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__ = '24.06.09'
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, **lon00_name):
303 '''(INTERNAL) Handle I{"polar"} longitude.
304 '''
305 return atan2d(y, x) if R else _xkwds_get(lon00_name, lon00=self.lon00)
307 def reverse(self, xyz, y=None, z=None, M=False, **lon00_name): # PYCHOK no cover
308 '''I{Must be overloaded}.'''
309 self._notOverloaded(xyz, y=y, z=z, M=M, **lon00_name)
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, **lon00_name): # 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 lon00_name: Optional C{B{name}=NN} (C{str}) and optional keyword argument
338 C{B{lon00}=INT0} (C{degrees}), an arbitrary I{"polar"} longitude
339 returned if C{B{x}=0} and C{B{y}=0}, see property C{lon00}.
341 @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with
342 geodetic coordinates C{(lat, lon, height)} for the given geocentric
343 ones C{(x, y, z)}, case C{C=1}, C{M=None} always and C{datum}
344 if available.
346 @raise EcefError: Invalid B{C{xyz}} or C{scalar} C{x} or B{C{y}} and/or B{C{z}}
347 not C{scalar} for C{scalar} B{C{xyz}} or C{sqrt} domain or
348 zero division error.
350 @see: L{EcefFarrell22} and L{EcefVeness}.
351 '''
352 x, y, z, name = _xyzn4(xyz, y, z, self._Geocentrics, **lon00_name)
354 E = self.ellipsoid
355 a = E.a
356 a2 = E.a2
357 b2 = E.b2
358 e2 = E.e2
359 e2_ = E.e2abs * E.a2_b2 # (E.e * E.a_b)**2 = 0.0820944... WGS84
360 e4 = E.e4
362 try: # names as page 29
363 z2 = z**2
364 ez = z2 * (_1_0 - e2) # E.e2s2(z)
366 p = hypot(x, y)
367 p2 = p**2
368 G = p2 + ez - e2 * (a2 - b2) # p2 + ez - e4 * a2
369 F = b2 * z2 * 54
370 t = e4 * p2 * F / G**3
371 t = cbrt(sqrt(t * (t + _2_0)) + t + _1_0)
372 G *= fsumf_(t , _1_0, _1_0 / t)
373 P = F / (G**2 * _3_0)
374 Q = sqrt(_2_0 * e4 * P + _1_0)
375 Q1 = Q + _1_0
376 r0 = P * p * e2 / Q1 - sqrt(fsumf_(a2 * (Q1 / Q) * _0_5,
377 -P * ez / (Q * Q1),
378 -P * p2 * _0_5))
379 r = p + e2 * r0
380 v = b2 / (sqrt(r**2 + ez) * a)
382 h = hypot(r, z) * (_1_0 - v)
383 lat = atan1d((e2_ * v + _1_0) * z, p)
384 lon = self._polon(y, x, p, **lon00_name)
385 # note, phi and lam are swapped on page 29
387 except (ValueError, ZeroDivisionError) as e:
388 raise EcefError(x=x, y=y, z=z, cause=e)
390 return Ecef9Tuple(x, y, z, lat, lon, h,
391 1, None, self.datum,
392 name=self._name__(name))
395class EcefFarrell22(_EcefBase):
396 '''Conversion between geodetic and geocentric, I{Earth-Centered, Earth-Fixed} (ECEF)
397 coordinates based on I{Jay A. Farrell}'s U{Table 2.2<https://Books.Google.com/
398 books?id=fW4foWASY6wC>}, page 30.
399 '''
401 def reverse(self, xyz, y=None, z=None, M=None, **lon00_name): # PYCHOK unused M
402 '''Convert from geocentric C{(x, y, z)} to geodetic C{(lat, lon, height)} using
403 I{Farrell}'s U{Table 2.2<https://Books.Google.com/books?id=fW4foWASY6wC>},
404 page 30.
406 @arg xyz: A geocentric (C{Cartesian}, L{Ecef9Tuple}) or C{scalar} ECEF C{x}
407 coordinate (C{meter}).
408 @kwarg y: ECEF C{y} coordinate for C{scalar} B{C{xyz}} and B{C{z}} (C{meter}).
409 @kwarg z: ECEF C{z} coordinate for C{scalar} B{C{xyz}} and B{C{y}} (C{meter}).
410 @kwarg M: I{Ignored}, rotation matrix C{M} not available.
411 @kwarg lon00_name: Optional C{B{name}=NN} (C{str}) and optional keyword argument
412 C{B{lon00}=INT0} (C{degrees}), an arbitrary I{"polar"} longitude
413 returned if C{B{x}=0} and C{B{y}=0}, see property C{lon00}.
415 @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with
416 geodetic coordinates C{(lat, lon, height)} for the given geocentric
417 ones C{(x, y, z)}, case C{C=1}, C{M=None} always and C{datum}
418 if available.
420 @raise EcefError: Invalid B{C{xyz}} or C{scalar} C{x} or B{C{y}} and/or B{C{z}}
421 not C{scalar} for C{scalar} B{C{xyz}} or C{sqrt} domain or
422 zero division error.
424 @see: L{EcefFarrell21} and L{EcefVeness}.
425 '''
426 x, y, z, name = _xyzn4(xyz, y, z, self._Geocentrics, **lon00_name)
428 E = self.ellipsoid
429 a = E.a
430 b = E.b
432 try: # see EcefVeness.reverse
433 p = hypot(x, y)
434 lon = self._polon(y, x, p, **lon00_name)
436 s, c = sincos2(atan2(z * a, p * b)) # == _norm3
437 lat = atan1d(z + s**3 * b * E.e22,
438 p - c**3 * a * E.e2)
440 s, c = sincos2d(lat)
441 if c: # E.roc1_(s) = E.a / sqrt(1 - E.e2 * s**2)
442 h = p / c - (E.roc1_(s) if s else a)
443 else: # polar
444 h = fabs(z) - b
445 # note, phi and lam are swapped on page 30
447 except (ValueError, ZeroDivisionError) as e:
448 raise EcefError(x=x, y=y, z=z, cause=e)
450 return Ecef9Tuple(x, y, z, lat, lon, h,
451 1, None, self.datum,
452 name=self._name__(name))
455class EcefKarney(_EcefBase):
456 '''Conversion between geodetic and geocentric, I{Earth-Centered, Earth-Fixed} (ECEF)
457 coordinates transcoded from I{Karney}'s C++ U{Geocentric<https://GeographicLib.SourceForge.io/
458 C++/doc/classGeographicLib_1_1Geocentric.html>} methods.
460 @note: On methods C{.forward} and C{.forwar_}, let C{v} be a unit vector located
461 at C{(lat, lon, h)}. We can express C{v} as column vectors in one of two
462 ways, C{v1} in East, North, Up (ENU) coordinates (where the components are
463 relative to a local coordinate system at C{C(lat0, lon0, h0)}) or as C{v0}
464 in geocentric C{x, y, z} coordinates. Then, M{v0 = M ⋅ v1} where C{M} is
465 the rotation matrix.
