# Coverage for pygeodesy/nvectorBase.py : 97%

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Classes L{LatLonNvectorBase} for C{n-vectorial} ellipsoidal and spherical C{LatLon}s, class L{NvectorBase} for C{Cartesian}s and function L{sumOf}. Pure Python implementation of C{n-vector}-based geodesy tools for ellipsoidal earth models, transcoded from JavaScript originals by I{(C) Chris Veness 2005-2016} and published under the same MIT Licence**, see U{Vector-based geodesy <https://www.Movable-Type.co.UK/scripts/latlong-vectors.html>}. ''' from pygeodesy.basics import len2, map1 from pygeodesy.datums import _spherical_datum from pygeodesy.errors import IntersectionError, _ValueError, VectorError, \ _xkwds, _xkwds_pop from pygeodesy.fmath import fidw, fsum, fsum_, hypot_ from pygeodesy.formy import n_xyz2latlon, n_xyz2philam from pygeodesy.interns import EPS, EPS1, EPS_2, MISSING, NN, R_M, \ _bearing_, _coincident_, _COMMASPACE_, \ _distance_, _intersection_, _no_, _NorthPole_, \ _points_, _pole_, _SPACE_, _SouthPole_, \ _1_, _2_, _3_, _2_0 from pygeodesy.latlonBase import LatLonBase from pygeodesy.lazily import _ALL_DOCS from pygeodesy.named import notImplemented, _xother3 from pygeodesy.namedTuples import Trilaterate5Tuple, Vector3Tuple, \ Vector4Tuple from pygeodesy.props import deprecated_method, property_doc_, Property_RO from pygeodesy.streprs import Fmt, hstr, unstr, _xattrs from pygeodesy.units import Bearing, Height, Radius_, Scalar from pygeodesy.utily import sincos2d from pygeodesy.vector3d import Vector3d, sumOf as _sumOf, _xyzhdn6 from math import fabs, sqrt # atan2, cos, sin __all__ = (_NorthPole_, _SouthPole_) # constants __version__ = '21.09.06' class NvectorBase(Vector3d): # XXX kept private '''Base class for ellipsoidal and spherical C{Nvector}s. ''' _datum = None # L{Datum}, overriden _h = 0 # height (C{meter}) _H = NN # height prefix (C{str}), '↑' in JS version def __init__(self, x, y=None, z=None, h=0, ll=None, datum=None, name=NN): '''New n-vector normal to the earth's surface. @arg x: An C{Nvector}, L{Vector3Tuple}, L{Vector4Tuple} or the C{X} coordinate (C{scalar}). @arg y: The C{Y} coordinate (C{scalar}) if B{C{x}} C{scalar}. @arg z: The C{Z} coordinate (C{scalar}) if B{C{x}} C{scalar}. @kwarg h: Optional height above surface (C{meter}). @kwarg ll: Optional, original latlon (C{LatLon}). @kwarg datum: Optional, I{pass-thru} datum (L{Datum}). @kwarg name: Optional name (C{str}). @raise TypeError: Non-scalar B{C{x}}, B{C{y}} or B{C{z}} coordinate or B{C{x}} not an C{Nvector}, L{Vector3Tuple} or L{Vector4Tuple} or invalid B{C{datum}}. @example: >>> from pygeodesy.sphericalNvector import Nvector >>> v = Nvector(0.5, 0.5, 0.7071, 1) >>> v.toLatLon() # 45.0°N, 045.0°E, +1.00m ''' x, y, z, h, d, n = _xyzhdn6(x, y, z, h, datum, ll) Vector3d.__init__(self, x, y, z, ll=ll, name=name or n) if h: self.h = h if d: self._datum = _spherical_datum(d, name=self.name) # pass-thru @Property_RO def datum(self): '''Get the I{pass-thru} datum (C{Datum}) or C{None}. ''' return self._datum @Property_RO def Ecef(self): '''Get the ECEF I{class} (L{EcefKarney}), I{lazily}. ''' from pygeodesy.ecef import EcefKarney return EcefKarney # default @property_doc_(''' the height above surface (C{meter}).''') def h(self): '''Get the height above surface (C{meter}). ''' return self._h @h.setter # PYCHOK setter! def h(self, h): '''Set the height above surface. @arg h: New height (C{meter}). @raise TypeError: If B{C{h}} invalid. @raise VectorError: