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 plane} as
57opposed to I{geocentric} (ECEF) ones.
58'''
60from pygeodesy.basics import copysign0, isscalar, issubclassof, neg, map1, \
61 _xinstanceof, _xsubclassof
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, 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, hypot, hypot1, hypot2_
71from pygeodesy.fsums import Fsum, fsumf_
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 _NamedBase, _NamedTuple, notOverloaded, _Pass, _xnamed
77from pygeodesy.namedTuples import LatLon2Tuple, LatLon3Tuple, \
78 PhiLam2Tuple, Vector3Tuple, Vector4Tuple
79from pygeodesy.props import deprecated_method, Property_RO, property_RO, property_doc_
80from pygeodesy.streprs import Fmt, unstr
81from pygeodesy.units import Degrees, Height, Int, Lam, Lat, Lon, Meter, Phi, \
82 Scalar, Scalar_
83from pygeodesy.utily import atan2d, degrees90, degrees180, sincos2, sincos2_, \
84 sincos2d, sincos2d_
86from math import atan2, cos, degrees, fabs, radians, sqrt
88__all__ = _ALL_LAZY.ecef
89__version__ = '23.09.07'
91_Ecef_ = 'Ecef'
92_prolate_ = 'prolate'
93_TRIPS = 17 # 8..9 sufficient, EcefSudano.reverse
94_xyz_y_z = _xyz_, _y_, _z_ # _xargs_names(_xyzn4)[:3]
97class EcefError(_ValueError):
98 '''An ECEF or C{Ecef*} related issue.
99 '''
100 pass
103def _llhn4(latlonh, lon, height, suffix=NN, Error=EcefError, name=NN): # in .ltp.LocalCartesian.forward and -.reset
104 '''(INTERNAL) Get C{lat, lon, h, name} as C{4-tuple}.
105 '''
106 try:
107 lat, lon = latlonh.lat, latlonh.lon
108 h = _xattr(latlonh, height=_xattr(latlonh, h=height))
109 n = _xattr(latlonh, name=NN)
110 except AttributeError:
111 lat, h, n = latlonh, height, NN
113 try:
114 llhn = Lat(lat), Lon(lon), Height(h), (name or n)
115 except (TypeError, ValueError) as x:
116 t = _lat_, _lon_, _height_
117 if suffix:
118 t = (_ + suffix for _ in t)
119 d = dict(zip(t, (lat, lon, h)))
120 raise Error(cause=x, **d)
121 return llhn
124# kwd lon00 unused but will throw a TypeError if misspelled, etc.
125def _xyzn4(xyz, y, z, Types, Error=EcefError, name=NN, # PYCHOK unused
126 _xyz_y_z_names=_xyz_y_z, lon00=0): # in .ltp
127 '''(INTERNAL) Get an C{(x, y, z, name)} 4-tuple.
128 '''
129 try:
130 try:
131 t = xyz.x, xyz.y, xyz.z, _xattr(xyz, name=name)
132 if not isinstance(xyz, Types):
133 raise _TypesError(_xyz_y_z_names[0], xyz, *Types)
134 except AttributeError:
135 t = map1(float, xyz, y, z) + (name,)
137 except (TypeError, ValueError) as x:
138 d = dict(zip(_xyz_y_z_names, (xyz, y, z)))
139 raise Error(cause=x, **d)
140 return t
142# assert _xyz_y_z == _xargs_names(_xyzn4)[:3]
145class _EcefBase(_NamedBase):
146 '''(INTERNAL) Base class for L{EcefFarrell21}, L{EcefFarrell22}, L{EcefKarney},
147 L{EcefSudano}, L{EcefVeness} and L{EcefYou}.
148 '''
149 _datum = _WGS84
150 _E = _EWGS84
151 _lon00 = INT0 # arbitrary, "polar" lon for LocalCartesian, Ltp
153 def __init__(self, a_ellipsoid=_EWGS84, f=None, name=NN, lon00=INT0):
154 '''New C{Ecef*} converter.
156 @arg a_ellipsoid: A (non-prolate) ellipsoid (L{Ellipsoid}, L{Ellipsoid2},
157 L{Datum} or L{a_f2Tuple}) or C{scalar} ellipsoid's
158 equatorial radius (C{meter}).
159 @kwarg f: C{None} or the ellipsoid flattening (C{scalar}), required
160 for C{scalar} B{C{a_ellipsoid}}, C{B{f}=0} represents a
161 sphere, negative B{C{f}} a prolate ellipsoid.
162 @kwarg name: Optional name (C{str}).
163 @kwarg lon00: An arbitrary, I{"polar"} longitude (C{degrees}), see the
164 methods C{reverse}.
166 @raise EcefError: If B{C{a_ellipsoid}} not L{Ellipsoid}, L{Ellipsoid2},
167 L{Datum} or L{a_f2Tuple} or C{scalar} or B{C{f}} not
168 C{scalar} or if C{scalar} B{C{a_ellipsoid}} not positive
169 or B{C{f}} not less than 1.0.
170 '''
171 try:
172 E = a_ellipsoid
173 if f is None:
174 if E is _EWGS84 or E is _WGS84:
175 raise AssertionError # "break"
176 elif isscalar(E) and isscalar(f):
177 E = a_f2Tuple(E, f)
178 else:
179 raise ValueError # _invalid_
181 d = _ellipsoidal_datum(E, name=name)
182 E = d.ellipsoid
183 if E.a < EPS or E.f > EPS1:
184 raise ValueError # _invalid_
186 self._datum = d
187 self._E = E
189 except AssertionError: # "break"
190 pass
191 except (TypeError, ValueError) as x:
192 t = unstr(self.classname, a=a_ellipsoid, f=f)
193 raise EcefError(_SPACE_(t, _ellipsoid_), cause=x)
195 if name:
196 self.name = name
197 if lon00 is not INT0:
198 self.lon00 = lon00
200 def __eq__(self, other):
201 '''Compare this and an other Ecef.
203 @arg other: The other ecef (C{Ecef*}).
205 @return: C{True} if equal, C{False} otherwise.
206 '''
207 return other is self or (isinstance(other, self.__class__) and
208 other.ellipsoid == self.ellipsoid)
210 @Property_RO
211 def datum(self):
212 '''Get the datum (L{Datum}).
213 '''
214 return self._datum
216 @Property_RO
217 def ellipsoid(self):
218 '''Get the ellipsoid (L{Ellipsoid} or L{Ellipsoid2}).
219 '''
220 return self._E
222 @Property_RO
223 def equatoradius(self):
224 '''Get the C{ellipsoid}'s equatorial radius, semi-axis (C{meter}).
225 '''
226 return self.ellipsoid.a
228 a = equatorialRadius = equatoradius # Karney property
230 @Property_RO
231 def flattening(self): # Karney property
232 '''Get the C{ellipsoid}'s flattening (C{scalar}), positive for
233 I{oblate}, negative for I{prolate} or C{0} for I{near-spherical}.
234 '''
235 return self.ellipsoid.f
237 f = flattening
239 def _forward(self, lat, lon, h, name, M=False, _philam=False): # in .ltp.LocalCartesian.forward and -.reset
240 '''(INTERNAL) Common for all C{Ecef*}.
241 '''
242 if _philam: # lat, lon in radians
243 sa, ca, sb, cb = sincos2_(lat, lon)
244 lat = Lat(degrees90( lat), Error=EcefError)
245 lon = Lon(degrees180(lon), Error=EcefError)
246 else:
247 sa, ca, sb, cb = sincos2d_(lat, lon)
249 E = self.ellipsoid
250 n = E.roc1_(sa, ca) if self._isYou else E.roc1_(sa)
251 z = (h + n * E.e21) * sa
252 x = (h + n) * ca
254 m = self._Matrix(sa, ca, sb, cb) if M else None
255 return Ecef9Tuple(x * cb, x * sb, z, lat, lon, h,
256 0, m, self.datum,
257 name=name or self.name)
259 def forward(self, latlonh, lon=None, height=0, M=False, name=NN):
260 '''Convert from geodetic C{(lat, lon, height)} to geocentric C{(x, y, z)}.