466 '''
468 @Property_RO
469 def hmax(self):
470 '''Get the distance or height limit (C{meter}, conventionally).
471 '''
472 return self.equatoradius / EPS_2 # self.equatoradius * _2_EPS, 12M lighyears
474 def reverse(self, xyz, y=None, z=None, M=False, **lon00_name):
475 '''Convert from geocentric C{(x, y, z)} to geodetic C{(lat, lon, height)}.
477 @arg xyz: A geocentric (C{Cartesian}, L{Ecef9Tuple}) or C{scalar} ECEF C{x}
478 coordinate (C{meter}).
479 @kwarg y: ECEF C{y} coordinate for C{scalar} B{C{xyz}} and B{C{z}} (C{meter}).
480 @kwarg z: ECEF C{z} coordinate for C{scalar} B{C{xyz}} and B{C{y}} (C{meter}).
481 @kwarg M: Optionally, return the rotation L{EcefMatrix} (C{bool}).
482 @kwarg lon00_name: Optional C{B{name}=NN} (C{str}) and optional keyword argument
483 C{B{lon00}=INT0} (C{degrees}), an arbitrary I{"polar"} longitude
484 returned if C{B{x}=0} and C{B{y}=0}, see property C{lon00}.
486 @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with
487 geodetic coordinates C{(lat, lon, height)} for the given geocentric
488 ones C{(x, y, z)}, case C{C}, optional C{M} (L{EcefMatrix}) and
489 C{datum} if available.
491 @raise EcefError: Invalid B{C{xyz}} or C{scalar} C{x} or B{C{y}} and/or B{C{z}}
492 not C{scalar} for C{scalar} B{C{xyz}}.
494 @note: In general, there are multiple solutions and the result which minimizes
495 C{height} is returned, i.e., the C{(lat, lon)} corresponding to the
496 closest point on the ellipsoid. If there are still multiple solutions
497 with different latitudes (applies only if C{z} = 0), then the solution
498 with C{lat} > 0 is returned. If there are still multiple solutions with
499 different longitudes (applies only if C{x} = C{y} = 0), then C{lon00} is
500 returned. The returned C{lon} is in the range [−180°, 180°] and C{height}
501 is not below M{−E.a * (1 − E.e2) / sqrt(1 − E.e2 * sin(lat)**2)}. Like
502 C{forward} above, M{v1 = Transpose(M) ⋅ v0}.
503 '''
504 def _norm3(y, x):
505 h = hypot(y, x) # EPS0, EPS_2
506 return (y / h, x / h, h) if h > 0 else (_0_0, _1_0, h)
508 x, y, z, name = _xyzn4(xyz, y, z, self._Geocentrics, **lon00_name)
510 E = self.ellipsoid
511 f = E.f
513 sb, cb, R = _norm3(y, x)
514 h = hypot(R, z) # distance to earth center
515 if h > self.hmax: # PYCHOK no cover
516 # We are really far away (> 12M light years). Treat the earth
517 # as a point and h above as an acceptable approximation to the
518 # height. This avoids overflow, e.g., in the computation of d
519 # below. It's possible that h has overflowed to INF, that's OK.
520 # Treat finite x, y, but R overflows to +INF by scaling by 2.
521 sb, cb, R = _norm3(y * _0_5, x * _0_5)
522 sa, ca, _ = _norm3(z * _0_5, R)
523 C = 1
525 elif E.e4: # E.isEllipsoidal
526 # Treat prolate spheroids by swapping R and Z here and by
527 # switching the arguments to phi = atan2(...) at the end.
528 p = (R / E.a)**2
529 q = (z / E.a)**2 * E.e21
530 if f < 0:
531 p, q = q, p
532 r = fsumf_(p, q, -E.e4)
533 e = E.e4 * q
534 if e or r > 0:
535 # Avoid possible division by zero when r = 0 by multiplying
536 # equations for s and t by r^3 and r, respectively.
537 s = d = e * p / _4_0 # s = r^3 * s
538 u = r = r / _6_0
539 r2 = r**2
540 r3 = r2 * r
541 t3 = r3 + s
542 d *= t3 + r3
543 if d < 0:
544 # t is complex, but the way u is defined, the result is real.
545 # There are three possible cube roots. We choose the root
546 # which avoids cancellation. Note, d < 0 implies r < 0.
547 u += cos(atan2(sqrt(-d), -t3) / _3_0) * r * _2_0
548 else:
549 # Pick the sign on the sqrt to maximize abs(t3). This
550 # minimizes loss of precision due to cancellation. The
551 # result is unchanged because of the way the t is used
552 # in definition of u.
553 if d > 0:
554 t3 += copysign0(sqrt(d), t3) # t3 = (r * t)^3
555 # N.B. cbrt always returns the real root, cbrt(-8) = -2.
556 t = cbrt(t3) # t = r * t
557 if t: # t can be zero; but then r2 / t -> 0.
558 u = fsumf_(u, t, r2 / t)
559 v = sqrt(e + u**2) # guaranteed positive
560 # Avoid loss of accuracy when u < 0. Underflow doesn't occur in
561 # E.e4 * q / (v - u) because u ~ e^4 when q is small and u < 0.
562 u = (e / (v - u)) if u < 0 else (u + v) # u+v, guaranteed positive
563 # Need to guard against w going negative due to roundoff in u - q.
564 w = E.e2abs * (u - q) / (_2_0 * v)
565 # Rearrange expression for k to avoid loss of accuracy due to
566 # subtraction. Division by 0 not possible because u > 0, w >= 0.