If B{C{h}} invalid. ''' h = Height(h=h, Error=VectorError) self._update(h != self._h) self._h = h @property_doc_(''' the height prefix (C{str}).''') def H(self): '''Get the height prefix (C{str}). ''' return self._H @H.setter # PYCHOK setter! def H(self, H): '''Set the height prefix. @arg H: New height prefix (C{str}). ''' self._H = str(H) if H else NN def hStr(self, prec=-2, m=NN): '''Return a string for the height B{C{h}}. @kwarg prec: Optional number of decimals, unstripped (C{int}). @kwarg m: Optional unit of the height (C{str}). @see: Function L{hstr}. ''' return NN(self.H, hstr(self.h, prec=prec, m=m)) @Property_RO def isEllipsoidal(self): '''Check whether this n-vector 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 n-vector is spherical (C{bool} or C{None} if unknown). ''' return self.datum.isSpherical if self.datum else None @Property_RO def lam(self): '''Get the (geodetic) longitude in C{radians} (C{float}). ''' return self.philam.lam @Property_RO def lat(self): '''Get the (geodetic) latitude in C{degrees} (C{float}). ''' return self.latlon.lat @Property_RO def latlon(self): '''Get the (geodetic) lat-, longitude in C{degrees} (L{LatLon2Tuple}C{(lat, lon)}). ''' return n_xyz2latlon(self.x, self.y, self.z, name=self.name) @Property_RO def latlonheight(self): '''Get the (geodetic) lat-, longitude in C{degrees} and height (L{LatLon3Tuple}C{(lat, lon, height)}). ''' return self.latlon.to3Tuple(self.h) @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 lon(self): '''Get the (geodetic) longitude in C{degrees} (C{float}). ''' return self.latlon.lon @Property_RO def phi(self): '''Get the (geodetic) latitude in C{radians} (C{float}). ''' return self.philam.phi @Property_RO def philam(self): '''Get the (geodetic) lat-, longitude in C{radians} (L{PhiLam2Tuple}C{(phi, lam)}). ''' return n_xyz2philam(self.x, self.y, self.z, name=self.name) @Property_RO def philamheight(self): '''Get the (geodetic) lat-, longitude in C{radians} and height (L{PhiLam3Tuple}C{(phi, lam, height)}). ''' return self.philam.to3Tuple(self.h) @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) @deprecated_method def to2ab(self): # PYCHOK no cover '''DEPRECATED, use property L{philam}. @return: A L{PhiLam2Tuple}C{(phi, lam)}. ''' return self.philam @deprecated_method def to3abh(self, height=None): # PYCHOK no cover '''DEPRECATED, use method L{philamheight} or C{philam.to3Tuple(B{height})}. @kwarg height: Optional height, overriding this n-vector's height (C{meter}). @return: A L{PhiLam3Tuple}C{(phi, lam, height)}. @raise ValueError: Invalid B{C{height}}. ''' return self.philamheight if height in (None, self.h) else \ self.philam.to3Tuple(height) def toCartesian(self, h=None, Cartesian=None, datum=None, **Cartesian_kwds): '''Convert this n-vector to C{Nvector}-based cartesian (ECEF) coordinates. @kwarg h: Optional height, overriding this n-vector's height (C{meter}). @kwarg Cartesian: Optional class to return the (ECEF) coordinates (C{Cartesian}). @kwarg datum: Optional datum (C{Datum}), overriding this datum. @kwarg Cartesian_kwds: Optional, additional B{C{Cartesian}} keyword arguments, ignored if C{B{Cartesian} is None}. @return: The cartesian (ECEF) coordinates (B{C{Cartesian}}) or if C{B{Cartesian} is 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{Cartesian}} or B{C{Cartesian_kwds}} argument. @raise ValueError: Invalid B{C{h}}. @example: >>> v = Nvector(0.5, 0.5, 0.7071) >>> c = v.toCartesian() # [3194434, 3194434, 4487327] >>> p = c.toLatLon() # 