262 @arg latlonh: Either a C{LatLon}, an L{Ecef9Tuple} or C{scalar}
263 latitude (C{degrees}).
264 @kwarg lon: Optional C{scalar} longitude for C{scalar} B{C{latlonh}}
265 (C{degrees}).
266 @kwarg height: Optional height (C{meter}), vertically above (or below)
267 the surface of the ellipsoid.
268 @kwarg M: Optionally, return the rotation L{EcefMatrix} (C{bool}).
269 @kwarg name: Optional name (C{str}).
271 @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with
272 geocentric C{(x, y, z)} coordinates for the given geodetic ones
273 C{(lat, lon, height)}, case C{C} 0, optional C{M} (L{EcefMatrix})
274 and C{datum} if available.
276 @raise EcefError: If B{C{latlonh}} not C{LatLon}, L{Ecef9Tuple} or
277 C{scalar} or B{C{lon}} not C{scalar} for C{scalar}
278 B{C{latlonh}} or C{abs(lat)} exceeds 90°.
280 @note: Use method C{.forward_} to specify C{lat} and C{lon} in C{radians}
281 and avoid double angle conversions.
282 '''
283 llhn = _llhn4(latlonh, lon, height, name=name)
284 return self._forward(*llhn, M=M)
286 def forward_(self, phi, lam, height=0, M=False, name=NN):
287 '''Like method C{.forward} except with geodetic lat- and longitude given
288 in I{radians}.
290 @arg phi: Latitude in I{radians} (C{scalar}).
291 @arg lam: Longitude in I{radians} (C{scalar}).
292 @kwarg height: Optional height (C{meter}), vertically above (or below)
293 the surface of the ellipsoid.
294 @kwarg M: Optionally, return the rotation L{EcefMatrix} (C{bool}).
295 @kwarg name: Optional name (C{str}).
297 @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)}
298 with C{lat} set to C{degrees90(B{phi})} and C{lon} to
299 C{degrees180(B{lam})}.
301 @raise EcefError: If B{C{phi}} or B{C{lam}} invalid or not C{scalar}.
302 '''
303 try: # like function C{_llhn4} above
304 plhn = Phi(phi), Lam(lam), Height(height), name
305 except (TypeError, ValueError) as x:
306 raise EcefError(phi=phi, lam=lam, height=height, cause=x)
307 return self._forward(*plhn, M=M, _philam=True)
309 @property_RO
310 def _Geocentrics(self):
311 '''(INTERNAL) Get the valid geocentric classes. I{once}.
312 '''
313 _EcefBase._Geocentrics = t = (Ecef9Tuple, # overwrite property_RO
314 _MODS.cartesianBase.CartesianBase)
315 return t
317 @Property_RO
318 def _isYou(self):
319 '''(INTERNAL) Is this an C{EcefYou}?.
320 '''
321 return isinstance(self, EcefYou)
323 @property
324 def lon00(self):
325 '''Get the I{"polar"} longitude (C{degrees}), see method C{reverse}.
326 '''
327 return self._lon00
329 @lon00.setter # PYCHOK setter!
330 def lon00(self, lon00):
331 '''Set the I{"polar"} longitude (C{degrees}), see method C{reverse}.
332 '''
333 self._lon00 = Degrees(lon00=lon00)
335 def _Matrix(self, sa, ca, sb, cb):
336 '''Creation a rotation matrix.
338 @arg sa: C{sin(phi)} (C{float}).
339 @arg ca: C{cos(phi)} (C{float}).
340 @arg sb: C{sin(lambda)} (C{float}).
341 @arg cb: C{cos(lambda)} (C{float}).
343 @return: An L{EcefMatrix}.
344 '''
345 return self._xnamed(EcefMatrix(sa, ca, sb, cb))
347 def _polon(self, y, x, R, **name_lon00):
348 '''(INTERNAL) Handle I{"polar"} longitude.
349 '''
350 return atan2d(y, x) if R else _xkwds_get(name_lon00, lon00=self.lon00)
352 def reverse(self, xyz, y=None, z=None, M=False, **name_lon00): # PYCHOK no cover
353 '''(INTERNAL) I{Must be overloaded}, see function C{notOverloaded}.
354 '''
355 notOverloaded(self, xyz, y=y, z=z, M=M, **name_lon00)
357 def toStr(self, prec=9, **unused): # PYCHOK signature
358 '''Return this C{Ecef*} as a string.
360 @kwarg prec: Precision, number of decimal digits (0..9).
362 @return: This C{Ecef*} (C{str}).
363 '''
364 return self.attrs(_a_, _f_, _datum_, _name_, prec=prec) # _ellipsoid_
367class EcefFarrell21(_EcefBase):
368 '''Conversion between geodetic and geocentric, I{Earth-Centered, Earth-Fixed} (ECEF)
369 coordinates based on I{Jay A. Farrell}'s U{Table 2.1<https://Books.Google.com/
370 books?id=fW4foWASY6wC>}, page 29.
371 '''
373 def reverse(self, xyz, y=None, z=None, M=None, **name_lon00): # PYCHOK unused M
374 '''Convert from geocentric C{(x, y, z)} to geodetic C{(lat, lon, height)} using
375 I{Farrell}'s U{Table 2.1<https://Books.Google.com/books?id=fW4foWASY6wC>},
376 page 29.
378 @arg xyz: A geocentric (C{Cartesian}, L{Ecef9Tuple}) or C{scalar} ECEF C{x}
379 coordinate (C{meter}).
380 @kwarg y: ECEF C{y} coordinate for C{scalar} B{C{xyz}} and B{C{z}} (C{meter}).
381 @kwarg z: ECEF C{z} coordinate for C{scalar} B{C{xyz}} and B{C{y}} (C{meter}).
382 @kwarg M: I{Ignored}, rotation matrix C{M} not available.
383 @kwarg name_lon00: Optional keyword arguments C{B{name}=NN} (C{str}) and
384 I{"polar"} longitude C{B{lon00}=INT0} (C{degrees}), overriding
385 the default and property C{lon00} setting and returned if
386 C{B{x}=0} and C{B{y}=0}.
388 @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with
389 geodetic coordinates C{(lat, lon, height)} for the given geocentric
390 ones C{(x, y, z)}, case C{C=1}, C{M=None} always and C{datum}
391 if available.
393 @raise EcefError: Invalid B{C{xyz}} or C{scalar} C{x} or B{C{y}} and/or B{C{z}}
394 not C{scalar} for C{scalar} B{C{xyz}} or C{sqrt} domain or
395 zero division error.
397 @see: L{EcefFarrell22} and L{EcefVeness}.
398 '''
399 x, y, z, name = _xyzn4(xyz, y, z, self._Geocentrics, **name_lon00)
401 E = self.ellipsoid
402 a = E.a
403 a2 = E.a2
404 b2 = E.b2
405 e2 = E.e2
406 e2_ = E.e2abs * E.a2_b2 # (E.e * E.a_b)**2 = 0.0820944... WGS84
407 e4 = E.e4
409 try: # names as page 29
410 z2 = z**2
411 ez = z2 * (_1_0 - e2) # E.e2s2(z)
413 p = hypot(x, y)
414 p2 = p**2
415 G = p2 + ez - e2 * (a2 - b2) # p2 + ez - e4 * a2
416 F = b2 * z2 * 54
417 c = e4 * p2 * F / G**3
418 s = cbrt(_1_0 + sqrt(c**2 + c + c) + c)
419 G *= fsumf_(s, _1_0, _1_0 / s)
420 P = F / (G**2 * _3_0)
421 Q = sqrt(_2_0 * e4 * P + _1_0)
422 Q1 = Q + _1_0
423 r0 = P * p * e2 / Q1 - sqrt(fsumf_(a2 * (Q1 / Q) * _0_5,
424 -P * ez / (Q * Q1),
425 -P * p2 * _0_5))
426 r = p + e2 * r0
427 v = b2 / (sqrt(r**2 + ez) * a)
429 h = hypot(r, z) * (_1_0 - v)
430 lat = atan2d((e2_ * v + _1_0) * z, p)
431 lon = self._polon(y, x, p, **name_lon00)
432 # note, phi and lam are swapped on page 29
434 except (ValueError, ZeroDivisionError) as e:
435 raise EcefError(x=x, y=y, z=z, cause=e)
437 return Ecef9Tuple(x, y, z, lat, lon, h,
438 1, None, self.datum,
439 name=name or self.name)
442class EcefFarrell22(_EcefBase):
443 '''Conversion between geodetic and geocentric, I{Earth-Centered, Earth-Fixed} (ECEF)
444 coordinates based on I{Jay A. Farrell}'s U{Table 2.2<https://Books.Google.com/
445 books?id=fW4foWASY6wC>}, page 30.
