Coverage for pygeodesy/ltp.py: 96%
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« prev ^ index » next coverage.py v7.2.2, created at 2023-12-02 13:46 -0500
2# -*- coding: utf-8 -*-
4u'''I{Local Tangent Plane} (LTP) and I{local} cartesian coordinates.
6I{Local cartesian} and I{local tangent plane} classes L{LocalCartesian}, approximations L{ChLVa}
7and L{ChLVe} and L{Ltp}, L{ChLV}, L{LocalError}, L{Attitude} and L{Frustum}.
9@see: U{Local tangent plane coordinates<https://WikiPedia.org/wiki/Local_tangent_plane_coordinates>}
10 and class L{LocalCartesian}, transcoded from I{Charles Karney}'s C++ classU{LocalCartesian
11 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1LocalCartesian.html>}.
12'''
13# make sure int/int division yields float quotient, see .basics
14from __future__ import division as _; del _ # PYCHOK semicolon
16from pygeodesy.basics import isscalar, issubclassof, map1, map2, \
17 _xargs_kwds_names
18from pygeodesy.constants import EPS, INT0, _umod_360, _0_0, _0_01, _0_5, _1_0, \
19 _2_0, _60_0, _90_0, _100_0, _180_0, _3600_0, \
20 _N_1_0 # PYCHOK used!
21from pygeodesy.datums import _WGS84, _xinstanceof
22from pygeodesy.ecef import _EcefBase, EcefKarney, _llhn4, _xyzn4
23from pygeodesy.errors import _NotImplementedError, _TypesError, _ValueError, \
24 _xattr, _xkwds, _xkwds_get
25from pygeodesy.fmath import fabs, fdot, Fhorner
26from pygeodesy.fsums import _floor, Fsum, fsumf_, fsum1f_
27from pygeodesy.interns import NN, _0_, _COMMASPACE_, _DOT_, _ecef_, _height_, \
28 _invalid_, _lat0_, _lon0_, _ltp_, _M_, _name_, _too_
29# from pygeodesy.lazily import _ALL_LAZY # from vector3d
30from pygeodesy.ltpTuples import Attitude4Tuple, ChLVEN2Tuple, ChLV9Tuple, \
31 ChLVYX2Tuple, Footprint5Tuple, Local9Tuple, \
32 ChLVyx2Tuple, _XyzLocals4, _XyzLocals5, Xyz4Tuple
33from pygeodesy.named import _NamedBase, notOverloaded
34from pygeodesy.namedTuples import LatLon3Tuple, LatLon4Tuple, Vector3Tuple
35from pygeodesy.props import Property, Property_RO, property_doc_, property_RO, \
36 _update_all
37from pygeodesy.streprs import Fmt, strs, unstr
38from pygeodesy.units import Bearing, Degrees, Meter
39from pygeodesy.utily import cotd, _loneg, sincos2d, sincos2d_, tand, tand_, \
40 wrap180, wrap360
41from pygeodesy.vector3d import _ALL_LAZY, Vector3d
43# from math import fabs, floor as _floor # from .fmath, .fsums
45__all__ = _ALL_LAZY.ltp
46__version__ = '23.11.16'
48_height0_ = _height_ + _0_
49_narrow_ = 'narrow'
50_wide_ = 'wide'
51_Xyz_ = 'Xyz'
54def _fov_2(**fov):
55 # Half a field-of-view angle in C{degrees}.
56 f = Degrees(Error=LocalError, **fov) * _0_5
57 if EPS < f < _90_0:
58 return f
59 t = _invalid_ if f < 0 else _too_(_wide_ if f > EPS else _narrow_)
60 raise LocalError(txt=t, **fov)
63class Attitude(_NamedBase):
64 '''The orientation of a plane or camera in space.
65 '''
66 _alt = Meter( alt =_0_0)
67 _roll = Degrees(roll=_0_0)
68 _tilt = Degrees(tilt=_0_0)
69 _yaw = Bearing(yaw =_0_0)
71 def __init__(self, alt_attitude=INT0, tilt=INT0, yaw=INT0, roll=INT0, name=NN):
72 '''New L{Attitude}.
74 @kwarg alt_attitude: An altitude (C{meter}) above earth or an attitude
75 (L{Attitude} or L{Attitude4Tuple}) with the
76 C{B{alt}itude}, B{C{tilt}}, B{C{yaw}} and B{C{roll}}.
77 @kwarg tilt: Pitch, elevation from horizontal (C{degrees180}), negative down
78 (clockwise rotation along and around the x- or East axis).
79 @kwarg yaw: Bearing, heading (compass C{degrees360}), clockwise from North
80 (counter-clockwise rotation along and around the z- or Up axis).
81 @kwarg roll: Roll, bank (C{degrees180}), positive to the right and down
82 (clockwise rotation along and around the y- or North axis).
83 @kwarg name: Optional name C{str}).
