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@note: The C{reverse} methods of all C{Ecef...} classes return by default C{INT0} as the (geodetic)
51longitude for I{polar} ECEF location C{x == y == 0}. Use keyword argument C{lon00} or property
52C{lon00} to configure that value.
54@see: Module L{ltp} and class L{LocalCartesian}, a transcription of I{Charles Karney}'s C++ class
55U{LocalCartesian<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1LocalCartesian.html>},
56for conversion between geodetic and I{local cartesian} coordinates in a I{local tangent
57plane} as opposed to I{geocentric} (ECEF) ones.
58'''
60from pygeodesy.basics import copysign0, isscalar, issubclassof, neg, map1, \
61 _xinstanceof, _xsubclassof # _args_kwds_names
62from pygeodesy.constants import EPS, EPS0, EPS02, EPS1, EPS2, EPS_2, INT0, PI, PI_2, \
63 _0_0, _0_0001, _0_01, _0_5, _1_0, _1_0_1T, _N_1_0, \
64 _2_0, _N_2_0, _3_0, _4_0, _6_0, _60_0, _90_0, _N_90_0, \
65 _100_0, _copysign_1_0, isnon0 # PYCHOK used!
66from pygeodesy.datums import a_f2Tuple, _ellipsoidal_datum, _WGS84, _EWGS84
67# from pygeodesy.ellipsoids import a_f2Tuple, _EWGS84 # from .datums
68from pygeodesy.errors import _IndexError, LenError, _ValueError, _TypesError, \
69 _xattr, _xdatum, _xkwds, _xkwds_get
70from pygeodesy.fmath import cbrt, fdot, Fpowers, hypot, hypot1, hypot2_, sqrt0
71from pygeodesy.fsums import Fsum, fsumf_, Fmt, unstr
72from pygeodesy.interns import NN, _a_, _C_, _datum_, _ellipsoid_, _f_, _height_, \
73 _lat_, _lon_, _M_, _name_, _singular_, _SPACE_, \
74 _x_, _xyz_, _y_, _z_
75from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS
76from pygeodesy.named import _name__, _name1__, _NamedBase, _NamedTuple, _Pass, _xnamed
77from pygeodesy.namedTuples import LatLon2Tuple, LatLon3Tuple, \
78 PhiLam2Tuple, Vector3Tuple, Vector4Tuple
79from pygeodesy.props import deprecated_method, Property_RO, property_RO, property_doc_
80# from pygeodesy.streprs import Fmt, unstr # from .fsums
81from pygeodesy.units import _isRadius, Degrees, Height, Int, Lam, Lat, Lon, Meter, \
82 Phi, Scalar, Scalar_
83from pygeodesy.utily import atan1, atan1d, atan2d, degrees90, degrees180, \
84 sincos2, sincos2_, sincos2d, sincos2d_
86from math import atan2, cos, degrees, fabs, radians, sqrt
88__all__ = _ALL_LAZY.ecef
89__version__ = '24.05.31'
91_Ecef_ = 'Ecef'
92_prolate_ = 'prolate'
93_TRIPS = 33 # 8..9 sufficient, EcefSudano.reverse
94_xyz_y_z = _xyz_, _y_, _z_ # _args_kwds_names(_xyzn4)[:3]
97class EcefError(_ValueError):
98 '''An ECEF or C{Ecef*} related issue.
99 '''
100 pass
103class _EcefBase(_NamedBase):
104 '''(INTERNAL) Base class for L{EcefFarrell21}, L{EcefFarrell22}, L{EcefKarney},
105 L{EcefSudano}, L{EcefVeness} and L{EcefYou}.
106 '''
107 _datum = _WGS84
108 _E = _EWGS84
109 _lon00 = INT0 # arbitrary, "polar" lon for LocalCartesian, Ltp
111 def __init__(self, a_ellipsoid=_EWGS84, f=None, lon00=INT0, **name):
112 '''New C{Ecef*} converter.
114 @arg a_ellipsoid: A (non-prolate) ellipsoid (L{Ellipsoid}, L{Ellipsoid2},
115 L{Datum} or L{a_f2Tuple}) or C{scalar} ellipsoid's
116 equatorial radius (C{meter}).
117 @kwarg f: C{None} or the ellipsoid flattening (C{scalar}), required
118 for C{scalar} B{C{a_ellipsoid}}, C{B{f}=0} represents a
119 sphere, negative B{C{f}} a prolate ellipsoid.
120 @kwarg lon00: An arbitrary, I{"polar"} longitude (C{degrees}), see the
121 C{reverse} method.
122 @kwarg name: Optional C{B{name}=NN} (C{str}).
124 @raise EcefError: If B{C{a_ellipsoid}} not L{Ellipsoid}, L{Ellipsoid2},
125 L{Datum} or L{a_f2Tuple} or C{scalar} or B{C{f}} not
126 C{scalar} or if C{scalar} B{C{a_ellipsoid}} not positive
127 or B{C{f}} not less than 1.0.
128 '''
129 try:
130 E = a_ellipsoid
131 if f is None:
132 pass
133 elif _isRadius(E) and isscalar(f):
134 E = a_f2Tuple(E, f)
135 else:
136 raise ValueError # _invalid_
138 if E not in (_EWGS84, _WGS84):
139 d = _ellipsoidal_datum(E, **name)
140 E = d.ellipsoid
141 if E.a < EPS or E.f > EPS1:
142 raise ValueError # _invalid_
143 self._datum = d
144 self._E = E
146 except (TypeError, ValueError) as x:
147 t = unstr(self.classname, a=a_ellipsoid, f=f)
148 raise EcefError(_SPACE_(t, _ellipsoid_), cause=x)
150 if name:
151 self.name = name
152 if lon00 is not INT0:
153 self.lon00 = lon00
155 def __eq__(self, other):
156 '''Compare this and an other Ecef.
158 @arg other: The other ecef (C{Ecef*}).
160 @return: C{True} if equal, C{False} otherwise.
161 '''
162 return other is self or (isinstance(other, self.__class__) and
163 other.ellipsoid == self.ellipsoid)
165 @Property_RO
166 def datum(self):
167 '''Get the datum (L{Datum}).
168 '''
169 return self._datum
171 @Property_RO
172 def ellipsoid(self):
173 '''Get the ellipsoid (L{Ellipsoid} or L{Ellipsoid2}).
174 '''
175 return self._E
177 @Property_RO
178 def equatoradius(self):
179 '''Get the C{ellipsoid}'s equatorial radius, semi-axis (C{meter}).
180 '''
181 return self.ellipsoid.a
183 a = equatorialRadius = equatoradius # Karney property
185 @Property_RO
186 def flattening(self): # Karney property
187 '''Get the C{ellipsoid}'s flattening (C{scalar}), positive for
188 I{oblate}, negative for I{prolate} or C{0} for I{near-spherical}.
189 '''
190 return self.ellipsoid.f
192 f = flattening
194 def _forward(self, lat, lon, h, name, M=False, _philam=False): # in .ltp.LocalCartesian.forward and -.reset
195 '''(INTERNAL) Common for all C{Ecef*}.
196 '''
197 if _philam: # lat, lon in radians
198 sa, ca, sb, cb = sincos2_(lat, lon)
199 lat = Lat(degrees90( lat), Error=EcefError)
200 lon = Lon(degrees180(lon), Error=EcefError)
201 else:
202 sa, ca, sb, cb = sincos2d_(lat, lon)
204 E = self.ellipsoid
205 n = E.roc1_(sa, ca) if self._isYou else E.roc1_(sa)
206 z = (h + n * E.e21) * sa
207 x = (h + n) * ca
209 m = self._Matrix(sa, ca, sb, cb) if M else None
210 return Ecef9Tuple(x * cb, x * sb, z, lat, lon, h,
211 0, m, self.datum,
212 name=self._name__(name))
214 def forward(self, latlonh, lon=None, height=0, M=False, **name):
215 '''Convert from geodetic C{(lat, lon, height)} to geocentric C{(x, y, z)}.
