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, _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, hypot, hypot1, hypot2_
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 _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_
80# from pygeodesy.streprs import Fmt, unstr # from .fsums
81from pygeodesy.units import Degrees, Height, Int, Lam, Lat, Lon, Meter, Phi, \
82 Scalar, Scalar_
83from pygeodesy.utily import atan1, atan1d, atan2d, degrees90, degrees180, sincos2, sincos2_, \
84 sincos2d, sincos2d_
86from math import atan2, cos, degrees, fabs, radians, sqrt
88__all__ = _ALL_LAZY.ecef
89__version__ = '23.09.29'
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 '''I{Must be overloaded}.'''
354 notOverloaded(self, xyz, y=y, z=z, M=M, **name_lon00)
356 def toStr(self, prec=9, **unused): # PYCHOK signature
357 '''Return this C{Ecef*} as a string.
359 @kwarg prec: Precision, number of decimal digits (0..9).
361 @return: This C{Ecef*} (C{str}).
362 '''
363 return self.attrs(_a_, _f_, _datum_, _name_, prec=prec) # _ellipsoid_
366class EcefFarrell21(_EcefBase):
367 '''Conversion between geodetic and geocentric, I{Earth-Centered, Earth-Fixed} (ECEF)
368 coordinates based on I{Jay A. Farrell}'s U{Table 2.1<https://Books.Google.com/
369 books?id=fW4foWASY6wC>}, page 29.
370 '''
372 def reverse(self, xyz, y=None, z=None, M=None, **name_lon00): # PYCHOK unused M
373 '''Convert from geocentric C{(x, y, z)} to geodetic C{(lat, lon, height)} using
374 I{Farrell}'s U{Table 2.1<https://Books.Google.com/books?id=fW4foWASY6wC>},
375 page 29.
377 @arg xyz: A geocentric (C{Cartesian}, L{Ecef9Tuple}) or C{scalar} ECEF C{x}
378 coordinate (C{meter}).
379 @kwarg y: ECEF C{y} coordinate for C{scalar} B{C{xyz}} and B{C{z}} (C{meter}).
380 @kwarg z: ECEF C{z} coordinate for C{scalar} B{C{xyz}} and B{C{y}} (C{meter}).
381 @kwarg M: I{Ignored}, rotation matrix C{M} not available.
382 @kwarg name_lon00: Optional keyword arguments C{B{name}=NN} (C{str}) and
383 I{"polar"} longitude C{B{lon00}=INT0} (C{degrees}), overriding
384 the default and property C{lon00} setting and returned if
385 C{B{x}=0} and C{B{y}=0}.
387 @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with
388 geodetic coordinates C{(lat, lon, height)} for the given geocentric
389 ones C{(x, y, z)}, case C{C=1}, C{M=None} always and C{datum}
390 if available.
392 @raise EcefError: Invalid B{C{xyz}} or C{scalar} C{x} or B{C{y}} and/or B{C{z}}
393 not C{scalar} for C{scalar} B{C{xyz}} or C{sqrt} domain or
394 zero division error.
396 @see: L{EcefFarrell22} and L{EcefVeness}.
397 '''
398 x, y, z, name = _xyzn4(xyz, y, z, self._Geocentrics, **name_lon00)
400 E = self.ellipsoid
401 a = E.a
402 a2 = E.a2
403 b2 = E.b2
404 e2 = E.e2
405 e2_ = E.e2abs * E.a2_b2 # (E.e * E.a_b)**2 = 0.0820944... WGS84
406 e4 = E.e4
408 try: # names as page 29
409 z2 = z**2
410 ez = z2 * (_1_0 - e2) # E.e2s2(z)
412 p = hypot(x, y)
413 p2 = p**2
414 G = p2 + ez - e2 * (a2 - b2) # p2 + ez - e4 * a2
415 F = b2 * z2 * 54
416 c = e4 * p2 * F / G**3
417 s = cbrt(_1_0 + sqrt(c**2 + c + c) + c)
418 G *= fsumf_(s, _1_0, _1_0 / s)
419 P = F / (G**2 * _3_0)
420 Q = sqrt(_2_0 * e4 * P + _1_0)
421 Q1 = Q + _1_0
422 r0 = P * p * e2 / Q1 - sqrt(fsumf_(a2 * (Q1 / Q) * _0_5,
423 -P * ez / (Q * Q1),
424 -P * p2 * _0_5))
425 r = p + e2 * r0
426 v = b2 / (sqrt(r**2 + ez) * a)
428 h = hypot(r, z) * (_1_0 - v)
429 lat = atan1d((e2_ * v + _1_0) * z, p)
430 lon = self._polon(y, x, p, **name_lon00)
431 # note, phi and lam are swapped on page 29
433 except (ValueError, ZeroDivisionError) as e:
434 raise EcefError(x=x, y=y, z=z, cause=e)
436 return Ecef9Tuple(x, y, z, lat, lon, h,
437 1, None, self.datum,
438 name=name or self.name)
441class EcefFarrell22(_EcefBase):
442 '''Conversion between geodetic and geocentric, I{Earth-Centered, Earth-Fixed} (ECEF)
443 coordinates based on I{Jay A. Farrell}'s U{Table 2.2<https://Books.Google.com/
444 books?id=fW4foWASY6wC>}, page 30.
445 '''
447 def reverse(self, xyz, y=None, z=None, M=None, **name_lon00): # PYCHOK unused M
448 '''Convert from geocentric C{(x, y, z)} to geodetic C{(lat, lon, height)} using
449 I{Farrell}'s U{Table 2.2<https://Books.Google.com/books?id=fW4foWASY6wC>},
450 page 30.
452 @arg xyz: A geocentric (C{Cartesian}, L{Ecef9Tuple}) or C{scalar} ECEF C{x}
453 coordinate (C{meter}).
454 @kwarg y: ECEF C{y} coordinate for C{scalar} B{C{xyz}} and B{C{z}} (C{meter}).
455 @kwarg z: ECEF C{z} coordinate for C{scalar} B{C{xyz}} and B{C{y}} (C{meter}).
456 @kwarg M: I{Ignored}, rotation matrix C{M} not available.
457 @kwarg name_lon00: Optional keyword arguments C{B{name}=NN} (C{str}) and
458 I{"polar"} longitude C{B{lon00}=INT0} (C{degrees}), overriding
459 the default and property C{lon00} setting and returned in case
460 C{B{x}=0} and C{B{y}=0}.
462 @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with
463 geodetic coordinates C{(lat, lon, height)} for the given geocentric
464 ones C{(x, y, z)}, case C{C=1}, C{M=None} always and C{datum}
465 if available.
