return LatLon2Tuple(self.lat, self.lon, name=self.name)
1082 @Property_RO
1083 def latlonheight(self):
1084 '''Get the lat-, longitude in C{degrees} and height (L{LatLon3Tuple}C{(lat, lon, height)}).
1085 '''
1086 return self.latlon.to3Tuple(self.height)
1088 @Property_RO
1089 def latlonheightdatum(self):
1090 '''Get the lat-, longitude in C{degrees} with height and datum (L{LatLon4Tuple}C{(lat, lon, height, datum)}).
1091 '''
1092 return self.latlonheight.to4Tuple(self.datum)
1094 @Property_RO
1095 def latlonVermeille(self):
1096 '''Get the latitude and I{Vermeille} longitude in C{degrees [-225..+225]} (L{LatLon2Tuple}C{(lat, lon)}).
1098 @see: Property C{lonVermeille}.
1099 '''
1100 return LatLon2Tuple(self.lat, self.lonVermeille, name=self.name)
1102 @Property_RO
1103 def lonVermeille(self):
1104 '''Get the longitude in C{degrees [-225..+225]} after U{Vermeille
1105 <https://Search.ProQuest.com/docview/639493848>} (2004), p 95.
1107 @see: Property C{lamVermeille}.
1108 '''
1109 return Lon(Vermeille=degrees(self.lamVermeille))
1111 def _T_x_M(self, T):
1112 '''(INTERNAL) Update M{self.M = T.multiply(self.M)}.
1113 '''
1114 t = list(self)
1115 M = self._IndexM
1116 t[M] = T.multiply(t[M])
1117 return self.classof(*t)
1119 @Property_RO
1120 def phi(self):
1121 '''Get the latitude in C{radians} (C{float}).
1122 '''
1123 return self.philam.phi
1125 @Property_RO
1126 def philam(self):
1127 '''Get the lat-, longitude in C{radians} (L{PhiLam2Tuple}C{(phi, lam)}).
1128 '''
1129 return PhiLam2Tuple(radians(self.lat), radians(self.lon), name=self.name)
1131 @Property_RO
1132 def philamheight(self):
1133 '''Get the lat-, longitude in C{radians} and height (L{PhiLam3Tuple}C{(phi, lam, height)}).
1134 '''
1135 return self.philam.to3Tuple(self.height)
1137 @Property_RO
1138 def philamheightdatum(self):
1139 '''Get the lat-, longitude in C{radians} with height and datum (L{PhiLam4Tuple}C{(phi, lam, height, datum)}).
1140 '''
1141 return self.philamheight.to4Tuple(self.datum)
1143 @Property_RO
1144 def philamVermeille(self):
1145 '''Get the latitude and I{Vermeille} longitude in C{radians [-PI*3/2..+PI*3/2]} (L{PhiLam2Tuple}C{(phi, lam)}).
1147 @see: Property C{lamVermeille}.
1148 '''
1149 return PhiLam2Tuple(radians(self.lat), self.lamVermeille, name=self.name)
1151 def toCartesian(self, Cartesian=None, **Cartesian_kwds):
1152 '''Return the geocentric C{(x, y, z)} coordinates as an ellipsoidal or spherical
1153 C{Cartesian}.
1155 @kwarg Cartesian: Optional class to return C{(x, y, z)} (L{ellipsoidalKarney.Cartesian},
1156 L{ellipsoidalNvector.Cartesian}, L{ellipsoidalVincenty.Cartesian},
1157 L{sphericalNvector.Cartesian} or L{sphericalTrigonometry.Cartesian})
1158 or C{None}.
1159 @kwarg Cartesian_kwds: Optional, additional B{C{Cartesian}} keyword arguments, ignored
1160 if C{B{Cartesian} is None}.
1162 @return: A C{B{Cartesian}(x, y, z, **B{Cartesian_kwds})} instance or
1163 a L{Vector4Tuple}C{(x, y, z, h)} if C{B{Cartesian} is None}.
1165 @raise TypeError: Invalid B{C{Cartesian}} or B{C{Cartesian_kwds}}.
1166 '''
1167 if Cartesian in (None, Vector4Tuple):
1168 r = self.xyzh
1169 elif Cartesian is Vector3Tuple:
1170 r = self.xyz
1171 else:
1172 _xsubclassof(self._CartesianBase, Cartesian=Cartesian)
1173 r = Cartesian(self, **_xkwds(Cartesian_kwds, name=self.name))
1174 return r
1176 def toDatum(self, datum2):
1177 '''Convert this C{Ecef9Tuple} to an other datum.
1179 @arg datum2: Datum to convert I{to} (L{Datum}).
1181 @return: The converted 9-Tuple (C{Ecef9Tuple}).
1183 @raise TypeError: The B{C{datum2}} is not a L{Datum}.
1184 '''
1185 if self.datum in (None, datum2): # PYCHOK _Names_
1186 r = self.copy()
1187 else:
1188 c = self._CartesianBase(self, datum=self.datum, name=self.name) # PYCHOK _Names_
1189 # c.toLatLon converts datum, x, y, z, lat, lon, etc.
1190 # and returns another Ecef9Tuple iff LatLon is None
1191 r = c.toLatLon(datum=datum2, LatLon=None)
1192 return r
1194 def toLatLon(self, LatLon=None, **LatLon_kwds):
1195 '''Return the geodetic C{(lat, lon, height[, datum])} coordinates.
1197 @kwarg LatLon: Optional class to return C{(lat, lon, height[, datum])}
1198 or C{None}.
