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# -*- coding: utf-8 -*- 

 

u'''I{Local Tangent Plane} (LTP) and I{local} cartesian coordinates. 

 

I{Local cartesian} and I{local tangent plane} classes L{LocalCartesian} and L{Ltp}, 

L{LocalError} and L{Frustum}. 

 

@see: U{Local tangent plane coordinates<https://WikiPedia.org/wiki/Local_tangent_plane_coordinates>} 

and class L{LocalCartesian}, transcoded from I{Charles Karney}'s C++ classU{LocalCartesian 

<https://GeographicLib.SourceForge.io/html/classGeographicLib_1_1LocalCartesian.html>}. 

''' 

 

# from pygeodesy.basics import issubclassof # from ecef 

from pygeodesy.datums import _WGS84, _xinstanceof 

from pygeodesy.ecef import _EcefBase, EcefKarney, issubclassof, \ 

_llhn4, _xyzn4 

from pygeodesy.errors import _TypesError, _ValueError 

from pygeodesy.interns import EPS, NN, _ltp_, _M_, _lat0_, \ 

_lon0_, _name_, _0_, _0_0, _0_5, \ 

_2_0, _90_0, _180_0, _360_0 

from pygeodesy.interns import _ecef_ # PYCHOK used! 

from pygeodesy.lazily import _ALL_LAZY 

from pygeodesy.ltpTuples import Footprint5Tuple, Local9Tuple, \ 

_XyzLocals4, _XyzLocals5, Xyz4Tuple 

from pygeodesy.named import _NamedBase 

from pygeodesy.props import Property, Property_RO 

from pygeodesy.units import Degrees, Meter 

from pygeodesy.utily import sincos2d 

 

from math import radians, tan 

 

__all__ = _ALL_LAZY.ltp 

__version__ = '21.06.25' 

 

_Xyz_ = 'Xyz' 

 

 

class LocalError(_ValueError): 

'''A L{LocalCartesian} or L{Ltp} related issue. 

''' 

pass 

 

 

class LocalCartesian(_NamedBase): 

'''Conversion between geodetic C{(lat, lon, height)} and I{local cartesian} 

C{(x, y, z)} coordinates with I{geodetic} origin C{(lat0, lon0, height0)}, 

transcoded 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 = -height0} is tangent to the ellipsoid. 

 

The conversions all take place via geocentric coordinates using a 

geocentric L{EcefKarney}, by default the WGS84 datum/ellipsoid. 

 

@see: Class L{Ltp}. 

''' 

_ecef = EcefKarney(_WGS84) 

_t0 = None # origin (..., lat0, lon0, height0, ...) L{Ecef9Tuple} 

 

def __init__(self, latlonh0=0, lon0=0, height0=0, ecef=None, name=NN): 

'''New L{LocalCartesian} converter. 

 

@kwarg latlonh0: Either a C{LatLon}, L{Ltp}, L{Ecef9Tuple} or 

C{scalar} latitude of the (goedetic) origin 

(C{degrees}). 

@kwarg lon0: Optional C{scalar} longitude of the (goedetic) origin 

C{scalar} B{C{latlonh0}} (C{degrees}). 

@kwarg height0: Optional origin height (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 LocalError: If B{C{latlonh0}} not C{LatLon}, L{Ecef9Tuple}, 

C{scalar} or invalid or if B{C{lon0}} not 

C{scalar} for C{scalar} B{C{latlonh0}} or 

invalid or if B{C{height0}} invalid. 

 

@raise TypeError: Invalid B{C{ecef}}, not L{EcefKarney}. 

 

@note: If BC{latlonh0} is L{Ltp}, only the lat-, longitude and 

height are duplicated, I{not} the ECEF converter. 

''' 

if ecef: 

_xinstanceof(EcefKarney, ecef=ecef) 

self._ecef = ecef 

self.reset(latlonh0, lon0, height0, name=name) 

 

@Property_RO 

def datum(self): 

'''Get the ECEF converter's datum (L{Datum}). 

''' 

return self.ecef.datum 

 

@Property_RO 

def ecef(self): 

'''Get the ECEF converter (L{EcefKarney}). 