85 @raise AttitudeError: Invalid B{C{alt_attitude}}, B{C{tilt}}, B{C{yaw}} or
86 B{C{roll}}.
88 @see: U{Principal axes<https://WikiPedia.org/wiki/Aircraft_principal_axes>} and
89 U{Yaw, pitch, and roll rotations<http://MSL.CS.UIUC.edu/planning/node102.html>}.
90 '''
91 if isscalar(alt_attitude):
92 t = Attitude4Tuple(alt_attitude, tilt, yaw, roll)
93 else:
94 try:
95 t = alt_attitude.atyr
96 except AttributeError:
97 raise AttitudeError(alt=alt_attitude, tilt=tilt, yaw=yaw, rol=roll)
98 for n, v in t.items():
99 if v:
100 setattr(self, n, v)
101 n = name or t.name
102 if n:
103 self.name = n
105 @property_doc_(' altitude above earth in C{meter}.')
106 def alt(self):
107 return self._alt
109 @alt.setter # PYCHOK setter!
110 def alt(self, alt): # PYCHOK no cover
111 a = Meter(alt=alt, Error=AttitudeError)
112 if self._alt != a:
113 _update_all(self)
114 self._alt = a
116 altitude = alt
118 @Property_RO
119 def atyr(self):
120 '''Return this attitude's alt[itude], tilt, yaw and roll as an L{Attitude4Tuple}.
121 '''
122 return Attitude4Tuple(self.alt, self.tilt, self.yaw, self.roll, name=self.name)
124 @Property_RO
125 def matrix(self):
126 '''Get the 3x3 rotation matrix C{R(yaw)·R(tilt)·R(roll)}, aka I{ZYX} (C{float}, row-order).
128 @see: Matrix M of case 10 in U{Appendix A
129 <https://ntrs.NASA.gov/api/citations/19770019231/downloads/19770019231.pdf>}.
130 '''
131 _f = fsum1f_
132 # to follow the definitions of rotation angles alpha, beta and gamma:
133 # negate yaw since yaw is counter-clockwise around the z-axis, swap
134 # tilt and roll since tilt is around the x- and roll around the y-axis
135 sa, ca, sb, cb, sg, cg = sincos2d_(-self.yaw, self.roll, self.tilt)
136 return ((ca * cb, _f(ca * sb * sg, -sa * cg), _f(ca * sb * cg, sa * sg)),
137 (sa * cb, _f(sa * sb * sg, ca * cg), _f(sa * sb * cg, -ca * sg)),
138 ( -sb, cb * sg, cb * cg))
140 @property_doc_(' roll/bank in C{degrees180}, positive to the right and down.')
141 def roll(self):
142 return self._roll
144 @roll.setter # PYCHOK setter!
145 def roll(self, roll):
146 r = Degrees(roll=roll, wrap=wrap180, Error=AttitudeError)
147 if self._roll != r:
148 _update_all(self)
149 self._roll = r
151 bank = roll
153 def rotate(self, x_xyz, y=None, z=None, Vector=None, **Vector_kwds):
154 '''Transform a (local) cartesian by this attitude's matrix.
156 @arg x_xyz: X component of vector (C{scalar}) or (3-D) vector
157 (C{Cartesian}, L{Vector3d} or L{Vector3Tuple}).
158 @kwarg y: Y component of vector (C{scalar}), same units as B{C{x}}.
159 @kwarg z: Z component of vector (C{scalar}), same units as B{C{x}}.
160 @kwarg Vector: Class to return transformed point (C{Cartesian},
161 L{Vector3d} or C{Vector3Tuple}) or C{None}.
162 @kwarg Vector_kwds: Optional, additional B{C{Vector}} keyword arguments,
163 ignored if C{B{Vector} is None}.
165 @return: A B{C{Vector}} instance or a L{Vector3Tuple}C{(x, y, z)} if
166 C{B{Vector}=None}.
168 @raise AttitudeError: Invalid B{C{x_xyz}}, B{C{y}} or B{C{z}}.
170 @see: U{Yaw, pitch, and roll rotations<http://MSL.CS.UIUC.edu/planning/node102.html>}.
171 '''
172 try:
173 try:
174 xyz = map2(float, x_xyz.xyz)
175 except AttributeError:
176 xyz = map1(float, x_xyz, y, z)
177 except (TypeError, ValueError) as x:
178 raise AttitudeError(x_xyz=x_xyz, y=y, z=z, cause=x)
180 x, y, z = (fdot(r, *xyz) for r in self.matrix)
181 return Vector3Tuple(x, y, z, name=self.name) if Vector is None else \
182 Vector(x, y, z, **_xkwds(Vector_kwds, name=self.name))
184 @property_doc_(' tilt/pitch/elevation from horizontal in C{degrees180}, negative down.')
185 def tilt(self):
186 return self._tilt
188 @tilt.setter # PYCHOK setter!
189 def tilt(self, tilt):
190 t = Degrees(tilt=tilt, wrap=wrap180, Error=AttitudeError)
191 if self._tilt != t:
192 _update_all(self)
193 self._tilt = t
195 elevation = pitch = tilt
197 def toStr(self, prec=6, sep=_COMMASPACE_, **unused): # PYCHOK signature
198 '''Format this attitude as string.
200 @kwarg prec: The C{float} precision, number of decimal digits (0..9).