45.0°N, 45.0°E ''' d = _spherical_datum(datum or self.datum, name=self.name) E = d.ellipsoid h = self.h if h is None else Height(h=h) x, y, z = self.x, self.y, self.z # Kenneth Gade eqn 22 n = E.b / hypot_(x * E.a_b, y * E.a_b, z) r = h + n * E.a2_b2 x *= r y *= r z *= n + h if Cartesian is None: r = self.Ecef(d).reverse(x, y, z, M=True) else: kwds = _xkwds(Cartesian_kwds, datum=d) # h=0 r = Cartesian(x, y, z, **kwds) return self._xnamed(r) @deprecated_method def to2ll(self): # PYCHOK no cover '''DEPRECATED, use property L{latlon}. @return: A L{LatLon2Tuple}C{(lat, lon)}. ''' return self.latlon @deprecated_method def to3llh(self, height=None): # PYCHOK no cover '''DEPRECATED, use property C{latlonheight} or C{latlon.to3Tuple}C{)}B{C{height}}C{)}. @kwarg height: Optional height, overriding this n-vector's height (C{meter}). @return: A L{LatLon3Tuple}C{(lat, lon, height)}. @raise ValueError: Invalid B{C{height}}. ''' return self.latlonheight if height in (None, self.h) else \ self.latlon.to3Tuple(height) def toLatLon(self, height=None, LatLon=None, datum=None, **LatLon_kwds): '''Convert this n-vector to an C{Nvector}-based geodetic point. @kwarg height: Optional height, overriding this n-vector's height (C{meter}). @kwarg LatLon: Optional class to return the geodetic point (C{LatLon}) or C{None}. @kwarg datum: Optional, spherical datum (C{Datum}). @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments, ignored if C{B{LatLon} is None}. @return: The geodetic point (C{LatLon}) or if C{B{LatLon} is 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{LatLon}} or B{C{LatLon_kwds}} argument. @raise ValueError: Invalid B{C{height}}. @example: >>> v = Nvector(0.5, 0.5, 0.7071) >>> p = v.toLatLon() # 45.0°N, 45.0°E ''' d = _spherical_datum(datum or self.datum, name=self.name) h = self.h if height is None else Height(height) # use self.Cartesian(Cartesian=None) for better accuracy of the height # than self.Ecef(d).forward(self.lat, self.lon, height=h, M=True) if LatLon is None: r = self.toCartesian(h=h, Cartesian=None, datum=d) else: kwds = _xkwds(LatLon_kwds, height=h, datum=d) r = self._xnamed(LatLon(self.lat, self.lon, **kwds)) return r def toStr(self, prec=5, fmt=Fmt.PAREN, sep=_COMMASPACE_): # PYCHOK expected '''Return a string representation of this n-vector. Height component is only included if non-zero. @kwarg prec: Optional number of decimals, unstripped (C{int}). @kwarg fmt: Optional enclosing backets format (C{str}). @kwarg sep: Optional separator between components (C{str}). @return: Comma-separated C{"(x, y, z [, h])"} enclosed in B{C{fmt}} brackets (C{str}). @example: >>> Nvector(0.5, 0.5, 0.7071).toStr() # (0.5, 0.5, 0.7071) >>> Nvector(0.5, 0.5, 0.7071, 1).toStr(-3) # (0.500, 0.500, 0.707, +1.00) ''' t = Vector3d.toStr(self, prec=prec, fmt=NN, sep=sep) if self.h: t = sep.join((t, self.hStr())) return (fmt % (t,)) if fmt else t def toVector3d(self, norm=True): '''Convert this n-vector to a 3-D vector, I{ignoring the height}. @kwarg norm: Normalize the 3-D vector (C{bool}). @return: The (normalized) vector (L{Vector3d}). ''' v = Vector3d.unit(self) if norm else self return Vector3d(v.x, v.y, v.z, name=self.name) @deprecated_method def to4xyzh(self, h=None): # PYCHOK no cover '''DEPRECATED, use property L{xyzh} or C{xyz.to4Tuple(B{h})}. ''' return self.xyzh if h in (None, self.h) else Vector4Tuple( self.x, self.y, self.z, h, name=self.name) def unit(self, ll=None): '''Normalize this n-vector to unit length. @kwarg ll: Optional, original latlon (C{LatLon}). @return: Normalized vector (C{Nvector}). ''' return _xattrs(Vector3d.unit(self, ll=ll), '_h') @Property_RO def xyzh(self): '''Get this n-vector's components (L{Vector4Tuple}C{(x, y, z, h)}) ''' return self.xyz.to4Tuple(self.h) NorthPole = NvectorBase(0, 0, +1, name=_NorthPole_) # North pole (C{Nvector}) SouthPole = NvectorBase(0, 0, -1, name=_SouthPole_) # South pole (C{Nvector}) class _N_vector_(NvectorBase): '''(INTERNAL) Minimal, low-overhead C{n-vector}. ''' def __init__(self, x, y, z, h=0, name=NN): self._x, self._y, self._z = x, y, z if h: self._h = h if name: self.name = name class LatLonNvectorBase(LatLonBase): '''(INTERNAL) Base class for n-vector-based ellipsoidal and spherical C{LatLon} classes. ''' def _update(self, updated, *attrs, **kwds): # PYCHOK _Nv=None '''(INTERNAL) Zap cached attributes if updated. @see: C{ellipsoidalNvector.LatLon} and C{sphericalNvector.LatLon} for the special case of B{C{_Nv}}. ''' if updated: _Nv = _xkwds_pop(kwds, _Nv=None) if _Nv is not None: if _Nv._fromll is not None: _Nv._fromll = None self._Nv = None LatLonBase._update(self, updated, *attrs) # def distanceTo(self, other, **kwds): # PYCHOK no cover # '''(INTERNAL) I{Must be overloaded}, see function C{notOverloaded}. # ''' # from pygeodesy.named import notOverloaded # notOverloaded(self, other, **kwds) def intersections2(self, radius1, other, radius2, **kwds): # PYCHOK expected '''B{Not implemented}, throws a C{NotImplementedError} always. ''' notImplemented(self, radius1, other, radius2, **kwds) def others(self, *other, **name_other_up): '''Refined class comparison. @arg other: The other instance (C{LatLonNvectorBase}). @kwarg name_other_up: Overriding C{name=other} and C{up=1} keyword arguments. @return: The B{C{other}} if compatible. @raise TypeError: Incompatible B{C{other}} C{type}. ''' if other: other0 = other[0] if isinstance(other0, (self.__class__, LatLonNvectorBase)): # XXX NvectorBase? return other0 other, name, up = _xother3(self, other, **name_other_up) if not isinstance(other, (self.__class__, LatLonNvectorBase)): # XXX NvectorBase? LatLonBase.others(self, other, name=name, up=up + 1) return other def toNvector(self, Nvector=NvectorBase, **Nvector_kwds): # PYCHOK signature '''Convert this point to C{Nvector} components, I{including height}. @kwarg Nvector_kwds: Optional, additional B{C{Nvector}} keyword arguments, ignored if C{B{Nvector} is None}. @return: An B{C{Nvector}} or a L{Vector4Tuple}C{(x, y, z, h)} if B{C{Nvector}} is C{None}. @raise TypeError: Invalid B{C{Nvector}} or B{C{Nvector_kwds}} argument. ''' return LatLonBase.toNvector(self, Nvector=Nvector, **Nvector_kwds) def triangulate(self, bearing1, other, bearing2, height=None): '''Locate a point given this and an other point and a bearing at this and the other point. @arg bearing1: Bearing at this point (compass C{degrees360}). @arg other: The other point (C{LatLon}). @arg bearing2: Bearing at the other point (compass C{degrees360}). @kwarg height: Optional height at the triangulated point, overriding the mean height (C{meter}). @return: Triangulated point (C{LatLon}). @raise TypeError: Invalid B{C{other}} point. @raise Valuerror: Points coincide. @example: >>> p = LatLon("47°18.228'N","002°34.326'W") # Basse Castouillet >>> q = LatLon("47°18.664'N","002°31.717'W") # Basse Hergo >>> t = p.triangulate(7, q, 295) # 47.323667°N, 002.568501°W' ''' return _triangulate(self, bearing1, self.others(other), bearing2, height=height, LatLon=self.classof) def