567 k1 = k2 = (u / (sqrt(u + w**2) + w)) if w > 0 else sqrt(u)
568 if f < 0:
569 k1 -= E.e2
570 else:
571 k2 += E.e2
572 sa, ca, h = _norm3(z / k1, R / k2)
573 h *= k1 - E.e21
574 C = 2
576 else: # e = E.e4 * q == 0 and r <= 0
577 # This leads to k = 0 (oblate, equatorial plane) and k + E.e^2 = 0
578 # (prolate, rotation axis) and the generation of 0/0 in the general
579 # formulas for phi and h, using the general formula and division
580 # by 0 in formula for h. Handle this case by taking the limits:
581 # f > 0: z -> 0, k -> E.e2 * sqrt(q) / sqrt(E.e4 - p)
582 # f < 0: r -> 0, k + E.e2 -> -E.e2 * sqrt(q) / sqrt(E.e4 - p)
583 q = E.e4 - p
584 if f < 0:
585 p, q = q, p
586 e = E.a
587 else:
588 e = E.b2_a
589 sa, ca, h = _norm3(sqrt(q * E._1_e21), sqrt(p))
590 if z < 0: # for tiny negative z, not for prolate
591 sa = neg(sa)
592 h *= neg(e / E.e2abs)
593 C = 3
595 else: # E.e4 == 0, spherical case
596 # Dealing with underflow in the general case with E.e2 = 0 is
597 # difficult. Origin maps to North pole, same as with ellipsoid.
598 sa, ca, _ = _norm3((z if h else _1_0), R)
599 h -= E.a
600 C = 4
602 # lon00 <https://GitHub.com/mrJean1/PyGeodesy/issues/77>
603 lon = self._polon(sb, cb, R, **lon00_name)
604 m = self._Matrix(sa, ca, sb, cb) if M else None
605 return Ecef9Tuple(x, y, z, atan1d(sa, ca), lon, h,
606 C, m, self.datum, name=self._name__(name))
609class EcefSudano(_EcefBase):
610 '''Conversion between geodetic and geocentric, I{Earth-Centered, Earth-Fixed} (ECEF) coordinates
611 based on I{John J. Sudano}'s U{paper<https://www.ResearchGate.net/publication/3709199>}.
612 '''
613 _tol = EPS2
615 def reverse(self, xyz, y=None, z=None, M=None, **lon00_name): # PYCHOK unused M
616 '''Convert from geocentric C{(x, y, z)} to geodetic C{(lat, lon, height)} using
617 I{Sudano}'s U{iterative method<https://www.ResearchGate.net/publication/3709199>}.
619 @arg xyz: A geocentric (C{Cartesian}, L{Ecef9Tuple}) or C{scalar} ECEF C{x}
620 coordinate (C{meter}).
621 @kwarg y: ECEF C{y} coordinate for C{scalar} B{C{xyz}} and B{C{z}} (C{meter}).
622 @kwarg z: ECEF C{z} coordinate for C{scalar} B{C{xyz}} and B{C{y}} (C{meter}).
623 @kwarg M: I{Ignored}, rotation matrix C{M} not available.
624 @kwarg lon00_name: Optional C{B{name}=NN} (C{str}) and optional keyword argument
625 C{B{lon00}=INT0} (C{degrees}), an arbitrary I{"polar"} longitude
626 returned if C{B{x}=0} and C{B{y}=0}, see property C{lon00}.
628 @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with geodetic
629 coordinates C{(lat, lon, height)} for the given geocentric ones C{(x, y, z)},
630 iteration C{C}, C{M=None} always and C{datum} if available.
632 @raise EcefError: Invalid B{C{xyz}} or C{scalar} C{x} or B{C{y}} and/or B{C{z}}
633 not C{scalar} for C{scalar} B{C{xyz}} or no convergence.
634 '''
635 x, y, z, name = _xyzn4(xyz, y, z, self._Geocentrics, **lon00_name)
637 E = self.ellipsoid
638 e = E.e2 * E.a
639 R = hypot(x, y) # Rh
640 d = e - R
642 _a = fabs
643 lat = atan1d(z, R * E.e21)
644 sa, ca = sincos2d(_a(lat))
645 # Sudano's Eq (A-6) and (A-7) refactored/reduced,
646 # replacing Rn from Eq (A-4) with n = E.a / ca:
647 # N = ca**2 * ((z + E.e2 * n * sa) * ca - R * sa)
648 # = ca**2 * (z * ca + E.e2 * E.a * sa - R * sa)
649 # = ca**2 * (z * ca + (E.e2 * E.a - R) * sa)
650 # D = ca**3 * (E.e2 * n / E.e2s2(sa)) - R
651 # = ca**2 * (E.e2 * E.a / E.e2s2(sa) - R / ca**2)
652 # N / D = (z * ca + (E.e2 * E.a - R) * sa) /
653 # (E.e2 * E.a / E.e2s2(sa) - R / ca**2)
654 _E = EPS_2
655 tol = self.tolerance
656 _S2 = Fsum(sa).fsum2f_
657 _rt = sqrt
658 for i in range(1, _TRIPS):
659 ca2 = _1_0 - sa**2
660 if ca2 < _E: # PYCHOK no cover
661 ca = _0_0
662 break
663 ca = _rt(ca2)
664 r = e / E.e2s2(sa) - R / ca2
665 if _a(r) < _E:
666 break
667 lat = None
668 sa, r = _S2(-z * ca / r, -d * sa / r)
669 if _a(r) < tol:
670 break
671 else:
672 t = unstr(self.reverse, x=x, y=y, z=z)
673 raise EcefError(t, txt=Fmt.no_convergence(r, tol))
675 if lat is None:
676 lat = copysign0(atan1d(_a(sa), ca), z)
677 lon = self._polon(y, x, R, **lon00_name)
679 h = fsumf_(R * ca, _a(z * sa), -E.a * E.e2s(sa)) # use Veness'
680 # because Sudano's Eq (7) doesn't produce the correct height
681 # h = (fabs(z) + R - E.a * cos(a + E.e21) * sa / ca) / (ca + sa)
682 return Ecef9Tuple(x, y, z, lat, lon, h,
683 i, None, self.datum, # C=i, M=None
684 iteration=i, name=self._name__(name))
686 @property_doc_(''' the convergence tolerance (C{float}).''')
687 def tolerance(self):
688 '''Get the convergence tolerance (C{scalar}).
689 '''
690 return self._tol
692 @tolerance.setter # PYCHOK setter!
693 def tolerance(self, tol):
694 '''Set the convergence tolerance (C{scalar}).
696 @raise EcefError: Non-scalar or invalid B{C{tol}}.
697 '''
698 self._tol = Scalar_(tolerance=tol, low=EPS, Error=EcefError)
701class EcefVeness(_EcefBase):
702 '''Conversion between geodetic and geocentric, I{Earth-Centered, Earth-Fixed} (ECEF) coordinates
703 transcoded from I{Chris Veness}' JavaScript classes U{LatLonEllipsoidal, Cartesian<https://
704 www.Movable-Type.co.UK/scripts/geodesy/docs/latlon-ellipsoidal.js.html>}.
