# Coverage for pygeodesy/ecef.py : 95%

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1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246 1247 1248 1249 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260 1261 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 1279 1280 1281 1282 1283 1284 1285 1286 1287 1288 1289 1290 1291 1292 1293 1294 1295 1296 1297 1298 1299 1300 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1311 1312 | # -*- coding: utf-8 -*- u'''I{Geocentric} Earth-Centered, Earth-Fixed (ECEF) coordinates. Geocentric conversions transcoded from I{Charles Karney}'s C++ class U{Geocentric <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Geocentric.html>} into pure Python class L{EcefKarney}, class L{EcefSudano} based on I{John Sudano}'s U{paper<https://www.ResearchGate.net/publication/ 3709199_An_exact_conversion_from_an_Earth-centered_coordinate_system_to_latitude_longitude_and_altitude>}, class L{EcefVeness} transcoded from I{Chris Veness}' JavaScript classes U{LatLonEllipsoidal, Cartesian<https://www.Movable-Type.co.UK/scripts/geodesy/docs/latlon-ellipsoidal.js.html>}, class L{EcefYou} implementing I{Rey-Jer You}'s U{transformations <https://www.ResearchGate.net/publication/240359424>} and classes L{EcefFarrell22} and L{EcefFarrell22} from I{Jay A. Farrell}'s U{Table 2.1 and 2.2 <https://Books.Google.com/books?id=fW4foWASY6wC>}, page 29-30. Following is a copy of I{Karney}'s U{Detailed Description <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Geocentric.html>}. Convert between geodetic coordinates C{lat}-, C{lon}gitude and height C{h} (measured vertically from the surface of the ellipsoid) to geocentric C{x}, C{y} and C{z} coordinates, also known as I{Earth-Centered, Earth-Fixed} (U{ECEF<https://WikiPedia.org/wiki/ECEF>}). The origin of geocentric coordinates is at the center of the earth. The C{z} axis goes thru the North pole, C{lat} = 90°. The C{x} axis goes thru C{lat} = 0°, C{lon} = 0°. The I{local (cartesian) origin} is at (C{lat0}, C{lon0}, C{height0}). The I{local} C{x} axis points East, the I{local} C{y} axis points North and the I{local} C{z} axis is normal to the ellipsoid. The plane C{z = -height0} is tangent to the ellipsoid, hence the alternate name I{local tangent plane}. Forward conversion from geodetic to geocentric (ECEF) coordinates is straightforward. For the reverse transformation we use Hugues Vermeille's U{I{Direct transformation from geocentric coordinates to geodetic coordinates}<https://DOI.org/10.1007/s00190-002-0273-6>}, J. Geodesy (2002) 76, page 451-454. Several changes have been made to ensure that the method returns accurate results for all finite inputs (even if h is infinite). The changes are described in Appendix B of C. F. F. Karney U{I{Geodesics on an ellipsoid of revolution}<https://ArXiv.org/abs/1102.1215v1>}, Feb. 2011, 85, 105-117 (U{preprint<https://ArXiv.org/abs/1102.1215v1>}). Vermeille similarly updated his method in U{I{An analytical method to transform geocentric into geodetic coordinates} <https://DOI.org/10.1007/s00190-010-0419-x>}, J. Geodesy (2011) 85, page 105-117. See U{Geocentric coordinates<https://GeographicLib.SourceForge.io/C++/doc/geocentric.html>} for more information. The errors in these routines are close to round-off. Specifically, for points within 5,000 km of the surface of the ellipsoid (either inside or outside the ellipsoid), the error is bounded by 7 nm (7 nanometers) for the WGS84 ellipsoid. See U{Geocentric coordinates <https://GeographicLib.SourceForge.io/C++/doc/geocentric.html>} for further information on the errors. @see: Module L{ltp} and class L{LocalCartesian}, a transcription of I{Charles Karney}'s C++ class U{LocalCartesian <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1LocalCartesian.html>}, providing conversion to and from I{local} cartesian cordinates in a I{local tangent plane} as opposed to I{geocentric} (ECEF) ones. ''' from pygeodesy.basics import copysign0, isscalar, issubclassof, neg, map1, \ _xinstanceof, _xsubclassof from pygeodesy.constants import EPS, EPS0, EPS02, EPS1, EPS2, EPS_2, PI, PI_2, \ _0_0, _0_0001, _0_01, _0_5, _1_0, _1_0_1T, _2_0, _3_0, _4_0, \ _6_0, _60_0, _90_0, _100_0, isnon0, \ _N_2_0 # PYCHOK used! from pygeodesy.datums import a_f2Tuple, _ellipsoidal_datum # from pygeodesy.ellipsoids import a_f2Tuple # from .datums from pygeodesy.errors import _IndexError, LenError, _ValueError, _TypesError, \ _xdatum, _xkwds from pygeodesy.fmath import cbrt, fdot, hypot, hypot1, hypot2_ from pygeodesy.fsums import Fsum, fsum_ from pygeodesy.interns import NN, _a_, _C_, _datum_, _ellipsoid_, _f_, _h_, \ _height_, _lat_, _lon_, _M_, _name_, _singular_, \ _SPACE_, _x_, _xyz_, _y_, _z_ from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS from pygeodesy.named import _NamedBase, _NamedTuple, notOverloaded, _Pass, _xnamed from pygeodesy.namedTuples import LatLon2Tuple, LatLon3Tuple, \ PhiLam2Tuple, Vector3Tuple, Vector4Tuple from pygeodesy.props import deprecated_method, Property_RO, property_RO, property_doc_ from pygeodesy.streprs import Fmt, unstr from pygeodesy.units import Height, Int, Lam, Lat, Lon, Meter, Phi, Scalar, Scalar_ from pygeodesy.utily import atan2d, degrees90, degrees180, sincos2, sincos2_, \ sincos2d_ from math import asin, atan2, cos, degrees, radians, sqrt __all__ = _ALL_LAZY.ecef __version__ = '22.10.12' _Ecef_ = 'Ecef' _prolate_ = 'prolate' _TRIPS = 17 # 8..9 sufficient, EcefSudano.reverse _xyz_y_z = _xyz_, _y_, _z_ # _xargs_names(_xyzn4)[:3] class EcefError(_ValueError): '''An ECEF or C{Ecef*} related issue. ''' pass def _llhn4(latlonh, lon, height, suffix=NN, Error=EcefError, name=NN): # in .ltp.LocalCartesian.forward and -.reset '''(INTERNAL) Get C{lat, lon, h, name} as C{4-tuple}. ''' try: lat, lon = latlonh.lat, latlonh.lon h = getattr(latlonh, _height_, getattr(latlonh, _h_, height)) n = getattr(latlonh, _name_, NN) except AttributeError: lat, h, n = latlonh, height, NN try: llhn = Lat(lat), Lon(lon), Height(h), (name or n) except (TypeError, ValueError) as x: t = _lat_, _lon_, _height_ if suffix: t = (_ + suffix for _ in t) d = dict(zip(t, (lat, lon, h))) raise Error(cause=x, **d) return llhn def _xyzn4(xyz, y, z, Types, Error=EcefError, name=NN, # in .ltp _xyz_y_z_names=_xyz_y_z): '''(INTERNAL) Get an C{(x, y, z, name)} 4-tuple. ''' try: try: t = xyz.x, xyz.y, xyz.z, getattr(xyz, _name_, name) if not isinstance(xyz, Types): raise _TypesError(_xyz_y_z_names[0], xyz, *Types) except AttributeError: t = map1(float, xyz, y, z) + (name,) except (TypeError, ValueError) as x: d = dict(zip(_xyz_y_z_names, (xyz, y, z))) raise Error(cause=x, **d) return t # assert _xyz_y_z == _xargs_names(_xyzn4)[:3] class _EcefBase(_NamedBase): '''(INTERNAL) Base class for L{EcefFarrell21}, L{EcefFarrell22}, L{EcefKarney}, L{EcefSudano}, L{EcefVeness} and L{EcefYou}. ''' _datum = None _E = None def __init__(self, a_ellipsoid, f=None, name=NN): '''New C{Ecef*} converter. @arg a_ellipsoid: A (non-prolate) ellipsoid (L{Ellipsoid}, L{Ellipsoid2}, L{Datum} or L{a_f2Tuple}) or C{scalar} ellipsoid's equatorial radius (C{meter}). @kwarg f: C{None} or the ellipsoid flattening (C{scalar}), required for C{scalar} B{C{a_ellipsoid}}, C{B{f}=0} represents a sphere, negative B{C{f}} a prolate ellipsoid. @kwarg name: Optional name (C{str}). @raise EcefError: If B{C{a_ellipsoid}} not L{Ellipsoid}, L{Ellipsoid2}, L{Datum} or L{a_f2Tuple} or C{scalar} or B{C{f}} not C{scalar} or if C{scalar} B{C{a_ellipsoid}} not positive or B{C{f}} not less than 1.0. ''' if name: self.name = name try: E = a_ellipsoid if f is None: pass elif isscalar(E) and isscalar(f): E = a_f2Tuple(E, f) else: raise ValueError # _invalid_ d = _ellipsoidal_datum(E, name=name) E = d.ellipsoid if E.a < EPS or E.f > EPS1: raise ValueError # _invalid_ except (TypeError, ValueError) as x: t = unstr(self.classname, a=a_ellipsoid, f=f) raise EcefError(_SPACE_(t, _ellipsoid_), cause=x) self._datum = d self._E = E def __eq__(self, other): '''Compare this and an other Ecef. @arg other: The other ecef (C{Ecef*}). @return: C{True} if equal, C{False} otherwise. ''' return other is self or (isinstance(other, self.__class__) and other.ellipsoid == self.ellipsoid) @Property_RO def equatoradius(self): '''Get the I{equatorial} radius, semi-axis (C{meter}). ''' return self.ellipsoid.a a = equatorialRadius = equatoradius # Karney property @Property_RO def datum(self): '''Get the datum (L{Datum}). ''' return self._datum @Property_RO def ellipsoid(self): '''Get the ellipsoid (L{Ellipsoid} or L{Ellipsoid2}). ''' return self._E @Property_RO def flattening(self): # Karney property '''Get the I{flattening} (C{float}), M{(a - b) / a}, positive for I{oblate}, negative for I{prolate} or C{0} for I{near-spherical}. ''' return self.ellipsoid.f f = flattening def _forward(self, lat, lon, h, name, M=False, _philam=False): # in .ltp.LocalCartesian.forward and -.reset '''(INTERNAL) Common for all C{Ecef*}. ''' E = self.ellipsoid if _philam: sa, ca, sb, cb = sincos2_(lat, lon) lat = Lat(degrees90( lat)) lon = Lon(degrees180(lon)) else: sa, ca, sb, cb = sincos2d_(lat, lon) n = E.roc1_(sa, ca) if self._isYou else E.roc1_(sa) z = (h + n * E.e21) * sa x = (h + n) * ca m = self._Matrix(sa, ca, sb, cb) if M else None return Ecef9Tuple(x * cb, x * sb, z, lat, lon, h, 0, m, self.datum, name=name or self.name) def forward(self, latlonh, lon=None, height=0, M=False, name=NN): '''Convert from geodetic C{(lat, lon, height)} to geocentric C{(x, y, z)}. @arg latlonh: Either a C{LatLon}, an L{Ecef9Tuple} or C{scalar} latitude (C{degrees}). @kwarg lon: Optional C{scalar} longitude for C{scalar} B{C{latlonh}} (C{degrees}). @kwarg height: Optional height (C{meter}), vertically above (or below) the surface of the ellipsoid. @kwarg M: Optionally, return the rotation L{EcefMatrix} (C{bool}). @kwarg name: Optional name (C{str}). @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with geocentric C{(x, y, z)} coordinates for the given geodetic ones C{(lat, lon, height)}, case C{C} 0, optional C{M} (L{EcefMatrix}) and C{datum} if available. @raise EcefError: If B{C{latlonh}} not C{LatLon}, L{Ecef9Tuple} or C{scalar} or B{C{lon}} not C{scalar} for C{scalar} B{C{latlonh}} or C{abs(lat)} exceeds 90°. @note: Use method C{.forward_} to specify C{lat} and C{lon} in C{radians} and avoid double angle conversions. ''' llhn = _llhn4(latlonh, lon, height, name=name) return _EcefBase._forward(self, *llhn, M=M) def forward_(self, phi, lam, height=0, M=False, name=NN): '''Like method C{.forward} except with geodetic lat- and longitude given in I{radians}. @arg phi: Latitude in I{radians} (C{scalar}). @arg lam: Longitude in I{radians} (C{scalar}). @kwarg height: Optional height (C{meter}), vertically above (or below) the surface of the ellipsoid. @kwarg M: Optionally, return the rotation L{EcefMatrix} (C{bool}). @kwarg name: Optional name (C{str}). @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with C{lat} set to C{degrees90(B{phi})} and C{lon} to C{degrees180(B{lam})}. @raise EcefError: If B{C{phi}} or B{C{lam}} invalid or not C{scalar}. ''' try: # like function C{_llhn4} above plhn = Phi(phi), Lam(lam), Height(height), name except (TypeError, ValueError) as x: raise