446 '''
448 def reverse(self, xyz, y=None, z=None, M=None, **name_lon00): # PYCHOK unused M
449 '''Convert from geocentric C{(x, y, z)} to geodetic C{(lat, lon, height)} using
450 I{Farrell}'s U{Table 2.2<https://Books.Google.com/books?id=fW4foWASY6wC>},
451 page 30.
453 @arg xyz: A geocentric (C{Cartesian}, L{Ecef9Tuple}) or C{scalar} ECEF C{x}
454 coordinate (C{meter}).
455 @kwarg y: ECEF C{y} coordinate for C{scalar} B{C{xyz}} and B{C{z}} (C{meter}).
456 @kwarg z: ECEF C{z} coordinate for C{scalar} B{C{xyz}} and B{C{y}} (C{meter}).
457 @kwarg M: I{Ignored}, rotation matrix C{M} not available.
458 @kwarg name_lon00: Optional keyword arguments C{B{name}=NN} (C{str}) and
459 I{"polar"} longitude C{B{lon00}=INT0} (C{degrees}), overriding
460 the default and property C{lon00} setting and returned in case
461 C{B{x}=0} and C{B{y}=0}.
463 @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with
464 geodetic coordinates C{(lat, lon, height)} for the given geocentric
465 ones C{(x, y, z)}, case C{C=1}, C{M=None} always and C{datum}
466 if available.
468 @raise EcefError: Invalid B{C{xyz}} or C{scalar} C{x} or B{C{y}} and/or B{C{z}}
469 not C{scalar} for C{scalar} B{C{xyz}} or C{sqrt} domain or
470 zero division error.
472 @see: L{EcefFarrell21} and L{EcefVeness}.
473 '''
474 x, y, z, name = _xyzn4(xyz, y, z, self._Geocentrics, **name_lon00)
476 E = self.ellipsoid
477 a = E.a
478 b = E.b
480 try: # see EcefVeness.reverse
481 p = hypot(x, y)
482 lon = self._polon(y, x, p, **name_lon00)
484 s, c = sincos2(atan2(z * a, p * b)) # == _norm3
485 lat = atan2d(z + s**3 * b * E.e22,
486 p - c**3 * a * E.e2)
488 s, c = sincos2d(lat)
489 if c: # E.roc1_(s) = E.a / sqrt(1 - E.e2 * s**2)
490 h = p / c - (E.roc1_(s) if s else a)
491 else: # polar
492 h = fabs(z) - b
493 # note, phi and lam are swapped on page 30
495 except (ValueError, ZeroDivisionError) as e:
496 raise EcefError(x=x, y=y, z=z, cause=e)
498 return Ecef9Tuple(x, y, z, lat, lon, h,
499 1, None, self.datum,
500 name=name or self.name)
503class EcefKarney(_EcefBase):
504 '''Conversion between geodetic and geocentric, I{Earth-Centered, Earth-Fixed} (ECEF)
505 coordinates transcoded from I{Karney}'s C++ U{Geocentric<https://GeographicLib.SourceForge.io/
506 C++/doc/classGeographicLib_1_1Geocentric.html>} methods.
508 @note: On methods C{.forward} and C{.forwar_}, let C{v} be a unit vector located
509 at C{(lat, lon, h)}. We can express C{v} as column vectors in one of two
510 ways, C{v1} in East, North, Up (ENU) coordinates (where the components are
511 relative to a local coordinate system at C{C(lat0, lon0, h0)}) or as C{v0}
512 in geocentric C{x, y, z} coordinates. Then, M{v0 = M ⋅ v1} where C{M} is
513 the rotation matrix.
514 '''
516 @Property_RO
517 def hmax(self):
518 '''Get the distance or height limit (C{meter}, conventionally).
519 '''
520 return self.equatoradius / EPS_2 # self.equatoradius * _2_EPS, 12M lighyears
522 def reverse(self, xyz, y=None, z=None, M=False, **name_lon00):
523 '''Convert from geocentric C{(x, y, z)} to geodetic C{(lat, lon, height)}.
525 @arg xyz: A geocentric (C{Cartesian}, L{Ecef9Tuple}) or C{scalar} ECEF C{x}
526 coordinate (C{meter}).
527 @kwarg y: ECEF C{y} coordinate for C{scalar} B{C{xyz}} and B{C{z}} (C{meter}).
528 @kwarg z: ECEF C{z} coordinate for C{scalar} B{C{xyz}} and B{C{y}} (C{meter}).
529 @kwarg M: Optionally, return the rotation L{EcefMatrix} (C{bool}).
530 @kwarg name_lon00: Optional keyword arguments C{B{name}=NN} (C{str}) and
531 I{"polar"} longitude C{B{lon00}=INT0} (C{degrees}), overriding
532 the default and property C{lon00} setting and returned in case
533 C{B{x}=0} and C{B{y}=0}.
535 @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with
536 geodetic coordinates C{(lat, lon, height)} for the given geocentric
537 ones C{(x, y, z)}, case C{C}, optional C{M} (L{EcefMatrix}) and
538 C{datum} if available.
540 @raise EcefError: Invalid B{C{xyz}} or C{scalar} C{x} or B{C{y}} and/or B{C{z}}
541 not C{scalar} for C{scalar} B{C{xyz}}.
543 @note: In general, there are multiple solutions and the result which minimizes
544 C{height} is returned, i.e., the C{(lat, lon)} corresponding to the
545 closest point on the ellipsoid. If there are still multiple solutions
546 with different latitudes (applies only if C{z} = 0), then the solution
547 with C{lat} > 0 is returned. If there are still multiple solutions with
548 different longitudes (applies only if C{x} = C{y} = 0), then C{lon00} is
549 returned. The returned C{lon} is in the range [−180°, 180°] and C{height}
550 is not below M{−E.a * (1 − E.e2) / sqrt(1 − E.e2 * sin(lat)**2)}. Like
551 C{forward} above, M{v1 = Transpose(M) ⋅ v0}.
552 '''
553 def _norm3(y, x):
554 h = hypot(y, x) # EPS0, EPS_2
555 return (y / h, x / h, h) if h > 0 else (_0_0, _1_0, h)
557 x, y, z, name = _xyzn4(xyz, y, z, self._Geocentrics, **name_lon00)
559 E = self.ellipsoid
560 f = E.f
562 sb, cb, R = _norm3(y, x)
563 h = hypot(R, z) # distance to earth center
564 if h > self.hmax: # PYCHOK no cover
565 # We are really far away (> 12M light years). Treat the earth
566 # as a point and h above as an acceptable approximation to the
567 # height. This avoids overflow, e.g., in the computation of d
568 # below. It's possible that h has overflowed to INF, that's OK.
569 # Treat finite x, y, but R overflows to +INF by scaling by 2.