217 @arg latlonh: Either a C{LatLon}, an L{Ecef9Tuple} or C{scalar}
218 latitude (C{degrees}).
219 @kwarg lon: Optional C{scalar} longitude for C{scalar} B{C{latlonh}}
220 (C{degrees}).
221 @kwarg height: Optional height (C{meter}), vertically above (or below)
222 the surface of the ellipsoid.
223 @kwarg M: Optionally, return the rotation L{EcefMatrix} (C{bool}).
224 @kwarg name: Optional C{B{name}=NN} (C{str}).
226 @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with
227 geocentric C{(x, y, z)} coordinates for the given geodetic ones
228 C{(lat, lon, height)}, case C{C} 0, optional C{M} (L{EcefMatrix})
229 and C{datum} if available.
231 @raise EcefError: If B{C{latlonh}} not C{LatLon}, L{Ecef9Tuple} or
232 C{scalar} or B{C{lon}} not C{scalar} for C{scalar}
233 B{C{latlonh}} or C{abs(lat)} exceeds 90°.
235 @note: Use method C{.forward_} to specify C{lat} and C{lon} in C{radians}
236 and avoid double angle conversions.
237 '''
238 llhn = _llhn4(latlonh, lon, height, **name)
239 return self._forward(*llhn, M=M)
241 def forward_(self, phi, lam, height=0, M=False, **name):
242 '''Like method C{.forward} except with geodetic lat- and longitude given
243 in I{radians}.
245 @arg phi: Latitude in I{radians} (C{scalar}).
246 @arg lam: Longitude in I{radians} (C{scalar}).
247 @kwarg height: Optional height (C{meter}), vertically above (or below)
248 the surface of the ellipsoid.
249 @kwarg M: Optionally, return the rotation L{EcefMatrix} (C{bool}).
250 @kwarg name: Optional C{B{name}=NN} (C{str}).
252 @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)}
253 with C{lat} set to C{degrees90(B{phi})} and C{lon} to
254 C{degrees180(B{lam})}.
256 @raise EcefError: If B{C{phi}} or B{C{lam}} invalid or not C{scalar}.
257 '''
258 try: # like function C{_llhn4} below
259 plhn = Phi(phi), Lam(lam), Height(height), _name__(name)
260 except (TypeError, ValueError) as x:
261 raise EcefError(phi=phi, lam=lam, height=height, cause=x)
262 return self._forward(*plhn, M=M, _philam=True)
264 @property_RO
265 def _Geocentrics(self):
266 '''(INTERNAL) Get the valid geocentric classes. I{once}.
267 '''
268 _EcefBase._Geocentrics = t = (Ecef9Tuple, # overwrite property_RO
269 _MODS.cartesianBase.CartesianBase)
270 return t
272 @Property_RO
273 def _isYou(self):
274 '''(INTERNAL) Is this an C{EcefYou}?.
275 '''
276 return isinstance(self, EcefYou)
278 @property
279 def lon00(self):
280 '''Get the I{"polar"} longitude (C{degrees}), see method C{reverse}.
281 '''
282 return self._lon00
284 @lon00.setter # PYCHOK setter!
285 def lon00(self, lon00):
286 '''Set the I{"polar"} longitude (C{degrees}), see method C{reverse}.
287 '''
288 self._lon00 = Degrees(lon00=lon00)
290 def _Matrix(self, sa, ca, sb, cb):
291 '''Creation a rotation matrix.
293 @arg sa: C{sin(phi)} (C{float}).
294 @arg ca: C{cos(phi)} (C{float}).
295 @arg sb: C{sin(lambda)} (C{float}).
296 @arg cb: C{cos(lambda)} (C{float}).
298 @return: An L{EcefMatrix}.
299 '''
300 return self._xnamed(EcefMatrix(sa, ca, sb, cb))
302 def _polon(self, y, x, R, **name_lon00):
303 '''(INTERNAL) Handle I{"polar"} longitude.
304 '''
305 return atan2d(y, x) if R else _xkwds_get(name_lon00, lon00=self.lon00)
307 def reverse(self, xyz, y=None, z=None, M=False, **name_lon00): # PYCHOK no cover
308 '''I{Must be overloaded}.'''
309 self._notOverloaded(xyz, y=y, z=z, M=M, **name_lon00)
311 def toStr(self, prec=9, **unused): # PYCHOK signature
312 '''Return this C{Ecef*} as a string.
314 @kwarg prec: Precision, number of decimal digits (0..9).
316 @return: This C{Ecef*} (C{str}).
317 '''
318 return self.attrs(_a_, _f_, _datum_, _name_, prec=prec) # _ellipsoid_
321class EcefFarrell21(_EcefBase):
322 '''Conversion between geodetic and geocentric, I{Earth-Centered, Earth-Fixed} (ECEF)
323 coordinates based on I{Jay A. Farrell}'s U{Table 2.1<https://Books.Google.com/
324 books?id=fW4foWASY6wC>}, page 29.
325 '''
327 def reverse(self, xyz, y=None, z=None, M=None, **name_lon00): # PYCHOK unused M
328 '''Convert from geocentric C{(x, y, z)} to geodetic C{(lat, lon, height)} using
329 I{Farrell}'s U{Table 2.1<https://Books.Google.com/books?id=fW4foWASY6wC>},
330 page 29.
332 @arg xyz: A geocentric (C{Cartesian}, L{Ecef9Tuple}) or C{scalar} ECEF C{x}
333 coordinate (C{meter}).
334 @kwarg y: ECEF C{y} coordinate for C{scalar} B{C{xyz}} and B{C{z}} (C{meter}).
335 @kwarg z: ECEF C{z} coordinate for C{scalar} B{C{xyz}} and B{C{y}} (C{meter}).
336 @kwarg M: I{Ignored}, rotation matrix C{M} not available.
337 @kwarg name_lon00: Optional keyword arguments C{B{name}=NN} (C{str}) and
338 I{"polar"} longitude C{B{lon00}=INT0} (C{degrees}), overriding
339 the default and property C{lon00} setting and returned if
340 C{B{x}=0} and C{B{y}=0}.
342 @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with
343 geodetic coordinates C{(lat, lon, height)} for the given geocentric
344 ones C{(x, y, z)}, case C{C=1}, C{M=None} always and C{datum}
345 if available.
347 @raise EcefError: Invalid B{C{xyz}} or C{scalar} C{x} or B{C{y}} and/or B{C{z}}
348 not C{scalar} for C{scalar} B{C{xyz}} or C{sqrt} domain or
349 zero division error.
351 @see: L{EcefFarrell22} and L{EcefVeness}.
352 '''
353 x, y, z, name = _xyzn4(xyz, y, z, self._Geocentrics, **name_lon00)
355 E = self.ellipsoid
356 a = E.a
357 a2 = E.a2
358 b2 = E.b2
359 e2 = E.e2
360 e2_ = E.e2abs * E.a2_b2 # (E.e * E.a_b)**2 = 0.0820944... WGS84
361 e4 = E.e4
363 try: # names as page 29
364 z2 = z**2
365 ez = z2 * (_1_0 - e2) # E.e2s2(z)
367 p = hypot(x, y)
368 p2 = p**2
369 G = p2 + ez - e2 * (a2 - b2) # p2 + ez - e4 * a2
370 F = b2 * z2 * 54
371 t = e4 * p2 * F / G**3
372 t = cbrt(sqrt(t * (t + _2_0)) + t + _1_0)
373 G *= fsumf_(t , _1_0, _1_0 / t)
374 P = F / (G**2 * _3_0)
375 Q = sqrt(_2_0 * e4 * P + _1_0)
376 Q1 = Q + _1_0
377 r0 = P * p * e2 / Q1 - sqrt(fsumf_(a2 * (Q1 / Q) * _0_5,
378 -P * ez / (Q * Q1),
379 -P * p2 * _0_5))
380 r = p + e2 * r0
381 v = b2 / (sqrt(r**2 + ez) * a)
383 h = hypot(r, z) * (_1_0 - v)
384 lat = atan1d((e2_ * v + _1_0) * z, p)
385 lon = self._polon(y, x, p, **name_lon00)
386 # note, phi and lam are swapped on page 29
388 except (ValueError, ZeroDivisionError) as e:
389 raise EcefError(x=x, y=y, z=z, cause=e)
391 return Ecef9Tuple(x, y, z, lat, lon, h,
392 1, None, self.datum,
393 name=self._name__(name))
396class EcefFarrell22(_EcefBase):
397 '''Conversion between geodetic and geocentric, I{Earth-Centered, Earth-Fixed} (ECEF)
398 coordinates based on I{Jay A. Farrell}'s U{Table 2.2<https://Books.Google.com/
399 books?id=fW4foWASY6wC>}, page 30.