EcefError(phi=phi, lam=lam, height=height, cause=x) return self._forward(*plhn, M=M, _philam=True) @property_RO def _Geocentrics(self): '''(INTERNAL) Valid geocentric classes. ''' t = Ecef9Tuple, _MODS.cartesianBase.CartesianBase _EcefBase._Geocentrics = t # overwrite the property return t @Property_RO def _isYou(self): '''(INTERNAL) Is this an C{EcefYou}?. ''' return isinstance(self, EcefYou) def _Matrix(self, sa, ca, sb, cb): '''Creation a rotation matrix. @arg sa: C{sin(phi)} (C{float}). @arg ca: C{cos(phi)} (C{float}). @arg sb: C{sin(lambda)} (C{float}). @arg cb: C{cos(lambda)} (C{float}). @return: An L{EcefMatrix}. ''' return self._xnamed(EcefMatrix(sa, ca, sb, cb)) def reverse(self, xyz, y=None, z=None, M=False, name=NN): # PYCHOK no cover '''(INTERNAL) I{Must be overloaded}, see function C{notOverloaded}. ''' notOverloaded(self, xyz, y=y, z=z, M=M, name=name) def toStr(self, prec=9, **unused): # PYCHOK signature '''Return this C{Ecef*} as a string. @kwarg prec: Precision, number of decimal digits (0..9). @return: This C{Ecef*} (C{str}). ''' return self.attrs(_a_, _f_, _datum_, _name_, prec=prec) # _ellipsoid_ class EcefFarrell21(_EcefBase): '''Conversion between geodetic and geocentric, I{Earth-Centered, Earth-Fixed} (ECEF) coordinates based on I{Jay A. Farrell}'s U{Table 2.1<https://Books.Google.com/ books?id=fW4foWASY6wC>}, page 29. ''' def reverse(self, xyz, y=None, z=None, M=None, name=NN): # PYCHOK unused M '''Convert from geocentric C{(x, y, z)} to geodetic C{(lat, lon, height)} using I{Farrell}'s U{Table 2.1<https://Books.Google.com/books?id=fW4foWASY6wC>}, page 29. @arg xyz: A geocentric (C{Cartesian}, L{Ecef9Tuple}) or C{scalar} ECEF C{x} coordinate (C{meter}). @kwarg y: ECEF C{y} coordinate for C{scalar} B{C{xyz}} and B{C{z}} (C{meter}). @kwarg z: ECEF C{z} coordinate for C{scalar} B{C{xyz}} and B{C{y}} (C{meter}). @kwarg M: I{Ignored}, rotation matrix C{M} not available. @kwarg name: Optional name (C{str}). @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with geodetic coordinates C{(lat, lon, height)} for the given geocentric ones C{(x, y, z)}, case C{C=1}, C{M=None} always and C{datum} if available. @raise EcefError: Invalid B{C{xyz}} or C{scalar} C{x} or B{C{y}} and/or B{C{z}} not C{scalar} for C{scalar} B{C{xyz}} or C{sqrt} domain or zero division error. @see: L{EcefFarrell22} and L{EcefVeness}. ''' x, y, z, name = _xyzn4(xyz, y, z, self._Geocentrics, name=name) E = self.ellipsoid a = E.a a2 = E.a2 b2 = E.b2 e_ = E.a_b * E.e # 0.0820944... WGS84 e2 = E.e2 e4 = E.e4 try: # names as page 29 z2 = z**2 ez = (_1_0 - e2) * z2 # E.e2s2(z) p = hypot(x, y) p2 = p**2 G = p2 + ez - e2 * (a2 - b2) # p2 + ez - e4 * a2 F = b2 * z2 * 54 c = e4 * p2 * F / G**3 s = cbrt(_1_0 + c + sqrt(c**2 + c * 2)) P = F / (_3_0 * (fsum_(_1_0, s, _1_0 / s) * G)**2) Q = sqrt(_1_0 + _2_0 * e4 * P) Q1 = Q + _1_0 r0 = P * e2 * p / Q1 - sqrt(fsum_(a2 * (Q1 / Q) * _0_5, -P * ez / (Q * Q1), -P * p2 * _0_5)) r = p + e2 * r0 v = b2 / (a * sqrt(r**2 + ez)) h = hypot(r, z) * (_1_0 - v) t = atan2(z + e_**2 * v * z, p) # note, phi and lam are swapped on page 29 except (ValueError, ZeroDivisionError) as e: raise EcefError(x=x, y=y, z=z, cause=e) return Ecef9Tuple(x, y, z, degrees90(t), atan2d(y, x), h, 1, None, self.datum, name=name or self.name) class EcefFarrell22(_EcefBase): '''Conversion between geodetic and geocentric, I{Earth-Centered, Earth-Fixed} (ECEF) coordinates based on I{Jay A. Farrell}'s U{Table 2.2<https://Books.Google.com/ books?id=fW4foWASY6wC>}, page 30. ''' def reverse(self, xyz, y=None, z=None, M=None, name=NN): # PYCHOK unused M '''Convert from geocentric C{(x, y, z)} to geodetic C{(lat, lon, height)} using I{Farrell}'s U{Table 2.2<https://Books.Google.com/books?id=fW4foWASY6wC>}, page 30. @arg xyz: A geocentric (C{Cartesian}, L{Ecef9Tuple}) or C{scalar} ECEF C{x} coordinate (C{meter}). @kwarg y: ECEF C{y} coordinate for C{scalar} B{C{xyz}} and B{C{z}} (C{meter}). @kwarg z: ECEF C{z} coordinate for C{scalar} B{C{xyz}} and B{C{y}} (C{meter}). @kwarg M: I{Ignored}, rotation matrix C{M} not available. @kwarg name: Optional name (C{str}). @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with geodetic coordinates C{(lat, lon, height)} for the given geocentric ones C{(x, y, z)}, case C{C=1}, C{M=None} always and C{datum} if available. @raise EcefError: Invalid B{C{xyz}} or C{scalar} C{x} or B{C{y}} and/or B{C{z}} not C{scalar} for C{scalar} B{C{xyz}} or C{sqrt} domain or zero division error. @see: L{EcefFarrell21} and L{EcefVeness}. ''' x, y, z, name = _xyzn4(xyz, y, z, self._Geocentrics, name=name) E = self.ellipsoid a = E.a b = E.b try: # see EcefVeness.reverse p = hypot(x, y) s, c = sincos2(atan2(z * a, p * b)) t = atan2(z + E.e22 * b * s**3, p - E.e2 * a * c**3) s, c = sincos2(t) if c: # E.roc1_(s) = E.a / sqrt(1 - E.e2 * s**2) h = p / c - (E.roc1_(s) if s else a) else: # polar h = abs(z) - b # note, phi and lam are swapped on page 30 except (ValueError, ZeroDivisionError) as e: raise EcefError(x=x, y=y, z=z, cause=e) return Ecef9Tuple(x, y, z, degrees90(t), atan2d(y, x), h, 1, None, self.datum, name=name or self.name) class EcefKarney(_EcefBase): '''Conversion between geodetic and geocentric, I{Earth-Centered, Earth-Fixed} (ECEF) coordinates transcoded from I{Karney}'s C++ U{Geocentric<https://GeographicLib.SourceForge.io/ C++/doc/classGeographicLib_1_1Geocentric.html>} methods. @note: On methods C{.forward} and C{.forwar_}, let C{v} be a unit vector located at C{(lat, lon, h)}. We can express C{v} as column vectors in one of two ways, C{v1} in east, north, up coordinates (where the components are