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1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1233 1234 | # -*- coding: utf-8 -*- u'''Geocentric conversions transcribed from I{Charles Karney}'s C++ classes U{Geocentric <https://GeographicLib.SourceForge.io/html/classGeographicLib_1_1Geocentric.html>} and U{LocalCartesian<https://GeographicLib.SourceForge.io/html/classGeographicLib_1_1LocalCartesian.html>} into pure Python classes L{EcefKarney} respectively L{EcefCartesian}, 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} transcribed from I{Chris Veness}' JavaScript classes U{LatLonEllipsoidal, Cartesian<https://www.Movable-Type.co.UK/scripts/geodesy/docs/latlon-ellipsoidal.js.html>} and class L{EcefYou} implementing I{Rey-Jer You}'s U{transformations <https://www.ResearchGate.net/publication/240359424>}. Following is a copy of I{Karney}'s U{Detailed Description <https://GeographicLib.SourceForge.io/html/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 local cartesian origin is at (C{lat0}, C{lon0}, C{height0}). The C{z} axis is normal to the ellipsoid, the C{y} axis points due North. The plane C{z = -height0} is tangent to the ellipsoid. Forward conversion from geodetic to geocentric (ECEF) coordinates is straightforward. For the reverse transformation we use Hugues Vermeille's U{Direct transformation from geocentric coordinates to geodetic coordinates <https://DOI.org/10.1007/s00190-002-0273-6>}, J. Geodesy (2002) 76, 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{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{An analytical method to transform geocentric into geodetic coordinates<https://DOI.org/10.1007/s00190-010-0419-x>}, J. Geodesy (2011) 85, 105-117. See U{Geocentric coordinates <https://GeographicLib.SourceForge.io/html/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/html/geocentric.html>} for further information on the errors. ''' from pygeodesy.basics import copysign, isscalar, neg, property_RO, \ _xinstanceof, _xsubclassof from pygeodesy.datums import Datums, _ellipsoidal_datum from pygeodesy.ellipsoids import a_f2Tuple from pygeodesy.errors import _datum_datum, LenError, _ValueError, _xkwds from pygeodesy.fmath import cbrt, fdot, Fsum, fsum_, hypot1, hypot2_ from pygeodesy.interns import EPS, EPS1, EPS_2, NN, PI, PI_2, _a_, _C_, \ _datum_, _ellipsoid_, _f_, _h_, _height_, \ joined_, _lat_, _lat0_, _lon_, _lon0_, _M_, \ _name_, _no_convergence_, _x_, _y_, _z_, _0_, \ _0_0, _0_5, _1_0, _2_0, _3_0, _4_0, _6_0, _90_0 from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _FOR_DOCS from pygeodesy.named import _NamedBase, _NamedTuple, notOverloaded, _Pass from pygeodesy.namedTuples import LatLon2Tuple, LatLon3Tuple, \ PhiLam2Tuple, Vector3Tuple from pygeodesy.streprs import unstr from pygeodesy.units import Height, Int, Lat, Lon, Meter, Scalar from pygeodesy.utily import atan2d, degrees90, sincos2, sincos2d from pygeodesy.vector3d import _xyzn4 from math import asin, atan2, cos, degrees, hypot, radians, sqrt __all__ = _ALL_LAZY.ecef __version__ = '20.10.29' _prolate_ = 'prolate' _singular_ = 'singular' _TRIPS = 17 # 8..9 sufficient, EcefSudano.reverse def _llhn4(latlonh, lon, height, suffix=NN): '''(INTERNAL) Get C{lat, lon, h, name} as C{4-tuple}. ''' try: llh = latlonh.lat, latlonh.lon, getattr(latlonh, _height_, getattr(latlonh, _h_, height)) except AttributeError: llh = latlonh, lon, height try: lat, lon, h = map(float, llh) except (TypeError, ValueError) as x: t = _lat_, _lon_, _height_ if suffix: t = (_ + suffix for _ in t) raise EcefError(txt=str(x), **dict(zip(t, llh))) if abs(lat) > _90_0: # XXX RangeError raise EcefError(_lat_ + suffix, lat) return lat, lon, h, getattr(latlonh, _name_, NN) def _sch3(y, x): '''(INTERNAL) Compute sin, cos and hypotenuse. ''' h = hypot(y, x) if h > 0: # EPS_2 s, c = y / h, x / h else: s, c = _0_0, _1_0 return s, c, h class EcefError(_ValueError): '''An ECEF or C{Ecef*} related issue. ''' pass class _EcefBase(_NamedBase): '''(INTERNAL) Base class for L{EcefKarney}, L{EcefVeness} and L{EcefYou}. ''' _datum = None _E = None def __init__(self, a_ellipsoid, f, name): '''(INTERNAL) New C{Ecef...