706 @see: U{I{A Guide to Coordinate Systems in Great Britain}<https://www.OrdnanceSurvey.co.UK/
707 documents/resources/guide-coordinate-systems-great-britain.pdf>}, section I{B) Converting
708 between 3D Cartesian and ellipsoidal latitude, longitude and height coordinates}.
709 '''
711 def reverse(self, xyz, y=None, z=None, M=None, **lon00_name): # PYCHOK unused M
712 '''Conversion from geocentric C{(x, y, z)} to geodetic C{(lat, lon, height)}
713 transcoded from I{Chris Veness}' U{JavaScript<https://www.Movable-Type.co.UK/
714 scripts/geodesy/docs/latlon-ellipsoidal.js.html>}.
716 Uses B. R. Bowring’s formulation for μm precision in concise form U{I{The accuracy
717 of geodetic latitude and height equations}<https://www.ResearchGate.net/publication/
718 233668213>}, Survey Review, Vol 28, 218, Oct 1985.
720 @arg xyz: A geocentric (C{Cartesian}, L{Ecef9Tuple}) or C{scalar} ECEF C{x}
721 coordinate (C{meter}).
722 @kwarg y: ECEF C{y} coordinate for C{scalar} B{C{xyz}} and B{C{z}} (C{meter}).
723 @kwarg z: ECEF C{z} coordinate for C{scalar} B{C{xyz}} and B{C{y}} (C{meter}).
724 @kwarg M: I{Ignored}, rotation matrix C{M} not available.
725 @kwarg lon00_name: Optional C{B{name}=NN} (C{str}) and optional keyword argument
726 C{B{lon00}=INT0} (C{degrees}), an arbitrary I{"polar"} longitude
727 returned if C{B{x}=0} and C{B{y}=0}, see property C{lon00}.
729 @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with
730 geodetic coordinates C{(lat, lon, height)} for the given geocentric
731 ones C{(x, y, z)}, case C{C}, C{M=None} always and C{datum} if available.
733 @raise EcefError: Invalid B{C{xyz}} or C{scalar} C{x} or B{C{y}} and/or B{C{z}}
734 not C{scalar} for C{scalar} B{C{xyz}}.
736 @see: Toms, Ralph M. U{I{An Efficient Algorithm for Geocentric to Geodetic
737 Coordinate Conversion}<https://www.OSTI.gov/scitech/biblio/110235>},
738 Sept 1995 and U{I{An Improved Algorithm for Geocentric to Geodetic
739 Coordinate Conversion}<https://www.OSTI.gov/scitech/servlets/purl/231228>},
740 Apr 1996, both from Lawrence Livermore National Laboratory (LLNL) and
741 Sudano, John J, U{I{An exact conversion from an Earth-centered coordinate
742 system to latitude longitude and altitude}<https://www.ResearchGate.net/
743 publication/3709199>}.
744 '''
745 x, y, z, name = _xyzn4(xyz, y, z, self._Geocentrics, **lon00_name)
747 E = self.ellipsoid
748 a = E.a
750 p = hypot(x, y) # distance from minor axis
751 r = hypot(p, z) # polar radius
752 if min(p, r) > EPS0:
753 b = E.b * E.e22
754 # parametric latitude (Bowring eqn 17, replaced)
755 t = (E.b * z) / (a * p) * (_1_0 + b / r)
756 c = _1_0 / hypot1(t)
757 s = c * t
758 # geodetic latitude (Bowring eqn 18)
759 lat = atan1d(z + s**3 * b,
760 p - c**3 * a * E.e2)
762 # height above ellipsoid (Bowring eqn 7)
763 sa, ca = sincos2d(lat)
764# r = a / E.e2s(sa) # length of normal terminated by minor axis
765# h = p * ca + z * sa - (a * a / r)
766 h = fsumf_(p * ca, z * sa, -a * E.e2s(sa))
767 C = 1
769 # see <https://GIS.StackExchange.com/questions/28446>
770 elif p > EPS: # lat arbitrarily zero, equatorial lon
771 C, lat, h = 2, _0_0, (p - a)
773 else: # polar lat, lon arbitrarily lon00
774 C, lat, h = 3, (_N_90_0 if z < 0 else _90_0), (fabs(z) - E.b)
776 lon = self._polon(y, x, p, **lon00_name)
777 return Ecef9Tuple(x, y, z, lat, lon, h,
778 C, None, self.datum, # M=None
779 name=self._name__(name))
782class EcefYou(_EcefBase):
783 '''Conversion between geodetic and geocentric, I{Earth-Centered, Earth-Fixed} (ECEF) coordinates
784 using I{Rey-Jer You}'s U{transformation<https://www.ResearchGate.net/publication/240359424>}
785 for I{non-prolate} ellipsoids.
787 @see: Featherstone, W.E., Claessens, S.J. U{I{Closed-form transformation between geodetic and
788 ellipsoidal coordinates}<https://Espace.Curtin.edu.AU/bitstream/handle/20.500.11937/
789 11589/115114_9021_geod2ellip_final.pdf>} Studia Geophysica et Geodaetica, 2008, 52,
790 pages 1-18 and U{PyMap3D <https://PyPI.org/project/pymap3d>}.
791 '''
793 def __init__(self, a_ellipsoid=_EWGS84, f=None, **lon00_name): # PYCHOK signature
794 _EcefBase.__init__(self, a_ellipsoid, f=f, **lon00_name) # inherited documentation
795 self._ee2 = EcefYou._ee2(self.ellipsoid)
797 @staticmethod
798 def _ee2(E):
799 e2 = E.a2 - E.b2
800 if e2 < 0 or E.f < 0:
801 raise EcefError(ellipsoid=E, txt=_prolate_)
802 return sqrt0(e2), e2
804 def reverse(self, xyz, y=None, z=None, M=None, **lon00_name): # PYCHOK unused M
805 '''Convert geocentric C{(x, y, z)} to geodetic C{(lat, lon, height)}
806 using I{Rey-Jer You}'s transformation.
808 @arg xyz: A geocentric (C{Cartesian}, L{Ecef9Tuple}) or C{scalar} ECEF C{x}
809 coordinate (C{meter}).
810 @kwarg y: ECEF C{y} coordinate for C{scalar} B{C{xyz}} and B{C{z}} (C{meter}).
