# Coverage for pygeodesy/cartesianBase.py : 92%

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After I{(C) Chris Veness 2011-2015} published under the same MIT Licence**, see U{https://www.Movable-Type.co.UK/scripts/latlong.html}, U{https://www.Movable-Type.co.UK/scripts/latlong-vectors.html} and U{https://www.Movable-Type.co.UK/scripts/geodesy/docs/latlon-ellipsoidal.js.html}.. ''' from pygeodesy.basics import isnear0, _xinstanceof from pygeodesy.datums import Datum, _spherical_datum, _WGS84 from pygeodesy.errors import _datum_datum, _IsnotError, \ _ValueError, _xkwds from pygeodesy.fmath import cbrt, Fmt, fsum_, hypot_, hypot2 # hypot from pygeodesy.interns import EPS0, NN, _COMMASPACE_, _height_, _not_, \ _1_0, _N_1_0, _2_0, _4_0, _6_0 from pygeodesy.interns import _ellipsoidal_, _spherical_ # PYCHOK used! from pygeodesy.lazily import _ALL_DOCS # from pygeodesy.named import _xnamed # from .vector3d from pygeodesy.namedTuples import Height, LatLon4Tuple, Vector4Tuple from pygeodesy.props import deprecated_method, Property, \ Property_RO, property_doc_ # from pygeodesy.streprs import Fmt # from .fmath # from pygeodesy.units import Height # from .namedTuples from pygeodesy.vector3d import Vector3d, _xnamed, _xyzhdn6 from math import sqrt __all__ = () __version__ = '21.10.08' class CartesianBase(Vector3d): '''(INTERNAL) Base class for ellipsoidal and spherical C{Cartesian}. ''' _datum = None # L{Datum}, to be overriden _height = None # height (L{Height}), set or approximated def __init__(self, x_xyz, y=None, z=None, datum=None, ll=None, name=NN): '''New C{Cartesian...}. @arg x_xyz: Cartesian X coordinate (C{scalar}) or a C{Cartesian}, L{Ecef9Tuple}, L{Vector3Tuple} or L{Vector4Tuple}. @kwarg y: Cartesian Y coordinate (C{scalar}), ignored if B{C{x_xyz}} is not C{scalar}, otherwise same units as B{C{x_xyz}}. @kwarg z: Cartesian Z coordinate (C{scalar}), ignored if B{C{x_xyz}} is not C{scalar}, otherwise same units as B{C{x_xyz}}. @kwarg datum: Optional datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}). @kwarg ll: Optional, original latlon (C{LatLon}). @kwarg name: Optional name (C{str}). @raise TypeError: Non-scalar B{C{x_xyz}}, B{C{y}} or B{C{z}} coordinate or B{C{x_xyz}} not an L{Ecef9Tuple}, L{Vector3Tuple} or L{Vector4Tuple}. ''' x, y, z, h, d, n = _xyzhdn6(x_xyz, y, z, None, datum, ll) Vector3d.__init__(self, x, y, z, ll=ll, name=name or n) if h is not None: self._height = Height(h) if d is not None: self.datum = d def _applyHelmert(self, transform, inverse=False, datum=None): '''(INTERNAL) Return a new cartesian by applying a Helmert transform to this cartesian. @arg transform: Transform to apply (L{Transform}). @kwarg inverse: Apply the inverse of the Helmert transform (C{bool}). @kwarg datum: Datum for the transformed point (L{Datum}), overriding this point's datum. @return: The transformed point (C{Cartesian}). @raise Valuerror: If C{B{inverse}=True} and B{C{datum}} is not L{Datums}C{.WGS84}. ''' d = datum or self.datum if inverse and d != _WGS84: raise _ValueError(inverse=inverse, datum=d, txt=_not_(_WGS84.name)) xyz = transform.transform(*self.xyz, inverse=inverse) return self.classof(xyz, datum=d) @property_doc_(''' this cartesian's datum (L{Datum}).''') def datum(self): '''Get this cartesian's datum (L{Datum}). ''' return self._datum @datum.setter # PYCHOK setter! def datum(self, datum): '''Set this cartesian's C{datum} I{without conversion}. @arg