467 @raise EcefError: Invalid B{C{xyz}} or C{scalar} C{x} or B{C{y}} and/or B{C{z}}
468 not C{scalar} for C{scalar} B{C{xyz}} or C{sqrt} domain or
469 zero division error.
471 @see: L{EcefFarrell21} and L{EcefVeness}.
472 '''
473 x, y, z, name = _xyzn4(xyz, y, z, self._Geocentrics, **name_lon00)
475 E = self.ellipsoid
476 a = E.a
477 b = E.b
479 try: # see EcefVeness.reverse
480 p = hypot(x, y)
481 lon = self._polon(y, x, p, **name_lon00)
483 s, c = sincos2(atan2(z * a, p * b)) # == _norm3
484 lat = atan1d(z + s**3 * b * E.e22,
485 p - c**3 * a * E.e2)
487 s, c = sincos2d(lat)
488 if c: # E.roc1_(s) = E.a / sqrt(1 - E.e2 * s**2)
489 h = p / c - (E.roc1_(s) if s else a)
490 else: # polar
491 h = fabs(z) - b
492 # note, phi and lam are swapped on page 30
494 except (ValueError, ZeroDivisionError) as e:
495 raise EcefError(x=x, y=y, z=z, cause=e)
497 return Ecef9Tuple(x, y, z, lat, lon, h,
498 1, None, self.datum,
499 name=name or self.name)
502class EcefKarney(_EcefBase):
503 '''Conversion between geodetic and geocentric, I{Earth-Centered, Earth-Fixed} (ECEF)
504 coordinates transcoded from I{Karney}'s C++ U{Geocentric<https://GeographicLib.SourceForge.io/
505 C++/doc/classGeographicLib_1_1Geocentric.html>} methods.
507 @note: On methods C{.forward} and C{.forwar_}, let C{v} be a unit vector located
508 at C{(lat, lon, h)}. We can express C{v} as column vectors in one of two
509 ways, C{v1} in East, North, Up (ENU) coordinates (where the components are
510 relative to a local coordinate system at C{C(lat0, lon0, h0)}) or as C{v0}
511 in geocentric C{x, y, z} coordinates. Then, M{v0 = M ⋅ v1} where C{M} is
512 the rotation matrix.
513 '''
515 @Property_RO
516 def hmax(self):
517 '''Get the distance or height limit (C{meter}, conventionally).
518 '''
519 return self.equatoradius / EPS_2 # self.equatoradius * _2_EPS, 12M lighyears
521 def reverse(self, xyz, y=None, z=None, M=False, **name_lon00):
522 '''Convert from geocentric C{(x, y, z)} to geodetic C{(lat, lon, height)}.
524 @arg xyz: A geocentric (C{Cartesian}, L{Ecef9Tuple}) or C{scalar} ECEF C{x}
525 coordinate (C{meter}).
526 @kwarg y: ECEF C{y} coordinate for C{scalar} B{C{xyz}} and B{C{z}} (C{meter}).
527 @kwarg z: ECEF C{z} coordinate for C{scalar} B{C{xyz}} and B{C{y}} (C{meter}).
528 @kwarg M: Optionally, return the rotation L{EcefMatrix} (C{bool}).
529 @kwarg name_lon00: Optional keyword arguments C{B{name}=NN} (C{str}) and
530 I{"polar"} longitude C{B{lon00}=INT0} (C{degrees}), overriding
531 the default and property C{lon00} setting and returned in case
532 C{B{x}=0} and C{B{y}=0}.
534 @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with
535 geodetic coordinates C{(lat, lon, height)} for the given geocentric
536 ones C{(x, y, z)}, case C{C}, optional C{M} (L{EcefMatrix}) and
537 C{datum} if available.
539 @raise EcefError: Invalid B{C{xyz}} or C{scalar} C{x} or B{C{y}} and/or B{C{z}}
540 not C{scalar} for C{scalar} B{C{xyz}}.
542 @note: In general, there are multiple solutions and the result which minimizes
543 C{height} is returned, i.e., the C{(lat, lon)} corresponding to the
544 closest point on the ellipsoid. If there are still multiple solutions
545 with different latitudes (applies only if C{z} = 0), then the solution
546 with C{lat} > 0 is returned. If there are still multiple solutions with
547 different longitudes (applies only if C{x} = C{y} = 0), then C{lon00} is
548 returned. The returned C{lon} is in the range [−180°, 180°] and C{height}
549 is not below M{−E.a * (1 − E.e2) / sqrt(1 − E.e2 * sin(lat)**2)}. Like
550 C{forward} above, M{v1 = Transpose(M) ⋅ v0}.
551 '''
552 def _norm3(y, x):
553 h = hypot(y, x) # EPS0, EPS_2
554 return (y / h, x / h, h) if h > 0 else (_0_0, _1_0, h)
556 x, y, z, name = _xyzn4(xyz, y, z, self._Geocentrics, **name_lon00)
558 E = self.ellipsoid
559 f = E.f
561 sb, cb, R = _norm3(y, x)
562 h = hypot(R, z) # distance to earth center
563 if h > self.hmax: # PYCHOK no cover
564 # We are really far away (> 12M light years). Treat the earth
565 # as a point and h above as an acceptable approximation to the
566 # height. This avoids overflow, e.g., in the computation of d
567 # below. It's possible that h has overflowed to INF, that's OK.
568 # Treat finite x, y, but R overflows to +INF by scaling by 2.
569 sb, cb, R = _norm3(y * _0_5, x * _0_5)
570 sa, ca, _ = _norm3(z * _0_5, R)
571 C = 1
573 elif E.e4: # E.isEllipsoidal
574 # Treat prolate spheroids by swapping R and Z here and by
575 # switching the arguments to phi = atan2(...) at the end.
576 p = (R / E.a)**2
577 q = (z / E.a)**2 * E.e21
578 if f < 0:
579 p, q = q, p
580 r = fsumf_(p, q, -E.e4)
581 e = E.e4 * q
582 if e or r > 0:
583 # Avoid possible division by zero when r = 0 by multiplying
584 # equations for s and t by r^3 and r, respectively.
585 s = d = e * p / _4_0 # s = r^3 * s
586 u = r = r / _6_0
587 r2 = r**2
588 r3 = r2 * r
589 t3 = r3 + s
590 d *= t3 + r3
591 if d < 0:
592 # t is complex, but the way u is defined, the result is real.