201 Trailing zero decimals are stripped for B{C{prec}} values
202 of 1 and above, but kept for negative B{C{prec}} values.
203 @kwarg sep: Separator to join (C{str}).
205 @return: This attitude (C{str}).
206 '''
207 return self.atyr.toStr(prec=prec, sep=sep)
209 @Property_RO
210 def tyr3d(self):
211 '''Get this attitude's (3-D) directional vector (L{Vector3d}).
213 @see: U{Yaw, pitch, and roll rotations<http://MSL.CS.UIUC.edu/planning/node102.html>}.
214 '''
215 def _r2d(r):
216 return fsumf_(_N_1_0, *r)
218 return Vector3d(*map(_r2d, self.matrix), name=tyr3d.__name__)
220 @property_doc_(' yaw/bearing/heading in compass C{degrees360}, clockwise from North.')
221 def yaw(self):
222 return self._yaw
224 @yaw.setter # PYCHOK setter!
225 def yaw(self, yaw):
226 y = Bearing(yaw=yaw, Error=AttitudeError)
227 if self._yaw != y:
228 _update_all(self)
229 self._yaw = y
231 bearing = heading = yaw
234class AttitudeError(_ValueError):
235 '''An L{Attitude} or L{Attitude4Tuple} issue.
236 '''
237 pass
240class Frustum(_NamedBase):
241 '''A rectangular pyramid, typically representing a camera's I{field-of-view}
242 (fov) and the intersection with (or projection to) a I{local tangent plane}.
244 @see: U{Viewing frustum<https://WikiPedia.org/wiki/Viewing_frustum>}.
245 '''
246 _h_2 = _0_0 # half hfov in degrees
247 _ltp = None # local tangent plane
248 _tan_h_2 = _0_0 # tan(_h_2)
249 _v_2 = _0_0 # half vfov in degrees
251 def __init__(self, hfov, vfov, ltp=None):
252 '''New L{Frustum}.
254 @arg hfov: Horizontal field-of-view (C{degrees180}).
255 @arg vfov: Vertical field-of-view (C{degrees180}).
256 @kwarg ltp: Optional I{local tangent plane} (L{Ltp}).
258 @raise LocalError: Invalid B{C{hfov}} or B{C{vfov}}.
259 '''
260 self._h_2 = h = _fov_2(hfov=hfov)
261 self._v_2 = _fov_2(vfov=vfov)
263 self._tan_h_2 = tand(h, hfov_2=h)
265 if ltp:
266 self._ltp = _xLtp(ltp)
268 def footprint5(self, alt_attitude, tilt=0, yaw=0, roll=0, z=_0_0, ltp=None): # MCCABE 15
269 '''Compute the center and corners of the intersection with (or projection
270 to) the I{local tangent plane} (LTP).
272 @arg alt_attitude: An altitude (C{meter}) above I{local tangent plane} or
273 an attitude (L{Attitude} or L{Attitude4Tuple}) with the
274 C{B{alt}itude}, B{C{tilt}}, B{C{yaw}} and B{C{roll}}.
275 @kwarg tilt: Pitch, elevation from horizontal (C{degrees}), negative down
276 (clockwise rotation along and around the x- or East axis).
277 @kwarg yaw: Bearing, heading (compass C{degrees}), clockwise from North
278 (counter-clockwise rotation along and around the z- or Up axis).
279 @kwarg roll: Roll, bank (C{degrees}), positive to the right and down
280 (clockwise rotation along and around the y- or North axis).
281 @kwarg z: Optional height of the footprint (C{meter}) above I{local tangent plane}.
282 @kwarg ltp: The I{local tangent plane} (L{Ltp}), overriding this
283 frustum's C{ltp}.
285 @return: A L{Footprint5Tuple}C{(center, upperleft, upperight, loweright,
286 lowerleft)} with the C{center} and 4 corners, each an L{Xyz4Tuple}.
288 @raise TypeError: Invalid B{C{ltp}}.
290 @raise UnitError: Invalid B{C{altitude}}, B{C{tilt}}, B{C{roll}} or B{C{z}}.
292 @raise ValueError: If B{C{altitude}} too low, B{C{z}} too high or B{C{tilt}}
293 or B{C{roll}} -including B{C{vfov}} respectively B{C{hfov}}-
294 over the horizon.
296 @see: U{Principal axes<https://WikiPedia.org/wiki/Aircraft_principal_axes>}.