relative to a local coordinate system at C{C(lat0, lon0, h0)}) or as C{v0} in geocentric C{x, y, z} coordinates. Then, M{v0 = M ⋅ v1} where C{M} is the rotation matrix. ''' @Property_RO def hmax(self): '''Get the distance or height limit (C{meter}, conventionally). ''' return self.equatoradius / EPS_2 # self.equatoradius * _2_EPS, 12M lighyears def reverse(self, xyz, y=None, z=None, M=False, name=NN): '''Convert from geocentric C{(x, y, z)} to geodetic C{(lat, lon, height)}. @arg xyz: A geocentric (C{Cartesian}, L{Ecef9Tuple}) or C{scalar} ECEF C{x} coordinate (C{meter}). @kwarg y: ECEF C{y} coordinate for C{scalar} B{C{xyz}} and B{C{z}} (C{meter}). @kwarg z: ECEF C{z} coordinate for C{scalar} B{C{xyz}} and B{C{y}} (C{meter}). @kwarg M: Optionally, return the rotation L{EcefMatrix} (C{bool}). @kwarg name: Optional name (C{str}). @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with geodetic coordinates C{(lat, lon, height)} for the given geocentric ones C{(x, y, z)}, case C{C}, optional C{M} (L{EcefMatrix}) and C{datum} if available. @raise EcefError: Invalid B{C{xyz}} or C{scalar} C{x} or B{C{y}} and/or B{C{z}} not C{scalar} for C{scalar} B{C{xyz}}. @note: In general, there are multiple solutions and the result which minimizes C{height} is returned, i.e., C{(lat, lon)} corresponds to the closest point on the ellipsoid. If there are still multiple solutions with different latitudes (applies only if C{z} = 0), then the solution with C{lat} > 0 is returned. If there are still multiple solutions with different longitudes (applies only if C{x} = C{y} = 0) then C{lon} = 0 is returned. The returned C{height} value is not below M{−E.a * (1 − E.e2) / sqrt(1 − E.e2 * sin(lat)**2)}. The returned C{lon} is in the range [−180°, 180°]. Like C{forward} above, M{v1 = Transpose(M) ⋅ v0}. ''' def norm3(y, x): h = hypot(y, x) # EPS0, EPS_2 return (y / h, x / h, h) if h > 0 else (_0_0, _1_0, h) x, y, z, name = _xyzn4(xyz, y, z, self._Geocentrics, name=name) E = self.ellipsoid sb, cb, R = norm3(y, x) h = hypot(R, z) # distance to earth center if h > self.hmax: # PYCHOK no cover # We are really far away (> 12M light years). Treat the earth # as a point and h, above as an acceptable approximation to the # height. This avoids overflow, e.g., in the computation of disc # below. It's possible that h has overflowed to INF, that's OK. # Treat finite x, y, but R overflows to +INF by scaling by 2. sb, cb, R = norm3(y * _0_5, x * _0_5) sa, ca, _ = norm3(z * _0_5, R) C = 1 elif E.e4: # E.isEllipsoidal # Treat prolate spheroids by swapping R and Z here and by # switching the arguments to phi = atan2(...) at the end. p = (R / E.a)**2 q = E.e21 * (z / E.a)**2 if E.isProlate: p, q = q, p r = p + q - E.e4 e = E.e4 * q if e or r > 0: # Avoid possible division by zero when r = 0 by multiplying # equations for s and t by r^3 and r, respectively. s = e * p / _4_0 # s = r^3 * s u = r = r / _6_0 r2 = r**2 r3 = r * r2 t3 = s + r3 disc = s * (r3 + t3) if disc < 0: # t is complex, but the way u is defined, the result is real. # There are three possible cube roots. We choose the root # which avoids cancellation. Note, disc < 0 implies r < 0. u += _2_0 * r * cos(atan2(sqrt(-disc), -t3) / _3_0) else: # Pick the sign on the sqrt to maximize abs(T3). This # minimizes loss of precision due to cancellation. The # result is unchanged because of the way the t is used # in definition of u. if disc > 0: t3 += copysign0(sqrt(disc), t3) # t3 = (r * t)^3 # N.B. cbrt always returns the real root, cbrt(-8) = -2. t = cbrt(t3) # t = r * t # t can be zero; but then r2 / t -> 0. if t: u = fsum_(u, t, r2 / t) v = sqrt(e + u**2) # guaranteed positive # Avoid loss of accuracy when u < 0. Underflow doesn't occur in # E.e4 * q / (v - u) because u ~ e^4 when q is small and u < 0. uv = (e / (v - u)) if u < 0 else (u + v) # u+v, guaranteed positive # Need to guard against w going negative due to roundoff in uv - q. w = max(_0_0, E.e2abs * (uv - q) / (_2_0 * v)) # Rearrange expression for k to avoid loss of accuracy due to # subtraction. Division by 0 not possible because uv > 0, w >= 0. k1 = k2 = uv / (sqrt(uv + w**2) + w) if E.isProlate: k1 -= E.e2 else: k2 += E.e2 sa, ca, h = norm3(z / k1, R / k2) h *= k1 - E.e21 C = 2 else: # e = E.e4 * q == 0 and r <= 0 # This leads to k = 0 (oblate, equatorial plane) and k + E.e^2 = 0 # (prolate, rotation axis) and the generation of 0/0 in the general # formulas for phi and h, using the general formula and division # by 0 in formula for h. Handle this case by taking the limits: # f > 0: z -> 0, k -> E.e2 * sqrt(q) / sqrt(E.e4 - p) # f < 0: r -> 0, k + E.e2 -> -E.e2 * sqrt(q) / sqrt(E.e4 - p) q = E.e4 - p if E.isProlate: p, q = q, p e = E.a else: e = E.b2_a sa, ca, h = norm3(sqrt(q * E._1_e21), sqrt(p)) if z < 0: sa = neg(sa) # for tiny negative z, not for prolate h *= neg(e / E.e2abs) C = 3 else: # E.e4 == 0, spherical case # Dealing with underflow in the general case with E.e2 = 0 is # difficult. Origin maps to North pole, same as with ellipsoid. sa, ca, _ = norm3((z if h else _1_0), R) h -= E.a C = 4 m = self._Matrix(sa, ca, sb, cb) if M else None return Ecef9Tuple(x, y, z, atan2d(sa, ca), atan2d(sb, cb), h, C, m, self.datum, name=name or self.name) class EcefSudano(_EcefBase): '''Conversion between geodetic and geocentric, I{Earth-Centered, Earth-Fixed} (ECEF) coordinates based on I{John J. Sudano}'s U{paper<https://www.ResearchGate.net/publication/ 3709199_An_exact_conversion_from_an_Earth-centered_coordinate_system_to_latitude_longitude_and_altitude>}. ''' _tol = EPS2 def reverse(self, xyz, y=None, z=None, M=None, name=NN): # PYCHOK