datum: New datum (L{Datum}), ellipsoidal or spherical. @raise TypeError: The B{C{datum}} is not a L{Datum}. ''' datum = _spherical_datum(datum, name=self.name) d = self.datum if d is not None: if d.isEllipsoidal and not datum.isEllipsoidal: raise _IsnotError(_ellipsoidal_, datum=datum) elif d.isSpherical and not datum.isSpherical: raise _IsnotError(_spherical_, datum=datum) self._update(datum != d) self._datum = datum def destinationXyz(self, delta, Cartesian=None, **Cartesian_kwds): '''Calculate the destination using a I{local} delta from this cartesian. @arg delta: Local delta to the destination (L{XyzLocal}, L{Enu}, L{Ned} or L{Local9Tuple}). @kwarg Cartesian: Optional (geocentric) class to return the destination or C{None}. @kwarg Cartesian_kwds: Optional, additional B{C{Cartesian}} keyword arguments, ignored if C{B{Cartesian} is None}. @return: Destination as a C{B{Cartesian}(x, y, z, **B{Cartesian_kwds})} instance or if C{B{Cartesian} is None}, an L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with C{M=None} always. @raise TypeError: Invalid B{C{delta}}, B{C{Cartesian}} or B{C{Cartesian_kwds}}. ''' if Cartesian is None: r = self._ltp._local2ecef(delta, nine=True) else: r = self._ltp._local2ecef(delta, nine=False) r = Cartesian(*r, **_xkwds(Cartesian_kwds, datum=self.datum)) return _xnamed(r, self.name) @Property_RO def Ecef(self): '''Get the ECEF I{class} (L{EcefKarney}), I{lazily}. ''' from pygeodesy.ecef import EcefKarney return EcefKarney # default @Property_RO def _ecef9(self): '''(INTERNAL) Helper for L{toEcef}, L{toLocal} and L{toLtp} (L{Ecef9Tuple}). ''' return self.Ecef(self.datum, name=self.name).reverse(self, M=True) def hartzell(self, los=None): '''Compute the intersection of a Line-Of-Sight from this certesian Point-Of-View (pov) with this C{datum}'s ellipsoid surface. @kwarg los: Line-Of-Sight, I{direction} to earth (L{Vector3d}) or C{None} to point to the ellipsoid's center. @return: The ellipsoid intersection (C{Cartesian}). @raise IntersectionError: Null C{pov} or B{C{los}} vector, this C{pov} is inside the ellipsoid or B{C{los}} points outside the ellipsoid or in an opposite direction. @raise TypeError: Invalid B{C{los}} or no B{C{datum}}. @see: Function C{hartzell} for further details. ''' from pygeodesy.formy import hartzell return hartzell(self, los=los, earth=self.datum) @Property def height(self): '''Get the height (C{meter}). ''' return self._height4.h if self._height is None else self._height @height.setter # PYCHOK setter! def height(self, height): '''Set the height. @arg height: New height (C{meter}). @raise TypeError: Invalid B{C{height}} C{type}. @raise ValueError: Invalid B{C{height}}. ''' h = Height(height) self._update(h != self.height) self._height = h @Property_RO def _height4(self): '''(INTERNAL) Get this C{height4}-tuple. ''' try: r = self.datum.ellipsoid.height4(self, normal=True) except (AttributeError, ValueError): # no datum, null cartesian, r = Vector4Tuple(self.x, self.y, self.z, 0, name=self.height4.