''' 

return self._ecef 

 

def _ecef2local(self, ecef, Xyz, Xyz_kwds): 

'''(INTERNAL) Convert geocentric/geodetic to local, like I{forward}. 

 

@arg ecef: Geocentric (and geodetic) (L{Ecef9Tuple}). 

@arg Xyz: An L{XyzLocal}, L{Enu} or L{Ned} I{class} or C{None}. 

@arg Xyz_kwds: B{C{Xyz}} keyword arguments, ignored if C{B{Xyz}=None}. 

 

@return: An C{B{Xyz}(x, y, z, ltp, **B{Xyz_kwds}} instance or if 

C{B{Xyz}=None}, an L{Local9Tuple}C{(x, y, z, lat, lon, 

height, ltp, ecef, M)} with this C{ltp}, B{C{ecef}} 

(L{Ecef9Tuple}) converted to this C{datum} and C{M=None}, 

always. 

''' 

ltp = self 

if ecef.datum != ltp.datum: 

ecef = ecef.toDatum(ltp.datum) 

x, y, z = self.M.rotate(ecef.xyz, *ltp._xyz0) 

r = Local9Tuple(x, y, z, ecef.lat, ecef.lon, ecef.height, 

ltp, ecef, None, name=ecef.name) 

if Xyz: 

if not issubclassof(Xyz, *_XyzLocals4): # Vector3d 

raise _TypesError(_Xyz_, Xyz, *_XyzLocals4) 

r = r.toXyz(Xyz=Xyz, **Xyz_kwds) 

return r 

 

def forward(self, latlonh, lon=None, height=0, M=False, name=NN): 

'''Convert I{geodetic} C{(lat, lon, height)} to I{local} cartesian 

C{(x, y, z)}. 

 

@arg latlonh: Either a C{LatLon}, a L{Ltp}, an L{Ecef9Tuple} or 

C{scalar} (geodetic) latitude (C{degrees}). 

@kwarg lon: Optional C{scalar} (geodetic) longitude for C{scalar} 

B{C{latlonh}} (C{degrees}). 

@kwarg height: Optional height (C{meter}), vertically above (or below) 

the surface of the ellipsoid. 

@kwarg M: Optionally, return the rotation L{EcefMatrix} (C{bool}). 

@kwarg name: Optional name (C{str}). 

 

@return: A L{Local9Tuple}C{(x, y, z, lat, lon, height, ltp, ecef, M)} 

with I{local} C{x}, C{y}, C{z}, I{geodetic} C{(lat}, C{lon}, 

C{height}, this C{ltp}, C{ecef} (L{Ecef9Tuple}) with 

I{geocentric} C{x}, C{y}, C{z} (and I{geodetic} C{lat}, 

C{lon}, C{height}) and the I{concatenated} rotation matrix 

C{M} (L{EcefMatrix}) if requested. 

 

@raise LocalError: If B{C{latlonh}} not C{scalar}, C{LatLon}, L{Ltp}, 

L{Ecef9Tuple} or invalid or if B{C{lon}} not 

C{scalar} for C{scalar} B{C{latlonh}} or invalid 

or if B{C{height}} invalid. 

 

@see: Note at method L{EcefKarney.forward}. 

''' 

lat, lon, h, n = _llhn4(latlonh, lon, height, Error=LocalError, name=name) 

t = self.ecef.forward(lat, lon, h, M=M) 

x, y, z = self.M.rotate(t.xyz, *self._xyz0) 

m = self.M.multiply(t.M) if M else None 

return Local9Tuple(x, y, z, lat, lon, h, self, t, m, name=n or self.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 

 

def _local2ecef(self, local, nine=False, M=False): 

'''(INTERNAL) Convert I{local} to geocentric/geodetic, like I{.reverse}. 

 

@arg local: Local (L{XyzLocal}, L{Enu}, L{Ned}, L{Aer} or L{Local9Tuple}). 

@kwarg nine: Return 3- or 9-tuple (C{bool}). 

@kwarg M: Include the rotation matrix (C{bool}). 

 

@return: A I{geocentric} 3-tuple C{(x, y, z)} or if C{B{nine}=True}, 

an L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)}, 

optionally including rotation matrix C{M} or C{None}. 