593 # There are three possible cube roots. We choose the root
594 # which avoids cancellation. Note, d < 0 implies r < 0.
595 u += cos(atan2(sqrt(-d), -t3) / _3_0) * r * _2_0
596 else:
597 # Pick the sign on the sqrt to maximize abs(t3). This
598 # minimizes loss of precision due to cancellation. The
599 # result is unchanged because of the way the t is used
600 # in definition of u.
601 if d > 0:
602 t3 += copysign0(sqrt(d), t3) # t3 = (r * t)^3
603 # N.B. cbrt always returns the real root, cbrt(-8) = -2.
604 t = cbrt(t3) # t = r * t
605 if t: # t can be zero; but then r2 / t -> 0.
606 u = fsumf_(u, t, r2 / t)
607 v = sqrt(e + u**2) # guaranteed positive
608 # Avoid loss of accuracy when u < 0. Underflow doesn't occur in
609 # E.e4 * q / (v - u) because u ~ e^4 when q is small and u < 0.
610 u = (e / (v - u)) if u < 0 else (u + v) # u+v, guaranteed positive
611 # Need to guard against w going negative due to roundoff in u - q.
612 w = E.e2abs * (u - q) / (_2_0 * v)
613 # Rearrange expression for k to avoid loss of accuracy due to
614 # subtraction. Division by 0 not possible because u > 0, w >= 0.
615 k1 = k2 = (u / (sqrt(u + w**2) + w)) if w > 0 else sqrt(u)
616 if f < 0:
617 k1 -= E.e2
618 else:
619 k2 += E.e2
620 sa, ca, h = _norm3(z / k1, R / k2)
621 h *= k1 - E.e21
622 C = 2
624 else: # e = E.e4 * q == 0 and r <= 0
625 # This leads to k = 0 (oblate, equatorial plane) and k + E.e^2 = 0
626 # (prolate, rotation axis) and the generation of 0/0 in the general
627 # formulas for phi and h, using the general formula and division
628 # by 0 in formula for h. Handle this case by taking the limits:
629 # f > 0: z -> 0, k -> E.e2 * sqrt(q) / sqrt(E.e4 - p)
630 # f < 0: r -> 0, k + E.e2 -> -E.e2 * sqrt(q) / sqrt(E.e4 - p)
631 q = E.e4 - p
632 if f < 0:
633 p, q = q, p
634 e = E.a
635 else:
636 e = E.b2_a
637 sa, ca, h = _norm3(sqrt(q * E._1_e21), sqrt(p))
638 if z < 0: # for tiny negative z, not for prolate
639 sa = neg(sa)
640 h *= neg(e / E.e2abs)
641 C = 3
643 else: # E.e4 == 0, spherical case
644 # Dealing with underflow in the general case with E.e2 = 0 is
645 # difficult. Origin maps to North pole, same as with ellipsoid.
646 sa, ca, _ = _norm3((z if h else _1_0), R)
647 h -= E.a
648 C = 4
650 # lon00 <https://GitHub.com/mrJean1/PyGeodesy/issues/77>
651 lon = self._polon(sb, cb, R, **name_lon00)
652 m = self._Matrix(sa, ca, sb, cb) if M else None
653 return Ecef9Tuple(x, y, z, atan1d(sa, ca), lon, h,
654 C, m, self.datum,
655 name=name or self.name)
658class EcefSudano(_EcefBase):
659 '''Conversion between geodetic and geocentric, I{Earth-Centered, Earth-Fixed} (ECEF) coordinates
660 based on I{John J. Sudano}'s U{paper<https://www.ResearchGate.net/publication/3709199>}.
661 '''
662 _tol = EPS2
664 def reverse(self, xyz, y=None, z=None, M=None, **name_lon00): # PYCHOK unused M
665 '''Convert from geocentric C{(x, y, z)} to geodetic C{(lat, lon, height)} using
666 I{Sudano}'s U{iterative method<https://www.ResearchGate.net/publication/3709199>}.
668 @arg xyz: A geocentric (C{Cartesian}, L{Ecef9Tuple}) or C{scalar} ECEF C{x}
669 coordinate (C{meter}).
670 @kwarg y: ECEF C{y} coordinate for C{scalar} B{C{xyz}} and B{C{z}} (C{meter}).
671 @kwarg z: ECEF C{z} coordinate for C{scalar} B{C{xyz}} and B{C{y}} (C{meter}).
672 @kwarg M: I{Ignored}, rotation matrix C{M} not available.
673 @kwarg name_lon00: Optional keyword arguments C{B{name}=NN} (C{str}) and
674 I{"polar"} longitude C{B{lon00}=INT0} (C{degrees}), overriding
675 the default and property C{lon00} setting and returned in case
676 C{B{x}=0} and C{B{y}=0}.
678 @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with geodetic
679 coordinates C{(lat, lon, height)} for the given geocentric ones C{(x, y, z)},
680 iteration C{C}, C{M=None} always and C{datum} if available.
682 @raise EcefError: Invalid B{C{xyz}} or C{scalar} C{x} or B{C{y}} and/or B{C{z}}
683 not C{scalar} for C{scalar} B{C{xyz}} or no convergence.
684 '''
685 x, y, z, name = _xyzn4(xyz, y, z, self._Geocentrics, **name_lon00)
687 E = self.ellipsoid
688 e = E.e2 * E.a
689 R = hypot(x, y) # Rh
690 d = e - R
692 lat = atan1d(z, R * E.e21)
693 sa, ca = sincos2d(fabs(lat))
694 # Sudano's Eq (A-6) and (A-7) refactored/reduced,
695 # replacing Rn from Eq (A-4) with n = E.a / ca:
696 # N = ca**2 * ((z + E.e2 * n * sa) * ca - R * sa)
697 # = ca**2 * (z * ca + E.e2 * E.a * sa - R * sa)
698 # = ca**2 * (z * ca + (E.e2 * E.a - R) * sa)
699 # D = ca**3 * (E.e2 * n / E.e2s2(sa)) - R
700 # = ca**2 * (E.e2 * E.a / E.e2s2(sa) - R / ca**2)
701 # N / D = (z * ca + (E.e2 * E.a - R) * sa) /
702 # (E.e2 * E.a / E.e2s2(sa) - R / ca**2)
703 tol = self.tolerance
704 _S2 = Fsum(sa).fsum2_
705 for i in range(1, _TRIPS):
706 ca2 = _1_0 - sa**2
707 if ca2 < EPS_2: # PYCHOK no cover
708 ca = _0_0
709 break
710 ca = sqrt(ca2)
711 r = e / E.e2s2(sa) - R / ca2
712 if fabs(r) < EPS_2:
713 break
714 lat = None
715 sa, r = _S2(-z * ca / r, -d * sa / r)
716 if fabs(r) < tol:
717 break
718 else:
719 t = unstr(self.reverse, x=x, y=y, z=z)
720 raise EcefError(Fmt.no_convergence(r, tol), txt=t)
722 if lat is None:
723 lat = copysign0(atan1d(fabs(sa), ca), z)
724 lon = self._polon(y, x, R, **name_lon00)
726 h = fsumf_(R * ca, fabs(z * sa), -E.a * E.e2s(sa)) # use Veness'
727 # because Sudano's Eq (7) doesn't produce the correct height
728 # h = (fabs(z) + R - E.a * cos(a + E.e21) * sa / ca) / (ca + sa)
729 r = Ecef9Tuple(x, y, z, lat, lon, h,
730 i, None, self.datum, # M=None
731 iteration=i, name=name or self.name)
732 return r
734 @property_doc_(''' the convergence tolerance (C{float}).''')