}. ''' try: E = a_ellipsoid if f is None: pass elif isscalar(E) and isscalar(f): E = a_f2Tuple(E, f) else: raise ValueError d = _ellipsoidal_datum(E, name=name) E = d.ellipsoid if E.a < EPS or E.f > EPS1: raise ValueError except (TypeError, ValueError) as x: t = unstr(self.classname, a=a_ellipsoid, f=f) raise EcefError(joined_(t, _ellipsoid_), txt=str(x)) self._datum = d self._E = E if name: self.name = name @property_RO def equatoradius(self): '''Get the I{equatorial} radius, semi-axis (C{meter}). ''' return self._E.a equatorialRadius = a = 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}, posiive for I{oblate}, negative for I{prolate} and C{0} for I{near-spherical}. ''' return self._E.f f = flattening def forward(self, latlonh, lon=None, height=0, M=False): # PYCHOK no cover '''(INTERNAL) I{Must be overloaded}. ''' notOverloaded(self, self.forward, latlonh, lon=lon, height=height, M=M) def _forward(self, latlonh, lon, height, M, You=False): '''(INTERNAL) Common C{EcefKarney}, C{EcefVeness}, C{EcefSudano} and C{EcefYou} forward. ''' lat, lon, h, name = _llhn4(latlonh, lon, height) sa, ca, sb, cb = sincos2d(lat, lon) E = self.ellipsoid n = E.roc1_(sa, ca) if You else E.roc1_(sa) z = (h + n * E.e12) * sa x = (h + n) * ca m = self._Matrix(sa, ca, sb, cb) if M else None r = Ecef9Tuple(x * cb, x * sb, z, lat, lon, h, 0, m, self.datum) return self._xnamed(r, name=name) 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): # PYCHOK no cover '''(INTERNAL) I{Must be overloaded}. ''' notOverloaded(self, self.reverse, xyz, y=y, z=z, M=M) def toStr(self, prec=9, **unused): # PYCHOK signature '''Return this C{Ecef*} as a string. @kwarg prec: Optional precision, number of decimal digits (0..9). @return: This C{Ecef*} representation (C{str}). ''' return self.attrs(_a_, _f_, _datum_, _ellipsoid_, _name_, prec=prec) class EcefKarney(_EcefBase): '''Conversion between geodetic and geocentric, aka I{Earth-Centered, Earth-Fixed} (ECEF) coordinates based on I{Karney}'s U{Geocentric <https://GeographicLib.SourceForge.io/html/classGeographicLib_1_1Geocentric.html>} methods. ''' _hmax = 0 # max height, 12M lightyears def __init__(self, a_ellipsoid, f=None, name=NN): '''New L{EcefKarney} converter. @arg a_ellipsoid: An ellipsoid (L{Ellipsoid}, L{Ellipsoid2}, L{Datum} or L{a_f2Tuple}) or C{scalar} for the equatorial radius of the ellipsoid (C{meter}). @kwarg f: C{None} or the ellipsoid flattening (C{scalar}), required for C{scalar} B{C{a_ellipsoid}}, B{C{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. ''' _EcefBase.__init__(self, a_ellipsoid, f, name) self._hmax = self.equatoradius / EPS_2 # self.equatoradius * _2_EPS def forward(self, latlonh, lon=None, height=0, M=False): '''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 in C{degrees}. @kwarg lon: Optional C{scalar} longitude in C{degrees} for C{scalar} B{C{latlonh}}. @kwarg height: Optional height in C{meter}, vertically above (or below) the surface of the ellipsoid. @kwarg M: Optionally, return the rotation L{EcefMatrix} (C{bool}). @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 L{EcefMatrix} C{M} 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: 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. ''' return _EcefBase._forward(self, latlonh, lon, height, M) @property_RO def hmax(self): '''Get the distance limit (C{float}). ''' return self._hmax def reverse(self, xyz, y=None, z=None, M=False): '''Convert from geocentric