''' 

t = self.M.unrotate(local.xyz, *self._xyz0) 

if nine: 

t = self.ecef.reverse(*t, M=M) 

return t 

 

@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 (geodetic) origin. 

 

@kwarg latlonh0: Either a C{LatLon}, an L{Ecef9Tuple} or C{scalar} 

latitude of the origin (C{degrees}). 

@kwarg lon0: Optional C{scalar} longitude of the origin for 

C{scalar} B{C{latlonh0}} (C{degrees}). 

@kwarg height0: Optional origin height (C{meter}), vertically 

above (or below) the surface of the ellipsoid. 

@kwarg name: Optional, new name (C{str}). 

 

@raise LocalError: If B{C{latlonh0}} not C{LatLon}, L{Ecef9Tuple}, 

C{scalar} or invalid or if B{C{lon0}} not 

C{scalar} for C{scalar} B{C{latlonh0}} or 

invalid or if B{C{height0}} invalid. 

''' 

self._update(True) # force reset 

 

lat0, lon0, height0, n = _llhn4(latlonh0, lon0, height0, 

suffix=_0_, Error=LocalError, name=name) 

if n: 

self.rename(n) 

else: 

n = self.name 

self._t0 = self.ecef.forward(lat0, lon0, height0, M=True, name=n) 

 

def reverse(self, xyz, y=None, z=None, M=False, name=NN): 

'''Convert I{local} C{(x, y, z)} to I{geodetic} C{(lat, lon, height)}. 

 

@arg xyz: A I{local} (L{XyzLocal}, L{Enu}, L{Ned}, L{Aer}, L{Local9Tuple}) or 

local C{x} coordinate (C{scalar}). 

@kwarg y: Local C{y} coordinate for C{scalar} B{C{xyz}} and B{C{z}} (C{meter}). 

@kwarg z: Local C{z} coordinate for C{scalar} B{C{xyz}} and B{C{y}} (C{meter}). 

@kwarg M: Optionally, return the I{concatenated} rotation L{EcefMatrix}, 

I{iff avaialble} (C{bool}). 

@kwarg name: Optional name (C{str}). 

 

@return: An L{Local9Tuple}C{(x, y, z, lat, lon, height, ltp, ecef, M)} with 

I{local} C{x}, C{y}, C{z}, I{geodetic} C{lat}, C{lon}, C{height}, 

this C{ltp}, an C{ecef} (L{Ecef9Tuple}) with the I{geocentric} C{x}, 

C{y}, C{z} (and I{geodetic} C{lat}, C{lon}, C{height}) and the 

I{concatenated} rotation matrix C{M} (L{EcefMatrix}) if requested. 

 

@raise LocalError: Invalid B{C{xyz}} or C{scalar} C{x} or B{C{y}} and/or B{C{z}} 

not C{scalar} for C{scalar} B{C{xyz}}. 

 

@see: Note at method L{EcefKarney.reverse}. 

''' 

x, y, z, n = _xyzn4(xyz, y, z, _XyzLocals5, Error=LocalError, name=name) 

c = self.M.unrotate((x, y, z), *self._xyz0) 

t = self.ecef.reverse(*c, M=M) 

m = self.M.multiply(t.M) if M else None 

return Local9Tuple(x, y, z, t.lat, t.lon, t.height, self, t, m, name=n or self.name) 

 

def toStr(self, prec=9): # PYCHOK signature 

'''Return this L{LocalCartesian} as a string. 

 

@kwarg prec: Optional precision, number of decimal digits (0..9). 

 

@return: This L{LocalCartesian} representation (C{str}). 

''' 

return self.attrs(_lat0_, _lon0_, 'height0', _M_, 'ecef', _name_, prec=prec) 

 

@Property_RO 

def _xyz0(self): 

'''(INTERNAL) Get C{(x0, y0, z0)} as L{Vector3Tuple}. 

''' 

return self._t0.xyz 

 

 

class Ltp(LocalCartesian): 

'''A I{local tangent plan} LTP, a sub-class of C{LocalCartesian} with 

configurable ECEF converter and without optional rotation matrix. 

''' 

def __init__(self, latlonh0=0, lon0=0, height0=0, ecef=None, name=NN): 

'''New C{Ltp}. 