811 @kwarg z: ECEF C{z} coordinate for C{scalar} B{C{xyz}} and B{C{y}} (C{meter}).
812 @kwarg M: I{Ignored}, rotation matrix C{M} not available.
813 @kwarg lon00_name: Optional C{B{name}=NN} (C{str}) and optional keyword argument
814 C{B{lon00}=INT0} (C{degrees}), an arbitrary I{"polar"} longitude
815 returned if C{B{x}=0} and C{B{y}=0}, see property C{lon00}.
817 @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with
818 geodetic coordinates C{(lat, lon, height)} for the given geocentric
819 ones C{(x, y, z)}, case C{C=1}, C{M=None} always and C{datum} if
820 available.
822 @raise EcefError: Invalid B{C{xyz}} or C{scalar} C{x} or B{C{y}} and/or
823 B{C{z}} not C{scalar} for C{scalar} B{C{xyz}} or the
824 ellipsoid is I{prolate}.
825 '''
826 x, y, z, name = _xyzn4(xyz, y, z, self._Geocentrics, **lon00_name)
828 E = self.ellipsoid
829 e, e2 = self._ee2
831 q = hypot(x, y) # R
832 u = Fpowers(2, x, y, z) - e2
833 u = u.fadd_(hypot(u, e * z * _2_0)).fover(_2_0)
834 if u > EPS02:
835 u = sqrt(u)
836 p = hypot(u, e)
837 B = atan1(p * z, u * q) # beta0 = atan(p / u * z / q)
838 sB, cB = sincos2(B)
839 if cB and sB:
840 p *= E.a
841 d = (p / cB - e2 * cB) / sB
842 if isnon0(d):
843 B += fsumf_(u * E.b, -p, e2) / d
844 sB, cB = sincos2(B)
845 elif u < (-EPS2):
846 raise EcefError(x=x, y=y, z=z, u=u, txt=_singular_)
847 else:
848 sB, cB = _copysign_1_0(z), _0_0
850 lat = atan1d(E.a * sB, E.b * cB) # atan(E.a_b * tan(B))
851 lon = self._polon(y, x, q, **lon00_name)
853 h = hypot(z - E.b * sB, q - E.a * cB)
854 if hypot2_(x, y, z * E.a_b) < E.a2:
855 h = neg(h) # inside ellipsoid
856 return Ecef9Tuple(x, y, z, lat, lon, h,
857 1, None, self.datum, # C=1, M=None
858 name=self._name__(name))
861class EcefMatrix(_NamedTuple):
862 '''A rotation matrix known as I{East-North-Up (ENU) to ECEF}.
864 @see: U{From ENU to ECEF<https://WikiPedia.org/wiki/
865 Geographic_coordinate_conversion#From_ECEF_to_ENU>} and
866 U{Issue #74<https://Github.com/mrJean1/PyGeodesy/issues/74>}.
867 '''
868 _Names_ = ('_0_0_', '_0_1_', '_0_2_', # row-order
869 '_1_0_', '_1_1_', '_1_2_',
870 '_2_0_', '_2_1_', '_2_2_')
871 _Units_ = (Scalar,) * len(_Names_)
873 def _validate(self, **unused): # PYCHOK unused
874 '''(INTERNAL) Allow C{_Names_} with leading underscore.
875 '''
876 _NamedTuple._validate(self, underOK=True)
878 def __new__(cls, sa, ca, sb, cb, *_more):
879 '''New L{EcefMatrix} matrix.
881 @arg sa: C{sin(phi)} (C{float}).
882 @arg ca: C{cos(phi)} (C{float}).
883 @arg sb: C{sin(lambda)} (C{float}).
884 @arg cb: C{cos(lambda)} (C{float}).
885 @arg _more: (INTERNAL) from C{.multiply}.
887 @raise EcefError: If B{C{sa}}, B{C{ca}}, B{C{sb}} or
888 B{C{cb}} outside M{[-1.0, +1.0]}.
889 '''
890 t = sa, ca, sb, cb
891 if _more: # all 9 matrix elements ...
892 t += _more # ... from .multiply
894 elif max(map(fabs, t)) > _1_0:
895 raise EcefError(unstr(EcefMatrix, *t))
897 else: # build matrix from the following quaternion operations
898 # qrot(lam, [0,0,1]) * qrot(phi, [0,-1,0]) * [1,1,1,1]/2
899 # or
900 # qrot(pi/2 + lam, [0,0,1]) * qrot(-pi/2 + phi, [-1,0,0])
901 # where
902 # qrot(t,v) = [cos(t/2), sin(t/2)*v[1], sin(t/2)*v[2], sin(t/2)*v[3]]
904 # Local X axis (East) in geocentric coords
905 # M[0] = -slam; M[3] = clam; M[6] = 0;
906 # Local Y axis (North) in geocentric coords
907 # M[1] = -clam * sphi; M[4] = -slam * sphi; M[7] = cphi;
908 # Local Z axis (Up) in geocentric coords
909 # M[2] = clam * cphi; M[5] = slam * cphi; M[8] = sphi;
910 t = (-sb, -cb * sa, cb * ca,
911 cb, -sb * sa, sb * ca,
912 _0_0, ca, sa)
914 return _NamedTuple.__new__(cls, *t)
916 def column(self, column):
917 '''Get this matrix' B{C{column}} 0, 1 or 2 as C{3-tuple}.
918 '''
919 if 0 <= column < 3:
920 return self[column::3]
921 raise _IndexError(column=column)
923 def copy(self, **unused): # PYCHOK signature
924 '''Make a shallow or deep copy of this instance.
926 @return: The copy (C{This class} or subclass thereof).
927 '''
928 return self.classof(*self)
930 __copy__ = __deepcopy__ = copy
932 @Property_RO
933 def matrix3(self):
934 '''Get this matrix' rows (C{3-tuple} of 3 C{3-tuple}s).
935 '''
936 return tuple(map(self.row, range(3)))
938 @Property_RO
939 def matrixTransposed3(self):
940 '''Get this matrix' I{Transposed} rows (C{3-tuple} of 3 C{3-tuple}s).
941 '''
942 return tuple(map(self.column, range(3)))
944 def multiply(self, other):
945 '''Matrix multiply M{M0' ⋅ M} this matrix I{Transposed}
946 with an other matrix.
948 @arg other: The other matrix (L{EcefMatrix}).
950 @return: The matrix product (L{EcefMatrix}).
952 @raise TypeError: If B{C{other}} is not L{EcefMatrix}.