C{(x, y, z)} to geodetic C{(lat, lon, height)}. @arg xyz: Either an L{Ecef9Tuple}, an C{(x, y, z)} 3-tuple or C{scalar} ECEF C{x} coordinate in C{meter}. @kwarg y: ECEF C{y} coordinate in C{meter} for C{scalar} B{C{xyz}} and B{C{z}}. @kwarg z: ECEF C{z} coordinate in C{meter} for C{scalar} B{C{xyz}} and B{C{y}}. @kwarg M: Optionally, return the rotation L{EcefMatrix} (C{bool}). @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 L{EcefMatrix} C{M} and C{datum} if available. @raise EcefError: If B{C{xyz}} not L{Ecef9Tuple} 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}. ''' E = self.ellipsoid x, y, z, name = _xyzn4(xyz, y, z, Error=EcefError) sb, cb, R = _sch3(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 = _sch3(y * _0_5, x * _0_5) sa, ca, _ = _sch3(z * _0_5, R) C = 1 elif E.e4: # E.isEllipsoidal prolate = E.isProlate # 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.e12 * (z / E.a)**2 if prolate: 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 += copysign(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 prolate: k1 -= E.e2 else: k2 += E.e2 sa, ca, h = _sch3(z / k1, R / k2) h *= k1 - E.e12 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 prolate: p, q = q, p e = E.a else: e = E.b2_a sa, ca, h = _sch3(sqrt(q / E.e12), 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, _ = _sch3(z if h else _1_0, R) h -= E.a C = 4 r = Ecef9Tuple(x, y, z, atan2d(sa, ca), atan2d(sb, cb), h, C, self._Matrix(sa, ca, sb, cb) if M else None, self.datum) return self._xnamed(r, name=name) class EcefCartesian(_NamedBase): '''Conversion between geodetic C{(lat, lon, height)} and local cartesian C{(x, y, z)} coordinates with a local cartesian origin at C{(lat0, lon0, height0)}, transcribed from I{Karney}'s C++ class U{LocalCartesian <https://GeographicLib.SourceForge.io/html/classGeographicLib_1_1LocalCartesian.html>}. The C{z} axis is normal to the ellipsoid, the C{y} axis points due North. The plane C{z = -heighth0} is tangent to the ellipsoid. The conversions all take place via geocentric coordinates using a geocentric L{EcefKarney}, by default the WGS84 datum/ellipsoid. ''' _ecef = EcefKarney(Datums.WGS84) _t0 = None # forward(lat0, lon0, height0) L{Ecef9Tuple} def __init__(self, latlonh0=0, lon0=0, height0=0, ecef=None, name=NN): '''New L{EcefCartesian} converter. @kwarg latlonh0: Either a C{LatLon}, an L{Ecef9Tuple} or C{scalar} latitude in C{degrees} of the cartesian origin. @kwarg lon0: Optional C{scalar} longitude of the cartesian origin in C{degrees} for C{scalar} B{C{latlonh0}}. @kwarg height0: Optional height of the cartesian origin in C{meter}, vertically above (or below) the surface of the ellipsoid. @kwarg ecef: An ECEF converter (L{EcefKarney}). @kwarg name: Optional name (C{str}). @raise EcefError: If B{C{latlonh0}} not C{LatLon}, L{Ecef9Tuple} or C{scalar} or B{C{lon0}} not C{scalar} for C{scalar} B{C{latlonh0}} or C{abs(lat)} exceeds 90°. @raise TypeError: Invalid B{C{ecef}}, not L{EcefKarney}. ''' if ecef: _xinstanceof(EcefKarney, ecef=ecef) self._ecef = ecef self.reset(latlonh0, lon0, height0, name=name) @property_RO def ecef(self): '''Get the ECEF converter (L{EcefKarney}). ''' return self._ecef def forward(self, latlonh, lon=None, height=0, M=False): '''Convert from geodetic C{(lat, lon, height)} to local cartesian C{(x, y, z)}. @arg latlonh: Either a C{LatLon}, an L{Ecef9Tuple} or C{scalar} latitude in C{degrees}. @kwarg lon: Optional C{scalar} longitude in C{degrees} for C{scalar} B{C{latlonh}}. @kwarg height: Optional height in C{meter}, vertically above (or below) the surface of the ellipsoid. @kwarg M: Optionally, return the rotation L{EcefMatrix} (C{bool}). @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 L{EcefMatrix} C{M} 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°. @see: Note at method L{EcefKarney.forward}. ''' lat, lon, h, name = _llhn4(latlonh, lon, height) t = self.ecef.forward(lat, lon, h, M=M) x, y, z = self.M.rotate(t[:3], *self._t0[:3]) # .x, .y, .z m = self.M.multiply(t.M) if M else None r = Ecef9Tuple(x, y, z, t.lat, t.lon, t.height, 0, m, self.ecef.datum) return self._xnamed(r, name=name) @property_RO def height0(self): '''Get origin's height (C{meter}). ''' return self._t0.height @property_RO def lat0(self): '''Get origin's latitude (C{degrees}). ''' return self._t0.lat @property_RO def lon0(self): '''Get origin's longitude (C{degrees}). ''' return self._t0.lon @property_RO def M(self): '''Get the rotation matrix (C{EcefMatrix}). ''' return self._t0.M def reset(self, latlonh0=0, lon0=0, height0=0, name=NN): '''Reset the local cartesian origin. @kwarg latlonh0: Either a C{LatLon}, an L{Ecef9Tuple} or C{scalar} latitude in C{degrees} of the cartesian origin. @kwarg lon0: Optional, C{scalar} longitude of the cartesian origin in C{degrees} for C{scalar} B{C{latlonh0}}. @kwarg height0: Optional, height of the cartesian origin in C{meter}, vertically above (or below) the surface of the ellipsoid. @kwarg name: Optional, new name (C{str}). @raise EcefError: If B{C{latlonh0}} not C{LatLon}, L{Ecef9Tuple} or C{scalar} or B{C{lon0}} not C{scalar} for C{scalar} B{C{latlonh0}} or C{abs(lat)} exceeds 90°. ''' lat0, lon0, height0, n = _llhn4(latlonh0, lon0, height0, suffix=_0_) if name or n: self.ecef.name = self.name = name or n self._t0 = self.ecef.forward(lat0, lon0, height0, M=True) def reverse(self, xyz, y=None, z=None, M=False): '''Convert from local cartesian C{(x, y, z)} to geodetic C{(lat, lon, height)}. @arg xyz: Either an L{Ecef9Tuple}, an C{(x, y, z)} 3-tuple or C{scalar} local cartesian C{x} coordinate in C{meter}. @kwarg y: Local cartesian C{y} coordinate in C{meter} for C{scalar} B{C{xyz}} and B{C{z}}. @kwarg z: Local cartesian C{z} coordinate in C{meter} for C{scalar} B{C{xyz}} and B{C{y}}. @kwarg M: Optionally, return the rotation L{EcefMatrix} (C{bool}). @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 L{EcefMatrix} C{M} and C{datum} if available. @raise EcefError: If B{C{xyz}} not L{Ecef9Tuple} or C{scalar} C{x} or B{C{y}} and/or B{C{z}} not C{scalar} for C{scalar} B{C{xyz}}. @see: Note at method L{EcefKarney.reverse}. ''' xyz_n = _xyzn4(xyz, y, z, Error=EcefError) x, y, z = self.M.unrotate(xyz_n[:3], *self._t0[:3]) # .x, .y, .z t = self.ecef.reverse(x, y, z, M=M) m = self.M.multiply(t.M) if M else None r = Ecef9Tuple(x, y, z, t.lat, t.lon, t.height, t.C, m, self.ecef.datum) return self._xnamed(r, name=xyz_n[3]) def toStr(self, prec=9): # PYCHOK signature '''Return this L{EcefCartesian} as a string. @kwarg prec: Optional precision, number of decimal digits (0..9). @return: This L{EcefCartesian} representation (C{str}). ''' return self.attrs(_lat0_, _lon0_, 'height0', _M_, 'ecef', _name_, prec=prec) 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, *_m): '''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 _m: (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 _m: # all 9 matrix elements ... t += _m # ... from .multiply elif max(map(abs, t)) > 1: 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 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/html/LocalCartesian_8cpp_source.html> M = (fdot(self[r::3], *other[c::3]) for r in range(3) for c in range(3)) return EcefMatrix(*M) 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[0::3]), fdot(xyz, *self[1::3]), fdot(xyz, *self[2::3])) 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,) + 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[0:3]), fdot(_xyz, xyz0[1], *self[3:6]), fdot(_xyz, xyz0[2], *self[6:])) 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[0:3]), fdot(xyz, *self[3:6]), fdot(xyz, *self[6:])) return