__name__) return r def height4(self, earth=None, normal=True, Cartesian=None, **Cartesian_kwds): '''Compute the height of this cartesian above or below and the projection on this datum's ellipsoid surface. @kwarg earth: A datum, ellipsoid or earth radius I{overriding} this datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2}, L{a_f2Tuple} or C{meter}, conventionally). @kwarg normal: If C{True} the projection is the nearest point on the ellipsoid's surface, otherwise the intersection of the radial line to the center and the ellipsoid's surface. @kwarg Cartesian: Optional class to return the height and projection (C{Cartesian}) or C{None}. @kwarg Cartesian_kwds: Optional, additional B{C{Cartesian}} keyword arguments, ignored if C{B{Cartesian} is None}. @note: Use keyword argument C{height=0} to override C{B{Cartesian}.height} to {0} or any other C{scalar}, conventionally in C{meter}. @return: An instance of B{C{Cartesian}} or if C{B{Cartesian} is None}, a L{Vector4Tuple}C{(x, y, z, h)} with the I{projection} C{x}, C{y} and C{z} coordinates and height C{h} in C{meter}, conventionally. @raise TypeError: Invalid B{C{earth}}. @see: L{Ellipsoid.height4} for more information. ''' r = self._height4 if normal and earth in (None, self.datum) else \ _spherical_datum(earth).ellipsoid.height4(self, normal=normal) if Cartesian is not None: kwds = Cartesian_kwds.copy() h = kwds.pop(_height_, None) r = Cartesian(r, **kwds) if h is not None: r.height = Height(height=h) return r @Property_RO def isEllipsoidal(self): '''Check whether this cartesian is ellipsoidal (C{bool} or C{None} if unknown). ''' return self.datum.isEllipsoidal if self._datum else None @Property_RO def isSpherical(self): '''Check whether this cartesian is spherical (C{bool} or C{None} if unknown). ''' return self.datum.isSpherical if self._datum else None @Property_RO def latlon(self): '''Get this cartesian's (geodetic) lat- and longitude in C{degrees} (L{LatLon2Tuple}C{(lat, lon)}). ''' return self.toEcef().latlon @Property_RO def latlonheight(self): '''Get this cartesian's (geodetic) lat-, longitude in C{degrees} with height (L{LatLon3Tuple}C{(lat, lon, height)}). ''' return self.toEcef().latlonheight @Property_RO def latlonheightdatum(self): '''Get this cartesian's (geodetic) lat-, longitude in C{degrees} with height and datum (L{LatLon4Tuple}C{(lat, lon, height, datum)}). ''' return self.toEcef().latlonheightdatum @Property_RO def _ltp(self): '''(INTERNAL) Cache for L{toLtp}. ''' from pygeodesy.ltp import Ltp return Ltp(self._ecef9, ecef=self.Ecef(self.datum), name=self.name) @Property_RO def _N_vector(self): '''(INTERNAL) Get the (C{nvectorBase._N_vector_}). ''' from pygeodesy.nvectorBase import _N_vector_ x, y, z, h = self._n_xyzh4(self.datum) return _N_vector_(x, y, z, h=h, name=self.name) def _n_xyzh4(self, datum): '''(INTERNAL) Get the n-vector components as L{Vector4Tuple}. ''' _xinstanceof(Datum, datum=datum) # <https://www.Movable-Type.co.UK/scripts/geodesy/docs/ # latlon-nvector-ellipsoidal.js.html#line309>, # <https://GitHub.com/pbrod/nvector>/src/nvector/core.py> # _equation23 and <https://www.NavLab.net/nvector> E = datum.ellipsoid x, y, z = self.xyz # Kenneth Gade eqn 23 p = hypot2(x, y) * E.a2_ q = (z**2 * E.e12) * E.a2_ r = fsum_(p, q, -E.e4) / _6_0 s = (p * q * E.e4) / (_4_0 * r**3) t = cbrt(fsum_(_1_0, s, sqrt(s * (_2_0 + s)))) if isnear0(t): raise _ValueError(origin=self, txt=Fmt.EPS0(t)) u = r * fsum_(_1_0, t, _1_0 / t) v = sqrt(u**2 + E.e4 * q) t = v * _2_0 if t < EPS0: # isnear0 raise _ValueError(origin=self, txt=Fmt.EPS0(t)) w = E.e2 * fsum_(u, v, -q) / t k = sqrt(fsum_(u, v, w**2)) - w if isnear0(k): raise _ValueError(origin=self, txt=Fmt.EPS0(k)) t = k + E.e2 if isnear0(t): raise _ValueError(origin=self, txt=Fmt.EPS0(t)) e = k / t # d = e * hypot(x, y) # tmp = 1 / hypot(d, z) == 1 / hypot(e * hypot(x, y), z) t = hypot_(x * e, y * e, z) # == 1 / tmp if t < EPS0: # isnear0 raise _ValueError(origin=self, txt=Fmt.EPS0(t)) h = fsum_(k, E.e2, _N_1_0) / k * t s = e / t # == e * tmp return Vector4Tuple(x * s, y * s, z / t, h, name=self.name) @Property_RO def philam(self): '''Get this cartesian's (geodetic) lat- and longitude in C{radians} (L{PhiLam2Tuple}C{(phi, lam)}). ''' return self.toEcef().philam @Property_RO def philamheight(self): '''Get this cartesian's (geodetic) lat-, longitude in C{radians} with height (L{PhiLam3Tuple}C{(phi, lam, height)}). ''' return self.toEcef().philamheight @Property_RO def philamheightdatum(self): '''Get this cartesian's (geodetic) lat-, longitude in C{radians} with height and datum (L{PhiLam4Tuple}C{(phi, lam, height, datum)}). ''' return self.toEcef().philamheightdatum @deprecated_method def to3llh(self, datum=None): # PYCHOK no cover '''DEPRECATED, use property L{latlonheightdatum} or L{latlonheight}. @return: A L{LatLon4Tuple}C{(lat, lon, height, datum)}. @note: This method returns a B{C{-4Tuple}} I{and not a} C{-3Tuple} as its name may suggest. ''' t = self.toLatLon(datum=datum, LatLon=None) return LatLon4Tuple(t.lat, t.lon, t.height, t.datum, name=self.name) # def _to3LLh(self, datum, LL, **pairs): # OBSOLETE # '''(INTERNAL) Helper for C{subclass.toLatLon} and C{.to3llh}. # ''' # r = self.to3llh(datum) # LatLon3Tuple # if LL is not None: # r = LL(r.lat, r.lon, height=r.height, datum=datum, name=self.name) # for n, v in pairs.items(): # setattr(r, n, v) # return r def toDatum(self, datum2, datum=None): '''Convert this cartesian from one datum to an other. @arg datum2: Datum to convert I{to} (L{Datum}). @kwarg datum: Datum to convert I{from} (L{Datum}). @return: The converted point (C{Cartesian}). @raise TypeError: B{C{datum2}} or B{C{datum}} invalid. ''' _xinstanceof(Datum, datum2=datum2) c = self if datum in (None, self.datum) else \ self.toDatum(datum) i, d = False, c.datum if d == datum2: return c.copy() if c is self else c elif d == _WGS84: d = datum2 # convert from WGS84 to datum2 elif datum2 == _WGS84: i = True # convert to WGS84 by inverse transformation else: # neither datum2 nor c.datum is WGS84, invert to WGS84 first c = c._applyHelmert(d.transform, inverse=True, datum=_WGS84) d = datum2 return c._applyHelmert(d.transform, inverse=i, datum=datum2) convertDatum = toDatum # for backward compatibility def toEcef(self): '''Convert this cartesian to I{geodetic} (lat-/longitude) coordinates. @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with C{C} and C{M} if available. @raise EcefError: A C{.datum} or an ECEF issue. ''' return self._ecef9 def toLatLon(self, datum=None, height=None, LatLon=None, **LatLon_kwds): # see .ecef.Ecef9Tuple.toDatum '''Convert this cartesian to a geodetic (lat-/longitude) point. @kwarg datum: Optional datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}). @kwarg height: Optional height, overriding the converted height (C{meter}), iff B{C{LatLon}} is not C{None}. @kwarg LatLon: Optional class to return the geodetic point (C{LatLon}) or C{None}. @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments, ignored if C{B{LatLon} is None}. @return: The geodetic point (B{C{LatLon}}) or if B{C{LatLon}} is C{None}, an L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with C{C} and C{M} if available. @raise TypeError: Invalid B{C{datum}} or B{C{LatLon_kwds}}. ''' d = _spherical_datum(datum or