400 '''
402 def reverse(self, xyz, y=None, z=None, M=None, **name_lon00): # PYCHOK unused M
403 '''Convert from geocentric C{(x, y, z)} to geodetic C{(lat, lon, height)} using
404 I{Farrell}'s U{Table 2.2<https://Books.Google.com/books?id=fW4foWASY6wC>},
405 page 30.
407 @arg xyz: A geocentric (C{Cartesian}, L{Ecef9Tuple}) or C{scalar} ECEF C{x}
408 coordinate (C{meter}).
409 @kwarg y: ECEF C{y} coordinate for C{scalar} B{C{xyz}} and B{C{z}} (C{meter}).
410 @kwarg z: ECEF C{z} coordinate for C{scalar} B{C{xyz}} and B{C{y}} (C{meter}).
411 @kwarg M: I{Ignored}, rotation matrix C{M} not available.
412 @kwarg name_lon00: Optional keyword arguments C{B{name}=NN} (C{str}) and
413 I{"polar"} longitude C{B{lon00}=INT0} (C{degrees}), overriding
414 the default and property C{lon00} setting and returned in case
415 C{B{x}=0} and C{B{y}=0}.
417 @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with
418 geodetic coordinates C{(lat, lon, height)} for the given geocentric
419 ones C{(x, y, z)}, case C{C=1}, C{M=None} always and C{datum}
420 if available.
422 @raise EcefError: Invalid B{C{xyz}} or C{scalar} C{x} or B{C{y}} and/or B{C{z}}
423 not C{scalar} for C{scalar} B{C{xyz}} or C{sqrt} domain or
424 zero division error.
426 @see: L{EcefFarrell21} and L{EcefVeness}.
427 '''
428 x, y, z, name = _xyzn4(xyz, y, z, self._Geocentrics, **name_lon00)
430 E = self.ellipsoid
431 a = E.a
432 b = E.b
434 try: # see EcefVeness.reverse
435 p = hypot(x, y)
436 lon = self._polon(y, x, p, **name_lon00)
438 s, c = sincos2(atan2(z * a, p * b)) # == _norm3
439 lat = atan1d(z + s**3 * b * E.e22,
440 p - c**3 * a * E.e2)
442 s, c = sincos2d(lat)
443 if c: # E.roc1_(s) = E.a / sqrt(1 - E.e2 * s**2)
444 h = p / c - (E.roc1_(s) if s else a)
445 else: # polar
446 h = fabs(z) - b
447 # note, phi and lam are swapped on page 30
449 except (ValueError, ZeroDivisionError) as e:
450 raise EcefError(x=x, y=y, z=z, cause=e)
452 return Ecef9Tuple(x, y, z, lat, lon, h,
453 1, None, self.datum,
454 name=self._name__(name))
457class EcefKarney(_EcefBase):
458 '''Conversion between geodetic and geocentric, I{Earth-Centered, Earth-Fixed} (ECEF)
459 coordinates transcoded from I{Karney}'s C++ U{Geocentric<https://GeographicLib.SourceForge.io/
460 C++/doc/classGeographicLib_1_1Geocentric.html>} methods.
462 @note: On methods C{.forward} and C{.forwar_}, let C{v} be a unit vector located
463 at C{(lat, lon, h)}. We can express C{v} as column vectors in one of two
464 ways, C{v1} in East, North, Up (ENU) coordinates (where the components are
465 relative to a local coordinate system at C{C(lat0, lon0, h0)}) or as C{v0}
466 in geocentric C{x, y, z} coordinates. Then, M{v0 = M ⋅ v1} where C{M} is
467 the rotation matrix.
468 '''
470 @Property_RO
471 def hmax(self):
472 '''Get the distance or height limit (C{meter}, conventionally).
473 '''
474 return self.equatoradius / EPS_2 # self.equatoradius * _2_EPS, 12M lighyears
476 def reverse(self, xyz, y=None, z=None, M=False, **name_lon00):
477 '''Convert from geocentric C{(x, y, z)} to geodetic C{(lat, lon, height)}.
479 @arg xyz: A geocentric (C{Cartesian}, L{Ecef9Tuple}) or C{scalar} ECEF C{x}
480 coordinate (C{meter}).
481 @kwarg y: ECEF C{y} coordinate for C{scalar} B{C{xyz}} and B{C{z}} (C{meter}).
482 @kwarg z: ECEF C{z} coordinate for C{scalar} B{C{xyz}} and B{C{y}} (C{meter}).
483 @kwarg M: Optionally, return the rotation L{EcefMatrix} (C{bool}).
484 @kwarg name_lon00: Optional keyword arguments C{B{name}=NN} (C{str}) and
485 I{"polar"} longitude C{B{lon00}=INT0} (C{degrees}), overriding
486 the default and property C{lon00} setting and returned in case
487 C{B{x}=0} and C{B{y}=0}.
489 @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with
490 geodetic coordinates C{(lat, lon, height)} for the given geocentric
491 ones C{(x, y, z)}, case C{C}, optional C{M} (L{EcefMatrix}) and
492 C{datum} if available.
494 @raise EcefError: Invalid B{C{xyz}} or C{scalar} C{x} or B{C{y}} and/or B{C{z}}
495 not C{scalar} for C{scalar} B{C{xyz}}.
497 @note: In general, there are multiple solutions and the result which minimizes
498 C{height} is returned, i.e., the C{(lat, lon)} corresponding to the
499 closest point on the ellipsoid. If there are still multiple solutions
500 with different latitudes (applies only if C{z} = 0), then the solution
501 with C{lat} > 0 is returned. If there are still multiple solutions with
502 different longitudes (applies only if C{x} = C{y} = 0), then C{lon00} is
503 returned. The returned C{lon} is in the range [−180°, 180°] and C{height}
504 is not below M{−E.a * (1 − E.e2) / sqrt(1 − E.e2 * sin(lat)**2)}. Like
505 C{forward} above, M{v1 = Transpose(M) ⋅ v0}.
506 '''
507 def _norm3(y, x):
508 h = hypot(y, x) # EPS0, EPS_2
509 return (y / h, x / h, h) if h > 0 else (_0_0, _1_0, h)
511 x, y, z, name = _xyzn4(xyz, y, z, self._Geocentrics, **name_lon00)
513 E = self.ellipsoid
514 f = E.f
516 sb, cb, R = _norm3(y, x)
517 h = hypot(R, z) # distance to earth center
518 if h > self.hmax: # PYCHOK no cover
519 # We are really far away (> 12M light years). Treat the earth
520 # as a point and h above as an acceptable approximation to the
521 # height. This avoids overflow, e.g., in the computation of d
522 # below. It's possible that h has overflowed to INF, that's OK.
523 # Treat finite x, y, but R overflows to +INF by scaling by 2.
524 sb, cb, R = _norm3(y * _0_5, x * _0_5)
525 sa, ca, _ = _norm3(z * _0_5, R)
526 C = 1
528 elif E.e4: # E.isEllipsoidal
529 # Treat prolate spheroids by swapping R and Z here and by
530 # switching the arguments to phi = atan2(...) at the end.