1199 @kwarg LatLon_kwds: Optional B{C{height}}, B{C{datum}} and other
1200 B{C{LatLon}} keyword arguments.
1202 @return: An instance of C{B{LatLon}(lat, lon, **B{LatLon_kwds})}
1203 or if B{C{LatLon}} is C{None}, a L{LatLon3Tuple}C{(lat, lon,
1204 height)} respectively L{LatLon4Tuple}C{(lat, lon, height,
1205 datum)} depending on whether C{datum} is un-/specified.
1207 @raise TypeError: Invalid B{C{LatLon}} or B{C{LatLon_kwds}}.
1208 '''
1209 kwds = _xkwds(LatLon_kwds, height=self.height, datum=self.datum, name=self.name) # PYCHOK Ecef9Tuple
1210 d = kwds[_datum_]
1211 if LatLon is None:
1212 r = LatLon3Tuple(self.lat, self.lon, kwds[_height_], name=kwds[_name_]) # PYCHOK Ecef9Tuple
1213 if d:
1214 r = r.to4Tuple(d) # checks type(d)
1215 else:
1216 if d is None: # remove None datum
1217 _ = kwds.pop[_datum_]
1218 r = LatLon(self.lat, self.lon, **kwds) # PYCHOK Ecef9Tuple
1219 _xdatum(_xattr(r, datum=self.datum), self.datum) # PYCHOK Ecef9Tuple
1220 return r
1222 def toLocal(self, ltp, Xyz=None, **Xyz_kwds):
1223 '''Convert this geocentric to I{local} C{x}, C{y} and C{z}.
1225 @kwarg ltp: The I{local tangent plane} (LTP) to use (L{Ltp}).
1226 @kwarg Xyz: Optional class to return C{x}, C{y} and C{z}
1227 (L{XyzLocal}, L{Enu}, L{Ned}) or C{None}.
1228 @kwarg Xyz_kwds: Optional, additional B{C{Xyz}} keyword
1229 arguments, ignored if C{B{Xyz} is None}.
1231 @return: An B{C{Xyz}} instance or if C{B{Xyz} is None},
1232 a L{Local9Tuple}C{(x, y, z, lat, lon, height,
1233 ltp, ecef, M)} with C{M=None}, always.
1235 @raise TypeError: Invalid B{C{ltp}}.
1236 '''
1237 return _MODS.ltp._xLtp(ltp)._ecef2local(self, Xyz, Xyz_kwds)
1239 def toVector(self, Vector=None, **Vector_kwds):
1240 '''Return the geocentric C{(x, y, z)} coordinates as vector.
1242 @kwarg Vector: Optional vector class to return C{(x, y, z)} or
1243 C{None}.
1244 @kwarg Vector_kwds: Optional, additional B{C{Vector}} keyword
1245 arguments, ignored if C{B{Vector} is None}.
1247 @return: A C{Vector}C{(x, y, z, **Vector_kwds)} instance or a
1248 L{Vector3Tuple}C{(x, y, z)} if B{C{Vector}} is C{None}.
1250 @see: Propertes C{xyz} and C{xyzh}
1251 '''
1252 return self.xyz if Vector is None else self._xnamed(
1253 Vector(self.x, self.y, self.z, **Vector_kwds)) # PYCHOK Ecef9Tuple
1255 @Property_RO
1256 def xyz(self):
1257 '''Get the geocentric C{(x, y, z)} coordinates (L{Vector3Tuple}C{(x, y, z)}).
1258 '''
1259 return Vector3Tuple(self.x, self.y, self.z, name=self.name)
1261 @Property_RO
1262 def xyzh(self):
1263 '''Get the geocentric C{(x, y, z)} coordinates and C{height} (L{Vector4Tuple}C{(x, y, z, h)})
1264 '''
1265 return self.xyz.to4Tuple(self.height)
1268def _4Ecef(this, Ecef): # in .datums.Datum.ecef, .ellipsoids.Ellipsoid.ecef
1269 '''Return an ECEF converter for C{this} L{Datum} or L{Ellipsoid}.
1270 '''
1271 if Ecef is None:
1272 Ecef = EcefKarney
1273 else:
1274 _xinstanceof(*_Ecefs, Ecef=Ecef)
1275 return Ecef(this, name=this.name)
1278def _xEcef(Ecef): # PYCHOK .latlonBase.py
1279 '''(INTERNAL) Validate B{C{Ecef}} I{class}.
1280 '''
1281 if issubclassof(Ecef, _EcefBase):
1282 return Ecef
1283 raise _TypesError(_Ecef_, Ecef, *_Ecefs)
1286_Ecefs = (EcefKarney, EcefSudano, EcefVeness, EcefYou,
1287 EcefFarrell21, EcefFarrell22)
1289__all__ += _ALL_DOCS(_EcefBase)
1291# **) MIT License
1292#
1293# Copyright (C) 2016-2023 -- mrJean1 at Gmail -- All Rights Reserved.
1294#
1295# Permission is hereby granted, free of charge, to any person obtaining a
1296# copy of this software and associated documentation files (the "Software"),
1297# to deal in the Software without restriction, including without limitation
1298# the rights to use, copy, modify, merge, publish, distribute, sublicense,
1299# and/or sell copies of the Software, and to permit persons to whom the
1300# Software is furnished to do so, subject to the following conditions:
1301#
1302# The above copyright notice and this permission notice shall be included
1303# in all copies or substantial portions of the Software.
1304#
1305# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
1306# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
1307# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
1308# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
1309# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
1310# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
1311# OTHER DEALINGS IN THE SOFTWARE.