xyz_ class Ecef9Tuple(_NamedTuple): # .ecef.py '''9-Tuple C{(x, y, z, lat, lon, height, C, M, datum)} with geocentric coordinates C{x}, C{y} and C{z}, geodetic coordinates C{lat}, C{lon} and C{height}, case C{C} (see the C{Ecef*.reverse} methods) and optionally, the L{EcefMatrix} C{M} 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) def convertDatum(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: from pygeodesy.cartesianBase import CartesianBase c = CartesianBase(self, datum=self.datum) # 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 self._xnamed(r) @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 radians M{[-PI*3/2..+PI*3/2]} after U{Vermeille <https://Search.ProQuest.com/docview/639493848>} (2004), p 95. @see: U{Karney<https://GeographicLib.SourceForge.io/html/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>}, p 7. ''' x, y = self.x, self.y if y > 0: r = -_2_0 * atan2(x, hypot(y, x) + y) + PI_2 elif y < 0: r = _2_0 * atan2(x, hypot(y, x) - y) - PI_2 else: # y == 0 r = PI if x < 0 else _0_0 return r @property_RO def latlon(self): '''Get the lat-, longitude in C{degrees} (L{LatLon2Tuple}C{(lat, lon)}). ''' return self._xnamed(LatLon2Tuple(self.lat, self.lon)) @property_RO def latlonheight(self): '''Get the lat-, longitude in C{degrees} and height (L{LatLon3Tuple}C{(lat, lon, height)}). ''' return self._xnamed(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._xnamed(self.latlon.to3Tuple(self.height).to4Tuple(self.datum)) @property_RO def lonVermeille(self): '''Get the longitude in degrees M{[-225..+225]} after U{Vermeille <https://Search.ProQuest.com/docview/639493848>} (2004), p 95. @see: Property C{lamVermeille}. ''' return degrees(self.lamVermeille) @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 self._xnamed(PhiLam2Tuple(radians(self.lat), radians(self.lon))) @property_RO def philamheight(self): '''Get the lat-, longitude in C{radians} and height (L{PhiLam3Tuple}C{(phi, lam, height)}). ''' return self._xnamed(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._xnamed(self.philam.to3Tuple(self.height).to4Tuple(self.datum)) def toCartesian(self, Cartesian, **Cartesian_kwds): '''Return the geocentric C{(x, y, z)} coordinates as an ellipsoidal or spherical C{Cartesian}. @arg Cartesian: L{ellipsoidalKarney.Cartesian}, L{ellipsoidalNvector.Cartesian}, L{ellipsoidalVincenty.Cartesian}, L{sphericalNvector.Cartesian} or L{sphericalTrigonometry.Cartesian} class to return the C{(x, y, z)} coordinates. @kwarg Cartesian_kwds: Optional B{C{Cartesian}} keyword arguments. @return: A B{C{Cartesian}}C{(x, y, z)} instance. @raise TypeError: Invalid B{C{Cartesian}} or B{C{Cartesian_kwds}}. ''' from pygeodesy.cartesianBase import CartesianBase _xsubclassof(CartesianBase, Cartesian=Cartesian) r = Cartesian(self, **Cartesian_kwds) return self._xnamed(r) def toLatLon(self, LatLon=None, **LatLon_height_datum_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_height_datum_kwds: Optional B{C{height}}, B{C{datum}} and other B{C{LatLon}} keyword arguments. @return: An instance of C{LatLon}C{(lat, lon, **_height_datum_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-/available. @raise TypeError: Invalid B{C{LatLon}} or B{C{LatLon_height_datum_kwds}}. ''' kwds = _xkwds(LatLon_height_datum_kwds, height=self.height, datum=self.datum) # PYCHOK Ecef9Tuple d = kwds[_datum_] if LatLon is None: r = LatLon3Tuple(self.lat, self.lon, kwds[_height_]) # PYCHOK Ecef9Tuple if d: r = r.to4Tuple(d) # checks type(d) else: if d is None: # remove datum _ = kwds.pop[_datum_] r = LatLon(self.lat, self.lon, **kwds) # PYCHOK Ecef9Tuple _datum_datum(getattr(r, _datum_, self.datum), self.datum) # PYCHOK Ecef9Tuple return self._xnamed(r) 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}=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 