531 p = (R / E.a)**2
532 q = (z / E.a)**2 * E.e21
533 if f < 0:
534 p, q = q, p
535 r = fsumf_(p, q, -E.e4)
536 e = E.e4 * q
537 if e or r > 0:
538 # Avoid possible division by zero when r = 0 by multiplying
539 # equations for s and t by r^3 and r, respectively.
540 s = d = e * p / _4_0 # s = r^3 * s
541 u = r = r / _6_0
542 r2 = r**2
543 r3 = r2 * r
544 t3 = r3 + s
545 d *= t3 + r3
546 if d < 0:
547 # t is complex, but the way u is defined, the result is real.
548 # There are three possible cube roots. We choose the root
549 # which avoids cancellation. Note, d < 0 implies r < 0.
550 u += cos(atan2(sqrt(-d), -t3) / _3_0) * r * _2_0
551 else:
552 # Pick the sign on the sqrt to maximize abs(t3). This
553 # minimizes loss of precision due to cancellation. The
554 # result is unchanged because of the way the t is used
555 # in definition of u.
556 if d > 0:
557 t3 += copysign0(sqrt(d), t3) # t3 = (r * t)^3
558 # N.B. cbrt always returns the real root, cbrt(-8) = -2.
559 t = cbrt(t3) # t = r * t
560 if t: # t can be zero; but then r2 / t -> 0.
561 u = fsumf_(u, t, r2 / t)
562 v = sqrt(e + u**2) # guaranteed positive
563 # Avoid loss of accuracy when u < 0. Underflow doesn't occur in
564 # E.e4 * q / (v - u) because u ~ e^4 when q is small and u < 0.
565 u = (e / (v - u)) if u < 0 else (u + v) # u+v, guaranteed positive
566 # Need to guard against w going negative due to roundoff in u - q.
567 w = E.e2abs * (u - q) / (_2_0 * v)
568 # Rearrange expression for k to avoid loss of accuracy due to
569 # subtraction. Division by 0 not possible because u > 0, w >= 0.
570 k1 = k2 = (u / (sqrt(u + w**2) + w)) if w > 0 else sqrt(u)
571 if f < 0:
572 k1 -= E.e2
573 else:
574 k2 += E.e2
575 sa, ca, h = _norm3(z / k1, R / k2)
576 h *= k1 - E.e21
577 C = 2
579 else: # e = E.e4 * q == 0 and r <= 0
580 # This leads to k = 0 (oblate, equatorial plane) and k + E.e^2 = 0
581 # (prolate, rotation axis) and the generation of 0/0 in the general
582 # formulas for phi and h, using the general formula and division
583 # by 0 in formula for h. Handle this case by taking the limits:
584 # f > 0: z -> 0, k -> E.e2 * sqrt(q) / sqrt(E.e4 - p)
585 # f < 0: r -> 0, k + E.e2 -> -E.e2 * sqrt(q) / sqrt(E.e4 - p)
586 q = E.e4 - p
587 if f < 0:
588 p, q = q, p
589 e = E.a
590 else:
591 e = E.b2_a
592 sa, ca, h = _norm3(sqrt(q * E._1_e21), sqrt(p))
593 if z < 0: # for tiny negative z, not for prolate
594 sa = neg(sa)
595 h *= neg(e / E.e2abs)
596 C = 3
598 else: # E.e4 == 0, spherical case
599 # Dealing with underflow in the general case with E.e2 = 0 is
600 # difficult. Origin maps to North pole, same as with ellipsoid.
601 sa, ca, _ = _norm3((z if h else _1_0), R)
602 h -= E.a
603 C = 4
605 # lon00 <https://GitHub.com/mrJean1/PyGeodesy/issues/77>
606 lon = self._polon(sb, cb, R, **name_lon00)
607 m = self._Matrix(sa, ca, sb, cb) if M else None
608 return Ecef9Tuple(x, y, z, atan1d(sa, ca), lon, h,
609 C, m, self.datum, name=self._name__(name))
612class EcefSudano(_EcefBase):
613 '''Conversion between geodetic and geocentric, I{Earth-Centered, Earth-Fixed} (ECEF) coordinates
614 based on I{John J. Sudano}'s U{paper<https://www.ResearchGate.net/publication/3709199>}.
615 '''
616 _tol = EPS2
618 def reverse(self, xyz, y=None, z=None, M=None, **name_lon00): # PYCHOK unused M
619 '''Convert from geocentric C{(x, y, z)} to geodetic C{(lat, lon, height)} using
620 I{Sudano}'s U{iterative method<https://www.ResearchGate.net/publication/3709199>}.
622 @arg xyz: A geocentric (C{Cartesian}, L{Ecef9Tuple}) or C{scalar} ECEF C{x}
623 coordinate (C{meter}).
624 @kwarg y: ECEF C{y} coordinate for C{scalar} B{C{xyz}} and B{C{z}} (C{meter}).
625 @kwarg z: ECEF C{z} coordinate for C{scalar} B{C{xyz}} and B{C{y}} (C{meter}).
626 @kwarg M: I{Ignored}, rotation matrix C{M} not available.
627 @kwarg name_lon00: Optional keyword arguments C{B{name}=NN} (C{str}) and
628 I{"polar"} longitude C{B{lon00}=INT0} (C{degrees}), overriding
629 the default and property C{lon00} setting and returned in case
630 C{B{x}=0} and C{B{y}=0}.
632 @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with geodetic
633 coordinates C{(lat, lon, height)} for the given geocentric ones C{(x, y, z)},
634 iteration C{C}, C{M=None} always and C{datum} if available.
636 @raise EcefError: Invalid B{C{xyz}} or C{scalar} C{x} or B{C{y}} and/or B{C{z}}
637 not C{scalar} for C{scalar} B{C{xyz}} or no convergence.
638 '''
639 x, y, z, name = _xyzn4(xyz, y, z, self._Geocentrics, **name_lon00)
641 E = self.ellipsoid
642 e = E.e2 * E.a
643 R = hypot(x, y) # Rh
644 d = e - R
646 _a = fabs
647 lat = atan1d(z, R * E.e21)
648 sa, ca = sincos2d(_a(lat))
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 - R * sa)
652 # = ca**2 * (z * ca + E.e2 * E.a * sa - R * sa)
653 # = ca**2 * (z * ca + (E.e2 * E.a - R) * sa)
654 # D = ca**3 * (E.e2 * n / E.e2s2(sa)) - R
655 # = ca**2 * (E.e2 * E.a / E.e2s2(sa) - R / ca**2)
656 # N / D = (z * ca + (E.e2 * E.a - R) * sa) /
657 # (E.e2 * E.a / E.e2s2(sa) - R / ca**2)
658 _E = EPS_2
659 tol = self.tolerance
660 _S2 = Fsum(sa).fsum2f_
661 _rt = sqrt
662 for i in range(1, _TRIPS):
663 ca2 = _1_0 - sa**2
664 if ca2 < _E: # PYCHOK no cover
665 ca = _0_0
666 break
667 ca = _rt(ca2)
668 r = e / E.e2s2(sa) - R / ca2
669 if _a(r) < _E:
670 break
671 lat = None
672 sa, r = _S2(-z * ca / r, -d * sa / r)
673 if _a(r) < tol:
674 break
675 else:
676 t = unstr(self.reverse, x=x, y=y, z=z)
677 raise EcefError(t, txt=Fmt.no_convergence(r, tol))
679 if lat is None:
680 lat = copysign0(atan1d(_a(sa), ca), z)
681 lon = self._polon(y, x, R, **name_lon00)
683 h = fsumf_(R * ca, _a(z * sa), -E.a * E.e2s(sa)) # use Veness'
684 # because Sudano's Eq (7) doesn't produce the correct height
685 # h = (fabs(z) + R - E.a * cos(a + E.e21) * sa / ca) / (ca + sa)
686 return Ecef9Tuple(x, y, z, lat, lon, h,
687 i, None, self.datum, # C=i, M=None
688 iteration=i, name=self._name__(name))
690 @property_doc_(''' the convergence tolerance (C{float}).''')