unused M '''Convert from geocentric C{(x, y, z)} to geodetic C{(lat, lon, height)} using I{Sudano}'s U{iterative method<https://www.ResearchGate.net/publication/ 3709199_An_exact_conversion_from_an_Earth-centered_coordinate_system_to_latitude_longitude_and_altitude>}. @arg xyz: A geocentric (C{Cartesian}, L{Ecef9Tuple}) or C{scalar} ECEF C{x} coordinate (C{meter}). @kwarg y: ECEF C{y} coordinate for C{scalar} B{C{xyz}} and B{C{z}} (C{meter}). @kwarg z: ECEF C{z} coordinate for C{scalar} B{C{xyz}} and B{C{y}} (C{meter}). @kwarg M: I{Ignored}, rotation matrix C{M} not available. @kwarg name: Optional name (C{str}). @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with geodetic coordinates C{(lat, lon, height)} for the given geocentric ones C{(x, y, z)}, iteration C{C}, C{M=None} always and C{datum} if available. @raise EcefError: Invalid B{C{xyz}} or C{scalar} C{x} or B{C{y}} and/or B{C{z}} not C{scalar} for C{scalar} B{C{xyz}} or no convergence. ''' x, y, z, name = _xyzn4(xyz, y, z, self._Geocentrics, name=name) E = self.ellipsoid e = E.e2 * E.a h = hypot(x, y) # Rh d = e - h a = atan2(z, h * E.e21) sa, ca = sincos2(abs(a)) # Sudano's Eq (A-6) and (A-7) refactored/reduced, # replacing Rn from Eq (A-4) with n = E.a / ca: # N = ca**2 * ((z + E.e2 * n * sa) * ca - h * sa) # = ca**2 * (z * ca + E.e2 * E.a * sa - h * sa) # = ca**2 * (z * ca + (E.e2 * E.a - h) * sa) # D = ca**3 * (E.e2 * n / E.e2s2(sa)) - h # = ca**2 * (E.e2 * E.a / E.e2s2(sa) - h / ca**2) # N / D = (z * ca + (E.e2 * E.a - h) * sa) / # (E.e2 * E.a / E.e2s2(sa) - h / ca**2) tol = self.tolerance _S2_ = Fsum(sa).fsum2_ for C in range(1, _TRIPS): ca2 = _1_0 - sa**2 if ca2 < EPS_2: # PYCHOK no cover ca = _0_0 break ca = sqrt(ca2) r = e / E.e2s2(sa) - h / ca2 if abs(r) < EPS_2: break a = None sa, r = _S2_(-z * ca / r, -d * sa / r) if abs(r) < tol: break else: t = unstr(self.reverse, x=x, y=y, z=z) raise EcefError(Fmt.no_convergence(r, tol), txt=t) if a is None: a = copysign0(asin(sa), z) h = fsum_(h * ca, abs(z * sa), -E.a * E.e2s(sa)) # use Veness', # since Sudano's Eq (7) doesn't provide the correct height # h = (abs(z) + h - E.a * cos(a + E.e21) * sa / ca) / (ca + sa) r = Ecef9Tuple(x, y, z, degrees90(a), atan2d(y, x), h, C, None, self.datum, name=name or self.name) r._iteration = C return r @property_doc_(''' the convergence tolerance (C{float}).''') def tolerance(self): '''Get the convergence tolerance (C{scalar}). ''' return self._tol @tolerance.setter # PYCHOK setter! def tolerance(self, tol): '''Set the convergence tolerance (C{scalar}). @raise EcefError: Non-scalar or invalid B{C{tol}}. ''' self._tol = Scalar_(tolerance=tol, low=EPS, Error=EcefError) class EcefVeness(_EcefBase): '''Conversion between geodetic and geocentric, I{Earth-Centered, Earth-Fixed} (ECEF) coordinates transcoded from I{Chris Veness}' JavaScript classes U{LatLonEllipsoidal, Cartesian<https:// www.Movable-Type.co.UK/scripts/geodesy/docs/latlon-ellipsoidal.js.html>}. @see: U{I{A Guide to Coordinate Systems in Great Britain}<https:// www.OrdnanceSurvey.co.UK/documents/resources/guide-coordinate-systems-great-britain.pdf>}, section I{B) Converting between 3D Cartesian and ellipsoidal latitude, longitude and height coordinates}. ''' def reverse(self, xyz, y=None, z=None, M=None, name=NN): # PYCHOK unused M '''Convert from geocentric C{(x, y, z)} to geodetic C{(lat, lon, height)} transcoded from I{Chris Veness}' U{JavaScript<https://www.Movable-Type.co.UK/ scripts/geodesy/docs/latlon-ellipsoidal.js.html>}. Uses B. R. Bowring’s formulation for μm precision in concise form U{I{The accuracy of geodetic latitude and height equations}<https://www.ResearchGate.net/publication/ 233668213_The_Accuracy_of_Geodetic_Latitude_and_Height_Equations>}, Survey Review, Vol 28, 218, Oct 1985. @arg xyz: A geocentric (C{Cartesian}, L{Ecef9Tuple}) or C{scalar} ECEF C{x} coordinate (C{meter}). @kwarg y: ECEF C{y} coordinate for C{scalar} B{C{xyz}} and B{C{z}} (C{meter}). @kwarg z: ECEF C{z} coordinate for C{scalar} B{C{xyz}} and B{C{y}} (C{meter}). @kwarg M: I{Ignored}, rotation matrix C{M} not available. @kwarg name: Optional name (C{str}). @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with geodetic coordinates C{(lat, lon, height)} for the given geocentric ones C{(x, y, z)}, case C{C}, C{M=None} always and C{datum} if available. @raise EcefError: Invalid B{C{xyz}} or C{scalar} C{x} or B{C{y}} and/or B{C{z}} not C{scalar} for C{scalar} B{C{xyz}}. @see: Toms, Ralph M. U{I{An Efficient Algorithm for Geocentric to Geodetic Coordinate Conversion}<https://www.OSTI.gov/scitech/biblio/110235>}, Sept 1995 and U{I{An Improved Algorithm for Geocentric to Geodetic Coordinate Conversion}<https://www.OSTI.gov/scitech/servlets/purl/231228>}, Apr 1996, both from Lawrence Livermore National Laboratory (LLNL) and Sudano, John J, U{I{An exact conversion from an Earth-centered coordinate system to latitude longitude and altitude}<https://www.ResearchGate.net/ publication/3709199_An_exact_conversion_from_an_Earth-centered_coordinate_system_to_latitude_longitude_and_altitude>}. ''' x, y, z, name = _xyzn4(xyz, y, z, self._Geocentrics, name=name) E = self.ellipsoid p = hypot(x, y) # distance from minor axis r = hypot(p, z) # polar radius if min(p, r) > EPS0: # parametric latitude (Bowring eqn 17, replaced) t = (E.b * z) / (E.a * p) * (_1_0 + E.e22 * E.b / r) c = _1_0 / hypot1(t) s = t * c # geodetic latitude (Bowring eqn 18) a = atan2(z + E.e22 * E.b * s**3, p - E.e2 * E.a * c**3) # height above ellipsoid (Bowring eqn 7) sa, ca = sincos2(a) # r = E.a / E.e2s(sa) # length of normal terminated by minor axis # h = p * ca + z * sa - (E.a * E.a / r) h = fsum_(p * ca, z * sa, -E.a * E.e2s(sa)) C, lat, lon = 1, degrees90(a), atan2d(y, x) # see <https://GIS.StackExchange.com/questions/28446> elif p > EPS: # lat arbitrarily zero C, lat, lon, h = 2, _0_0, atan2d(y, x), p - E.a else: # polar lat, lon arbitrarily zero C, lat, lon, h = 3, copysign0(_90_0, z), _0_0, abs(z) - E.b return Ecef9Tuple(x, y, z, lat, lon, h, C, None, # M=None self.datum, name=name or self.name) class EcefYou(_EcefBase): '''Conversion between geodetic and geocentric, I{Earth-Centered, Earth-Fixed} (ECEF) coordinates using I{Rey-Jer You}'s U{transformation<https://www.ResearchGate.net/publication/240359424>}. @see: Featherstone, W.E., Claessens, S.J. U{I{Closed-form transformation between geodetic and ellipsoidal coordinates}<https://Espace.Curtin.edu.AU/bitstream/handle/20.500.11937/ 11589/115114_9021_geod2ellip_final.pdf>} Studia Geophysica et Geodaetica, 2008, 52, pages 1-18 and U{PyMap3D <https://PyPI.org/project/pymap3d>}. ''' def __init__(self, a_ellipsoid, f=None, name=NN): _EcefBase.__init__(self, a_ellipsoid, f=f, name=name) # inherited documentation E = self.ellipsoid if E.isProlate or (E.a2 - E.b2) < 0: raise EcefError(ellipsoid=E, txt=_prolate_) def reverse(self, xyz, y=None, z=None, M=None, name=NN): # PYCHOK unused M '''Convert geocentric C{(x, y, z)} to geodetic C{(lat, lon, height)} using I{Rey-Jer You}'s transformation. @arg xyz: A geocentric (C{Cartesian}, L{Ecef9Tuple}) or C{scalar} ECEF C{x} coordinate (C{meter}). @kwarg y: ECEF C{y} coordinate for C{scalar} B{C{xyz}} and B{C{z}} (C{meter}). @kwarg z: ECEF C{z} coordinate for C{scalar} B{C{xyz}} and B{C{y}} (C{meter}). @kwarg M: I{Ignored}, rotation matrix C{M} not available. @kwarg name: Optional name (C{str}). @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with geodetic coordinates C{(lat, lon, height)} for the given geocentric ones C{(x, y, z)}, case C{C=1}, C{M=None} always and C{datum} if available. @raise EcefError: Invalid B{C{xyz}} or C{scalar} C{x} or B{C{y}} and/or B{C{z}} not C{scalar} for C{scalar} B{C{xyz}}. ''' x, y, z, name = _xyzn4(xyz, y, z, self._Geocentrics, name=name) r2 = hypot2_(x, y, z) E = self.ellipsoid e2 = E.a2 - E.b2 # == E.e2 * E.a2 if e2 < 0: raise EcefError(ellipsoid=E, txt=_prolate_) e = sqrt(e2) # XXX sqrt0(e2)? q = hypot(x, y) u = fsum_(r2, -e2, hypot(r2 - e2, 2 * e * z)) * _0_5 if u > EPS02: u = sqrt(u) p = hypot(u, e) B = atan2(p * z, u * q) # beta0 = atan(p / u * z / q) sB, cB = sincos2(B) if cB and sB: p *= E.a d = (p / cB - e2 * cB) / sB if isnon0(d): B += fsum_(u * E.b, -p, e2) / d sB, cB = sincos2(B) elif u < 0: raise EcefError(x=x, y=y, z=z, txt=_singular_) else: sB, cB = copysign0(_1_0, z), _0_0 h = hypot(z - E.b * sB, q - E.a * cB) if hypot2_(x, y, z * E.a_b) < E.a2: h = neg(h) # inside ellipsoid return Ecef9Tuple(x, y, z, atan2d(E.a * sB, E.b * cB), # atan(E.a_b * tan(B)) atan2d(y, x), h, 1, None, # C=1, M=None self.datum, name=name or self.name) class EcefMatrix(_NamedTuple): '''A rotation matrix. ''' _Names_ = ('_0_0_', '_0_1_', '_0_2_', # row-order '_1_0_', '_1_1_', '_1_2_', '_2_0_', '_2_1_', '_2_2_') _Units_ = (Scalar,) * len(_Names_) def _validate(self, **_OK): # PYCHOK unused '''(INTERNAL) Allow C{_Names_} with leading underscore. ''' _NamedTuple._validate(self, _OK=True) def __new__(cls, sa, ca, sb, cb, *_more): '''New L{EcefMatrix} matrix. @arg sa: C{sin(phi)} (C{float}). @arg ca: C{cos(phi)} (C{float}). @arg sb: C{sin(lambda)} (C{float}). @arg cb: C{cos(lambda)} (C{float}). @arg _more: (INTERNAL) from C{.multiply}. @raise EcefError: If B{C{sa}}, B{C{ca}}, B{C{sb}} or B{C{cb}} outside M{[-1.0, +1.0]}. ''' t = sa, ca, sb, cb if _more: # all 9 matrix elements ... t += _more # ... from .multiply elif max(map(abs, t)) > _1_0: raise EcefError(unstr(EcefMatrix.__name__, *t)) else: # build matrix from the following quaternion operations # qrot(lam, [0,0,1]) * qrot(phi, [0,-1,0]) * [1,1,1,1]/2 # or # qrot(pi/2 + lam, [0,0,1]) * qrot(-pi/2 + phi, [-1,0,0]) # where # qrot(t,v) = [cos(t/2), sin(t/2)*v[1], sin(t/2)*v[2], sin(t/2)*v[3]] # Local X axis (east) in geocentric coords # M[0] = -slam; M[3] = clam; M[6] = 0; # Local Y axis (north) in geocentric coords # M[1] = -clam * sphi; M[4] = -slam * sphi; M[7] = cphi; # Local Z axis (up) in geocentric coords # M[2] = clam * cphi; M[5] = slam * cphi; M[8] = sphi; t = (-sb, -cb * sa, cb * ca, cb, -sb * sa, sb * ca, _0_0, ca, sa) return _NamedTuple.__new__(cls, *t) def column(self, column): '''Get matrix B{C{column}} as 3-tuple. ''' if 0 <= column < 3: return self[column::3] raise _IndexError(column=column) @Property_RO def _column_0(self): return self.column(0) @Property_RO def _column_1(self): return self.column(1) @Property_RO def _column_2(self): return self.column(2) def copy(self, **unused): # PYCHOK signature '''Make a shallow or deep copy of this instance. @return: The copy (C{This class} or subclass thereof). ''' return self.classof(*self) __copy__ = __deepcopy__ = copy def multiply(self, other): '''Matrix multiply M{M0' ⋅ M} this matrix transposed with an other matrix. @arg other: The other matrix (L{EcefMatrix}). @return: The matrix product (L{EcefMatrix}). @raise TypeError: If B{C{other}} is not L{EcefMatrix}. ''' _xinstanceof(EcefMatrix, other=other) # like LocalCartesian.MatrixMultiply, transposed(self) X other # <https://GeographicLib.SourceForge.io/C++/doc/LocalCartesian_8cpp_source.html> M = (fdot(self[r::3], *other[c::3]) for r in range(3) for c in range(3)) return _xnamed(EcefMatrix(*M), EcefMatrix.multiply.