570 sb, cb, R = _norm3(y * _0_5, x * _0_5)
571 sa, ca, _ = _norm3(z * _0_5, R)
572 C = 1
574 elif E.e4: # E.isEllipsoidal
575 # Treat prolate spheroids by swapping R and Z here and by
576 # switching the arguments to phi = atan2(...) at the end.
577 p = (R / E.a)**2
578 q = (z / E.a)**2 * E.e21
579 if f < 0:
580 p, q = q, p
581 r = fsumf_(p, q, -E.e4)
582 e = E.e4 * q
583 if e or r > 0:
584 # Avoid possible division by zero when r = 0 by multiplying
585 # equations for s and t by r^3 and r, respectively.
586 s = d = e * p / _4_0 # s = r^3 * s
587 u = r = r / _6_0
588 r2 = r**2
589 r3 = r2 * r
590 t3 = r3 + s
591 d *= t3 + r3
592 if d < 0:
593 # t is complex, but the way u is defined, the result is real.
594 # There are three possible cube roots. We choose the root
595 # which avoids cancellation. Note, d < 0 implies r < 0.
596 u += cos(atan2(sqrt(-d), -t3) / _3_0) * r * _2_0
597 else:
598 # Pick the sign on the sqrt to maximize abs(t3). This
599 # minimizes loss of precision due to cancellation. The
600 # result is unchanged because of the way the t is used
601 # in definition of u.
602 if d > 0:
603 t3 += copysign0(sqrt(d), t3) # t3 = (r * t)^3
604 # N.B. cbrt always returns the real root, cbrt(-8) = -2.
605 t = cbrt(t3) # t = r * t
606 if t: # t can be zero; but then r2 / t -> 0.
607 u = fsumf_(u, t, r2 / t)
608 v = sqrt(e + u**2) # guaranteed positive
609 # Avoid loss of accuracy when u < 0. Underflow doesn't occur in
610 # E.e4 * q / (v - u) because u ~ e^4 when q is small and u < 0.
611 u = (e / (v - u)) if u < 0 else (u + v) # u+v, guaranteed positive
612 # Need to guard against w going negative due to roundoff in u - q.
613 w = E.e2abs * (u - q) / (_2_0 * v)
614 # Rearrange expression for k to avoid loss of accuracy due to
615 # subtraction. Division by 0 not possible because u > 0, w >= 0.
616 k1 = k2 = (u / (sqrt(u + w**2) + w)) if w > 0 else sqrt(u)
617 if f < 0:
618 k1 -= E.e2
619 else:
620 k2 += E.e2
621 sa, ca, h = _norm3(z / k1, R / k2)
622 h *= k1 - E.e21
623 C = 2
625 else: # e = E.e4 * q == 0 and r <= 0
626 # This leads to k = 0 (oblate, equatorial plane) and k + E.e^2 = 0
627 # (prolate, rotation axis) and the generation of 0/0 in the general
628 # formulas for phi and h, using the general formula and division
629 # by 0 in formula for h. Handle this case by taking the limits:
630 # f > 0: z -> 0, k -> E.e2 * sqrt(q) / sqrt(E.e4 - p)
631 # f < 0: r -> 0, k + E.e2 -> -E.e2 * sqrt(q) / sqrt(E.e4 - p)
632 q = E.e4 - p
633 if f < 0:
634 p, q = q, p
635 e = E.a
636 else:
637 e = E.b2_a
638 sa, ca, h = _norm3(sqrt(q * E._1_e21), sqrt(p))
639 if z < 0: # for tiny negative z, not for prolate
640 sa = neg(sa)
641 h *= neg(e / E.e2abs)
642 C = 3
644 else: # E.e4 == 0, spherical case
645 # Dealing with underflow in the general case with E.e2 = 0 is
646 # difficult. Origin maps to North pole, same as with ellipsoid.
647 sa, ca, _ = _norm3((z if h else _1_0), R)
648 h -= E.a
649 C = 4
651 # lon00 <https://GitHub.com/mrJean1/PyGeodesy/issues/77>
652 lon = self._polon(sb, cb, R, **name_lon00)
653 m = self._Matrix(sa, ca, sb, cb) if M else None
654 return Ecef9Tuple(x, y, z, atan2d(sa, ca), lon, h,
655 C, m, self.datum,
656 name=name or self.name)
659class EcefSudano(_EcefBase):
660 '''Conversion between geodetic and geocentric, I{Earth-Centered, Earth-Fixed} (ECEF) coordinates
661 based on I{John J. Sudano}'s U{paper<https://www.ResearchGate.net/publication/3709199>}.
662 '''
663 _tol = EPS2
665 def reverse(self, xyz, y=None, z=None, M=None, **name_lon00): # PYCHOK unused M
666 '''Convert from geocentric C{(x, y, z)} to geodetic C{(lat, lon, height)} using
667 I{Sudano}'s U{iterative method<https://www.ResearchGate.net/publication/3709199>}.
669 @arg xyz: A geocentric (C{Cartesian}, L{Ecef9Tuple}) or C{scalar} ECEF C{x}
670 coordinate (C{meter}).
671 @kwarg y: ECEF C{y} coordinate for C{scalar} B{C{xyz}} and B{C{z}} (C{meter}).
672 @kwarg z: ECEF C{z} coordinate for C{scalar} B{C{xyz}} and B{C{y}} (C{meter}).
673 @kwarg M: I{Ignored}, rotation matrix C{M} not available.
674 @kwarg name_lon00: Optional keyword arguments C{B{name}=NN} (C{str}) and
675 I{"polar"} longitude C{B{lon00}=INT0} (C{degrees}), overriding
676 the default and property C{lon00} setting and returned in case
677 C{B{x}=0} and C{B{y}=0}.
679 @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with geodetic
680 coordinates C{(lat, lon, height)} for the given geocentric ones C{(x, y, z)},
681 iteration C{C}, C{M=None} always and C{datum} if available.
683 @raise EcefError: Invalid B{C{xyz}} or C{scalar} C{x} or B{C{y}} and/or B{C{z}}
684 not C{scalar} for C{scalar} B{C{xyz}} or no convergence.
685 '''
686 x, y, z, name = _xyzn4(xyz, y, z, self._Geocentrics, **name_lon00)
688 E = self.ellipsoid
689 e = E.e2 * E.a
690 R = hypot(x, y) # Rh
691 d = e - R
693 lat = atan2d(z, R * E.e21)
694 sa, ca = sincos2d(fabs(lat))
695 # Sudano's Eq (A-6) and (A-7) refactored/reduced,
696 # replacing Rn from Eq (A-4) with n = E.a / ca:
697 # N = ca**2 * ((z + E.e2 * n * sa) * ca - R * sa)
698 # = ca**2 * (z * ca + E.e2 * E.a * sa - R * sa)
699 # = ca**2 * (z * ca + (E.e2 * E.a - R) * sa)
700 # D = ca**3 * (E.e2 * n / E.e2s2(sa)) - R
701 # = ca**2 * (E.e2 * E.a / E.e2s2(sa) - R / ca**2)
702 # N / D = (z * ca + (E.e2 * E.a - R) * sa) /
703 # (E.e2 * E.a / E.e2s2(sa) - R / ca**2)
704 tol = self.tolerance
705 _S2 = Fsum(sa).fsum2_
706 for i in range(1, _TRIPS):
707 ca2 = _1_0 - sa**2
708 if ca2 < EPS_2: # PYCHOK no cover
709 ca = _0_0
710 break
711 ca = sqrt(ca2)
712 r = e / E.e2s2(sa) - R / ca2
713 if fabs(r) < EPS_2:
714 break
715 lat = None
716 sa, r = _S2(-z * ca / r, -d * sa / r)
717 if fabs(r) < tol:
718 break
719 else:
720 t = unstr(self.reverse, x=x, y=y, z=z)
721 raise EcefError(Fmt.no_convergence(r, tol), txt=t)
723 if lat is None:
724 lat = copysign0(atan2d(fabs(sa), ca), z)
725 lon = self._polon(y, x, R, **name_lon00)
727 h = fsumf_(R * ca, fabs(z * sa), -E.a * E.e2s(sa)) # use Veness'
728 # because Sudano's Eq (7) doesn't produce the correct height
729 # h = (fabs(z) + R - E.a * cos(a + E.e21) * sa / ca) / (ca + sa)
730 r = Ecef9Tuple(x, y, z, lat, lon, h,
731 i, None, self.datum, # M=None
732 iteration=i, name=name or self.name)
733 return r
735 @property_doc_(''' the convergence tolerance (C{float}).''')