691 def tolerance(self):
692 '''Get the convergence tolerance (C{scalar}).
693 '''
694 return self._tol
696 @tolerance.setter # PYCHOK setter!
697 def tolerance(self, tol):
698 '''Set the convergence tolerance (C{scalar}).
700 @raise EcefError: Non-scalar or invalid B{C{tol}}.
701 '''
702 self._tol = Scalar_(tolerance=tol, low=EPS, Error=EcefError)
705class EcefVeness(_EcefBase):
706 '''Conversion between geodetic and geocentric, I{Earth-Centered, Earth-Fixed} (ECEF) coordinates
707 transcoded from I{Chris Veness}' JavaScript classes U{LatLonEllipsoidal, Cartesian<https://
708 www.Movable-Type.co.UK/scripts/geodesy/docs/latlon-ellipsoidal.js.html>}.
710 @see: U{I{A Guide to Coordinate Systems in Great Britain}<https://www.OrdnanceSurvey.co.UK/
711 documents/resources/guide-coordinate-systems-great-britain.pdf>}, section I{B) Converting
712 between 3D Cartesian and ellipsoidal latitude, longitude and height coordinates}.
713 '''
715 def reverse(self, xyz, y=None, z=None, M=None, **name_lon00): # PYCHOK unused M
716 '''Conversion 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>}, Survey Review, Vol 28, 218, Oct 1985.
724 @arg xyz: A geocentric (C{Cartesian}, L{Ecef9Tuple}) or C{scalar} ECEF C{x}
725 coordinate (C{meter}).
726 @kwarg y: ECEF C{y} coordinate for C{scalar} B{C{xyz}} and B{C{z}} (C{meter}).
727 @kwarg z: ECEF C{z} coordinate for C{scalar} B{C{xyz}} and B{C{y}} (C{meter}).
728 @kwarg M: I{Ignored}, rotation matrix C{M} not available.
729 @kwarg name_lon00: Optional keyword arguments C{B{name}=NN} (C{str}) and
730 I{"polar"} longitude C{B{lon00}=INT0} (C{degrees}), overriding
731 the default and property C{lon00} setting and returned in case
732 C{B{x}=0} and C{B{y}=0}.
734 @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with
735 geodetic coordinates C{(lat, lon, height)} for the given geocentric
736 ones C{(x, y, z)}, case C{C}, C{M=None} always and C{datum} if available.
738 @raise EcefError: Invalid B{C{xyz}} or C{scalar} C{x} or B{C{y}} and/or B{C{z}}
739 not C{scalar} for C{scalar} B{C{xyz}}.
741 @see: Toms, Ralph M. U{I{An Efficient Algorithm for Geocentric to Geodetic
742 Coordinate Conversion}<https://www.OSTI.gov/scitech/biblio/110235>},
743 Sept 1995 and U{I{An Improved Algorithm for Geocentric to Geodetic
744 Coordinate Conversion}<https://www.OSTI.gov/scitech/servlets/purl/231228>},
745 Apr 1996, both from Lawrence Livermore National Laboratory (LLNL) and
746 Sudano, John J, U{I{An exact conversion from an Earth-centered coordinate
747 system to latitude longitude and altitude}<https://www.ResearchGate.net/
748 publication/3709199>}.
749 '''
750 x, y, z, name = _xyzn4(xyz, y, z, self._Geocentrics, **name_lon00)
752 E = self.ellipsoid
753 a = E.a
755 p = hypot(x, y) # distance from minor axis
756 r = hypot(p, z) # polar radius
757 if min(p, r) > EPS0:
758 b = E.b * E.e22
759 # parametric latitude (Bowring eqn 17, replaced)
760 t = (E.b * z) / (a * p) * (_1_0 + b / r)
761 c = _1_0 / hypot1(t)
762 s = c * t
763 # geodetic latitude (Bowring eqn 18)
764 lat = atan1d(z + s**3 * b,
765 p - c**3 * a * E.e2)
767 # height above ellipsoid (Bowring eqn 7)
768 sa, ca = sincos2d(lat)
769# r = a / E.e2s(sa) # length of normal terminated by minor axis
770# h = p * ca + z * sa - (a * a / r)
771 h = fsumf_(p * ca, z * sa, -a * E.e2s(sa))
772 C = 1
774 # see <https://GIS.StackExchange.com/questions/28446>
775 elif p > EPS: # lat arbitrarily zero, equatorial lon
776 C, lat, h = 2, _0_0, (p - a)
778 else: # polar lat, lon arbitrarily lon00
779 C, lat, h = 3, (_N_90_0 if z < 0 else _90_0), (fabs(z) - E.b)
781 lon = self._polon(y, x, p, **name_lon00)
782 return Ecef9Tuple(x, y, z, lat, lon, h,
783 C, None, self.datum, # M=None
784 name=self._name__(name))
787class EcefYou(_EcefBase):
788 '''Conversion between geodetic and geocentric, I{Earth-Centered, Earth-Fixed} (ECEF) coordinates
789 using I{Rey-Jer You}'s U{transformation<https://www.ResearchGate.net/publication/240359424>}
790 for I{non-prolate} ellipsoids.
792 @see: Featherstone, W.E., Claessens, S.J. U{I{Closed-form transformation between geodetic and
793 ellipsoidal coordinates}<https://Espace.Curtin.edu.AU/bitstream/handle/20.500.11937/
794 11589/115114_9021_geod2ellip_final.pdf>} Studia Geophysica et Geodaetica, 2008, 52,
795 pages 1-18 and U{PyMap3D <https://PyPI.org/project/pymap3d>}.
796 '''
798 def __init__(self, a_ellipsoid=_EWGS84, f=None, **name_lon00): # PYCHOK signature
799 _EcefBase.__init__(self, a_ellipsoid, f=f, **name_lon00) # inherited documentation
800 self._ee2 = EcefYou._ee2(self.ellipsoid)
802 @staticmethod
803 def _ee2(E):
804 e2 = E.a2 - E.b2
805 if e2 < 0 or E.f < 0:
806 raise EcefError(ellipsoid=E, txt=_prolate_)
807 return sqrt0(e2), e2
809 def reverse(self, xyz, y=None, z=None, M=None, **name_lon00): # PYCHOK unused M
810 '''Convert geocentric C{(x, y, z)} to geodetic C{(lat, lon, height)}
811 using I{Rey-Jer You}'s transformation.
813 @arg xyz: A geocentric (C{Cartesian}, L{Ecef9Tuple}) or C{scalar} ECEF C{x}
814 coordinate (C{meter}).
815 @kwarg y: ECEF C{y} coordinate for C{scalar} B{C{xyz}} and B{C{z}} (C{meter}).
816 @kwarg z: ECEF C{z} coordinate for C{scalar} B{C{xyz}} and B{C{y}} (C{meter}).
817 @kwarg M: I{Ignored}, rotation matrix C{M} not available.
818 @kwarg name_lon00: Optional keyword arguments C{B{name}=NN} (C{str}) and
819 I{"polar"} longitude C{B{lon00}=INT0} (C{degrees}), overriding
820 the default and property C{lon00} setting and returned in case
821 C{B{x}=0} and C{B{y}=0}.
823 @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with
824 geodetic coordinates C{(lat, lon, height)} for the given geocentric
825 ones C{(x, y, z)}, case C{C=1}, C{M=None} always and C{datum} if
826 available.
828 @raise EcefError: Invalid B{C{xyz}} or C{scalar} C{x} or B{C{y}} and/or
829 B{C{z}} not C{scalar} for C{scalar} B{C{xyz}} or the
830 ellipsoid is I{prolate}.