297 '''
298 def _xy2(a, e, h_2, tan_h_2, r):
299 # left and right corners, or swapped
300 if r < EPS: # no roll
301 r = a * tan_h_2
302 l = -r # PYCHOK l is ell
303 else: # roll
304 r, l = tand_(r - h_2, r + h_2, roll_hfov=r) # PYCHOK l is ell
305 r *= -a # negate right positive
306 l *= -a # PYCHOK l is ell
307 y = a * cotd(e, tilt_vfov=e)
308 return (l, y), (r, y)
310 def _xyz5(b, xy5, z, ltp):
311 # rotate (x, y)'s by bearing, clockwise
312 s, c = sincos2d(b)
313 _f = fsum1f_
314 for x, y in xy5:
315 yield Xyz4Tuple(_f(x * c, y * s),
316 _f(y * c, -x * s), z, ltp)
318 try:
319 a, t, y, r = alt_attitude.atyr
320 except AttributeError:
321 a, t, y, r = alt_attitude, tilt, yaw, roll
323 a = Meter(altitude=a)
324 if a < EPS: # too low
325 raise _ValueError(altitude=a)
326 if z: # PYCHOK no cover
327 z = Meter(z=z)
328 a -= z
329 if a < EPS: # z above a
330 raise _ValueError(altitude_z=a)
331 else:
332 z = _0_0
334 b = Degrees(yaw=y, wrap=wrap360) # bearing
335 e = -Degrees(tilt=t, wrap=wrap180) # elevation, pitch
336 if not EPS < e < _180_0:
337 raise _ValueError(tilt=t)
338 if e > _90_0:
339 e = _loneg(e)
340 b = _umod_360(b + _180_0)
342 r = Degrees(roll=r, wrap=wrap180) # roll center
343 x = (-a * tand(r, roll=r)) if r else _0_0
344 y = a * cotd(e, tilt=t) # ground range
345 if fabs(y) < EPS:
346 y = _0_0
348 v, h, t = self._v_2, self._h_2, self._tan_h_2
349 # center and corners, clockwise from upperleft, rolled
350 xy5 = ((x, y),) + _xy2(a, e - v, h, t, r) \
351 + _xy2(a, e + v, -h, -t, r) # swapped
352 # turn center and corners by yaw, clockwise
353 p = self.ltp if ltp is None else ltp # None OK
354 return Footprint5Tuple(_xyz5(b, xy5, z, p)) # *_xyz5
356 @Property_RO
357 def hfov(self):
358 '''Get the horizontal C{fov} (C{degrees}).
359 '''
360 return Degrees(hfov=self._h_2 * _2_0)
362 @Property_RO
363 def ltp(self):
364 '''Get the I{local tangent plane} (L{Ltp}) or C{None}.
365 '''
366 return self._ltp
368 def toStr(self, prec=3, fmt=Fmt.F, sep=_COMMASPACE_): # PYCHOK signature
369 '''Convert this frustum to a "hfov, vfov, ltp" string.
371 @kwarg prec: Number of (decimal) digits, unstripped (0..8 or C{None}).
372 @kwarg fmt: Optional, C{float} format (C{str}).
373 @kwarg sep: Separator to join (C{str}).
375 @return: Frustum in the specified form (C{str}).
376 '''
377 t = self.hfov, self.vfov
378 if self.ltp:
379 t += self.ltp,
380 t = strs(t, prec=prec, fmt=fmt)
381 return sep.join(t) if sep else t
383 @Property_RO
384 def vfov(self):
385 '''Get the vertical C{fov} (C{degrees}).
386 '''
387 return Degrees(vfov=self._v_2 * _2_0)
390class LocalError(_ValueError):
391 '''A L{LocalCartesian} or L{Ltp} related issue.
392 '''
393 pass
396class LocalCartesian(_NamedBase):
397 '''Conversion between geodetic C{(lat, lon, height)} and I{local
398 cartesian} C{(x, y, z)} coordinates with I{geodetic} origin
399 C{(lat0, lon0, height0)}, transcoded from I{Karney}'s C++ class
400 U{LocalCartesian<https://GeographicLib.SourceForge.io/C++/doc/
401 classGeographicLib_1_1LocalCartesian.html>}.
403 The C{z} axis is normal to the ellipsoid, the C{y} axis points due
404 North. The plane C{z = -height0} is tangent to the ellipsoid.
406 The conversions all take place via geocentric coordinates using a
407 geocentric L{EcefKarney}, by default the WGS84 datum/ellipsoid.
409 @see: Class L{Ltp}.
410 '''
411 _ecef = EcefKarney(_WGS84)
412 _Ecef = EcefKarney
413 _lon00 = INT0 # self.lon0
414 _t0 = None # origin (..., lat0, lon0, height0, ...) L{Ecef9Tuple}
415 _9Tuple = Local9Tuple
417 def __init__(self, latlonh0=INT0, lon0=INT0, height0=INT0, ecef=None, name=NN, **lon00):
418 '''New L{LocalCartesian} converter.
420 @kwarg latlonh0: The (geodetic) origin (C{LatLon}, L{LatLon4Tuple}, L{Ltp}
421 L{LocalCartesian} or L{Ecef9Tuple}) or the C{scalar}
422 latitude of the (goedetic) origin (C{degrees}).
423 @kwarg lon0: Longitude of the (goedetic) origin (C{degrees}) for C{scalar}
424 B{C{latlonh0}}, ignored otherwise.
425 @kwarg height0: Optional height (C{meter}, conventionally) at the (goedetic)
426 origin perpendicular to and above (or below) the ellipsoid's
427 surface and for C{scalar} B{C{latlonh0}}, ignored otherwise.
428 @kwarg ecef: An ECEF converter (L{EcefKarney} I{only}) for C{scalar}
429 B{C{latlonh0}}, ignored otherwise.
430 @kwarg name: Optional name (C{str}).