736 def tolerance(self):
737 '''Get the convergence tolerance (C{scalar}).
738 '''
739 return self._tol
741 @tolerance.setter # PYCHOK setter!
742 def tolerance(self, tol):
743 '''Set the convergence tolerance (C{scalar}).
745 @raise EcefError: Non-scalar or invalid B{C{tol}}.
746 '''
747 self._tol = Scalar_(tolerance=tol, low=EPS, Error=EcefError)
750class EcefVeness(_EcefBase):
751 '''Conversion between geodetic and geocentric, I{Earth-Centered, Earth-Fixed} (ECEF) coordinates
752 transcoded from I{Chris Veness}' JavaScript classes U{LatLonEllipsoidal, Cartesian<https://
753 www.Movable-Type.co.UK/scripts/geodesy/docs/latlon-ellipsoidal.js.html>}.
755 @see: U{I{A Guide to Coordinate Systems in Great Britain}<https://www.OrdnanceSurvey.co.UK/
756 documents/resources/guide-coordinate-systems-great-britain.pdf>}, section I{B) Converting
757 between 3D Cartesian and ellipsoidal latitude, longitude and height coordinates}.
758 '''
760 def reverse(self, xyz, y=None, z=None, M=None, **name_lon00): # PYCHOK unused M
761 '''Conversion from geocentric C{(x, y, z)} to geodetic C{(lat, lon, height)}
762 transcoded from I{Chris Veness}' U{JavaScript<https://www.Movable-Type.co.UK/
763 scripts/geodesy/docs/latlon-ellipsoidal.js.html>}.
765 Uses B. R. Bowring’s formulation for μm precision in concise form U{I{The accuracy
766 of geodetic latitude and height equations}<https://www.ResearchGate.net/publication/
767 233668213>}, Survey Review, Vol 28, 218, Oct 1985.
769 @arg xyz: A geocentric (C{Cartesian}, L{Ecef9Tuple}) or C{scalar} ECEF C{x}
770 coordinate (C{meter}).
771 @kwarg y: ECEF C{y} coordinate for C{scalar} B{C{xyz}} and B{C{z}} (C{meter}).
772 @kwarg z: ECEF C{z} coordinate for C{scalar} B{C{xyz}} and B{C{y}} (C{meter}).
773 @kwarg M: I{Ignored}, rotation matrix C{M} not available.
774 @kwarg name_lon00: Optional keyword arguments C{B{name}=NN} (C{str}) and
775 I{"polar"} longitude C{B{lon00}=INT0} (C{degrees}), overriding
776 the default and property C{lon00} setting and returned in case
777 C{B{x}=0} and C{B{y}=0}.
779 @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with
780 geodetic coordinates C{(lat, lon, height)} for the given geocentric
781 ones C{(x, y, z)}, case C{C}, C{M=None} always and C{datum} if available.
783 @raise EcefError: Invalid B{C{xyz}} or C{scalar} C{x} or B{C{y}} and/or B{C{z}}
784 not C{scalar} for C{scalar} B{C{xyz}}.
786 @see: Toms, Ralph M. U{I{An Efficient Algorithm for Geocentric to Geodetic
787 Coordinate Conversion}<https://www.OSTI.gov/scitech/biblio/110235>},
788 Sept 1995 and U{I{An Improved Algorithm for Geocentric to Geodetic
789 Coordinate Conversion}<https://www.OSTI.gov/scitech/servlets/purl/231228>},
790 Apr 1996, both from Lawrence Livermore National Laboratory (LLNL) and
791 Sudano, John J, U{I{An exact conversion from an Earth-centered coordinate
792 system to latitude longitude and altitude}<https://www.ResearchGate.net/
793 publication/3709199>}.
794 '''
795 x, y, z, name = _xyzn4(xyz, y, z, self._Geocentrics, **name_lon00)
797 E = self.ellipsoid
799 p = hypot(x, y) # distance from minor axis
800 r = hypot(p, z) # polar radius
801 if min(p, r) > EPS0:
802 b = E.b * E.e22
803 # parametric latitude (Bowring eqn 17, replaced)
804 t = (E.b * z) / (E.a * p) * (_1_0 + b / r)
805 c = _1_0 / hypot1(t)
806 s = c * t
808 # geodetic latitude (Bowring eqn 18)
809 lat = atan2d(z + b * s**3,
810 p - E.e2 * E.a * c**3)
812 # height above ellipsoid (Bowring eqn 7)
813 sa, ca = sincos2d(lat)
814# r = E.a / E.e2s(sa) # length of normal terminated by minor axis
815# h = p * ca + z * sa - (E.a * E.a / r)
816 h = fsumf_(p * ca, z * sa, -E.a * E.e2s(sa))
817 C = 1
819 # see <https://GIS.StackExchange.com/questions/28446>
820 elif p > EPS: # lat arbitrarily zero, equatorial lon
821 C, lat, h = 2, _0_0, (p - E.a)
823 else: # polar lat, lon arbitrarily lon00
824 C, lat, h = 3, (_N_90_0 if z < 0 else _90_0), (fabs(z) - E.b)
826 lon = self._polon(y, x, p, **name_lon00)
827 return Ecef9Tuple(x, y, z, lat, lon, h,
828 C, None, self.datum, # M=None
829 name=name or self.name)
832class EcefYou(_EcefBase):
833 '''Conversion between geodetic and geocentric, I{Earth-Centered, Earth-Fixed} (ECEF) coordinates
834 using I{Rey-Jer You}'s U{transformation<https://www.ResearchGate.net/publication/240359424>}
835 for I{non-prolate} ellipsoids.
837 @see: Featherstone, W.E., Claessens, S.J. U{I{Closed-form transformation between geodetic and
838 ellipsoidal coordinates}<https://Espace.Curtin.edu.AU/bitstream/handle/20.500.11937/
839 11589/115114_9021_geod2ellip_final.pdf>} Studia Geophysica et Geodaetica, 2008, 52,
840 pages 1-18 and U{PyMap3D <https://PyPI.org/project/pymap3d>}.
841 '''
843 def __init__(self, a_ellipsoid=_EWGS84, f=None, **name_lon00): # PYCHOK signature
844 _EcefBase.__init__(self, a_ellipsoid, f=f, **name_lon00) # inherited documentation
845 _ = EcefYou._e2(self.ellipsoid)
847 @staticmethod
848 def _e2(E):
849 e2 = E.a2 - E.b2
850 if E.f < 0 or e2 < 0:
851 raise EcefError(ellipsoid=E, txt=_prolate_)
852 return e2
854 def reverse(self, xyz, y=None, z=None, M=None, **name_lon00): # PYCHOK unused M
855 '''Convert geocentric C{(x, y, z)} to geodetic C{(lat, lon, height)}
856 using I{Rey-Jer You}'s transformation.
858 @arg xyz: A geocentric (C{Cartesian}, L{Ecef9Tuple}) or C{scalar} ECEF C{x}
859 coordinate (C{meter}).
860 @kwarg y: ECEF C{y} coordinate for C{scalar} B{C{xyz}} and B{C{z}} (C{meter}).
861 @kwarg z: ECEF C{z} coordinate for C{scalar} B{C{xyz}} and B{C{y}} (C{meter}).
862 @kwarg M: I{Ignored}, rotation matrix C{M} not available.