831 '''
832 x, y, z, name = _xyzn4(xyz, y, z, self._Geocentrics, **name_lon00)
834 E = self.ellipsoid
835 e, e2 = self._ee2
837 q = hypot(x, y) # R
838 u = Fpowers(2, x, y, z) - e2
839 u = u.fadd_(hypot(u, e * z * _2_0)).fover(_2_0)
840 if u > EPS02:
841 u = sqrt(u)
842 p = hypot(u, e)
843 B = atan1(p * z, u * q) # beta0 = atan(p / u * z / q)
844 sB, cB = sincos2(B)
845 if cB and sB:
846 p *= E.a
847 d = (p / cB - e2 * cB) / sB
848 if isnon0(d):
849 B += fsumf_(u * E.b, -p, e2) / d
850 sB, cB = sincos2(B)
851 elif u < (-EPS2):
852 raise EcefError(x=x, y=y, z=z, u=u, txt=_singular_)
853 else:
854 sB, cB = _copysign_1_0(z), _0_0
856 lat = atan1d(E.a * sB, E.b * cB) # atan(E.a_b * tan(B))
857 lon = self._polon(y, x, q, **name_lon00)
859 h = hypot(z - E.b * sB, q - E.a * cB)
860 if hypot2_(x, y, z * E.a_b) < E.a2:
861 h = neg(h) # inside ellipsoid
862 return Ecef9Tuple(x, y, z, lat, lon, h,
863 1, None, self.datum, # C=1, M=None
864 name=self._name__(name))
867class EcefMatrix(_NamedTuple):
868 '''A rotation matrix known as I{East-North-Up (ENU) to ECEF}.
870 @see: U{From ENU to ECEF<https://WikiPedia.org/wiki/
871 Geographic_coordinate_conversion#From_ECEF_to_ENU>} and
872 U{Issue #74<https://Github.com/mrJean1/PyGeodesy/issues/74>}.
873 '''
874 _Names_ = ('_0_0_', '_0_1_', '_0_2_', # row-order
875 '_1_0_', '_1_1_', '_1_2_',
876 '_2_0_', '_2_1_', '_2_2_')
877 _Units_ = (Scalar,) * len(_Names_)
879 def _validate(self, **unused): # PYCHOK unused
880 '''(INTERNAL) Allow C{_Names_} with leading underscore.
881 '''
882 _NamedTuple._validate(self, underOK=True)
884 def __new__(cls, sa, ca, sb, cb, *_more):
885 '''New L{EcefMatrix} matrix.
887 @arg sa: C{sin(phi)} (C{float}).
888 @arg ca: C{cos(phi)} (C{float}).
889 @arg sb: C{sin(lambda)} (C{float}).
890 @arg cb: C{cos(lambda)} (C{float}).
891 @arg _more: (INTERNAL) from C{.multiply}.
893 @raise EcefError: If B{C{sa}}, B{C{ca}}, B{C{sb}} or
894 B{C{cb}} outside M{[-1.0, +1.0]}.
895 '''
896 t = sa, ca, sb, cb
897 if _more: # all 9 matrix elements ...
898 t += _more # ... from .multiply
900 elif max(map(fabs, t)) > _1_0:
901 raise EcefError(unstr(EcefMatrix.__name__, *t))
903 else: # build matrix from the following quaternion operations
904 # qrot(lam, [0,0,1]) * qrot(phi, [0,-1,0]) * [1,1,1,1]/2
905 # or
906 # qrot(pi/2 + lam, [0,0,1]) * qrot(-pi/2 + phi, [-1,0,0])
907 # where
908 # qrot(t,v) = [cos(t/2), sin(t/2)*v[1], sin(t/2)*v[2], sin(t/2)*v[3]]
910 # Local X axis (East) in geocentric coords
911 # M[0] = -slam; M[3] = clam; M[6] = 0;
912 # Local Y axis (North) in geocentric coords
913 # M[1] = -clam * sphi; M[4] = -slam * sphi; M[7] = cphi;
914 # Local Z axis (Up) in geocentric coords
915 # M[2] = clam * cphi; M[5] = slam * cphi; M[8] = sphi;
916 t = (-sb, -cb * sa, cb * ca,
917 cb, -sb * sa, sb * ca,
918 _0_0, ca, sa)
920 return _NamedTuple.__new__(cls, *t)
922 def column(self, column):
923 '''Get this matrix' B{C{column}} 0, 1 or 2 as C{3-tuple}.
924 '''
925 if 0 <= column < 3:
926 return self[column::3]
927 raise _IndexError(column=column)
929 def copy(self, **unused): # PYCHOK signature
930 '''Make a shallow or deep copy of this instance.
932 @return: The copy (C{This class} or subclass thereof).
933 '''
934 return self.classof(*self)
936 __copy__ = __deepcopy__ = copy
938 @Property_RO
939 def matrix3(self):
940 '''Get this matrix' rows (C{3-tuple} of 3 C{3-tuple}s).
941 '''
942 return tuple(map(self.row, range(3)))
944 @Property_RO
945 def matrixTransposed3(self):
946 '''Get this matrix' I{Transposed} rows (C{3-tuple} of 3 C{3-tuple}s).
947 '''
948 return tuple(map(self.column, range(3)))
950 def multiply(self, other):
951 '''Matrix multiply M{M0' ⋅ M} this matrix I{Transposed}
952 with an other matrix.
954 @arg other: The other matrix (L{EcefMatrix}).
956 @return: The matrix product (L{EcefMatrix}).
958 @raise TypeError: If B{C{other}} is not L{EcefMatrix}.
959 '''
960 _xinstanceof(EcefMatrix, other=other)
961 # like LocalCartesian.MatrixMultiply, C{self.matrixTransposed3 X other.matrix3}
962 # <https://GeographicLib.SourceForge.io/C++/doc/LocalCartesian_8cpp_source.html>
963 # X = (fdot(self.column(r), *other.column(c)) for r in (0,1,2) for c in (0,1,2))
964 X = (fdot(self[r::3], *other[c::3]) for r in range(3) for c in range(3))
965 return _xnamed(EcefMatrix(*X), EcefMatrix.multiply.__name__)
967 def rotate(self, xyz, *xyz0):
968 '''Forward rotation M{M0' ⋅ ([x, y, z] - [x0, y0, z0])'}.
970 @arg xyz: Local C{(x, y, z)} coordinates (C{3-tuple}).
971 @arg xyz0: Optional, local C{(x0, y0, z0)} origin (C{3-tuple}).
973 @return: Rotated C{(x, y, z)} location (C{3-tuple}).
975 @raise LenError: Unequal C{len(B{xyz})} and C{len(B{xyz0})}.
976 '''
977 if xyz0:
978 if len(xyz0) != len(xyz):
979 raise LenError(self.rotate, xyz0=len(xyz0), xyz=len(xyz))
980 xyz = tuple(c - c0 for c, c0 in zip(xyz, xyz0))
982 # x' = M[0] * x + M[3] * y + M[6] * z
983 # y' = M[1] * x + M[4] * y + M[7] * z
984 # z' = M[2] * x + M[5] * y + M[8] * z
985 return (fdot(xyz, *self[0::3]), # .column(0)
986 fdot(xyz, *self[1::3]), # .column(1)
987 fdot(xyz, *self[2::3])) # .column(2)
989 def row(self, row):
990 '''Get this matrix' B{C{row}} 0, 1 or 2 as C{3-tuple}.