self._xnamed(Vector3Tuple(self.x, self.y, self.z)) @property_RO def xyzh(self): '''Get the geocentric C{(x, y, z)} coordinates and height (L{Vector4Tuple}C{(x, y, z, h)}) ''' return self._xnamed(self.xyz.to4Tuple(self.height)) class EcefVeness(_EcefBase): '''Conversion between geodetic and geocentric, aka I{Earth-Centered, Earth-Fixed} (ECEF) coordinates transcribed from I{Chris Veness}' JavaScript classes U{LatLonEllipsoidal, Cartesian <https://www.Movable-Type.co.UK/scripts/geodesy/docs/latlon-ellipsoidal.js.html>}. @see: U{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 __init__(self, a_ellipsoid, f=None, name=NN): '''New L{EcefVeness}/L{EcefSudano} converter. @arg a_ellipsoid: An ellipsoid (L{Ellipsoid}, L{Ellipsoid2}, L{Datum} or L{a_f2Tuple}) or C{scalar} for the equatorial radius of the ellipsoid (C{meter}). @kwarg f: C{None} or the ellipsoid flattening (C{scalar}), required for C{scalar} B{C{a_ellipsoid}}, B{C{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. ''' _EcefBase.__init__(self, a_ellipsoid, f, name) def forward(self, latlonh, lon=None, height=0, M=False): '''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 in C{degrees}. @kwarg lon: Optional C{scalar} longitude in C{degrees} for C{scalar} B{C{latlonh}}. @kwarg height: Optional height in C{meter}, vertically above (or below) the surface of the ellipsoid. @kwarg M: Optionally, return the rotation L{EcefMatrix} (C{bool}). @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, L{EcefMatrix} C{M} 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°. ''' return _EcefBase._forward(self, latlonh, lon, height, M) def reverse(self, xyz, y=None, z=None, **no_M): # PYCHOK unused M '''Convert from geocentric C{(x, y, z)} to geodetic C{(lat, lon, height)} transcribed 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{'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: Either an L{Ecef9Tuple}, an C{(x, y, z)} 3-tuple or C{scalar} ECEF C{x} coordinate in C{meter}. @kwarg y: ECEF C{y} coordinate in C{meter} for C{scalar} B{C{xyz}} and B{C{z}}. @kwarg z: ECEF C{z} coordinate in C{meter} for C{scalar} B{C{xyz}} and B{C{y}}. @kwarg no_M: Rotation matrix C{M} not available. @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}, L{EcefMatrix} C{M} always C{None} and C{datum} if available. @raise EcefError: If B{C{xyz}} not L{Ecef9Tuple} or C{scalar} C{x} or B{C{y}} and/or B{C{z}} not C{scalar} for C{scalar} B{C{xyz}}. @see: Ralph M. Toms U{'An Efficient Algorithm for Geocentric to Geodetic Coordinate Conversion'<https://www.OSTI.gov/scitech/biblio/110235>}, Sept 1995 and U{'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 John J. Sudano U{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, Error=EcefError) E = self.ellipsoid p = hypot(x, y) # distance from minor axis r = hypot(p, z) # polar radius if min(p, r) > EPS: # 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, copysign(_90_0, z), _0_0, abs(z) - E.b r = Ecef9Tuple(x, y, z, lat, lon, h, C, None, self.datum) return self._xnamed(r, name=name) class EcefSudano(EcefVeness): '''Conversion between geodetic and geocentric, aka 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>}. ''' if _FOR_DOCS: __init__ = EcefVeness.__init__ forward = EcefVeness.forward def reverse(self, xyz, y=None, z=None, **no_M): # 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: Either an L{Ecef9Tuple}, an C{(x, y, z)} 3-tuple or C{scalar} ECEF C{x} coordinate in C{meter}. @kwarg y: ECEF C{y} coordinate in C{meter} for C{scalar} B{C{xyz}} and B{C{z}}. @kwarg z: ECEF C{z} coordinate in C{meter} for C{scalar} B{C{xyz}} and B{C{y}}. @kwarg no_M: Rotation matrix C{M} not available. @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}, L{EcefMatrix} C{M} always C{None} and C{datum} if available. @raise EcefError: If B{C{xyz}} not L{Ecef9Tuple} 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, Error=EcefError) E = self.ellipsoid e = E.e2 * E.a h = hypot(x, y) # Rh d = e - h a = atan2(z, h * E.e12) 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) S = Fsum(sa) 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) t = e / E.e2s2(sa) - h / ca2 if abs(t) < EPS_2: break a = None sa, t = S.fsum2_(-(z * ca + d * sa) / t) if abs(t) < EPS: break else: raise EcefError(unstr(self.reverse.