__name__) def rotate(self, xyz, *xyz0): '''Forward rotation M{M0' ⋅ ([x, y, z] - [x0, y0, z0])'}. @arg xyz: Local C{(x, y, z)} coordinates (C{3-tuple}). @arg xyz0: Optional, local C{(x0, y0, z0)} origin (C{3-tuple}). @return: Rotated C{(x, y, z)} location (C{3-tuple}). @raise LenError: Unequal C{len(B{xyz})} and C{len(B{xyz0})}. ''' if xyz0: if len(xyz0) != len(xyz): raise LenError(self.rotate, xyz0=len(xyz0), xyz=len(xyz)) xyz = tuple(c - c0 for c, c0 in zip(xyz, xyz0)) # x' = M[0] * x + M[3] * y + M[6] * z # y' = M[1] * x + M[4] * y + M[7] * z # z' = M[2] * x + M[5] * y + M[8] * z return (fdot(xyz, *self._column_0), fdot(xyz, *self._column_1), fdot(xyz, *self._column_2)) def row(self, row): '''Get matrix B{C{row}} as 3-tuple. ''' if 0 <= row < 3: r = row * 3 return self[r: r+3] raise _IndexError(row=row) @Property_RO def _row_0(self): return self.row(0) @Property_RO def _row_1(self): return self.row(1) @Property_RO def _row_2(self): return self.row(2) def unrotate(self, xyz, *xyz0): '''Inverse rotation M{[x0, y0, z0] + M0 ⋅ [x,y,z]'}. @arg xyz: Local C{(x, y, z)} coordinates (C{3-tuple}). @arg xyz0: Optional, local C{(x0, y0, z0)} origin (C{3-tuple}). @return: Unrotated C{(x, y, z)} location (C{3-tuple}). @raise LenError: Unequal C{len(B{xyz})} and C{len(B{xyz0})}. ''' if xyz0: if len(xyz0) != len(xyz): raise LenError(self.unrotate, xyz0=len(xyz0), xyz=len(xyz)) _xyz = _1_0_1T + xyz # x' = x0 + M[0] * x + M[1] * y + M[2] * z # y' = y0 + M[3] * x + M[4] * y + M[5] * z # z' = z0 + M[6] * x + M[7] * y + M[8] * z xyz_ = (fdot(_xyz, xyz0[0], *self._row_0), fdot(_xyz, xyz0[1], *self._row_1), fdot(_xyz, xyz0[2], *self._row_2)) else: # x' = M[0] * x + M[1] * y + M[2] * z # y' = M[3] * x + M[4] * y + M[5] * z # z' = M[6] * x + M[7] * y + M[8] * z xyz_ = (fdot(xyz, *self._row_0), fdot(xyz, *self._row_1), fdot(xyz, *self._row_2)) return xyz_ class Ecef9Tuple(_NamedTuple): '''9-Tuple C{(x, y, z, lat, lon, height, C, M, datum)} with I{geocentric} C{x}, C{y} and C{z} plus I{geodetic} C{lat}, C{lon} and C{height}, case C{C} (see the C{Ecef*.reverse} methods) and optionally, the rotation matrix C{M} (L{EcefMatrix}) and C{datum}, with C{lat} and C{lon} in C{degrees} and C{x}, C{y}, C{z} and C{height} in C{meter}, conventionally. ''' _Names_ = (_x_, _y_, _z_, _lat_, _lon_, _height_, _C_, _M_, _datum_) _Units_ = ( Meter, Meter, Meter, Lat, Lon, Height, Int, _Pass, _Pass) _IndexM = _Names_.index(_M_) # for ._M_x_M @property_RO def _CartesianBase(self): '''(INTERNAL) Get/cache class C{CartesianBase}. ''' Ecef9Tuple._CartesianBase = C = _MODS.cartesianBase.CartesianBase # overwrite property return C @deprecated_method def convertDatum(self, datum2): # for backward compatibility '''DEPRECATED, use method L{toDatum}.''' return self.toDatum(datum2) @Property_RO def lam(self): '''Get the longitude in C{radians} (C{float}). ''' return self.philam.lam @Property_RO def lamVermeille(self): '''Get the longitude in C{radians [-PI*3/2..+PI*3/2]} after U{Vermeille <https://Search.ProQuest.com/docview/639493848>} (2004), page 95. @see: U{Karney<https://GeographicLib.SourceForge.io/C++/doc/geocentric.html>}, U{Vermeille<https://Search.ProQuest.com/docview/847292978>} 2011, pp 112-113, 116 and U{Featherstone, et.al.<https://Search.ProQuest.com/docview/872827242>}, page 7. ''' x, y = self.x, self.y if y > EPS0: r = _N_2_0 * atan2(x, hypot(y, x) + y) + PI_2 elif y < -EPS0: r = _2_0 * atan2(x, hypot(y, x) - y) - PI_2 else: # y == 0 r = PI if x < 0 else _0_0 return Lam(Vermeille=r) @Property_RO def latlon(self): '''Get the lat-, longitude in C{degrees} (L{LatLon2Tuple}C{(lat, lon)}). ''' return LatLon2Tuple(self.lat, self.lon, name=self.name) @Property_RO def latlonheight(self): '''Get the lat-, longitude in C{degrees} and height (L{LatLon3Tuple}C{(lat, lon, height)}). ''' return self.latlon.to3Tuple(self.height) @Property_RO def latlonheightdatum(self): '''Get the lat-, longitude in C{degrees} with height and datum (L{LatLon4Tuple}C{(lat, lon, height, datum)}). ''' return self.latlonheight.to4Tuple(self.datum) @Property_RO def latlonVermeille(self): '''Get the latitude and I{Vermeille} longitude in C{degrees [-225..+225]} (L{LatLon2Tuple}C{(lat, lon)}). @see: Property C{lonVermeille}. ''' return LatLon2Tuple(self.lat, self.lonVermeille, name=self.name) @Property_RO def lonVermeille(self): '''Get the longitude in C{degrees [-225..+225]} after U{Vermeille <https://Search.ProQuest.com/docview/639493848>} (2004), p 95. @see: Property C{lamVermeille}. ''' return Lon(Vermeille=degrees(self.lamVermeille)) def _T_x_M(self, T): '''(INTERNAL) Update M{self.M = T.multiply(self.M)}. ''' t = list(self) M = self._IndexM t[M] = T.multiply(t[M]) return self.classof(*t) @Property_RO def phi(self): '''Get the latitude in C{radians} (C{float}). ''' return self.philam.phi @Property_RO def philam(self): '''Get the lat-, longitude in C{radians} (L{PhiLam2Tuple}C{(phi, lam)}). ''' return PhiLam2Tuple(radians(self.lat), radians(self.lon), name=self.name) @Property_RO def philamheight(self): '''Get the lat-, longitude in C{radians} and height (L{PhiLam3Tuple}C{(phi, lam, height)}). ''' return self.philam.to3Tuple(self.height) @Property_RO def philamheightdatum(self): '''Get the lat-, longitude in C{radians} with height and datum (L{PhiLam4Tuple}C{(phi, lam, height, datum)}). ''' return self.philamheight.to4Tuple(self.datum) @Property_RO def philamVermeille(self): '''Get the latitude and I{Vermeille} longitude in C{radians [-PI*3/2..