953 '''
954 _xinstanceof(EcefMatrix, other=other)
955 # like LocalCartesian.MatrixMultiply, C{self.matrixTransposed3 X other.matrix3}
956 # <https://GeographicLib.SourceForge.io/C++/doc/LocalCartesian_8cpp_source.html>
957 # X = (fdot(self.column(r), *other.column(c)) for r in (0,1,2) for c in (0,1,2))
958 X = (fdot(self[r::3], *other[c::3]) for r in range(3) for c in range(3))
959 return _xnamed(EcefMatrix(*X), EcefMatrix.multiply.__name__)
961 def rotate(self, xyz, *xyz0):
962 '''Forward rotation M{M0' ⋅ ([x, y, z] - [x0, y0, z0])'}.
964 @arg xyz: Local C{(x, y, z)} coordinates (C{3-tuple}).
965 @arg xyz0: Optional, local C{(x0, y0, z0)} origin (C{3-tuple}).
967 @return: Rotated C{(x, y, z)} location (C{3-tuple}).
969 @raise LenError: Unequal C{len(B{xyz})} and C{len(B{xyz0})}.
970 '''
971 if xyz0:
972 if len(xyz0) != len(xyz):
973 raise LenError(self.rotate, xyz0=len(xyz0), xyz=len(xyz))
974 xyz = tuple(c - c0 for c, c0 in zip(xyz, xyz0))
976 # x' = M[0] * x + M[3] * y + M[6] * z
977 # y' = M[1] * x + M[4] * y + M[7] * z
978 # z' = M[2] * x + M[5] * y + M[8] * z
979 return (fdot(xyz, *self[0::3]), # .column(0)
980 fdot(xyz, *self[1::3]), # .column(1)
981 fdot(xyz, *self[2::3])) # .column(2)
983 def row(self, row):
984 '''Get this matrix' B{C{row}} 0, 1 or 2 as C{3-tuple}.
985 '''
986 if 0 <= row < 3:
987 r = row * 3
988 return self[r:r+3]
989 raise _IndexError(row=row)
991 def unrotate(self, xyz, *xyz0):
992 '''Inverse rotation M{[x0, y0, z0] + M0 ⋅ [x,y,z]'}.
994 @arg xyz: Local C{(x, y, z)} coordinates (C{3-tuple}).
995 @arg xyz0: Optional, local C{(x0, y0, z0)} origin (C{3-tuple}).
997 @return: Unrotated C{(x, y, z)} location (C{3-tuple}).
999 @raise LenError: Unequal C{len(B{xyz})} and C{len(B{xyz0})}.
1000 '''
1001 if xyz0:
1002 if len(xyz0) != len(xyz):
1003 raise LenError(self.unrotate, xyz0=len(xyz0), xyz=len(xyz))
1004 _xyz = _1_0_1T + xyz
1005 # x' = x0 + M[0] * x + M[1] * y + M[2] * z
1006 # y' = y0 + M[3] * x + M[4] * y + M[5] * z
1007 # z' = z0 + M[6] * x + M[7] * y + M[8] * z
1008 xyz_ = (fdot(_xyz, xyz0[0], *self[0:3]), # .row(0)
1009 fdot(_xyz, xyz0[1], *self[3:6]), # .row(1)
1010 fdot(_xyz, xyz0[2], *self[6:9])) # .row(2)
1011 else:
1012 # x' = M[0] * x + M[1] * y + M[2] * z
1013 # y' = M[3] * x + M[4] * y + M[5] * z
1014 # z' = M[6] * x + M[7] * y + M[8] * z
1015 xyz_ = (fdot(xyz, *self[0:3]), # .row(0)
1016 fdot(xyz, *self[3:6]), # .row(1)
1017 fdot(xyz, *self[6:9])) # .row(2)
1018 return xyz_
1021class Ecef9Tuple(_NamedTuple):
1022 '''9-Tuple C{(x, y, z, lat, lon, height, C, M, datum)} with I{geocentric}
1023 C{x}, C{y} and C{z} plus I{geodetic} C{lat}, C{lon} and C{height}, case
1024 C{C} (see the C{Ecef*.reverse} methods) and optionally, the rotation
1025 matrix C{M} (L{EcefMatrix}) and C{datum}, with C{lat} and C{lon} in
1026 C{degrees} and C{x}, C{y}, C{z} and C{height} in C{meter}, conventionally.
1027 '''
1028 _Names_ = (_x_, _y_, _z_, _lat_, _lon_, _height_, _C_, _M_, _datum_)
1029 _Units_ = ( Meter, Meter, Meter, Lat, Lon, Height, Int, _Pass, _Pass)
1031 @property_RO
1032 def _CartesianBase(self):
1033 '''(INTERNAL) Get class C{CartesianBase}, I{once}.
1034 '''
1035 Ecef9Tuple._CartesianBase = C = _MODS.cartesianBase.CartesianBase # overwrite property_RO
1036 return C
1038 @deprecated_method
1039 def convertDatum(self, datum2): # for backward compatibility
1040 '''DEPRECATED, use method L{toDatum}.'''
1041 return self.toDatum(datum2)
1043 @Property_RO
1044 def lam(self):
1045 '''Get the longitude in C{radians} (C{float}).
1046 '''
1047 return self.philam.lam
1049 @Property_RO
1050 def lamVermeille(self):
1051 '''Get the longitude in C{radians} M{[-PI*3/2..+PI*3/2]} after U{Vermeille
1052 <https://Search.ProQuest.com/docview/639493848>} (2004), page 95.
1054 @see: U{Karney<https://GeographicLib.SourceForge.io/C++/doc/geocentric.html>},
1055 U{Vermeille<https://Search.ProQuest.com/docview/847292978>} 2011, pp 112-113, 116
1056 and U{Featherstone, et.al.<https://Search.ProQuest.com/docview/872827242>}, page 7.
1057 '''
1058 x, y = self.x, self.y
1059 if y > EPS0:
1060 r = atan2(x, hypot(y, x) + y) * _N_2_0 + PI_2
1061 elif y < -EPS0:
1062 r = atan2(x, hypot(y, x) - y) * _2_0 - PI_2
1063 else: # y == 0
1064 r = PI if x < 0 else _0_0
1065 return Lam(Vermeille=r)
1067 @Property_RO
1068 def latlon(self):
1069 '''Get the lat-, longitude in C{degrees} (L{LatLon2Tuple}C{(lat, lon)}).