self.datum, name=self.name) if d == self.datum: r = self.toEcef() else: c = self.toDatum(d) r = c.Ecef(d, name=self.name).reverse(c, M=LatLon is None) if LatLon: # class or .classof h = r.height if height is None else Height(height) r = LatLon(r.lat, r.lon, datum=r.datum, height=h, **_xkwds(LatLon_kwds, name=r.name)) _datum_datum(r.datum, d) return r def toLocal(self, Xyz=None, ltp=None, **Xyz_kwds): '''Convert this I{geocentric} cartesian to I{local} C{X}, C{Y} and C{Z}. @kwarg Xyz: Optional class to return C{X}, C{Y} and C{Z} (L{XyzLocal}, L{Enu}, L{Ned}) or C{None}. @kwarg ltp: The I{local tangent plane} (LTP) to use, overriding this cartesian's LTP (L{Ltp}). @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}}. ''' p = self._ltp if ltp is None else self._xLtp(ltp) return p._ecef2local(self._ecef9, Xyz, Xyz_kwds) def toLtp(self, Ecef=None): '''Return the I{local tangent plane} (LTP) for this cartesian. @kwarg Ecef: Optional ECEF I{class} (L{EcefKarney}, ... L{EcefYou}), overriding this cartesian's C{Ecef}. ''' if Ecef in (None, self.Ecef): r = self._ltp else: from pygeodesy.ltp import Ltp r = Ltp(self._ecef9, ecef=Ecef(self.datum), name=self.name) return r def toNvector(self, Nvector=None, datum=None, **Nvector_kwds): '''Convert this cartesian to C{n-vector} components. @kwarg Nvector: Optional class to return the C{n-vector} components (C{Nvector}) or C{None}. @kwarg datum: Optional datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}) overriding this cartesian's datum. @kwarg Nvector_kwds: Optional, additional B{C{Nvector}} keyword arguments, ignored if C{B{Nvector} is None}. @return: The C{unit, n-vector} components (B{C{Nvector}}) or a L{Vector4Tuple}C{(x, y, z, h)} if B{C{Nvector}} is C{None}. @raise TypeError: Invalid B{C{datum}}. @raise ValueError: The B{C{Cartesian}} at origin. @example: >>> c = Cartesian(3980581, 97, 4966825) >>> n = c.toNvector() # (x=0.622818, y=0.00002, z=0.782367, h=0.242887) ''' d = _spherical_datum(datum or self.datum, name=self.name) r = self._N_vector.xyzh if d == self.datum else self._n_xyzh4(d) if Nvector is not None: kwds = _xkwds(Nvector_kwds, h=r.h, datum=d) r = self._xnamed(Nvector(r.x, r.y, r.z, **kwds)) return r def toStr(self, prec=3, fmt=Fmt.SQUARE, sep=_COMMASPACE_): # PYCHOK expected '''Return the string representation of this cartesian. @kwarg prec: Optional number of decimals, unstripped (C{int}). @kwarg fmt: Optional enclosing backets format (string). @kwarg sep: Optional separator to join (string). @return: Cartesian represented as "[x, y, z]" (string). ''' return Vector3d.toStr(self, prec=prec, fmt=fmt, sep=sep) def toVector(self, Vector=None, **Vector_kwds): '''Return this cartesian's components as vector. @kwarg Vector: Optional class to return the C{n-vector} components (L{Vector3d}) or C{None}. @kwarg Vector_kwds: Optional, additional B{C{Vector}} keyword arguments, ignored if C{B{Vector} is None}. @return: A B{C{Vector}} or an L{Vector3Tuple}C{(x, y, z)} if B{C{Vector}} is C{None}. @raise TypeError: Invalid B{C{Vector}} or B{C{Vector_kwds}}. ''' return self.xyz if Vector is None else self._xnamed( Vector(self.x, self.y, self.z, **Vector_kwds)) @Property_RO def _xLtp(self): '''(INTERNAL) Import and cache function C{ltp._xLtp}. ''' from pygeodesy.ltp import _xLtp return _xLtp __all__ += _ALL_DOCS(CartesianBase) # **) MIT License # # Copyright (C) 2016-2021 -- 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.