431 @kwarg lon00: An arbitrary, I{polar} longitude (C{degrees}), overriding
432 the default C{B{lon00}=B{lon0}}, see method C{reverse}.
434 @raise LocalError: If B{C{latlonh0}} not C{LatLon}, L{LatLon4Tuple}, L{Ltp},
435 L{LocalCartesian} or L{Ecef9Tuple} or B{C{latlonh0}},
436 B{C{lon0}}, B{C{height0}} or B{C{lon00}} invalid.
438 @raise TypeError: Invalid B{C{ecef}} or not L{EcefKarney}.
440 @note: If BC{latlonh0} is an L{Ltp} or L{LocalCartesian}, only C{lat0}, C{lon0},
441 C{height0} and I{polar} C{lon00} are copied, I{not} the ECEF converter.
442 '''
443 self.reset(latlonh0, lon0=lon0, height0=height0, ecef=ecef, name=name, **lon00)
445 def __eq__(self, other):
446 '''Compare this and an other instance.
448 @arg other: The other ellipsoid (L{LocalCartesian} or L{Ltp}).
450 @return: C{True} if equal, C{False} otherwise.
451 '''
452 return other is self or (isinstance(other, self.__class__) and
453 other.ecef == self.ecef and
454 other._t0 == self._t0)
456 @Property_RO
457 def datum(self):
458 '''Get the ECEF converter's datum (L{Datum}).
459 '''
460 return self.ecef.datum
462 @Property_RO
463 def ecef(self):
464 '''Get the ECEF converter (L{EcefKarney}).
465 '''
466 return self._ecef
468 def _ecef2local(self, ecef, Xyz, Xyz_kwds):
469 '''(INTERNAL) Convert geocentric/geodetic to local, like I{forward}.
471 @arg ecef: Geocentric (and geodetic) (L{Ecef9Tuple}).
472 @arg Xyz: An L{XyzLocal}, L{Enu} or L{Ned} I{class} or C{None}.
473 @arg Xyz_kwds: B{C{Xyz}} keyword arguments, ignored if C{B{Xyz} is None}.
475 @return: An C{B{Xyz}(x, y, z, ltp, **B{Xyz_kwds}} instance or if
476 C{B{Xyz} is None}, a L{Local9Tuple}C{(x, y, z, lat, lon,
477 height, ltp, ecef, M)} with this C{ltp}, B{C{ecef}}
478 (L{Ecef9Tuple}) converted to this C{datum} and C{M=None},
479 always.
480 '''
481 ltp = self
482 if ecef.datum != ltp.datum:
483 ecef = ecef.toDatum(ltp.datum)
484 x, y, z = self.M.rotate(ecef.xyz, *ltp._t0_xyz)
485 r = Local9Tuple(x, y, z, ecef.lat, ecef.lon, ecef.height,
486 ltp, ecef, None, name=ecef.name)
487 if Xyz:
488 if not issubclassof(Xyz, *_XyzLocals4): # Vector3d
489 raise _TypesError(_Xyz_, Xyz, *_XyzLocals4)
490 r = r.toXyz(Xyz=Xyz, **Xyz_kwds)
491 return r
493 @Property_RO
494 def ellipsoid(self):
495 '''Get the ECEF converter's ellipsoid (L{Ellipsoid}).
496 '''
497 return self.ecef.datum.ellipsoid
499 def forward(self, latlonh, lon=None, height=0, M=False, name=NN):
500 '''Convert I{geodetic} C{(lat, lon, height)} to I{local} cartesian
501 C{(x, y, z)}.
503 @arg latlonh: Either a C{LatLon}, L{Ltp}, L{Ecef9Tuple} or C{scalar}
504 (geodetic) latitude (C{degrees}).
505 @kwarg lon: Optional C{scalar} (geodetic) longitude for C{scalar}
506 B{C{latlonh}} (C{degrees}).
507 @kwarg height: Optional height (C{meter}, conventionally) perpendicular
508 to and above (or below) the ellipsoid's surface.
509 @kwarg M: Optionally, return the I{concatenated} rotation L{EcefMatrix},
510 iff available (C{bool}).
511 @kwarg name: Optional name (C{str}).
513 @return: A L{Local9Tuple}C{(x, y, z, lat, lon, height, ltp, ecef, M)}
514 with I{local} C{x}, C{y}, C{z}, I{geodetic} C{(lat}, C{lon},
515 C{height}, this C{ltp}, C{ecef} (L{Ecef9Tuple}) with
516 I{geocentric} C{x}, C{y}, C{z} (and I{geodetic} C{lat},
517 C{lon}, C{height}) and the I{concatenated} rotation matrix
518 C{M} (L{EcefMatrix}) if requested.
520 @raise LocalError: If B{C{latlonh}} not C{scalar}, C{LatLon}, L{Ltp},
521 L{Ecef9Tuple} or invalid or if B{C{lon}} not
522 C{scalar} for C{scalar} B{C{latlonh}} or invalid
523 or if B{C{height}} invalid.