991 '''
992 if 0 <= row < 3:
993 r = row * 3
994 return self[r:r+3]
995 raise _IndexError(row=row)
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))
1010 _xyz = _1_0_1T + xyz
1011 # x' = x0 + M[0] * x + M[1] * y + M[2] * z
1012 # y' = y0 + M[3] * x + M[4] * y + M[5] * z
1013 # z' = z0 + M[6] * x + M[7] * y + M[8] * z
1014 xyz_ = (fdot(_xyz, xyz0[0], *self[0:3]), # .row(0)
1015 fdot(_xyz, xyz0[1], *self[3:6]), # .row(1)
1016 fdot(_xyz, xyz0[2], *self[6:9])) # .row(2)
1017 else:
1018 # x' = M[0] * x + M[1] * y + M[2] * z
1019 # y' = M[3] * x + M[4] * y + M[5] * z
1020 # z' = M[6] * x + M[7] * y + M[8] * z
1021 xyz_ = (fdot(xyz, *self[0:3]), # .row(0)
1022 fdot(xyz, *self[3:6]), # .row(1)
1023 fdot(xyz, *self[6:9])) # .row(2)
1024 return xyz_
1027class Ecef9Tuple(_NamedTuple):
1028 '''9-Tuple C{(x, y, z, lat, lon, height, C, M, datum)} with I{geocentric}
1029 C{x}, C{y} and C{z} plus I{geodetic} C{lat}, C{lon} and C{height}, case
1030 C{C} (see the C{Ecef*.reverse} methods) and optionally, the rotation
1031 matrix C{M} (L{EcefMatrix}) and C{datum}, with C{lat} and C{lon} in
1032 C{degrees} and C{x}, C{y}, C{z} and C{height} in C{meter}, conventionally.
1033 '''
1034 _Names_ = (_x_, _y_, _z_, _lat_, _lon_, _height_, _C_, _M_, _datum_)
1035 _Units_ = ( Meter, Meter, Meter, Lat, Lon, Height, Int, _Pass, _Pass)
1037 @property_RO
1038 def _CartesianBase(self):
1039 '''(INTERNAL) Get class C{CartesianBase}, I{once}.
1040 '''
1041 Ecef9Tuple._CartesianBase = C = _MODS.cartesianBase.CartesianBase # overwrite property_RO
1042 return C
1044 @deprecated_method
1045 def convertDatum(self, datum2): # for backward compatibility
1046 '''DEPRECATED, use method L{toDatum}.'''
1047 return self.toDatum(datum2)
1049 @Property_RO
1050 def lam(self):
1051 '''Get the longitude in C{radians} (C{float}).
1052 '''
1053 return self.philam.lam
1055 @Property_RO
1056 def lamVermeille(self):
1057 '''Get the longitude in C{radians} M{[-PI*3/2..+PI*3/2]} after U{Vermeille
1058 <https://Search.ProQuest.com/docview/639493848>} (2004), page 95.
1060 @see: U{Karney<https://GeographicLib.SourceForge.io/C++/doc/geocentric.html>},
1061 U{Vermeille<https://Search.ProQuest.com/docview/847292978>} 2011, pp 112-113, 116
1062 and U{Featherstone, et.al.<https://Search.ProQuest.com/docview/872827242>}, page 7.
1063 '''
1064 x, y = self.x, self.y
1065 if y > EPS0:
1066 r = atan2(x, hypot(y, x) + y) * _N_2_0 + PI_2
1067 elif y < -EPS0:
1068 r = atan2(x, hypot(y, x) - y) * _2_0 - PI_2
1069 else: # y == 0
1070 r = PI if x < 0 else _0_0
1071 return Lam(Vermeille=r)
1073 @Property_RO
1074 def latlon(self):
1075 '''Get the lat-, longitude in C{degrees} (L{LatLon2Tuple}C{(lat, lon)}).
1076 '''
1077 return LatLon2Tuple(self.lat, self.lon, name=self.name)
1079 @Property_RO
1080 def latlonheight(self):
1081 '''Get the lat-, longitude in C{degrees} and height (L{LatLon3Tuple}C{(lat, lon, height)}).
1082 '''
1083 return self.latlon.to3Tuple(self.height)
1085 @Property_RO
1086 def latlonheightdatum(self):
1087 '''Get the lat-, longitude in C{degrees} with height and datum (L{LatLon4Tuple}C{(lat, lon, height, datum)}).
1088 '''
1089 return self.latlonheight.to4Tuple(self.datum)
1091 @Property_RO
1092 def latlonVermeille(self):
1093 '''Get the latitude and I{Vermeille} longitude in C{degrees [-225..+225]} (L{LatLon2Tuple}C{(lat, lon)}).
1095 @see: Property C{lonVermeille}.
1096 '''
1097 return LatLon2Tuple(self.lat, self.lonVermeille, name=self.name)
1099 @Property_RO
1100 def lonVermeille(self):
1101 '''Get the longitude in C{degrees [-225..+225]} after U{Vermeille
1102 <https://Search.ProQuest.com/docview/639493848>} (2004), p 95.
1104 @see: Property C{lamVermeille}.
1105 '''
1106 return Lon(Vermeille=degrees(self.lamVermeille))
1108 @Property_RO
1109 def phi(self):
1110 '''Get the latitude in C{radians} (C{float}).
1111 '''
1112 return self.philam.phi
1114 @Property_RO
1115 def philam(self):
1116 '''Get the lat-, longitude in C{radians} (L{PhiLam2Tuple}C{(phi, lam)}).
1117 '''
1118 return PhiLam2Tuple(radians(self.lat), radians(self.lon), name=self.name)
1120 @Property_RO
1121 def philamheight(self):
1122 '''Get the lat-, longitude in C{radians} and height (L{PhiLam3Tuple}C{(phi, lam, height)}).
1123 '''
1124 return self.philam.to3Tuple(self.height)
1126 @Property_RO
1127 def philamheightdatum(self):
1128 '''Get the lat-, longitude in C{radians} with height and datum (L{PhiLam4Tuple}C{(phi, lam, height, datum)}).
1129 '''
1130 return self.philamheight.to4Tuple(self.datum)
1132 @Property_RO
1133 def philamVermeille(self):
1134 '''Get the latitude and I{Vermeille} longitude in C{radians [-PI*3/2..+PI*3/2]} (L{PhiLam2Tuple}C{(phi, lam)}).
1136 @see: Property C{lamVermeille}.
1137 '''
1138 return PhiLam2Tuple(radians(self.lat), self.lamVermeille, name=self.name)
1140 def toCartesian(self, Cartesian=None, **Cartesian_kwds):
1141 '''Return the geocentric C{(x, y, z)} coordinates as an ellipsoidal or spherical
1142 C{Cartesian}.
1144 @kwarg Cartesian: Optional class to return C{(x, y, z)} (L{ellipsoidalKarney.Cartesian},
1145 L{ellipsoidalNvector.Cartesian}, L{ellipsoidalVincenty.Cartesian},
1146 L{sphericalNvector.Cartesian} or L{sphericalTrigonometry.Cartesian})
1147 or C{None}.
1148 @kwarg Cartesian_kwds: Optional, additional B{C{Cartesian}} keyword arguments, ignored
1149 if C{B{Cartesian} is None}.
1151 @return: A C{B{Cartesian}(x, y, z, **B{Cartesian_kwds})} instance or
1152 a L{Vector4Tuple}C{(x, y, z, h)} if C{B{Cartesian} is None}.
1154 @raise TypeError: Invalid B{C{Cartesian}} or B{C{Cartesian_kwds}}.
1155 '''
1156 if Cartesian in (None, Vector4Tuple):
1157 r = self.xyzh
1158 elif Cartesian is Vector3Tuple:
1159 r = self.xyz
1160 else:
1161 _xsubclassof(self._CartesianBase, Cartesian=Cartesian)
1162 r = Cartesian(self, **_name1__(Cartesian_kwds, _or_nameof=self))
1163 return r
1165 def toDatum(self, datum2, **name):
1166 '''Convert this C{Ecef9Tuple} to an other datum.
1168 @arg datum2: Datum to convert I{to} (L{Datum}).
1169 @kwarg name: Optional C{B{name}=NN} (C{str}).
1171 @return: The converted 9-Tuple (C{Ecef9Tuple}).
1173 @raise TypeError: The B{C{datum2}} is not a L{Datum}.
1174 '''
1175 n = _name__(name, _or_nameof=self)
1176 if self.datum in (None, datum2): # PYCHOK _Names_
1177 r = self.copy(name=n)
1178 else:
1179 c = self._CartesianBase(self, datum=self.datum, name=n) # PYCHOK _Names_
1180 # c.toLatLon converts datum, x, y, z, lat, lon, etc.