863 @kwarg name_lon00: Optional keyword arguments C{B{name}=NN} (C{str}) and
864 I{"polar"} longitude C{B{lon00}=INT0} (C{degrees}), overriding
865 the default and property C{lon00} setting and returned in case
866 C{B{x}=0} and C{B{y}=0}.
868 @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with
869 geodetic coordinates C{(lat, lon, height)} for the given geocentric
870 ones C{(x, y, z)}, case C{C=1}, C{M=None} always and C{datum} if
871 available.
873 @raise EcefError: Invalid B{C{xyz}} or C{scalar} C{x} or B{C{y}} and/or
874 B{C{z}} not C{scalar} for C{scalar} B{C{xyz}} or the
875 ellipsoid is I{prolate}.
876 '''
877 x, y, z, name = _xyzn4(xyz, y, z, self._Geocentrics, **name_lon00)
879 E = self.ellipsoid
880 e2 = EcefYou._e2(E)
881 e = sqrt(e2) if e2 > 0 else _0_0 # XXX sqrt0(e2)?
883 q = hypot( x, y) # R
884 r2 = hypot2_(x, y, z)
885 u = fsumf_(r2, -e2, hypot(r2 - e2, e * z * _2_0)) * _0_5
886 if u > EPS02:
887 u = sqrt(u)
888 p = hypot(u, e)
889 B = atan2(p * z, u * q) # beta0 = atan(p / u * z / q)
890 sB, cB = sincos2(B)
891 if cB and sB:
892 p *= E.a
893 d = (p / cB - e2 * cB) / sB
894 if isnon0(d):
895 B += fsumf_(u * E.b, -p, e2) / d
896 sB, cB = sincos2(B)
897 elif u < 0:
898 raise EcefError(x=x, y=y, z=z, txt=_singular_)
899 else:
900 sB, cB = (_N_1_0 if z < 0 else _1_0), _0_0
902 lat = atan2d(E.a * sB, E.b * cB) # atan(E.a_b * tan(B))
903 lon = self._polon(y, x, q, **name_lon00)
905 h = hypot(z - E.b * sB, q - E.a * cB)
906 if hypot2_(x, y, z * E.a_b) < E.a2:
907 h = neg(h) # inside ellipsoid
908 return Ecef9Tuple(x, y, z, lat, lon, h,
909 1, None, self.datum, # C=1, M=None
910 name=name or self.name)
913class EcefMatrix(_NamedTuple):
914 '''A rotation matrix known as I{East-North-Up (ENU) to ECEF}.
916 @see: U{From ENU to ECEF<https://WikiPedia.org/wiki/
917 Geographic_coordinate_conversion#From_ECEF_to_ENU>} and
918 U{Issue #74<https://Github.com/mrJean1/PyGeodesy/issues/74>}.
919 '''
920 _Names_ = ('_0_0_', '_0_1_', '_0_2_', # row-order
921 '_1_0_', '_1_1_', '_1_2_',
922 '_2_0_', '_2_1_', '_2_2_')
923 _Units_ = (Scalar,) * len(_Names_)
925 def _validate(self, **_OK): # PYCHOK unused
926 '''(INTERNAL) Allow C{_Names_} with leading underscore.
927 '''
928 _NamedTuple._validate(self, _OK=True)
930 def __new__(cls, sa, ca, sb, cb, *_more):
931 '''New L{EcefMatrix} matrix.
933 @arg sa: C{sin(phi)} (C{float}).
934 @arg ca: C{cos(phi)} (C{float}).
935 @arg sb: C{sin(lambda)} (C{float}).
936 @arg cb: C{cos(lambda)} (C{float}).
937 @arg _more: (INTERNAL) from C{.multiply}.
939 @raise EcefError: If B{C{sa}}, B{C{ca}}, B{C{sb}} or
940 B{C{cb}} outside M{[-1.0, +1.0]}.
941 '''
942 t = sa, ca, sb, cb
943 if _more: # all 9 matrix elements ...
944 t += _more # ... from .multiply
946 elif max(map(fabs, t)) > _1_0:
947 raise EcefError(unstr(EcefMatrix.__name__, *t))
949 else: # build matrix from the following quaternion operations
950 # qrot(lam, [0,0,1]) * qrot(phi, [0,-1,0]) * [1,1,1,1]/2
951 # or
952 # qrot(pi/2 + lam, [0,0,1]) * qrot(-pi/2 + phi, [-1,0,0])
953 # where
954 # qrot(t,v) = [cos(t/2), sin(t/2)*v[1], sin(t/2)*v[2], sin(t/2)*v[3]]
956 # Local X axis (East) in geocentric coords
957 # M[0] = -slam; M[3] = clam; M[6] = 0;
958 # Local Y axis (North) in geocentric coords
959 # M[1] = -clam * sphi; M[4] = -slam * sphi; M[7] = cphi;
960 # Local Z axis (Up) in geocentric coords
961 # M[2] = clam * cphi; M[5] = slam * cphi; M[8] = sphi;
962 t = (-sb, -cb * sa, cb * ca,
963 cb, -sb * sa, sb * ca,
964 _0_0, ca, sa)
966 return _NamedTuple.__new__(cls, *t)
968 def column(self, column):
969 '''Get this matrix' B{C{column}} 0, 1 or 2 as C{3-tuple}.
970 '''
971 if 0 <= column < 3:
972 return self[column::3]
973 raise _IndexError(column=column)
975 def copy(self, **unused): # PYCHOK signature
976 '''Make a shallow or deep copy of this instance.
978 @return: The copy (C{This class} or subclass thereof).
979 '''
980 return self.classof(*self)
982 __copy__ = __deepcopy__ = copy
984 @Property_RO
985 def matrix3(self):
986 '''Get this matrix' rows (C{3-tuple} of 3 C{3-tuple}s).
987 '''
988 return tuple(map(self.row, range(3)))
990 @Property_RO
991 def matrixTransposed3(self):
992 '''Get this matrix' I{Transposed} rows (C{3-tuple} of 3 C{3-tuple}s).
993 '''
994 return tuple(map(self.column, range(3)))
996 def multiply(self, other):
997 '''Matrix multiply M{M0' ⋅ M} this matrix I{Transposed}
998 with an other matrix.
1000 @arg other: The other matrix (L{EcefMatrix}).
1002 @return: The matrix product (L{EcefMatrix}).
1004 @raise TypeError: If B{C{other}} is not L{EcefMatrix}.
1005 '''
1006 _xinstanceof(EcefMatrix, other=other)
1007 # like LocalCartesian.MatrixMultiply, C{self.matrixTransposed3 X other.matrix3}
1008 # <https://GeographicLib.SourceForge.io/C++/doc/LocalCartesian_8cpp_source.html>
1009 # X = (fdot(self.column(r), *other.column(c)) for r in (0,1,2) for c in (0,1,2))
1010 X = (fdot(self[r::3], *other[c::3]) for r in range(3) for c in range(3))
1011 return _xnamed(EcefMatrix(*X), EcefMatrix.multiply.__name__)
1013 def rotate(self, xyz, *xyz0):
1014 '''Forward rotation M{M0' ⋅ ([x, y, z] - [x0, y0, z0])'}.
1016 @arg xyz: Local C{(x, y, z)} coordinates (C{3-tuple}).
1017 @arg xyz0: Optional, local C{(x0, y0, z0)} origin (C{3-tuple}).
1019 @return: Rotated C{(x, y, z)} location (C{3-tuple}).
1021 @raise LenError: Unequal C{len(B{xyz})} and C{len(B{xyz0})}.
1022 '''
1023 if xyz0:
1024 if len(xyz0) != len(xyz):
1025 raise LenError(self.rotate, xyz0=len(xyz0), xyz=len(xyz))
1026 xyz = tuple(c - c0 for c, c0 in zip(xyz, xyz0))
1028 # x' = M[0] * x + M[3] * y + M[6] * z
1029 # y' = M[1] * x + M[4] * y + M[7] * z
1030 # z' = M[2] * x + M[5] * y + M[8] * z
1031 return (fdot(xyz, *self[0::3]), # .column(0)
1032 fdot(xyz, *self[1::3]), # .column(1)
1033 fdot(xyz, *self[2::3])) # .column(2)
1035 def row(self, row):
1036 '''Get this matrix' B{C{row}} 0, 1 or 2 as C{3-tuple}.