524 '''
525 lat, lon, h, n = _llhn4(latlonh, lon, height, Error=LocalError, name=name)
526 t = self.ecef._forward(lat, lon, h, n, M=M)
527 x, y, z = self.M.rotate(t.xyz, *self._t0_xyz)
528 m = self.M.multiply(t.M) if M else None
529 return self._9Tuple(x, y, z, lat, lon, h, self, t, m, name=n or self.name)
531 @Property_RO
532 def height0(self):
533 '''Get the origin's height (C{meter}).
534 '''
535 return self._t0.height
537 @Property_RO
538 def lat0(self):
539 '''Get the origin's latitude (C{degrees}).
540 '''
541 return self._t0.lat
543 @Property_RO
544 def latlonheight0(self):
545 '''Get the origin's lat-, longitude and height (L{LatLon3Tuple}C{(lat, lon, height)}).
546 '''
547 return LatLon3Tuple(self.lat0, self.lon0, self.height0, name=self.name)
549 def _local2ecef(self, local, nine=False, M=False):
550 '''(INTERNAL) Convert I{local} to geocentric/geodetic, like I{.reverse}.
552 @arg local: Local (L{XyzLocal}, L{Enu}, L{Ned}, L{Aer} or L{Local9Tuple}).
553 @kwarg nine: Return 3- or 9-tuple (C{bool}).
554 @kwarg M: Include the rotation matrix (C{bool}).
556 @return: A I{geocentric} 3-tuple C{(x, y, z)} or if C{B{nine}=True},
557 an L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)},
558 optionally including rotation matrix C{M} or C{None}.
559 '''
560 t = self.M.unrotate(local.xyz, *self._t0_xyz)
561 if nine:
562 t = self.ecef.reverse(*t, M=M)
563 return t
565 @Property_RO
566 def lon0(self):
567 '''Get the origin's longitude (C{degrees}).
568 '''
569 return self._t0.lon
571 @Property
572 def lon00(self):
573 '''Get the arbitrary, I{polar} longitude (C{degrees}).
574 '''
575 return self._lon00
577 @lon00.setter # PYCHOK setter!
578 def lon00(self, lon00):
579 '''Set the arbitrary, I{polar} longitude (C{degrees}).
580 '''
581 # lon00 <https://GitHub.com/mrJean1/PyGeodesy/issues/77>
582 self._lon00 = Degrees(lon00=lon00)
584 @Property_RO
585 def M(self):
586 '''Get the rotation matrix (C{EcefMatrix}).
587 '''
588 return self._t0.M
590 def reset(self, latlonh0=INT0, lon0=INT0, height0=INT0, ecef=None, name=NN, **lon00):
591 '''Reset this converter, see L{LocalCartesian.__init__} and L{Ltp.__init__} for more details.
592 '''
593 if isinstance(latlonh0, LocalCartesian):
594 if self._t0:
595 _update_all(self)
596 self._ecef = latlonh0.ecef
597 self._lon00 = latlonh0.lon00
598 self._t0 = latlonh0._t0
599 n = name or latlonh0.name
600 else:
601 lat0, lon0, height0, n = _llhn4(latlonh0, lon0, height0, suffix=_0_,
602 Error=LocalError, name=name or self.name)
603 if ecef: # PYCHOK no cover
604 _xinstanceof(self._Ecef, ecef=ecef)
605 _update_all(self)
606 self._ecef = ecef
607 elif self._t0:
608 _update_all(self)
609 self._t0 = self.ecef._forward(lat0, lon0, height0, n, M=True)
610 self.lon00 = _xattr(latlonh0, lon00=_xkwds_get(lon00, lon00=lon0))
611 if n:
612 self.rename(n)
614 def reverse(self, xyz, y=None, z=None, M=False, name=NN, **lon00):
615 '''Convert I{local} C{(x, y, z)} to I{geodetic} C{(lat, lon, height)}.
617 @arg xyz: A I{local} (L{XyzLocal}, L{Enu}, L{Ned}, L{Aer}, L{Local9Tuple}) or
618 local C{x} coordinate (C{scalar}).
619 @kwarg y: Local C{y} coordinate for C{scalar} B{C{xyz}} and B{C{z}} (C{meter}).
620 @kwarg z: Local C{z} coordinate for C{scalar} B{C{xyz}} and B{C{y}} (C{meter}).
621 @kwarg M: Optionally, return the I{concatenated} rotation L{EcefMatrix}, iff
622 available (C{bool}).
623 @kwarg name: Optional name (C{str}).
624 @kwarg lon00: An arbitrary, I{polar} longitude (C{degrees}), returned for local
625 C{B{x}=0} and C{B{y}=0} at I{polar} latitudes C{abs(B{lat0}) == 90},
626 overriding property C{lon00} and default C{B{lon00}=B{lon0}}.