735 def tolerance(self):
736 '''Get the convergence tolerance (C{scalar}).
737 '''
738 return self._tol
740 @tolerance.setter # PYCHOK setter!
741 def tolerance(self, tol):
742 '''Set the convergence tolerance (C{scalar}).
744 @raise EcefError: Non-scalar or invalid B{C{tol}}.
745 '''
746 self._tol = Scalar_(tolerance=tol, low=EPS, Error=EcefError)
749class EcefVeness(_EcefBase):
750 '''Conversion between geodetic and geocentric, I{Earth-Centered, Earth-Fixed} (ECEF) coordinates
751 transcoded from I{Chris Veness}' JavaScript classes U{LatLonEllipsoidal, Cartesian<https://
752 www.Movable-Type.co.UK/scripts/geodesy/docs/latlon-ellipsoidal.js.html>}.
754 @see: U{I{A Guide to Coordinate Systems in Great Britain}<https://www.OrdnanceSurvey.co.UK/
755 documents/resources/guide-coordinate-systems-great-britain.pdf>}, section I{B) Converting
756 between 3D Cartesian and ellipsoidal latitude, longitude and height coordinates}.
757 '''
759 def reverse(self, xyz, y=None, z=None, M=None, **name_lon00): # PYCHOK unused M
760 '''Conversion from geocentric C{(x, y, z)} to geodetic C{(lat, lon, height)}
761 transcoded from I{Chris Veness}' U{JavaScript<https://www.Movable-Type.co.UK/
762 scripts/geodesy/docs/latlon-ellipsoidal.js.html>}.
764 Uses B. R. Bowring’s formulation for μm precision in concise form U{I{The accuracy
765 of geodetic latitude and height equations}<https://www.ResearchGate.net/publication/
766 233668213>}, Survey Review, Vol 28, 218, Oct 1985.
768 @arg xyz: A geocentric (C{Cartesian}, L{Ecef9Tuple}) or C{scalar} ECEF C{x}
769 coordinate (C{meter}).
770 @kwarg y: ECEF C{y} coordinate for C{scalar} B{C{xyz}} and B{C{z}} (C{meter}).
771 @kwarg z: ECEF C{z} coordinate for C{scalar} B{C{xyz}} and B{C{y}} (C{meter}).
772 @kwarg M: I{Ignored}, rotation matrix C{M} not available.
773 @kwarg name_lon00: Optional keyword arguments C{B{name}=NN} (C{str}) and
774 I{"polar"} longitude C{B{lon00}=INT0} (C{degrees}), overriding
775 the default and property C{lon00} setting and returned in case
776 C{B{x}=0} and C{B{y}=0}.
778 @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with
779 geodetic coordinates C{(lat, lon, height)} for the given geocentric
780 ones C{(x, y, z)}, case C{C}, C{M=None} always and C{datum} if available.
782 @raise EcefError: Invalid B{C{xyz}} or C{scalar} C{x} or B{C{y}} and/or B{C{z}}
783 not C{scalar} for C{scalar} B{C{xyz}}.
785 @see: Toms, Ralph M. U{I{An Efficient Algorithm for Geocentric to Geodetic
786 Coordinate Conversion}<https://www.OSTI.gov/scitech/biblio/110235>},
787 Sept 1995 and U{I{An Improved Algorithm for Geocentric to Geodetic
788 Coordinate Conversion}<https://www.OSTI.gov/scitech/servlets/purl/231228>},
789 Apr 1996, both from Lawrence Livermore National Laboratory (LLNL) and
790 Sudano, John J, U{I{An exact conversion from an Earth-centered coordinate
791 system to latitude longitude and altitude}<https://www.ResearchGate.net/
792 publication/3709199>}.
793 '''
794 x, y, z, name = _xyzn4(xyz, y, z, self._Geocentrics, **name_lon00)
796 E = self.ellipsoid
798 p = hypot(x, y) # distance from minor axis
799 r = hypot(p, z) # polar radius
800 if min(p, r) > EPS0:
801 b = E.b * E.e22
802 # parametric latitude (Bowring eqn 17, replaced)
803 t = (E.b * z) / (E.a * p) * (_1_0 + b / r)
804 c = _1_0 / hypot1(t)
805 s = c * t
807 # geodetic latitude (Bowring eqn 18)
808 lat = atan1d(z + b * s**3,
809 p - E.e2 * E.a * c**3)
811 # height above ellipsoid (Bowring eqn 7)
812 sa, ca = sincos2d(lat)
813# r = E.a / E.e2s(sa) # length of normal terminated by minor axis
814# h = p * ca + z * sa - (E.a * E.a / r)
815 h = fsumf_(p * ca, z * sa, -E.a * E.e2s(sa))
816 C = 1
818 # see <https://GIS.StackExchange.com/questions/28446>
819 elif p > EPS: # lat arbitrarily zero, equatorial lon
820 C, lat, h = 2, _0_0, (p - E.a)
822 else: # polar lat, lon arbitrarily lon00
823 C, lat, h = 3, (_N_90_0 if z < 0 else _90_0), (fabs(z) - E.b)
825 lon = self._polon(y, x, p, **name_lon00)
826 return Ecef9Tuple(x, y, z, lat, lon, h,
827 C, None, self.datum, # M=None
828 name=name or self.name)
831class EcefYou(_EcefBase):
832 '''Conversion between geodetic and geocentric, I{Earth-Centered, Earth-Fixed} (ECEF) coordinates
833 using I{Rey-Jer You}'s U{transformation<https://www.ResearchGate.net/publication/240359424>}
834 for I{non-prolate} ellipsoids.