trilaterate(self, distance1, point2, distance2, point3, distance3, radius=R_M, height=None, useZ=False): '''Locate a point at given distances from this and two other points. @arg distance1: Distance to this point (C{meter}, same units as B{C{radius}}). @arg point2: Second reference point (C{LatLon}). @arg distance2: Distance to point2 (C{meter}, same units as B{C{radius}}). @arg point3: Third reference point (C{LatLon}). @arg distance3: Distance to point3 (C{meter}, same units as B{C{radius}}). @kwarg radius: Mean earth radius (C{meter}). @kwarg height: Optional height at trilaterated point, overriding the mean height (C{meter}, same units as B{C{radius}}). @kwarg useZ: Include Z component iff non-NaN, non-zero (C{bool}). @return: Trilaterated point (C{LatLon}). @raise IntersectionError: No intersection, trilateration failed. @raise TypeError: Invalid B{C{point2}} or B{C{point3}}. @raise ValueError: Some B{C{points}} coincide or invalid B{C{distance1}}, B{C{distance2}}, B{C{distance3}} or B{C{radius}}. @see: U{Trilateration<https://WikiPedia.org/wiki/Trilateration>}, Veness' JavaScript U{Trilateration<https://www.Movable-Type.co.UK/ scripts/latlong-vectors.html>} and method C{LatLon.trilaterate2} of other, non-C{Nvector LatLon} classes. ''' return _trilaterate(self, distance1, self.others(point2=point2), distance2, self.others(point3=point3), distance3, radius=radius, height=height, useZ=useZ, LatLon=self.classof) def trilaterate5(self, distance1, point2, distance2, point3, distance3, # PYCHOK signature area=False, eps=EPS1, radius=R_M, wrap=False): '''B{Not implemented} for C{B{area}=True} or C{B{wrap}=True} and falls back to method C{trilaterate} otherwise. @return: A L{Trilaterate5Tuple}C{(min, minPoint, max, maxPoint, n)} with a single trilaterated intersection C{minPoint I{is} maxPoint}, C{min I{is} max} the nearest intersection margin and count C{n = 1}. @raise IntersectionError: No intersection, trilateration failed. @raise NotImplementedError: Keyword argument C{B{area}=True} or C{B{wrap}=True} not (yet) supported. @raise TypeError: Invalid B{C{point2}} or B{C{point3}}. @raise ValueError: Coincident B{C{points}} or invalid B{C{distance1}}, B{C{distance2}}, B{C{distance3}} or B{C{radius}}. ''' if area or wrap: notImplemented(self, area=area, wrap=wrap) t = _trilaterate(self, distance1, self.others(point2=point2), distance2, self.others(point3=point3), distance3, radius=radius, height=None, useZ=True, LatLon=self.classof) # ... and handle B{C{eps}} and C{IntersectionError} # like function C{.latlonBase._trilaterate5} d = self.distanceTo(t, radius=radius, wrap=wrap) # PYCHOK distanceTo d = min(fabs(distance1 - d), fabs(distance2 - d), fabs(distance3 - d)) if d < eps: # min is max, minPoint is maxPoint return Trilaterate5Tuple(d, t, d, t, 1) # n = 1 t = _SPACE_(_no_(_intersection_), Fmt.PAREN(min.__name__, Fmt.f(d, prec=3))) raise IntersectionError(area=area, eps=eps, wrap=wrap, txt=t) def sumOf(nvectors, Vector=None, h=None, **Vector_kwds): '''Return the vectorial sum of two or more n-vectors. @arg nvectors: Vectors to be added (C{Nvector}[]). @kwarg Vector: Optional class for the vectorial sum (C{Nvector}) or C{None}. @kwarg h: Optional height, overriding the mean height (C{meter}). @kwarg Vector_kwds: Optional, additional B{C{Vector}} keyword arguments, ignored if C{B{Vector} is None}. @return: Vectorial sum (B{C{Vector}}) or a L{Vector4Tuple}C{(x, y, z, h)} if B{C{Vector}} is C{None}. @raise VectorError: No