 

@kwarg latlonh0: Either a C{LatLon}, L{Ltp}, L{Ecef9Tuple} or 

C{scalar} latitude of the (goedetic) origin 

(C{degrees}). 

@kwarg lon0: Optional C{scalar} longitude of the (goedetic) origin 

for C{scalar} B{C{latlonh0}} (C{degrees}). 

@kwarg height0: Optional origin height (C{meter}), vertically 

above (or below) the surface of the ellipsoid. 

@kwarg ecef: Optional ECEF converter (L{EcefKarney}, l{EcefFarrell21}, 

L{EcefFarrell22}, L{EcefSudano}, L{EcefVeness} or 

L{EcefYou} I{instance}), overriding default 

L{EcefKarney}C{(datum=Datums.WGS84)}. 

@kwarg name: Optional name (C{str}). 

 

@return: New instance (C{Ltp}). 

 

@raise LocalError: If B{C{latlonh0}} not C{LatLon}, L{Ecef9Tuple}, 

C{scalar} or invalid or if B{C{lon0}} not 

C{scalar} for C{scalar} B{C{latlonh0}} or 

invalid or if B{C{height0}} invalid. 

 

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

''' 

if isinstance(latlonh0, Ltp): 

self._ecef = latlonh0.ecef 

self._t0 = latlonh0._to 

self.name = name or latlonh0.name 

else: 

LocalCartesian.__init__(self, latlonh0, lon0=lon0, height0=height0, name=name) 

if ecef: 

self.ecef = ecef 

 

@Property 

def ecef(self): 

'''Get this LTP's ECEF converter (C{Ecef...} I{instance}). 

''' 

return self._ecef 

 

@ecef.setter # PYCHOK setter! 

def ecef(self, ecef): 

'''Set this LTP's ECEF converter. 

 

@arg ecef: New ECEF converter (C{Ecef...} I{instance}). 

 

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

''' 

_xinstanceof(_EcefBase, ecef=ecef) 

if ecef != self._ecef: 

self._ecef = ecef 

self.reset(self._t0) 

 

 

class Frustum(_NamedBase): 

'''A rectangular pyramid, typically representing a camera's I{field of view} 

(fov) and the intersection with (or projection to) a I{local tangent plane}. 

 

@see: U{Viewing frustum<https://WikiPedia.org/wiki/Viewing_frustum>}. 

''' 

_h_2 = _0_0 # half hfov 

_ltp = None # local tangent plane 

_tan_h_2 = _0_0 # tan(_h_2) 

_v_2 = _0_0 # half vfov 

 

def __init__(self, hfov, vfov, ltp=None): 

'''New L{Frustum}. 

 

@arg hfov: Horizontal field of view (C{degrees180}). 

@arg vfov: Vertical field of view (C{degrees180}). 

@kwarg ltp: Optional I{local tangent plane} (L{Ltp}). 

 

@raise UnitError: Invalid B{C{hfov}} or B{C{vfov}}. 

 

@raise ValueError: Invalid B{C{hfov}} or B{C{vfov}}. 

''' 

self._h_2 = h = Degrees(hfov=hfov) * _0_5 

if not EPS < h < _90_0: 

raise _ValueError(hfov=hfov) 

 

self._v_2 = v = Degrees(vfov=vfov) * _0_5 

if not EPS < v < _90_0: 

raise _ValueError(vfov=vfov) 

 

self._tan_h_2 = t = tan(radians(h)) 

if t < EPS: 

raise _ValueError(hfov=hfov) 

 

if ltp: 

self._ltp = _xLtp(ltp) 

 

@Property_RO 

def hfov(self): 

'''Get the horizontal C{fov} (C{degrees}). 

''' 

return Degrees(hfov=self._h_2 * _2_0) 

 

def footprint5(self, altitude, tilt, yaw=0, roll=0, z=_0_0, ltp=None): # MCCABE 15 

'''Compute the center and corners of the intersection with (or projection 

to) the I{local tangent plane} (LTP). 

 

@arg altitude: Altitude (C{meter}) above I{local tangent plane}. 

@arg tilt: Pitch, elevation from horizontal (C{degrees180}), negative down. 