836 @see: Featherstone, W.E., Claessens, S.J. U{I{Closed-form transformation between geodetic and
837 ellipsoidal coordinates}<https://Espace.Curtin.edu.AU/bitstream/handle/20.500.11937/
838 11589/115114_9021_geod2ellip_final.pdf>} Studia Geophysica et Geodaetica, 2008, 52,
839 pages 1-18 and U{PyMap3D <https://PyPI.org/project/pymap3d>}.
840 '''
842 def __init__(self, a_ellipsoid=_EWGS84, f=None, **name_lon00): # PYCHOK signature
843 _EcefBase.__init__(self, a_ellipsoid, f=f, **name_lon00) # inherited documentation
844 _ = EcefYou._e2(self.ellipsoid)
846 @staticmethod
847 def _e2(E):
848 e2 = E.a2 - E.b2
849 if E.f < 0 or e2 < 0:
850 raise EcefError(ellipsoid=E, txt=_prolate_)
851 return e2
853 def reverse(self, xyz, y=None, z=None, M=None, **name_lon00): # PYCHOK unused M
854 '''Convert geocentric C{(x, y, z)} to geodetic C{(lat, lon, height)}
855 using I{Rey-Jer You}'s transformation.
857 @arg xyz: A geocentric (C{Cartesian}, L{Ecef9Tuple}) or C{scalar} ECEF C{x}
858 coordinate (C{meter}).
859 @kwarg y: ECEF C{y} coordinate for C{scalar} B{C{xyz}} and B{C{z}} (C{meter}).
860 @kwarg z: ECEF C{z} coordinate for C{scalar} B{C{xyz}} and B{C{y}} (C{meter}).
861 @kwarg M: I{Ignored}, rotation matrix C{M} not available.
862 @kwarg name_lon00: Optional keyword arguments C{B{name}=NN} (C{str}) and
863 I{"polar"} longitude C{B{lon00}=INT0} (C{degrees}), overriding
864 the default and property C{lon00} setting and returned in case
865 C{B{x}=0} and C{B{y}=0}.
867 @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with
868 geodetic coordinates C{(lat, lon, height)} for the given geocentric
869 ones C{(x, y, z)}, case C{C=1}, C{M=None} always and C{datum} if
870 available.
872 @raise EcefError: Invalid B{C{xyz}} or C{scalar} C{x} or B{C{y}} and/or
873 B{C{z}} not C{scalar} for C{scalar} B{C{xyz}} or the
874 ellipsoid is I{prolate}.
875 '''
876 x, y, z, name = _xyzn4(xyz, y, z, self._Geocentrics, **name_lon00)
878 E = self.ellipsoid
879 e2 = EcefYou._e2(E)
880 e = sqrt(e2) if e2 > 0 else _0_0 # XXX sqrt0(e2)?
882 q = hypot( x, y) # R
883 r2 = hypot2_(x, y, z)
884 u = fsumf_(r2, -e2, hypot(r2 - e2, e * z * _2_0)) * _0_5
885 if u > EPS02:
886 u = sqrt(u)
887 p = hypot(u, e)
888 B = atan1(p * z, u * q) # beta0 = atan(p / u * z / q)
889 sB, cB = sincos2(B)
890 if cB and sB:
891 p *= E.a
892 d = (p / cB - e2 * cB) / sB
893 if isnon0(d):
894 B += fsumf_(u * E.b, -p, e2) / d
895 sB, cB = sincos2(B)
896 elif u < 0:
897 raise EcefError(x=x, y=y, z=z, txt=_singular_)
898 else:
899 sB, cB = _copysign_1_0(z), _0_0
901 lat = atan1d(E.a * sB, E.b * cB) # atan(E.a_b * tan(B))
902 lon = self._polon(y, x, q, **name_lon00)
904 h = hypot(z - E.b * sB, q - E.a * cB)
905 if hypot2_(x, y, z * E.a_b) < E.a2:
906 h = neg(h) # inside ellipsoid
907 return Ecef9Tuple(x, y, z, lat, lon, h,
908 1, None, self.datum, # C=1, M=None
909 name=name or self.name)
912class EcefMatrix(_NamedTuple):
913 '''A rotation matrix known as I{East-North-Up (ENU) to ECEF}.
915 @see: U{From ENU to ECEF<https://WikiPedia.org/wiki/
916 Geographic_coordinate_conversion#From_ECEF_to_ENU>} and
917 U{Issue #74<https://Github.com/mrJean1/PyGeodesy/issues/74>}.
918 '''
919 _Names_ = ('_0_0_', '_0_1_', '_0_2_', # row-order
920 '_1_0_', '_1_1_', '_1_2_',
921 '_2_0_', '_2_1_', '_2_2_')
922 _Units_ = (Scalar,) * len(_Names_)
924 def _validate(self, **_OK): # PYCHOK unused
925 '''(INTERNAL) Allow C{_Names_} with leading underscore.
926 '''
927 _NamedTuple._validate(self, _OK=True)
929 def __new__(cls, sa, ca, sb, cb, *_more):
930 '''New L{EcefMatrix} matrix.
932 @arg sa: C{sin(phi)} (C{float}).
933 @arg ca: C{cos(phi)} (C{float}).
934 @arg sb: C{sin(lambda)} (C{float}).
935 @arg cb: C{cos(lambda)} (C{float}).
936 @arg _more: (INTERNAL) from C{.multiply}.
938 @raise EcefError: If B{C{sa}}, B{C{ca}}, B{C{sb}} or
939 B{C{cb}} outside M{[-1.0, +1.0]}.
940 '''
941 t = sa, ca, sb, cb
942 if _more: # all 9 matrix elements ...