1070 '''
1071 return LatLon2Tuple(self.lat, self.lon, name=self.name)
1073 @Property_RO
1074 def latlonheight(self):
1075 '''Get the lat-, longitude in C{degrees} and height (L{LatLon3Tuple}C{(lat, lon, height)}).
1076 '''
1077 return self.latlon.to3Tuple(self.height)
1079 @Property_RO
1080 def latlonheightdatum(self):
1081 '''Get the lat-, longitude in C{degrees} with height and datum (L{LatLon4Tuple}C{(lat, lon, height, datum)}).
1082 '''
1083 return self.latlonheight.to4Tuple(self.datum)
1085 @Property_RO
1086 def latlonVermeille(self):
1087 '''Get the latitude and I{Vermeille} longitude in C{degrees [-225..+225]} (L{LatLon2Tuple}C{(lat, lon)}).
1089 @see: Property C{lonVermeille}.
1090 '''
1091 return LatLon2Tuple(self.lat, self.lonVermeille, name=self.name)
1093 @Property_RO
1094 def lonVermeille(self):
1095 '''Get the longitude in C{degrees [-225..+225]} after U{Vermeille
1096 <https://Search.ProQuest.com/docview/639493848>} (2004), p 95.
1098 @see: Property C{lamVermeille}.
1099 '''
1100 return Lon(Vermeille=degrees(self.lamVermeille))
1102 @Property_RO
1103 def phi(self):
1104 '''Get the latitude in C{radians} (C{float}).
1105 '''
1106 return self.philam.phi
1108 @Property_RO
1109 def philam(self):
1110 '''Get the lat-, longitude in C{radians} (L{PhiLam2Tuple}C{(phi, lam)}).
1111 '''
1112 return PhiLam2Tuple(radians(self.lat), radians(self.lon), name=self.name)
1114 @Property_RO
1115 def philamheight(self):
1116 '''Get the lat-, longitude in C{radians} and height (L{PhiLam3Tuple}C{(phi, lam, height)}).
1117 '''
1118 return self.philam.to3Tuple(self.height)
1120 @Property_RO
1121 def philamheightdatum(self):
1122 '''Get the lat-, longitude in C{radians} with height and datum (L{PhiLam4Tuple}C{(phi, lam, height, datum)}).
1123 '''
1124 return self.philamheight.to4Tuple(self.datum)
1126 @Property_RO
1127 def philamVermeille(self):
1128 '''Get the latitude and I{Vermeille} longitude in C{radians [-PI*3/2..+PI*3/2]} (L{PhiLam2Tuple}C{(phi, lam)}).
1130 @see: Property C{lamVermeille}.
1131 '''
1132 return PhiLam2Tuple(radians(self.lat), self.lamVermeille, name=self.name)
1134 def toCartesian(self, Cartesian=None, **Cartesian_kwds):
1135 '''Return the geocentric C{(x, y, z)} coordinates as an ellipsoidal or spherical
1136 C{Cartesian}.
1138 @kwarg Cartesian: Optional class to return C{(x, y, z)} (L{ellipsoidalKarney.Cartesian},
1139 L{ellipsoidalNvector.Cartesian}, L{ellipsoidalVincenty.Cartesian},
1140 L{sphericalNvector.Cartesian} or L{sphericalTrigonometry.Cartesian})
1141 or C{None}.
1142 @kwarg Cartesian_kwds: Optional, additional B{C{Cartesian}} keyword arguments, ignored
1143 if C{B{Cartesian} is None}.
1145 @return: A C{B{Cartesian}(x, y, z, **B{Cartesian_kwds})} instance or
1146 a L{Vector4Tuple}C{(x, y, z, h)} if C{B{Cartesian} is None}.
1148 @raise TypeError: Invalid B{C{Cartesian}} or B{C{Cartesian_kwds}}.
1149 '''
1150 if Cartesian in (None, Vector4Tuple):
1151 r = self.xyzh
1152 elif Cartesian is Vector3Tuple:
1153 r = self.xyz
1154 else:
1155 _xsubclassof(self._CartesianBase, Cartesian=Cartesian)
1156 r = Cartesian(self, **_name1__(Cartesian_kwds, _or_nameof=self))
1157 return r
1159 def toDatum(self, datum2, **name):
1160 '''Convert this C{Ecef9Tuple} to an other datum.
1162 @arg datum2: Datum to convert I{to} (L{Datum}).
1163 @kwarg name: Optional C{B{name}=NN} (C{str}).
1165 @return: The converted 9-Tuple (C{Ecef9Tuple}).
1167 @raise TypeError: The B{C{datum2}} is not a L{Datum}.
1168 '''
1169 n = _name__(name, _or_nameof=self)
1170 if self.datum in (None, datum2): # PYCHOK _Names_
1171 r = self.copy(name=n)
1172 else:
1173 c = self._CartesianBase(self, datum=self.datum, name=n) # PYCHOK _Names_
1174 # c.toLatLon converts datum, x, y, z, lat, lon, etc.
1175 # and returns another Ecef9Tuple iff LatLon is None
1176 r = c.toLatLon(datum=datum2, LatLon=None)
1177 return r
1179 def toLatLon(self, LatLon=None, **LatLon_kwds):
1180 '''Return the geodetic C{(lat, lon, height[, datum])} coordinates.
1182 @kwarg LatLon: Optional class to return C{(lat, lon, height[, datum])}
1183 or C{None}.
1184 @kwarg LatLon_kwds: Optional B{C{height}}, B{C{datum}} and other
1185 B{C{LatLon}} keyword arguments.
1187 @return: An instance of C{B{LatLon}(lat, lon, **B{LatLon_kwds})}
1188 or if B{C{LatLon}} is C{None}, a L{LatLon3Tuple}C{(lat, lon,
1189 height)} respectively L{LatLon4Tuple}C{(lat, lon, height,
1190 datum)} depending on whether C{datum} is un-/specified.
1192 @raise TypeError: Invalid B{C{LatLon}} or B{C{LatLon_kwds}}.
1193 '''
1194 lat, lon, D = self.lat, self.lon, self.datum # PYCHOK Ecef9Tuple
1195 kwds = _name1__(LatLon_kwds, _or_nameof=self)
1196 kwds = _xkwds(kwds, height=self.height, datum=D) # PYCHOK Ecef9Tuple
1197 d = kwds.get(_datum_, LatLon)
1198 if LatLon is None:
1199 r = LatLon3Tuple(lat, lon, kwds[_height_], name=kwds[_name_])
1200 if d is not None:
1201 # assert d is not LatLon
1202 r = r.to4Tuple(d) # checks type(d)
1203 else:
1204 if d is None:
1205 _ = kwds.pop(_datum_) # remove None datum
1206 r = LatLon(lat, lon, **kwds)
1207 _xdatum(_xattr(r, datum=D), D)
1208 return r
1210 def toLocal(self, ltp, Xyz=None, **Xyz_kwds):
1211 '''Convert this geocentric to I{local} C{x}, C{y} and C{z}.