@kwarg yaw: Bearing, heading (compass C{degrees360}), clockwise from North. 

@kwarg roll: Roll, bank (C{degrees}), positive to the right and down. 

kwarg z: Optional height of the footprint (C{meter}) above I{local tangent plane}. 

@kwarg ltp: The I{local tangent plane} (L{Ltp}), overriding this 

frustum's C{ltp}. 

 

@return: A L{Footprint5Tuple}C{(center, upperleft, upperight, loweright, 

lowerleft)} with the C{center} and 4 corners each an L{Xyz4Tuple}. 

 

@raise TypeError: Invalid B{C{ltp}}. 

 

@raise UnitError: Invalid B{C{altitude}}, B{C{tilt}}, B{C{roll}} or B{C{z}}. 

 

@raise ValueError: If B{C{altitude}} too low, B{C{z}} too high or B{C{tilt}} 

or B{C{roll}} -including B{C{vfov}} respectively B{C{hfov}}- 

over the horizon. 

 

@see: U{Principal axes<https://WikiPedia.org/wiki/Aircraft_principal_axes>}. 

''' 

def _xy2(a, t, h_2, tan_h_2, r): 

# left and right corners, or swapped 

if r < EPS: # no roll 

r = a * tan_h_2 

l = -r # PYCHOK l is ell 

else: # roll 

sl, cl, sr, cr = sincos2d(r + h_2, r - h_2) 

if cl < EPS or cr < EPS: 

raise _ValueError(roll_hfov=r) 

r = -a * sr / cr # negate right positive 

l = -a * sl / cl # PYCHOK l is ell 

s, c = sincos2d(t) 

if abs(s) < EPS: 

raise _ValueError(tilt_vfov=t) 

y = a * c / s 

return (l, y), (r, y) 

 

def _xys(b, *xys): 

# rotate (x, y)'s by bearing, clockwise 

s, c = sincos2d(b) 

for x, y in xys: 

yield (x * c + y * s), (y * c - x * s) 

 

a = Meter(altitude=altitude) 

if a < EPS: # too low 

raise _ValueError(altitude=altitude) 

if z: 

z = Meter(z=z) 

a -= z 

if a < EPS: # z above a 

raise _ValueError(altitude_z=a) 

else: 

z = _0_0 

 

b = Degrees(yaw=yaw) % _360_0 

t = -Degrees(tilt=tilt) 

if not EPS < t < _180_0: 

raise _ValueError(tilt=tilt) 

if t > _90_0: 

t = _180_0 - t 

b = (_180_0 + b) % _360_0 

 

r = Degrees(roll=roll) % _360_0 # center 

if r: # roll center 

s, c = sincos2d(r) 

if c < EPS: 

raise _ValueError(roll=r) 

x = -a * s / c 

else: 

x = _0_0 

# ground range 

s, c = sincos2d(t) 

if s < EPS: 

raise _ValueError(tilt=tilt) 

y = a * c / s 

if abs(y) < EPS: 

y = _0_0 

 

# center and corners, clockwise from upperleft, rolled 

xy5 = ((x, y),) + _xy2(a, t - self._v_2, self._h_2, self._tan_h_2, r) \ 

+ _xy2(a, t + self._v_2, -self._h_2, -self._tan_h_2, r) # swapped 

# turn center and corners by yaw, clockwise 

p = self.ltp if ltp is None else _xLtp(ltp) 

return Footprint5Tuple(*(Xyz4Tuple(x, y, z, p) for 

x, y in _xys(b, *xy5))) 

 

@Property_RO 

def ltp(self): 

'''Get the I{local tangent plane} (L{Ltp}) or C{None}. 

''' 

return self._ltp 

 

@Property_RO 

def vfov(self): 

'''Get the vertical C{fov} (C{degrees}). 

''' 

return Degrees(vfov=self._v_2 * _2_0) 

 

 

def _xLtp(ltp): 

'''(INTERNAL) Validate B{C{ltp}}. 

''' 

if isinstance(ltp, (LocalCartesian, Ltp)): 

return ltp 

raise _TypesError(_ltp_, ltp, Ltp, LocalCartesian) 

 

# **) 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.