+PI*3/2]} (L{PhiLam2Tuple}C{(phi, lam)}). @see: Property C{lamVermeille}. ''' return PhiLam2Tuple(radians(self.lat), self.lamVermeille, name=self.name) def toCartesian(self, Cartesian=None, **Cartesian_kwds): '''Return the geocentric C{(x, y, z)} coordinates as an ellipsoidal or spherical C{Cartesian}. @kwarg Cartesian: Optional class to return C{(x, y, z)} (L{ellipsoidalKarney.Cartesian}, L{ellipsoidalNvector.Cartesian}, L{ellipsoidalVincenty.Cartesian}, L{sphericalNvector.Cartesian} or L{sphericalTrigonometry.Cartesian}) or C{None}. @kwarg Cartesian_kwds: Optional, additional B{C{Cartesian}} keyword arguments, ignored if C{B{Cartesian} is None}. @return: A C{B{Cartesian}(x, y, z, **B{Cartesian_kwds})} instance or a L{Vector4Tuple}C{(x, y, z, h)} if C{B{Cartesian} is None}. @raise TypeError: Invalid B{C{Cartesian}} or B{C{Cartesian_kwds}}. ''' if Cartesian in (None, Vector4Tuple): r = self.xyzh elif Cartesian is Vector3Tuple: r = self.xyz else: _xsubclassof(self._CartesianBase, Cartesian=Cartesian) r = Cartesian(self, **_xkwds(Cartesian_kwds, name=self.name)) return r def toDatum(self, datum2): '''Convert this C{Ecef9Tuple} to an other datum. @arg datum2: Datum to convert I{to} (L{Datum}). @return: The converted 9-Tuple (C{Ecef9Tuple}). @raise TypeError: The B{C{datum2}} is not a L{Datum}. ''' if self.datum in (None, datum2): # PYCHOK _Names_ r = self.copy() else: c = self._CartesianBase(self, datum=self.datum, name=self.name) # PYCHOK _Names_ # c.toLatLon converts datum, x, y, z, lat, lon, etc. # and returns another Ecef9Tuple iff LatLon is None r = c.toLatLon(datum=datum2, LatLon=None) return r def toLatLon(self, LatLon=None, **LatLon_kwds): '''Return the geodetic C{(lat, lon, height[, datum])} coordinates. @kwarg LatLon: Optional class to return C{(lat, lon, height[, datum])} or C{None}. @kwarg LatLon_kwds: Optional B{C{height}}, B{C{datum}} and other B{C{LatLon}} keyword arguments. @return: An instance of C{B{LatLon}(lat, lon, **B{LatLon_kwds})} or if B{C{LatLon}} is C{None}, a L{LatLon3Tuple}C{(lat, lon, height)} respectively L{LatLon4Tuple}C{(lat, lon, height, datum)} depending on whether C{datum} is un-/specified. @raise TypeError: Invalid B{C{LatLon}} or B{C{LatLon_kwds}}. ''' kwds = _xkwds(LatLon_kwds, height=self.height, datum=self.datum, name=self.name) # PYCHOK Ecef9Tuple d = kwds[_datum_] if LatLon is None: r = LatLon3Tuple(self.lat, self.lon, kwds[_height_], name=kwds[_name_]) # PYCHOK Ecef9Tuple if d: r = r.to4Tuple(d) # checks type(d) else: if d is None: # remove None datum _ = kwds.pop[_datum_] r = LatLon(self.lat, self.lon, **kwds) # PYCHOK Ecef9Tuple _xdatum(getattr(r, _datum_, self.datum), self.datum) # PYCHOK Ecef9Tuple return r def toLocal(self, ltp, Xyz=None, **Xyz_kwds): '''Convert this geocentric to I{local} C{x}, C{y} and C{z}. @kwarg ltp: The I{local tangent plane} (LTP) to use (L{Ltp}). @kwarg Xyz: Optional class to return C{x}, C{y} and C{z} (L{XyzLocal}, L{Enu}, L{Ned}) or C{None}. @kwarg Xyz_kwds: Optional, additional B{C{Xyz}} keyword arguments, ignored if C{B{Xyz} is None}. @return: An B{C{Xyz}} instance or if C{B{Xyz} is None}, a L{Local9Tuple}C{(x, y, z, lat, lon, height, ltp, ecef, M)} with C{M=None}, always. @raise TypeError: Invalid B{C{ltp}}. ''' return _MODS.ltp._xLtp(ltp)._ecef2local(self, Xyz, Xyz_kwds) def toVector(self, Vector=None, **Vector_kwds): '''Return the geocentric C{(x, y, z)} coordinates as vector. @kwarg Vector: Optional vector class to return C{(x, y, z)} or C{None}. @kwarg Vector_kwds: Optional, additional B{C{Vector}} keyword arguments, ignored if C{B{Vector} is None}. @return: A C{Vector}C{(x, y, z, **Vector_kwds)} instance or a L{Vector3Tuple}C{(x, y, z)} if B{C{Vector}} is C{None}. @see: Propertes C{xyz} and C{xyzh} ''' return self.xyz if Vector is None else self._xnamed( Vector(self.x, self.y, self.z, **Vector_kwds)) # PYCHOK Ecef9Tuple @Property_RO def xyz(self): '''Get the geocentric C{(x, y, z)} coordinates (L{Vector3Tuple}C{(x, y, z)}). ''' return Vector3Tuple(self.x, self.y, self.z, name=self.name) @Property_RO def xyzh(self): '''Get the geocentric C{(x, y, z)} coordinates and C{height} (L{Vector4Tuple}C{(x, y, z, h)}) ''' return self.xyz.to4Tuple(self.height) def _4Ecef(this, Ecef): # in .datums.Datum.ecef, .ellipsoids.Ellipsoid.ecef '''Return an ECEF converter for C{this} L{Datum} or L{Ellipsoid}. ''' if Ecef is None: Ecef = EcefKarney else: _xinstanceof(*_Ecefs, Ecef=Ecef) return Ecef(this, name=this.name) def _xEcef(Ecef): # PYCHOK .latlonBase.py '''(INTERNAL) Validate B{C{Ecef}} I{class}. ''' if issubclassof(Ecef, _EcefBase): return Ecef raise _TypesError(_Ecef_, Ecef, *_Ecefs) _Ecefs = (EcefKarney, EcefSudano, EcefVeness, EcefYou, EcefFarrell21, EcefFarrell22) __all__ += _ALL_DOCS(_EcefBase) # **) MIT License # # Copyright (C) 2016-2022 -- mrJean1 at Gmail -- All Rights Reserved. # # Permission is hereby granted, free of charge, to any person obtaining a # copy of this software and associated documentation files (the "Software"), # to deal in the Software without restriction, including without limitation # the rights to use, copy, modify, merge, publish, distribute, sublicense, # and/or sell copies of the Software, and to permit persons to whom the # Software is furnished to do so, subject to the following conditions: # # The above copyright notice and this permission notice shall be included # in all copies or substantial portions of the Software. # # THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS # OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, # FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL # THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR # OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, # ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR # OTHER DEALINGS IN THE SOFTWARE.