1181 # and returns another Ecef9Tuple iff LatLon is None
1182 r = c.toLatLon(datum=datum2, LatLon=None)
1183 return r
1185 def toLatLon(self, LatLon=None, **LatLon_kwds):
1186 '''Return the geodetic C{(lat, lon, height[, datum])} coordinates.
1188 @kwarg LatLon: Optional class to return C{(lat, lon, height[, datum])}
1189 or C{None}.
1190 @kwarg LatLon_kwds: Optional B{C{height}}, B{C{datum}} and other
1191 B{C{LatLon}} keyword arguments.
1193 @return: An instance of C{B{LatLon}(lat, lon, **B{LatLon_kwds})}
1194 or if B{C{LatLon}} is C{None}, a L{LatLon3Tuple}C{(lat, lon,
1195 height)} respectively L{LatLon4Tuple}C{(lat, lon, height,
1196 datum)} depending on whether C{datum} is un-/specified.
1198 @raise TypeError: Invalid B{C{LatLon}} or B{C{LatLon_kwds}}.
1199 '''
1200 lat, lon, D = self.lat, self.lon, self.datum # PYCHOK Ecef9Tuple
1201 kwds = _name1__(LatLon_kwds, _or_nameof=self)
1202 kwds = _xkwds(kwds, height=self.height, datum=D) # PYCHOK Ecef9Tuple
1203 d = kwds.get(_datum_, LatLon)
1204 if LatLon is None:
1205 r = LatLon3Tuple(lat, lon, kwds[_height_], name=kwds[_name_])
1206 if d is not None:
1207 # assert d is not LatLon
1208 r = r.to4Tuple(d) # checks type(d)
1209 else:
1210 if d is None:
1211 _ = kwds.pop(_datum_) # remove None datum
1212 r = LatLon(lat, lon, **kwds)
1213 _xdatum(_xattr(r, datum=D), D)
1214 return r
1216 def toLocal(self, ltp, Xyz=None, **Xyz_kwds):
1217 '''Convert this geocentric to I{local} C{x}, C{y} and C{z}.
1219 @kwarg ltp: The I{local tangent plane} (LTP) to use (L{Ltp}).
1220 @kwarg Xyz: Optional class to return C{x}, C{y} and C{z}
1221 (L{XyzLocal}, L{Enu}, L{Ned}) or C{None}.
1222 @kwarg Xyz_kwds: Optional, additional B{C{Xyz}} keyword
1223 arguments, ignored if C{B{Xyz} is None}.
1225 @return: An B{C{Xyz}} instance or if C{B{Xyz} is None},
1226 a L{Local9Tuple}C{(x, y, z, lat, lon, height,
1227 ltp, ecef, M)} with C{M=None}, always.
1229 @raise TypeError: Invalid B{C{ltp}}.
1230 '''
1231 return _MODS.ltp._xLtp(ltp)._ecef2local(self, Xyz, Xyz_kwds)
1233 def toVector(self, Vector=None, **Vector_kwds):
1234 '''Return the geocentric C{(x, y, z)} coordinates as vector.
1236 @kwarg Vector: Optional vector class to return C{(x, y, z)} or
1237 C{None}.
1238 @kwarg Vector_kwds: Optional, additional B{C{Vector}} keyword
1239 arguments, ignored if C{B{Vector} is None}.
1241 @return: A C{Vector}C{(x, y, z, **Vector_kwds)} instance or a
1242 L{Vector3Tuple}C{(x, y, z)} if B{C{Vector}} is C{None}.
1244 @see: Propertes C{xyz} and C{xyzh}
1245 '''
1246 return self.xyz if Vector is None else Vector(
1247 *self.xyz, **_name1__(Vector_kwds, _or_nameof=self)) # PYCHOK Ecef9Tuple
1249# def _T_x_M(self, T):
1250# '''(INTERNAL) Update M{self.M = T.multiply(self.M)}.
1251# '''
1252# return self.dup(M=T.multiply(self.M))
1254 @Property_RO
1255 def xyz(self):
1256 '''Get the geocentric C{(x, y, z)} coordinates (L{Vector3Tuple}C{(x, y, z)}).
1257 '''
1258 return Vector3Tuple(self.x, self.y, self.z, name=self.name)
1260 @Property_RO
1261 def xyzh(self):
1262 '''Get the geocentric C{(x, y, z)} coordinates and C{height} (L{Vector4Tuple}C{(x, y, z, h)})
1263 '''
1264 return self.xyz.to4Tuple(self.height)
1267def _4Ecef(this, Ecef): # in .datums.Datum.ecef, .ellipsoids.Ellipsoid.ecef
1268 '''Return an ECEF converter for C{this} L{Datum} or L{Ellipsoid}.
1269 '''
1270 if Ecef is None:
1271 Ecef = EcefKarney
1272 else:
1273 _xinstanceof(*_Ecefs, Ecef=Ecef)
1274 return Ecef(this, name=this.name)
1277def _llhn4(latlonh, lon, height, suffix=NN, Error=EcefError, **name): # in .ltp
1278 '''(INTERNAL) Get a C{(lat, lon, h, name)} 4-tuple.
1279 '''
1280 try:
1281 lat, lon = latlonh.lat, latlonh.lon
1282 h = _xattr(latlonh, height=_xattr(latlonh, h=height))
1283 n = _name__(name, _or_nameof=latlonh) # == latlonh._name__(name)
1284 except AttributeError:
1285 lat, h, n = latlonh, height, _name__(**name)
1286 try:
1287 return Lat(lat), Lon(lon), Height(h), n
1288 except (TypeError, ValueError) as x:
1289 t = _lat_, _lon_, _height_
1290 if suffix:
1291 t = (_ + suffix for _ in t)
1292 d = dict(zip(t, (lat, lon, h)))
1293 raise Error(cause=x, **d)
1296def _xEcef(Ecef): # PYCHOK .latlonBase
1297 '''(INTERNAL) Validate B{C{Ecef}} I{class}.
1298 '''
1299 if issubclassof(Ecef, _EcefBase):
1300 return Ecef
1301 raise _TypesError(_Ecef_, Ecef, *_Ecefs)
1304# kwd lon00 unused but will throw a TypeError if misspelled, etc.
1305def _xyzn4(xyz, y, z, Types, Error=EcefError, lon00=0, # PYCHOK unused
1306 _xyz_y_z_names=_xyz_y_z, **name): # in .ltp
1307 '''(INTERNAL) Get an C{(x, y, z, name)} 4-tuple.
1308 '''
1309 try:
1310 n = _name__(name, _or_nameof=xyz) # == xyz._name__(name)
1311 try:
1312 t = xyz.x, xyz.y, xyz.z, n
1313 if not isinstance(xyz, Types):
1314 raise _TypesError(_xyz_y_z_names[0], xyz, *Types)
1315 except AttributeError:
1316 t = map1(float, xyz, y, z) + (n,)
1317 except (TypeError, ValueError) as x:
1318 d = dict(zip(_xyz_y_z_names, (xyz, y, z)))
1319 raise Error(cause=x, **d)
1320 return t
1321# assert _xyz_y_z == _args_kwds_names(_xyzn4)[:3]
1324_Ecefs = (EcefKarney, EcefSudano, EcefVeness, EcefYou,
1325 EcefFarrell21, EcefFarrell22)
1326__all__ += _ALL_DOCS(_EcefBase)
1328# **) MIT License
1329#
1330# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.
1331#
1332# Permission is hereby granted, free of charge, to any person obtaining a
1333# copy of this software and associated documentation files (the "Software"),
1334# to deal in the Software without restriction, including without limitation
1335# the rights to use, copy, modify, merge, publish, distribute, sublicense,
1336# and/or sell copies of the Software, and to permit persons to whom the
1337# Software is furnished to do so, subject to the following conditions:
1338#
1339# The above copyright notice and this permission notice shall be included
1340# in all copies or substantial portions of the Software.
1341#
1342# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
1343# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
1344# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
1345# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
1346# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
1347# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
1348# OTHER DEALINGS IN THE SOFTWARE.