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# -*- coding: utf-8 -*- 

 

u'''(INTERNAL) Base classes for elliposiodal, spherical and N-/vectorial 

C{Cartesian}s. 

 

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}.. 

 

@newfield example: Example, Examples 

''' 

 

from pygeodesy.datum import Datum, Datums 

from pygeodesy.ecef import EcefKarney 

from pygeodesy.fmath import EPS, cbrt, fsum_, _IsNotError 

from pygeodesy.lazily import _ALL_DOCS 

from pygeodesy.named import LatLon4Tuple, Vector4Tuple 

from pygeodesy.utily import property_RO, _TypeError 

from pygeodesy.vector3d import Vector3d, _xyzhdn6 

 

from math import hypot, sqrt 

 

# XXX the following classes are listed only to get 

# Epydoc to include class and method documentation 

__all__ = _ALL_DOCS('CartesianBase') 

__version__ = '20.01.22' 

 

 

class CartesianBase(Vector3d): 

'''(INTERNAL) Base class for ellipsoidal and spherical C{Cartesian}. 

''' 

_datum = None #: (INTERNAL) L{Datum}, to be overriden. 

_Ecef = EcefKarney #: (INTERNAL) Preferred C{Ecef...} class. 

_e9t = None #: (INTERNAL) Cached toEcef (L{Ecef9Tuple}). 

_v4t = None #: (INTERNAL) Cached toNvector (L{Vector4Tuple}). 

 

def __init__(self, xyz, y=None, z=None, datum=None, ll=None, name=''): 

'''New C{Cartesian...}. 

 

@param xyz: An L{Ecef9Tuple}, L{Vector3Tuple}, L{Vector4Tuple} 

or the C{X} coordinate (C{scalar}). 

@param y: The C{Y} coordinate (C{scalar}) if B{C{xyz}} C{scalar}. 

@param z: The C{Z} coordinate (C{scalar}) if B{C{xyz}} C{scalar}. 

@keyword datum: Optional datum (L{Datum}). 

@keyword ll: Optional, original latlon (C{LatLon}). 

@keyword name: Optional name (C{str}). 

 

@raise TypeError: Non-scalar B{C{xyz}}, B{C{y}} or B{C{z}} 

coordinate or B{C{xyz}} not an L{Ecef9Tuple}, 

L{Vector3Tuple} or L{Vector4Tuple}. 

''' 

x, y, z, _, d, n = _xyzhdn6(xyz, y, z, None, datum, ll) 

Vector3d.__init__(self, x, y, z, ll=ll, name=name or n) 

if d: 

self.datum = d 

 

def _update(self, updated): 

if updated: # reset cached attrs 

self._e9t = self._v4t = None 

Vector3d._update(self, updated) 

 

def _applyHelmert(self, transform, inverse=False, **datum): 

'''(INTERNAL) Return a new cartesian point by applying a 

Helmert transform to this point. 

 

@param transform: Transform to apply (L{Transform}). 

@keyword inverse: Optionally, apply the inverse 

Helmert transform (C{bool}). 

@keyword datum: Optional datum of the returned point, 

(C{B{datum}=}L{Datum}). 

 

@return: The transformed point (C{Cartesian}). 

 

@note: For C{B{inverse}=True} keyword B{C{datum}} must 

be C{B{datum}=Datums.WGS84}. 

''' 

xyz = transform.transform(self.x, self.y, self.z, inverse) 

return self._xnamed(self.classof(xyz, **datum)) 

 

def convertDatum(self, datum2, datum=None): 

'''Convert this cartesian point from one to an other datum. 

 

@param datum2: Datum to convert I{to} (L{Datum}). 

@keyword datum: Datum to convert I{from} (L{Datum}). 

 

@return: The converted point (C{Cartesian}). 

 

@raise TypeError: B{C{datum2}} or B{C{datum}} not a 

L{Datum}. 

''' 

_TypeError(Datum, datum2=datum2) 

 

if datum and self.datum != datum: 

c = self.convertDatum(datum) 

else: 

c = self 

 

i, d = False, c.datum 

if d == datum2: 

return c.copy() if c is self else c 

 

elif d == Datums.WGS84: 

d = datum2 # convert from WGS84 to datum2 

 

elif datum2 == Datums.WGS84: 

i = True # convert to WGS84 by inverse transform 

 

else: # neither datum2 nor c.datum is WGS84, invert to WGS84 first 

c = c._applyHelmert(d.transform, True) 

d = datum2 

 

return c._applyHelmert(d.transform, i, datum=datum2) 

 

@property 

def datum(self): 

'''Get this point's datum (L{Datum}). 

''' 

return self._datum 

 

@datum.setter # PYCHOK setter! 

def datum(self, datum): 

'''Set this geocentric point's C{datum} I{without conversion}. 

 

@param datum: New datum (L{Datum}). 