628 @return: An L{Local9Tuple}C{(x, y, z, lat, lon, height, ltp, ecef, M)} with
629 I{local} C{x}, C{y}, C{z}, I{geodetic} C{lat}, C{lon}, C{height},
630 this C{ltp}, an C{ecef} (L{Ecef9Tuple}) with the I{geocentric} C{x},
631 C{y}, C{z} (and I{geodetic} C{lat}, C{lon}, C{height}) and the
632 I{concatenated} rotation matrix C{M} (L{EcefMatrix}) if requested.
634 @raise LocalError: Invalid B{C{xyz}} or C{scalar} C{x} or B{C{y}} and/or B{C{z}}
635 not C{scalar} for C{scalar} B{C{xyz}}.
636 '''
637 x, y, z, n = _xyzn4(xyz, y, z, _XyzLocals5, Error=LocalError, name=name)
638 c = self.M.unrotate((x, y, z), *self._t0_xyz)
639 t = self.ecef.reverse(*c, M=M, lon00=_xkwds_get(lon00, lon00=self.lon00))
640 m = self.M.multiply(t.M) if M else None
641 return self._9Tuple(x, y, z, t.lat, t.lon, t.height, self, t, m, name=n or self.name)
643 @Property_RO
644 def _t0_xyz(self):
645 '''(INTERNAL) Get C{(x0, y0, z0)} as L{Vector3Tuple}.
646 '''
647 return self._t0.xyz
649 def toStr(self, prec=9, **unused): # PYCHOK signature
650 '''Return this L{LocalCartesian} as a string.
652 @kwarg prec: Precision, number of (decimal) digits (0..9).
654 @return: This L{LocalCartesian} representation (C{str}).
655 '''
656 return self.attrs(_lat0_, _lon0_, _height0_, _M_, _ecef_, _name_, prec=prec)
659class Ltp(LocalCartesian):
660 '''A I{local tangent plan} (LTP), a sub-class of C{LocalCartesian} with
661 (re-)configurable ECEF converter.
662 '''
663 _Ecef = _EcefBase
665 def __init__(self, latlonh0=INT0, lon0=INT0, height0=INT0, ecef=None, name=NN, **lon00):
666 '''New C{Ltp}, see L{LocalCartesian.__init__} for more details.
668 @kwarg ecef: Optional ECEF converter (L{EcefKarney}, L{EcefFarrell21},
669 L{EcefFarrell22}, L{EcefSudano}, L{EcefVeness} or
670 L{EcefYou} I{instance}), overriding the default
671 L{EcefKarney}C{(datum=Datums.WGS84)} for C{scalar}.
673 @raise TypeError: Invalid B{C{ecef}}.
674 '''
675 LocalCartesian.reset(self, latlonh0, lon0=lon0, height0=height0,
676 ecef=ecef, name=name, **lon00)
678 @Property
679 def ecef(self):
680 '''Get this LTP's ECEF converter (C{Ecef...} I{instance}).
681 '''
682 return self._ecef
684 @ecef.setter # PYCHOK setter!
685 def ecef(self, ecef):
686 '''Set this LTP's ECEF converter (C{Ecef...} I{instance}).
688 @raise TypeError: Invalid B{C{ecef}}.
689 '''
690 _xinstanceof(_EcefBase, ecef=ecef)
691 if ecef != self._ecef: # PYCHOK no cover
692 self.reset(self._t0)
693 self._ecef = ecef
696class _ChLV(object):
697 '''(INTERNAL) Base class for C{ChLV*} classes.
698 '''
699 _03_falsing = ChLVyx2Tuple(0.6e6, 0.2e6)
700# _92_falsing = ChLVYX2Tuple(2.0e6, 1.0e6) # _95_ - _03_
701 _95_falsing = ChLVEN2Tuple(2.6e6, 1.2e6)
703 def _ChLV9Tuple(self, fw, M, name, *Y_X_h_lat_lon_h):
704 '''(INTERNAL) Helper for C{ChLVa/e.forward} and C{.reverse}.
705 '''
706 if bool(M): # PYCHOK no cover
707 m = self.forward if fw else self.reverse # PYCHOK attr
708 n = _DOT_(self.__class__.__name__, m.__name__)
709 raise _NotImplementedError(unstr(n, M=M), txt=None)
710 t = Y_X_h_lat_lon_h + (self, self._t0, None) # PYCHOK _t0
711 return ChLV9Tuple(t, name=name)
713 @property_RO
714 def _enh_n_h(self):
715 '''(INTERNAL) Get C{ChLV*.reverse} args[1:4] names, I{once}.
716 '''
717 _ChLV._enh_n_h = t = _xargs_kwds_names(_ChLV.reverse)[1:4] # overwrite property_RO
718 # assert _xargs_kwds_names( ChLV.reverse)[1:4] == t
719 # assert _xargs_kwds_names(ChLVa.reverse)[1:4] == t
720 # assert _xargs_kwds_names(ChLVe.reverse)[1:4] == t
721 return t
723 def forward(self, latlonh, lon=None, height=0, M=None, name=NN): # PYCHOK no cover
724 '''Convert WGS84 geodetic to I{Swiss} projection coordinates. I{Must be overloaded}.
726 @arg latlonh: Either a C{LatLon}, L{Ltp} or C{scalar} (geodetic) latitude (C{degrees}).
727 @kwarg lon: Optional, C{scalar} (geodetic) longitude for C{scalar} B{C{latlonh}} (C{degrees}).