943 t += _more # ... from .multiply
945 elif max(map(fabs, t)) > _1_0:
946 raise EcefError(unstr(EcefMatrix.__name__, *t))
948 else: # build matrix from the following quaternion operations
949 # qrot(lam, [0,0,1]) * qrot(phi, [0,-1,0]) * [1,1,1,1]/2
950 # or
951 # qrot(pi/2 + lam, [0,0,1]) * qrot(-pi/2 + phi, [-1,0,0])
952 # where
953 # qrot(t,v) = [cos(t/2), sin(t/2)*v[1], sin(t/2)*v[2], sin(t/2)*v[3]]
955 # Local X axis (East) in geocentric coords
956 # M[0] = -slam; M[3] = clam; M[6] = 0;
957 # Local Y axis (North) in geocentric coords
958 # M[1] = -clam * sphi; M[4] = -slam * sphi; M[7] = cphi;
959 # Local Z axis (Up) in geocentric coords
960 # M[2] = clam * cphi; M[5] = slam * cphi; M[8] = sphi;
961 t = (-sb, -cb * sa, cb * ca,
962 cb, -sb * sa, sb * ca,
963 _0_0, ca, sa)
965 return _NamedTuple.__new__(cls, *t)
967 def column(self, column):
968 '''Get this matrix' B{C{column}} 0, 1 or 2 as C{3-tuple}.
969 '''
970 if 0 <= column < 3:
971 return self[column::3]
972 raise _IndexError(column=column)
974 def copy(self, **unused): # PYCHOK signature
975 '''Make a shallow or deep copy of this instance.
977 @return: The copy (C{This class} or subclass thereof).
978 '''
979 return self.classof(*self)
981 __copy__ = __deepcopy__ = copy
983 @Property_RO
984 def matrix3(self):
985 '''Get this matrix' rows (C{3-tuple} of 3 C{3-tuple}s).
986 '''
987 return tuple(map(self.row, range(3)))
989 @Property_RO
990 def matrixTransposed3(self):
991 '''Get this matrix' I{Transposed} rows (C{3-tuple} of 3 C{3-tuple}s).
992 '''
993 return tuple(map(self.column, range(3)))
995 def multiply(self, other):
996 '''Matrix multiply M{M0' ⋅ M} this matrix I{Transposed}
997 with an other matrix.
999 @arg other: The other matrix (L{EcefMatrix}).
1001 @return: The matrix product (L{EcefMatrix}).
1003 @raise TypeError: If B{C{other}} is not L{EcefMatrix}.
1004 '''
1005 _xinstanceof(EcefMatrix, other=other)
1006 # like LocalCartesian.MatrixMultiply, C{self.matrixTransposed3 X other.matrix3}
1007 # <https://GeographicLib.SourceForge.io/C++/doc/LocalCartesian_8cpp_source.html>
1008 # X = (fdot(self.column(r), *other.column(c)) for r in (0,1,2) for c in (0,1,2))
1009 X = (fdot(self[r::3], *other[c::3]) for r in range(3) for c in range(3))
1010 return _xnamed(EcefMatrix(*X), EcefMatrix.multiply.__name__)
1012 def rotate(self, xyz, *xyz0):
1013 '''Forward rotation M{M0' ⋅ ([x, y, z] - [x0, y0, z0])'}.
1015 @arg xyz: Local C{(x, y, z)} coordinates (C{3-tuple}).
1016 @arg xyz0: Optional, local C{(x0, y0, z0)} origin (C{3-tuple}).
1018 @return: Rotated C{(x, y, z)} location (C{3-tuple}).
1020 @raise LenError: Unequal C{len(B{xyz})} and C{len(B{xyz0})}.
1021 '''
1022 if xyz0:
1023 if len(xyz0) != len(xyz):
1024 raise LenError(self.rotate, xyz0=len(xyz0), xyz=len(xyz))
1025 xyz = tuple(c - c0 for c, c0 in zip(xyz, xyz0))
1027 # x' = M[0] * x + M[3] * y + M[6] * z
1028 # y' = M[1] * x + M[4] * y + M[7] * z
1029 # z' = M[2] * x + M[5] * y + M[8] * z
1030 return (fdot(xyz, *self[0::3]), # .column(0)
1031 fdot(xyz, *self[1::3]), # .column(1)
1032 fdot(xyz, *self[2::3])) # .column(2)
1034 def row(self, row):
1035 '''Get this matrix' B{C{row}} 0, 1 or 2 as C{3-tuple}.
1036 '''
1037 if 0 <= row < 3:
1038 r = row * 3
1039 return self[r:r+3]
1040 raise _IndexError(row=row)
1042 def unrotate(self, xyz, *xyz0):
1043 '''Inverse rotation M{[x0, y0, z0] + M0 ⋅ [x,y,z]'}.
1045 @arg xyz: Local C{(x, y, z)} coordinates (C{3-tuple}).
1046 @arg xyz0: Optional, local C{(x0, y0, z0)} origin (C{3-tuple}).
1048 @return: Unrotated C{(x, y, z)} location (C{3-tuple}).
1050 @raise LenError: Unequal C{len(B{xyz})} and C{len(B{xyz0})}.
1051 '''
1052 if xyz0:
1053 if len(xyz0) != len(xyz):
1054 raise LenError(self.unrotate, xyz0=len(xyz0), xyz=len(xyz))
1055 _xyz = _1_0_1T + xyz
1056 # x' = x0 + M[0] * x + M[1] * y + M[2] * z
1057 # y' = y0 + M[3] * x + M[4] * y + M[5] * z
1058 # z' = z0 + M[6] * x + M[7] * y + M[8] * z
1059 xyz_ = (fdot(_xyz, xyz0[0], *self[0:3]), # .row(0)
1060 fdot(_xyz, xyz0[1], *self[3:6]), # .row(1)
1061 fdot(_xyz, xyz0[2], *self[6:9])) # .row(2)
1062 else:
1063 # x' = M[0] * x + M[1] * y + M[2] * z
1064 # y' = M[3] * x + M[4] * y + M[5] * z
1065 # z' = M[6] * x + M[7] * y + M[8] * z
1066 xyz_ = (fdot(xyz, *self[0:3]), # .row(0)
1067 fdot(xyz, *self[3:6]), # .row(1)
1068 fdot(xyz, *self[6:9])) # .row(2)
1069 return xyz_
1072class Ecef9Tuple(_NamedTuple):
1073 '''9-Tuple C{(x, y, z, lat, lon, height, C, M, datum)} with I{geocentric}
1074 C{x}, C{y} and C{z} plus I{geodetic} C{lat}, C{lon} and C{height}, case
1075 C{C} (see the C{Ecef*.reverse} methods) and optionally, the rotation
1076 matrix C{M} (L{EcefMatrix}) and C{datum}, with C{lat} and C{lon} in
1077 C{degrees} and C{x}, C{y}, C{z} and C{height} in C{meter}, conventionally.
1078 '''
1079 _Names_ = (_x_, _y_, _z_, _lat_, _lon_, _height_, _C_, _M_, _datum_)
1080 _Units_ = ( Meter, Meter, Meter, Lat, Lon, Height, Int, _Pass, _Pass)
1082 @property_RO
1083 def _CartesianBase(self):
1084 '''(INTERNAL) Get class C{CartesianBase}, I{once}.