1037 '''
1038 if 0 <= row < 3:
1039 r = row * 3
1040 return self[r:r+3]
1041 raise _IndexError(row=row)
1043 def unrotate(self, xyz, *xyz0):
1044 '''Inverse rotation M{[x0, y0, z0] + M0 ⋅ [x,y,z]'}.
1046 @arg xyz: Local C{(x, y, z)} coordinates (C{3-tuple}).
1047 @arg xyz0: Optional, local C{(x0, y0, z0)} origin (C{3-tuple}).
1049 @return: Unrotated C{(x, y, z)} location (C{3-tuple}).
1051 @raise LenError: Unequal C{len(B{xyz})} and C{len(B{xyz0})}.
1052 '''
1053 if xyz0:
1054 if len(xyz0) != len(xyz):
1055 raise LenError(self.unrotate, xyz0=len(xyz0), xyz=len(xyz))
1056 _xyz = _1_0_1T + xyz
1057 # x' = x0 + M[0] * x + M[1] * y + M[2] * z
1058 # y' = y0 + M[3] * x + M[4] * y + M[5] * z
1059 # z' = z0 + M[6] * x + M[7] * y + M[8] * z
1060 xyz_ = (fdot(_xyz, xyz0[0], *self[0:3]), # .row(0)
1061 fdot(_xyz, xyz0[1], *self[3:6]), # .row(1)
1062 fdot(_xyz, xyz0[2], *self[6:9])) # .row(2)
1063 else:
1064 # x' = M[0] * x + M[1] * y + M[2] * z
1065 # y' = M[3] * x + M[4] * y + M[5] * z
1066 # z' = M[6] * x + M[7] * y + M[8] * z
1067 xyz_ = (fdot(xyz, *self[0:3]), # .row(0)
1068 fdot(xyz, *self[3:6]), # .row(1)
1069 fdot(xyz, *self[6:9])) # .row(2)
1070 return xyz_
1073class Ecef9Tuple(_NamedTuple):
1074 '''9-Tuple C{(x, y, z, lat, lon, height, C, M, datum)} with I{geocentric}
1075 C{x}, C{y} and C{z} plus I{geodetic} C{lat}, C{lon} and C{height}, case
1076 C{C} (see the C{Ecef*.reverse} methods) and optionally, the rotation
1077 matrix C{M} (L{EcefMatrix}) and C{datum}, with C{lat} and C{lon} in
1078 C{degrees} and C{x}, C{y}, C{z} and C{height} in C{meter}, conventionally.
1079 '''
1080 _Names_ = (_x_, _y_, _z_, _lat_, _lon_, _height_, _C_, _M_, _datum_)
1081 _Units_ = ( Meter, Meter, Meter, Lat, Lon, Height, Int, _Pass, _Pass)
1083 @property_RO
1084 def _CartesianBase(self):
1085 '''(INTERNAL) Get class C{CartesianBase}, I{once}.
1086 '''
1087 Ecef9Tuple._CartesianBase = C = _MODS.cartesianBase.CartesianBase # overwrite property_RO
1088 return C
1090 @deprecated_method
1091 def convertDatum(self, datum2): # for backward compatibility
1092 '''DEPRECATED, use method L{toDatum}.'''
1093 return self.toDatum(datum2)
1095 @Property_RO
1096 def lam(self):
1097 '''Get the longitude in C{radians} (C{float}).
1098 '''
1099 return self.philam.lam
1101 @Property_RO
1102 def lamVermeille(self):
1103 '''Get the longitude in C{radians [-PI*3/2..+PI*3/2]} after U{Vermeille
1104 <https://Search.ProQuest.com/docview/639493848>} (2004), page 95.
1106 @see: U{Karney<https://GeographicLib.SourceForge.io/C++/doc/geocentric.html>},
1107 U{Vermeille<https://Search.ProQuest.com/docview/847292978>} 2011, pp 112-113, 116
1108 and U{Featherstone, et.al.<https://Search.ProQuest.com/docview/872827242>}, page 7.
1109 '''
1110 x, y = self.x, self.y
1111 if y > EPS0:
1112 r = atan2(x, hypot(y, x) + y) * _N_2_0 + PI_2
1113 elif y < -EPS0:
1114 r = atan2(x, hypot(y, x) - y) * _2_0 - PI_2
1115 else: # y == 0
1116 r = PI if x < 0 else _0_0
1117 return Lam(Vermeille=r)
1119 @Property_RO
1120 def latlon(self):
1121 '''Get the lat-, longitude in C{degrees} (L{LatLon2Tuple}C{(lat, lon)}).
1122 '''
1123 return LatLon2Tuple(self.lat, self.lon, name=self.name)
1125 @Property_RO
1126 def latlonheight(self):
1127 '''Get the lat-, longitude in C{degrees} and height (L{LatLon3Tuple}C{(lat, lon, height)}).
1128 '''
1129 return self.latlon.to3Tuple(self.height)
1131 @Property_RO
1132 def latlonheightdatum(self):
1133 '''Get the lat-, longitude in C{degrees} with height and datum (L{LatLon4Tuple}C{(lat, lon, height, datum)}).
1134 '''
1135 return self.latlonheight.to4Tuple(self.datum)
1137 @Property_RO
1138 def latlonVermeille(self):
1139 '''Get the latitude and I{Vermeille} longitude in C{degrees [-225..+225]} (L{LatLon2Tuple}C{(lat, lon)}).
1141 @see: Property C{lonVermeille}.
1142 '''
1143 return LatLon2Tuple(self.lat, self.lonVermeille, name=self.name)
1145 @Property_RO
1146 def lonVermeille(self):
1147 '''Get the longitude in C{degrees [-225..+225]} after U{Vermeille
1148 <https://Search.ProQuest.com/docview/639493848>} (2004), p 95.
1150 @see: Property C{lamVermeille}.
1151 '''
1152 return Lon(Vermeille=degrees(self.lamVermeille))
1154 @Property_RO
1155 def phi(self):
1156 '''Get the latitude in C{radians} (C{float}).
1157 '''
1158 return self.philam.phi
1160 @Property_RO
1161 def philam(self):
1162 '''Get the lat-, longitude in C{radians} (L{PhiLam2Tuple}C{(phi, lam)}).
1163 '''
1164 return PhiLam2Tuple(radians(self.lat), radians(self.lon), name=self.name)
1166 @Property_RO
1167 def philamheight(self):
1168 '''Get the lat-, longitude in C{radians} and height (L{PhiLam3Tuple}C{(phi, lam, height)}).
1169 '''
1170 return self.philam.to3Tuple(self.height)
1172 @Property_RO
1173 def philamheightdatum(self):
1174 '''Get the lat-, longitude in C{radians} with height and datum (L{PhiLam4Tuple}C{(phi, lam, height, datum)}).
1175 '''
1176 return self.philamheight.to4Tuple(self.datum)
1178 @Property_RO
1179 def philamVermeille(self):
1180 '''Get the latitude and I{Vermeille} longitude in C{radians [-PI*3/2..+PI*3/2]} (L{PhiLam2Tuple}C{(phi, lam)}).
1182 @see: Property C{lamVermeille}.
1183 '''
1184 return PhiLam2Tuple(radians(self.lat), self.lamVermeille, name=self.name)
1186 def toCartesian(self, Cartesian=None, **Cartesian_kwds):
1187 '''Return the geocentric C{(x, y, z)} coordinates as an ellipsoidal or spherical
1188 C{Cartesian}.
1190 @kwarg Cartesian: Optional class to return C{(x, y, z)} (L{ellipsoidalKarney.Cartesian},
1191 L{ellipsoidalNvector.Cartesian}, L{ellipsoidalVincenty.Cartesian},
1192 L{sphericalNvector.Cartesian} or L{sphericalTrigonometry.Cartesian})
1193 or C{None}.