1213 @kwarg ltp: The I{local tangent plane} (LTP) to use (L{Ltp}).
1214 @kwarg Xyz: Optional class to return C{x}, C{y} and C{z}
1215 (L{XyzLocal}, L{Enu}, L{Ned}) or C{None}.
1216 @kwarg Xyz_kwds: Optional, additional B{C{Xyz}} keyword
1217 arguments, ignored if C{B{Xyz} is None}.
1219 @return: An B{C{Xyz}} instance or if C{B{Xyz} is None},
1220 a L{Local9Tuple}C{(x, y, z, lat, lon, height,
1221 ltp, ecef, M)} with C{M=None}, always.
1223 @raise TypeError: Invalid B{C{ltp}}.
1224 '''
1225 return _MODS.ltp._xLtp(ltp)._ecef2local(self, Xyz, Xyz_kwds)
1227 def toVector(self, Vector=None, **Vector_kwds):
1228 '''Return the geocentric C{(x, y, z)} coordinates as vector.
1230 @kwarg Vector: Optional vector class to return C{(x, y, z)} or
1231 C{None}.
1232 @kwarg Vector_kwds: Optional, additional B{C{Vector}} keyword
1233 arguments, ignored if C{B{Vector} is None}.
1235 @return: A C{Vector}C{(x, y, z, **Vector_kwds)} instance or a
1236 L{Vector3Tuple}C{(x, y, z)} if B{C{Vector}} is C{None}.
1238 @see: Propertes C{xyz} and C{xyzh}
1239 '''
1240 return self.xyz if Vector is None else Vector(
1241 *self.xyz, **_name1__(Vector_kwds, _or_nameof=self)) # PYCHOK Ecef9Tuple
1243# def _T_x_M(self, T):
1244# '''(INTERNAL) Update M{self.M = T.multiply(self.M)}.
1245# '''
1246# return self.dup(M=T.multiply(self.M))
1248 @Property_RO
1249 def xyz(self):
1250 '''Get the geocentric C{(x, y, z)} coordinates (L{Vector3Tuple}C{(x, y, z)}).
1251 '''
1252 return Vector3Tuple(self.x, self.y, self.z, name=self.name)
1254 @Property_RO
1255 def xyzh(self):
1256 '''Get the geocentric C{(x, y, z)} coordinates and C{height} (L{Vector4Tuple}C{(x, y, z, h)})
1257 '''
1258 return self.xyz.to4Tuple(self.height)
1261def _4Ecef(this, Ecef): # in .datums.Datum.ecef, .ellipsoids.Ellipsoid.ecef
1262 '''Return an ECEF converter for C{this} L{Datum} or L{Ellipsoid}.
1263 '''
1264 if Ecef is None:
1265 Ecef = EcefKarney
1266 else:
1267 _xinstanceof(*_Ecefs, Ecef=Ecef)
1268 return Ecef(this, name=this.name)
1271def _llhn4(latlonh, lon, height, suffix=NN, Error=EcefError, **name): # in .ltp
1272 '''(INTERNAL) Get a C{(lat, lon, h, name)} 4-tuple.
1273 '''
1274 try:
1275 lat, lon = latlonh.lat, latlonh.lon
1276 h = _xattr(latlonh, height=_xattr(latlonh, h=height))
1277 n = _name__(name, _or_nameof=latlonh) # == latlonh._name__(name)
1278 except AttributeError:
1279 lat, h, n = latlonh, height, _name__(**name)
1280 try:
1281 return Lat(lat), Lon(lon), Height(h), n
1282 except (TypeError, ValueError) as x:
1283 t = _lat_, _lon_, _height_
1284 if suffix:
1285 t = (_ + suffix for _ in t)
1286 d = dict(zip(t, (lat, lon, h)))
1287 raise Error(cause=x, **d)
1290def _xEcef(Ecef): # PYCHOK .latlonBase
1291 '''(INTERNAL) Validate B{C{Ecef}} I{class}.
1292 '''
1293 if issubclassof(Ecef, _EcefBase):
1294 return Ecef
1295 raise _TypesError(_Ecef_, Ecef, *_Ecefs)
1298# kwd lon00 unused but will throw a TypeError if misspelled, etc.
1299def _xyzn4(xyz, y, z, Types, Error=EcefError, lon00=0, # PYCHOK unused
1300 _xyz_y_z_names=_xyz_y_z, **name): # in .ltp
1301 '''(INTERNAL) Get an C{(x, y, z, name)} 4-tuple.
1302 '''
1303 try:
1304 n = _name__(name, _or_nameof=xyz) # == xyz._name__(name)
1305 try:
1306 t = xyz.x, xyz.y, xyz.z, n
1307 if not isinstance(xyz, Types):
1308 raise _TypesError(_xyz_y_z_names[0], xyz, *Types)
1309 except AttributeError:
1310 t = map1(float, xyz, y, z) + (n,)
1311 except (TypeError, ValueError) as x:
1312 d = dict(zip(_xyz_y_z_names, (xyz, y, z)))
1313 raise Error(cause=x, **d)
1314 return t
1315# assert _xyz_y_z == _args_kwds_names(_xyzn4)[:3]
1318_Ecefs = (EcefKarney, EcefSudano, EcefVeness, EcefYou,
1319 EcefFarrell21, EcefFarrell22)
1320__all__ += _ALL_DOCS(_EcefBase)
1322# **) MIT License
1323#
1324# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.
1325#
1326# Permission is hereby granted, free of charge, to any person obtaining a
1327# copy of this software and associated documentation files (the "Software"),
1328# to deal in the Software without restriction, including without limitation
1329# the rights to use, copy, modify, merge, publish, distribute, sublicense,
1330# and/or sell copies of the Software, and to permit persons to whom the
1331# Software is furnished to do so, subject to the following conditions:
1332#
1333# The above copyright notice and this permission notice shall be included
1334# in all copies or substantial portions of the Software.
1335#
1336# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
1337# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
1338# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
1339# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
1340# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
1341# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
1342# OTHER DEALINGS IN THE SOFTWARE.