1085 '''
1086 Ecef9Tuple._CartesianBase = C = _MODS.cartesianBase.CartesianBase # overwrite property_RO
1087 return C
1089 @deprecated_method
1090 def convertDatum(self, datum2): # for backward compatibility
1091 '''DEPRECATED, use method L{toDatum}.'''
1092 return self.toDatum(datum2)
1094 @Property_RO
1095 def lam(self):
1096 '''Get the longitude in C{radians} (C{float}).
1097 '''
1098 return self.philam.lam
1100 @Property_RO
1101 def lamVermeille(self):
1102 '''Get the longitude in C{radians} M{[-PI*3/2..+PI*3/2]} after U{Vermeille
1103 <https://Search.ProQuest.com/docview/639493848>} (2004), page 95.
1105 @see: U{Karney<https://GeographicLib.SourceForge.io/C++/doc/geocentric.html>},
1106 U{Vermeille<https://Search.ProQuest.com/docview/847292978>} 2011, pp 112-113, 116
1107 and U{Featherstone, et.al.<https://Search.ProQuest.com/docview/872827242>}, page 7.
1108 '''
1109 x, y = self.x, self.y
1110 if y > EPS0:
1111 r = atan2(x, hypot(y, x) + y) * _N_2_0 + PI_2
1112 elif y < -EPS0:
1113 r = atan2(x, hypot(y, x) - y) * _2_0 - PI_2
1114 else: # y == 0
1115 r = PI if x < 0 else _0_0
1116 return Lam(Vermeille=r)
1118 @Property_RO
1119 def latlon(self):
1120 '''Get the lat-, longitude in C{degrees} (L{LatLon2Tuple}C{(lat, lon)}).
1121 '''
1122 return LatLon2Tuple(self.lat, self.lon, name=self.name)
1124 @Property_RO
1125 def latlonheight(self):
1126 '''Get the lat-, longitude in C{degrees} and height (L{LatLon3Tuple}C{(lat, lon, height)}).
1127 '''
1128 return self.latlon.to3Tuple(self.height)
1130 @Property_RO
1131 def latlonheightdatum(self):
1132 '''Get the lat-, longitude in C{degrees} with height and datum (L{LatLon4Tuple}C{(lat, lon, height, datum)}).
1133 '''
1134 return self.latlonheight.to4Tuple(self.datum)
1136 @Property_RO
1137 def latlonVermeille(self):
1138 '''Get the latitude and I{Vermeille} longitude in C{degrees [-225..+225]} (L{LatLon2Tuple}C{(lat, lon)}).
1140 @see: Property C{lonVermeille}.
1141 '''
1142 return LatLon2Tuple(self.lat, self.lonVermeille, name=self.name)
1144 @Property_RO
1145 def lonVermeille(self):
1146 '''Get the longitude in C{degrees [-225..+225]} after U{Vermeille
1147 <https://Search.ProQuest.com/docview/639493848>} (2004), p 95.
1149 @see: Property C{lamVermeille}.
1150 '''
1151 return Lon(Vermeille=degrees(self.lamVermeille))
1153 @Property_RO
1154 def phi(self):
1155 '''Get the latitude in C{radians} (C{float}).
1156 '''
1157 return self.philam.phi
1159 @Property_RO
1160 def philam(self):
1161 '''Get the lat-, longitude in C{radians} (L{PhiLam2Tuple}C{(phi, lam)}).
1162 '''
1163 return PhiLam2Tuple(radians(self.lat), radians(self.lon), name=self.name)
1165 @Property_RO
1166 def philamheight(self):
1167 '''Get the lat-, longitude in C{radians} and height (L{PhiLam3Tuple}C{(phi, lam, height)}).
1168 '''
1169 return self.philam.to3Tuple(self.height)
1171 @Property_RO
1172 def philamheightdatum(self):
1173 '''Get the lat-, longitude in C{radians} with height and datum (L{PhiLam4Tuple}C{(phi, lam, height, datum)}).
1174 '''
1175 return self.philamheight.to4Tuple(self.datum)
1177 @Property_RO
1178 def philamVermeille(self):
1179 '''Get the latitude and I{Vermeille} longitude in C{radians [-PI*3/2..+PI*3/2]} (L{PhiLam2Tuple}C{(phi, lam)}).
1181 @see: Property C{lamVermeille}.
1182 '''
1183 return PhiLam2Tuple(radians(self.lat), self.lamVermeille, name=self.name)
1185 def toCartesian(self, Cartesian=None, **Cartesian_kwds):
1186 '''Return the geocentric C{(x, y, z)} coordinates as an ellipsoidal or spherical
1187 C{Cartesian}.
1189 @kwarg Cartesian: Optional class to return C{(x, y, z)} (L{ellipsoidalKarney.Cartesian},
1190 L{ellipsoidalNvector.Cartesian}, L{ellipsoidalVincenty.Cartesian},
1191 L{sphericalNvector.Cartesian} or L{sphericalTrigonometry.Cartesian})
1192 or C{None}.
1193 @kwarg Cartesian_kwds: Optional, additional B{C{Cartesian}} keyword arguments, ignored
1194 if C{B{Cartesian} is None}.
1196 @return: A C{B{Cartesian}(x, y, z, **B{Cartesian_kwds})} instance or
1197 a L{Vector4Tuple}C{(x, y, z, h)} if C{B{Cartesian} is None}.
1199 @raise TypeError: Invalid B{C{Cartesian}} or B{C{Cartesian_kwds}}.
1200 '''
1201 if Cartesian in (None, Vector4Tuple):
1202 r = self.xyzh
1203 elif Cartesian is Vector3Tuple:
1204 r = self.xyz
1205 else:
1206 _xsubclassof(self._CartesianBase, Cartesian=Cartesian)
1207 r = Cartesian(self, **_xkwds(Cartesian_kwds, name=self.name))
1208 return r
1210 def toDatum(self, datum2):
1211 '''Convert this C{Ecef9Tuple} to an other datum.
1213 @arg datum2: Datum to convert I{to} (L{Datum}).
1215 @return: The converted 9-Tuple (C{Ecef9Tuple}).
1217 @raise TypeError: The B{C{datum2}} is not a L{Datum}.