1194 @kwarg Cartesian_kwds: Optional, additional B{C{Cartesian}} keyword arguments, ignored
1195 if C{B{Cartesian} is None}.
1197 @return: A C{B{Cartesian}(x, y, z, **B{Cartesian_kwds})} instance or
1198 a L{Vector4Tuple}C{(x, y, z, h)} if C{B{Cartesian} is None}.
1200 @raise TypeError: Invalid B{C{Cartesian}} or B{C{Cartesian_kwds}}.
1201 '''
1202 if Cartesian in (None, Vector4Tuple):
1203 r = self.xyzh
1204 elif Cartesian is Vector3Tuple:
1205 r = self.xyz
1206 else:
1207 _xsubclassof(self._CartesianBase, Cartesian=Cartesian)
1208 r = Cartesian(self, **_xkwds(Cartesian_kwds, name=self.name))
1209 return r
1211 def toDatum(self, datum2):
1212 '''Convert this C{Ecef9Tuple} to an other datum.
1214 @arg datum2: Datum to convert I{to} (L{Datum}).
1216 @return: The converted 9-Tuple (C{Ecef9Tuple}).
1218 @raise TypeError: The B{C{datum2}} is not a L{Datum}.
1219 '''
1220 if self.datum in (None, datum2): # PYCHOK _Names_
1221 r = self.copy()
1222 else:
1223 c = self._CartesianBase(self, datum=self.datum, name=self.name) # PYCHOK _Names_
1224 # c.toLatLon converts datum, x, y, z, lat, lon, etc.
1225 # and returns another Ecef9Tuple iff LatLon is None
1226 r = c.toLatLon(datum=datum2, LatLon=None)
1227 return r
1229 def toLatLon(self, LatLon=None, **LatLon_kwds):
1230 '''Return the geodetic C{(lat, lon, height[, datum])} coordinates.
1232 @kwarg LatLon: Optional class to return C{(lat, lon, height[, datum])}
1233 or C{None}.
1234 @kwarg LatLon_kwds: Optional B{C{height}}, B{C{datum}} and other
1235 B{C{LatLon}} keyword arguments.
1237 @return: An instance of C{B{LatLon}(lat, lon, **B{LatLon_kwds})}
1238 or if B{C{LatLon}} is C{None}, a L{LatLon3Tuple}C{(lat, lon,
1239 height)} respectively L{LatLon4Tuple}C{(lat, lon, height,
1240 datum)} depending on whether C{datum} is un-/specified.
1242 @raise TypeError: Invalid B{C{LatLon}} or B{C{LatLon_kwds}}.
1243 '''
1244 lat, lon, D = self.lat, self.lon, self.datum # PYCHOK Ecef9Tuple
1245 kwds = _xkwds(LatLon_kwds, height=self.height, datum=D, name=self.name) # PYCHOK Ecef9Tuple
1246 d = kwds.get(_datum_, LatLon)
1247 if LatLon is None:
1248 r = LatLon3Tuple(lat, lon, kwds[_height_], name=kwds[_name_])
1249 if d is not None:
1250 # assert d is not LatLon
1251 r = r.to4Tuple(d) # checks type(d)
1252 else:
1253 if d is None:
1254 _ = kwds.pop(_datum_) # remove None datum
1255 r = LatLon(lat, lon, **kwds)
1256 _xdatum(_xattr(r, datum=D), D)
1257 return r
1259 def toLocal(self, ltp, Xyz=None, **Xyz_kwds):
1260 '''Convert this geocentric to I{local} C{x}, C{y} and C{z}.
1262 @kwarg ltp: The I{local tangent plane} (LTP) to use (L{Ltp}).
1263 @kwarg Xyz: Optional class to return C{x}, C{y} and C{z}
1264 (L{XyzLocal}, L{Enu}, L{Ned}) or C{None}.
1265 @kwarg Xyz_kwds: Optional, additional B{C{Xyz}} keyword
1266 arguments, ignored if C{B{Xyz} is None}.
1268 @return: An B{C{Xyz}} instance or if C{B{Xyz} is None},
1269 a L{Local9Tuple}C{(x, y, z, lat, lon, height,
1270 ltp, ecef, M)} with C{M=None}, always.
1272 @raise TypeError: Invalid B{C{ltp}}.
1273 '''
1274 return _MODS.ltp._xLtp(ltp)._ecef2local(self, Xyz, Xyz_kwds)
1276 def toVector(self, Vector=None, **Vector_kwds):
1277 '''Return the geocentric C{(x, y, z)} coordinates as vector.
1279 @kwarg Vector: Optional vector class to return C{(x, y, z)} or
1280 C{None}.
1281 @kwarg Vector_kwds: Optional, additional B{C{Vector}} keyword
1282 arguments, ignored if C{B{Vector} is None}.
1284 @return: A C{Vector}C{(x, y, z, **Vector_kwds)} instance or a
1285 L{Vector3Tuple}C{(x, y, z)} if B{C{Vector}} is C{None}.
1287 @see: Propertes C{xyz} and C{xyzh}
1288 '''
1289 return self.xyz if Vector is None else self._xnamed(
1290 Vector(self.x, self.y, self.z, **Vector_kwds)) # PYCHOK Ecef9Tuple
1292# def _T_x_M(self, T):
1293# '''(INTERNAL) Update M{self.M = T.multiply(self.M)}.
1294# '''
1295# return self.dup(M=T.multiply(self.M))
1297 @Property_RO
1298 def xyz(self):
1299 '''Get the geocentric C{(x, y, z)} coordinates (L{Vector3Tuple}C{(x, y, z)}).
1300 '''
1301 return Vector3Tuple(self.x, self.y, self.z, name=self.name)
1303 @Property_RO
1304 def xyzh(self):
1305 '''Get the geocentric C{(x, y, z)} coordinates and C{height} (L{Vector4Tuple}C{(x, y, z, h)})
1306 '''
1307 return self.xyz.to4Tuple(self.height)
1310def _4Ecef(this, Ecef): # in .datums.Datum.ecef, .ellipsoids.Ellipsoid.ecef
1311 '''Return an ECEF converter for C{this} L{Datum} or L{Ellipsoid}.
1312 '''
1313 if Ecef is None:
1314 Ecef = EcefKarney
1315 else:
1316 _xinstanceof(*_Ecefs, Ecef=Ecef)
1317 return Ecef(this, name=this.name)
1320def _xEcef(Ecef): # PYCHOK .latlonBase.py
1321 '''(INTERNAL) Validate B{C{Ecef}} I{class}.
1322 '''
1323 if issubclassof(Ecef, _EcefBase):
1324 return Ecef
1325 raise _TypesError(_Ecef_, Ecef, *_Ecefs)
1328_Ecefs = (EcefKarney, EcefSudano, EcefVeness, EcefYou,
1329 EcefFarrell21, EcefFarrell22)
1331__all__ += _ALL_DOCS(_EcefBase)
1333# **) MIT License
1334#
1335# Copyright (C) 2016-2023 -- mrJean1 at Gmail -- All Rights Reserved.
1336#
1337# Permission is hereby granted, free of charge, to any person obtaining a
1338# copy of this software and associated documentation files (the "Software"),
1339# to deal in the Software without restriction, including without limitation
1340# the rights to use, copy, modify, merge, publish, distribute, sublicense,
1341# and/or sell copies of the Software, and to permit persons to whom the
1342# Software is furnished to do so, subject to the following conditions:
1343#
1344# The above copyright notice and this permission notice shall be included
1345# in all copies or substantial portions of the Software.
1346#
1347# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
1348# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
1349# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
1350# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
1351# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
1352# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
1353# OTHER DEALINGS IN THE SOFTWARE.