B{C{nvectors}}. ''' n, nvectors = len2(nvectors) if n < 1: raise VectorError(nvectors=n, txt=MISSING) if h is None: h = fsum(v.h for v in nvectors) / float(n) if Vector is None: r = _sumOf(nvectors, Vector=Vector3Tuple).to4Tuple(h) else: r = _sumOf(nvectors, Vector=Vector, **_xkwds(Vector_kwds, h=h)) return r def _triangulate(point1, bearing1, point2, bearing2, height=None, **LatLon_LatLon_kwds): # (INTERNAL) Locate a point given two known points and initial # bearings from those points, see C{LatLon.triangulate} above def _gc(p, b, _i_): n = p.toNvector() de = NorthPole.cross(n, raiser=_pole_).unit() # east vector @ n dn = n.cross(de) # north vector @ n s, c = sincos2d(Bearing(b, name=_bearing_ + _i_)) dest = de.times(s) dnct = dn.times(c) d = dnct.plus(dest) # direction vector @ n return n.cross(d) # great circle point + bearing if point1.isequalTo(point2, EPS): raise _ValueError(points=point2, txt=_coincident_) gc1 = _gc(point1, bearing1, _1_) # great circle p1 + b1 gc2 = _gc(point2, bearing2, _2_) # great circle p2 + b2 n = gc1.cross(gc2, raiser=_points_) # n-vector of intersection point h = point1._havg(point2) if height is None else Height(height) kwds = _xkwds(LatLon_LatLon_kwds, height=h) return n.toLatLon(**kwds) # Nvector(n.x, n.y, n.z).toLatLon(...) def _trilaterate(point1, distance1, point2, distance2, point3, distance3, radius=R_M, height=None, useZ=False, **LatLon_LatLon_kwds): # (INTERNAL) Locate a point at given distances from # three other points, see LatLon.triangulate above def _nd2(p, d, r, _i_, *qs): # .toNvector and angular distance squared for q in qs: if p.isequalTo(q, EPS): raise _ValueError(points=p, txt=_coincident_) return p.toNvector(), (Scalar(d, name=_distance_ + _i_) / r)**2 r = Radius_(radius) n1, r12 = _nd2(point1, distance1, r, _1_) n2, r22 = _nd2(point2, distance2, r, _2_, point1) n3, r32 = _nd2(point3, distance3, r, _3_, point1, point2) # the following uses x,y coordinate system with origin at n1, x axis n1->n2 y = n3.minus(n1) x = n2.minus(n1) z = None d = x.length # distance n1->n2 if d > EPS_2: # and y.length > EPS_2: X = x.unit() # unit vector in x direction n1->n2 i = X.dot(y) # signed magnitude of x component of n1->n3 Y = y.minus(X.times(i)).unit() # unit vector in y direction j = Y.dot(y) # signed magnitude of y component of n1->n3 if abs(j) > EPS_2: # courtesy Carlos Freitas <https://GitHub.com/mrJean1/PyGeodesy/issues/33> x = fsum_(r12, -r22, d**2) / (_2_0 * d) # n1->intersection x- and ... y = fsum_(r12, -r32, i**2, j**2, -2 * x * i) / (_2_0 * j) # ... y-component # courtesy AleixDev <https://GitHub.com/mrJean1/PyGeodesy/issues/43> z = fsum_(max(r12, r22, r32), -(x**2), -(y**2)) # XXX not just r12! if z > EPS: n = n1.plus(X.times(x)).plus(Y.times(y)) if useZ: # include Z component Z = X.cross(Y) # unit vector perpendicular to plane n = n.plus(Z.times(sqrt(z))) if height is None: h = fidw((point1.height, point2.height, point3.height), map1(fabs, distance1, distance2, distance3)) else: h = Height(height) kwds = _xkwds(LatLon_LatLon_kwds, height=h) return n.toLatLon(**kwds) # Nvector(n.x, n.y, n.z).toLatLon(...) # no intersection, d < EPS_2 or abs(j) < EPS_2 or z < EPS t = _SPACE_(_no_, _intersection_, NN) raise IntersectionError(point1=point1, distance1=distance1, point2=point2, distance2=distance2, point3=point3, distance3=distance3, txt=unstr(t, z=z, useZ=useZ)) __all__ += _ALL_DOCS(LatLonNvectorBase, NvectorBase, sumOf) # classes # **) 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.