1218 '''
1219 if self.datum in (None, datum2): # PYCHOK _Names_
1220 r = self.copy()
1221 else:
1222 c = self._CartesianBase(self, datum=self.datum, name=self.name) # PYCHOK _Names_
1223 # c.toLatLon converts datum, x, y, z, lat, lon, etc.
1224 # and returns another Ecef9Tuple iff LatLon is None
1225 r = c.toLatLon(datum=datum2, LatLon=None)
1226 return r
1228 def toLatLon(self, LatLon=None, **LatLon_kwds):
1229 '''Return the geodetic C{(lat, lon, height[, datum])} coordinates.
1231 @kwarg LatLon: Optional class to return C{(lat, lon, height[, datum])}
1232 or C{None}.
1233 @kwarg LatLon_kwds: Optional B{C{height}}, B{C{datum}} and other
1234 B{C{LatLon}} keyword arguments.
1236 @return: An instance of C{B{LatLon}(lat, lon, **B{LatLon_kwds})}
1237 or if B{C{LatLon}} is C{None}, a L{LatLon3Tuple}C{(lat, lon,
1238 height)} respectively L{LatLon4Tuple}C{(lat, lon, height,
1239 datum)} depending on whether C{datum} is un-/specified.
1241 @raise TypeError: Invalid B{C{LatLon}} or B{C{LatLon_kwds}}.
1242 '''
1243 lat, lon, D = self.lat, self.lon, self.datum # PYCHOK Ecef9Tuple
1244 kwds = _xkwds(LatLon_kwds, height=self.height, datum=D, name=self.name) # PYCHOK Ecef9Tuple
1245 d = kwds.get(_datum_, LatLon)
1246 if LatLon is None:
1247 r = LatLon3Tuple(lat, lon, kwds[_height_], name=kwds[_name_])
1248 if d is not None:
1249 # assert d is not LatLon
1250 r = r.to4Tuple(d) # checks type(d)
1251 else:
1252 if d is None:
1253 _ = kwds.pop(_datum_) # remove None datum
1254 r = LatLon(lat, lon, **kwds)
1255 _xdatum(_xattr(r, datum=D), D)
1256 return r
1258 def toLocal(self, ltp, Xyz=None, **Xyz_kwds):
1259 '''Convert this geocentric to I{local} C{x}, C{y} and C{z}.
1261 @kwarg ltp: The I{local tangent plane} (LTP) to use (L{Ltp}).
1262 @kwarg Xyz: Optional class to return C{x}, C{y} and C{z}
1263 (L{XyzLocal}, L{Enu}, L{Ned}) or C{None}.
1264 @kwarg Xyz_kwds: Optional, additional B{C{Xyz}} keyword
1265 arguments, ignored if C{B{Xyz} is None}.
1267 @return: An B{C{Xyz}} instance or if C{B{Xyz} is None},
1268 a L{Local9Tuple}C{(x, y, z, lat, lon, height,
1269 ltp, ecef, M)} with C{M=None}, always.
1271 @raise TypeError: Invalid B{C{ltp}}.
1272 '''
1273 return _MODS.ltp._xLtp(ltp)._ecef2local(self, Xyz, Xyz_kwds)
1275 def toVector(self, Vector=None, **Vector_kwds):
1276 '''Return the geocentric C{(x, y, z)} coordinates as vector.
1278 @kwarg Vector: Optional vector class to return C{(x, y, z)} or
1279 C{None}.
1280 @kwarg Vector_kwds: Optional, additional B{C{Vector}} keyword
1281 arguments, ignored if C{B{Vector} is None}.
1283 @return: A C{Vector}C{(x, y, z, **Vector_kwds)} instance or a
1284 L{Vector3Tuple}C{(x, y, z)} if B{C{Vector}} is C{None}.
1286 @see: Propertes C{xyz} and C{xyzh}
1287 '''
1288 return self.xyz if Vector is None else self._xnamed(
1289 Vector(*self.xyz, **Vector_kwds)) # PYCHOK Ecef9Tuple
1291# def _T_x_M(self, T):
1292# '''(INTERNAL) Update M{self.M = T.multiply(self.M)}.
1293# '''
1294# return self.dup(M=T.multiply(self.M))
1296 @Property_RO
1297 def xyz(self):
1298 '''Get the geocentric C{(x, y, z)} coordinates (L{Vector3Tuple}C{(x, y, z)}).
1299 '''
1300 return Vector3Tuple(self.x, self.y, self.z, name=self.name)
1302 @Property_RO
1303 def xyzh(self):
1304 '''Get the geocentric C{(x, y, z)} coordinates and C{height} (L{Vector4Tuple}C{(x, y, z, h)})
1305 '''
1306 return self.xyz.to4Tuple(self.height)
1309def _4Ecef(this, Ecef): # in .datums.Datum.ecef, .ellipsoids.Ellipsoid.ecef
1310 '''Return an ECEF converter for C{this} L{Datum} or L{Ellipsoid}.
1311 '''
1312 if Ecef is None:
1313 Ecef = EcefKarney
1314 else:
1315 _xinstanceof(*_Ecefs, Ecef=Ecef)
1316 return Ecef(this, name=this.name)
1319def _xEcef(Ecef): # PYCHOK .latlonBase.py
1320 '''(INTERNAL) Validate B{C{Ecef}} I{class}.
1321 '''
1322 if issubclassof(Ecef, _EcefBase):
1323 return Ecef
1324 raise _TypesError(_Ecef_, Ecef, *_Ecefs)
1327_Ecefs = (EcefKarney, EcefSudano, EcefVeness, EcefYou,
1328 EcefFarrell21, EcefFarrell22)
1330__all__ += _ALL_DOCS(_EcefBase)
1332# **) MIT License
1333#
1334# Copyright (C) 2016-2023 -- mrJean1 at Gmail -- All Rights Reserved.
1335#
1336# Permission is hereby granted, free of charge, to any person obtaining a
1337# copy of this software and associated documentation files (the "Software"),
1338# to deal in the Software without restriction, including without limitation
1339# the rights to use, copy, modify, merge, publish, distribute, sublicense,
1340# and/or sell copies of the Software, and to permit persons to whom the
1341# Software is furnished to do so, subject to the following conditions:
1342#
1343# The above copyright notice and this permission notice shall be included
1344# in all copies or substantial portions of the Software.
1345#
1346# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
1347# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
1348# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
1349# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
1350# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
1351# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
1352# OTHER DEALINGS IN THE SOFTWARE.