__name__, x=x, y=y, z=z), txt=_no_convergence_) if a is None: a = copysign(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.e12) * sa / ca) / (ca + sa) r = Ecef9Tuple(x, y, z, degrees90(a), atan2d(y, x), h, C, None, self.datum) r._iteration = C return self._xnamed(r, name=name) class EcefYou(_EcefBase): '''Conversion between geodetic and geocentric, aka I{Earth-Centered, Earth-Fixed} (ECEF) coordinates using I{Rey-Jer You}'s U{transformations <https://www.ResearchGate.net/publication/240359424>}. @see: W.E. Featherstone, S.J. (Sten) Claessens U{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, 1-18 and U{PyMap3D <https://PyPI.org/project/pymap3d>}. ''' def __init__(self, a_ellipsoid, f=None, name=NN): '''New L{EcefYou} converter. @arg a_ellipsoid: An ellipsoid (L{Ellipsoid}, L{Ellipsoid2}, L{Datum} or L{a_f2Tuple}) or C{scalar} for the equatorial radius of the ellipsoid (C{meter}). @kwarg f: C{None} or the ellipsoid flattening (C{scalar}), required for C{scalar} B{C{a_ellipsoid}}, B{C{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 or if ellipsoid is prolate. ''' _EcefBase.__init__(self, a_ellipsoid, f, name) E = self.ellipsoid if (E.a2 - E.b2) < 0: raise EcefError(ellipsoid=E, txt=_prolate_) def forward(self, latlonh, lon=None, height=0, M=False): '''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 in C{degrees}. @kwarg lon: Optional C{scalar} longitude in C{degrees} for C{scalar} B{C{latlonh}}. @kwarg height: Optional height in C{meter}, vertically above (or below) the surface of the ellipsoid. @kwarg M: Optionally, return the rotation L{EcefMatrix} (C{bool}). @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, L{EcefMatrix} C{M} 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°. ''' return _EcefBase._forward(self, latlonh, lon, height, M, You=True) def reverse(self, xyz, y=None, z=None, **no_M): # PYCHOK unused M '''Convert from geocentric C{(x, y, z)} to geodetic C{(lat, lon, height)} using I{Rey-Jer You}'s transformation. @arg xyz: Either an L{Ecef9Tuple}, an C{(x, y, z)} 3-tuple or C{scalar} ECEF C{x} coordinate in C{meter}. @kwarg y: ECEF C{y} coordinate in C{meter} for C{scalar} B{C{xyz}} and B{C{z}}. @kwarg z: ECEF C{z} coordinate in C{meter} for C{scalar} B{C{xyz}} and B{C{y}}. @kwarg no_M: Rotation matrix C{M} not available. @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, L{EcefMatrix} C{M} always C{None} and C{datum} if available. @raise EcefError: If B{C{xyz}} not L{Ecef9Tuple} 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, Error=EcefError) r2 = hypot2_(x, y, z) E = self.ellipsoid e2 = E.a2 - E.b2 if e2 < 0: raise EcefError(ellipsoid=E, txt=_prolate_) e = sqrt(e2) u = fsum_(r2, -e2, hypot(r2 - e2, 2 * e * z)) if u < 0: raise EcefError(x=x, y=y, z=z, txt=_singular_) u = sqrt(u * _0_5) p = hypot(u, e) q = hypot(x, y) 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 abs(d) > EPS: B += fsum_(u * E.b, -p, e2) / d sB, cB = sincos2(B) 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 r = Ecef9Tuple(x, y, z, atan2d(E.a * sB, E.b * cB), # atan(E.a_b * tan(B)) atan2d(y, x), h, 1, # C=1 None, # M=None self.datum) return self._xnamed(r, name=name) __all__ += _ALL_DOCS(_EcefBase) # **) MIT License # # Copyright (C) 2016-2020 -- 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.