 

@raise TypeError: The B{C{datum}} is not a L{Datum}. 

''' 

_TypeError(Datum, datum=datum) 

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 

 

@property_RO 

def Ecef(self): 

'''Get the ECEF I{class} (L{EcefKarney} or L{EcefVeness}). 

''' 

return self._Ecef 

 

def toEcef(self): 

'''Convert this cartesian to geodetic 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. 

''' 

if self._e9t is None: 

r = self.Ecef(self.datum).reverse(self, M=True) 

self._e9t = self._xnamed(r) 

return self._e9t 

 

def to3llh(self, datum=None): 

'''DEPRECATED, use method C{toLatLon}. 

 

Convert this cartesian to geodetic lat-, longitude and 

height. 

 

@keyword datum: Optional datum to use (L{Datum}). 

 

@return: A L{LatLon4Tuple}C{(lat, lon, height, datum)}. 

 

@raise TypeError: Invalid B{C{datum}}. 

''' 

t = self.toLatLon(datum=datum, LatLon=None) 

r = LatLon4Tuple(t.lat, t.lon, t.height, t.datum) 

return self._xnamed(r) 

 

# 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) 

# for n, v in pairs.items(): 

# setattr(r, n, v) 

# r = self._xnamed(r) 

# return r 

 

def toLatLon(self, datum=None, LatLon=None, **kwds): 

'''Convert this cartesian point to a geodetic point. 

 

@keyword datum: Optional datum (L{Datum}) or C{None}. 

@keyword LatLon: Optional (sub-)class to return the 

geodetic point (C{LatLon}) or C{None}. 

@keyword kwds: Optional, additional B{C{LatLon}} keyword 

arguments, ignored if C{B{LatLon}=None}. 

 

@return: The B{C{LatLon}} point or if C{B{LatLon}=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{kwds}}. 

''' 

c = self 

if datum is not None: 

_TypeError(Datum, datum=datum) 

if datum != self.datum: 

c = self.convertDatum(datum) 

 

r = c.Ecef(c.datum).reverse(c, M=True) 

if LatLon is not None: # class or .classof 

r = LatLon(r.lat, r.lon, height=r.height, 

datum=c.datum, **kwds) 

return self._xnamed(r) 

 

def toNvector(self, Nvector=None, datum=None, **kwds): # PYCHOK Datums.WGS84 

'''Convert this cartesian to C{n-vector} components. 

 

@keyword Nvector: Optional (sub-)class to return the 

C{n-vector} components (C{Nvector}) 

or C{None}. 

@keyword datum: Optional datum (L{Datum}) overriding this 

cartesian's datum. 

@keyword kwds: Optional, additional B{C{Nvector}} keyword 

arguments, ignored if C{B{Nvector}=None}. 

 

@return: Unit vector B{C{Nvector}} or a L{Vector4Tuple}C{(x, 

y, z, h)} if B{C{Nvector}=None}. 

 

@raise ValueError: The B{C{Cartesian}} at origin. 

''' 

d = datum or self.datum 

r = self._v4t 

if r is None or self.datum != d: 

E = d.ellipsoid 

x, y, z = self.to3xyz() 

 

# Kenneth Gade eqn 23 

p = (x**2 + y**2) * E.a2_ 

q = (z**2 * E.e12) * E.a2_ 

r = fsum_(p, q, -E.e4) / 6 

s = (p * q * E.e4) / (4 * r**3) 

t = cbrt(fsum_(1, s, sqrt(s * (2 + s)))) 

 

u = r * fsum_(1, t, 1 / t) 

v = sqrt(u**2 + E.e4 * q) 

w = E.e2 * fsum_(u, v, -q) / (2 * v) 

 

k = sqrt(fsum_(u, v, w**2)) - w 

if abs(k) < EPS: 

raise ValueError('%s: %r' % ('origin', self)) 

e = k / (k + E.e2) 

 

t = hypot(e * hypot(x, y), z) 

if t < EPS: 

raise ValueError('%s: %r' % ('origin', self)) 

h = fsum_(k, E.e2, -1) / k * t 

 

s = e / t 

r = Vector4Tuple(x * s, y * s, z / t, h) 

self._v4t = r if d == self.datum else None 

 

if Nvector is not None: 

r = Nvector(r.x, r.y, r.z, h=r.h, datum=d, **kwds) 

return self._xnamed(r) 

 

def toStr(self, prec=3, fmt='[%s]', sep=', '): # PYCHOK expected 

'''Return the string representation of this cartesian. 

 

@keyword prec: Optional number of decimals, unstripped (C{int}). 

@keyword fmt: Optional enclosing backets format (string). 

@keyword sep: Optional separator to join (string). 

 

@return: Cartesian represented as "[x, y, z]" (string). 

''' 

return Vector3d.toStr(self, prec=prec, fmt=fmt, sep=sep) 

 

# **) 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.