728 @kwarg height: Optional, height, vertically above (or below) the surface of the ellipsoid
729 (C{meter}) for C{scalar} B{C{latlonh}} and B{C{lon}}.
730 @kwarg M: If C{True}, return the I{concatenated} rotation L{EcefMatrix} iff available
731 for C{ChLV} only, C{None} otherwise (C{bool}).
732 @kwarg name: Optional name (C{str}).
734 @return: A L{ChLV9Tuple}C{(Y, X, h_, lat, lon, height, ltp, ecef, M)} with the unfalsed
735 I{Swiss Y, X} coordinates, I{Swiss h_} height, the given I{geodetic} C{lat},
736 C{lon} and C{height}, this C{ChLV*} instance and C{ecef} (L{Ecef9Tuple}) at
737 I{Bern, Ch} and rotation matrix C{M}. The returned C{ltp} is this C{ChLV},
738 C{ChLVa} or C{ChLVe} instance.
740 @raise LocalError: Invalid or non-C{scalar} B{C{latlonh}}, B{C{lon}} or B{C{height}}.
741 '''
742 notOverloaded(self, latlonh, lon=lon, height=height, M=M, name=name)
744 def reverse(self, enh_, n=None, h_=0, M=None, **name): # PYCHOK no cover
745 '''Convert I{Swiss} projection to WGS84 geodetic coordinates.
747 @arg enh_: A Swiss projection (L{ChLV9Tuple}) or the C{scalar}, falsed I{Swiss E_LV95}
748 or I{y_LV03} easting (C{meter}).
749 @kwarg n: Falsed I{Swiss N_LV85} or I{x_LV03} northing for C{scalar} B{C{enh_}} and
750 B{C{h_}} (C{meter}).
751 @kwarg h_: I{Swiss h'} height for C{scalar} B{C{enh_}} and B{C{n}} (C{meter}).
752 @kwarg M: If C{True}, return the I{concatenated} rotation L{EcefMatrix} iff available
753 for C{ChLV} only, C{None} otherwise (C{bool}).
754 @kwarg name: Optional name (C{str}).
756 @return: A L{ChLV9Tuple}C{(Y, X, h_, lat, lon, height, ltp, ecef, M)} with the unfalsed
757 I{Swiss Y, X} coordinates, I{Swiss h_} height, the given I{geodetic} C{lat},
758 C{lon} and C{height}, this C{ChLV*} instance and C{ecef} (L{Ecef9Tuple}) at
759 I{Bern, Ch} and rotation matrix C{M}. The returned C{ltp} is this C{ChLV},
760 C{ChLVa} or C{ChLVe} instance.
762 @raise LocalError: Invalid or non-C{scalar} B{C{enh_}}, B{C{n}} or B{C{h_}}.
763 '''
764 notOverloaded(self, enh_, n=n, h_=h_, M=M, **name)
766 @staticmethod
767 def _falsing2(LV95):
768 '''(INTERNAL) Get the C{LV95} or C{LV03} falsing.
769 '''
770 return _ChLV._95_falsing if LV95 in (True, 95) else (
771 _ChLV._03_falsing if LV95 in (False, 3) else ChLVYX2Tuple(0, 0))
773 @staticmethod
774 def _llh2abh_3(lat, lon, h):
775 '''(INTERNAL) Helper for C{ChLVa/e.forward}.
776 '''
777 def _deg2ab(deg, sLL):
778 # convert degrees to arc-seconds
779 def _dms(ds, p, q, swap):
780 d = _floor(ds)
781 t = (ds - d) * p
782 m = _floor(t)
783 s = (t - m) * p
784 if swap:
785 d, s = s, d
786 return d + (m + s * q) * q
788 s = _dms(deg, _60_0, _0_01, False) # deg2sexag
789 s = _dms( s, _100_0, _60_0, True) # sexag2asec
790 return (s - sLL) / ChLV._s_ab
792 a = _deg2ab(lat, ChLV._sLat) # phi', lat_aux
793 b = _deg2ab(lon, ChLV._sLon) # lam', lng_aux
794 h_ = fsumf_(h, -ChLV.Bern.height, 2.73 * b, 6.94 * a)
795 return a, b, h_
797 @staticmethod
798 def _YXh_2abh3(Y, X, h_):
799 '''(INTERNAL) Helper for C{ChLVa/e.reverse}.
800 '''
801 def _YX2ab(YX):
802 return YX * ChLV._ab_m
804 a, b = map1(_YX2ab, Y, X)
805 h = fsumf_(h_, ChLV.Bern.height, -12.6 * a, -22.64 * b)
806 return a, b, h
808 def _YXh_n4(self, enh_, n, h_, **name):
809 '''(INTERNAL) Helper for C{ChLV*.reverse}.
810 '''
811 Y, X, h_, name = _xyzn4(enh_, n, h_, ChLV9Tuple,
812 _xyz_y_z_names=self._enh_n_h, **name)
813 if isinstance(enh_, ChLV9Tuple):
814 Y, X = enh_.Y, enh_.X
815 else: # isscalar(enh_)
816 Y, X = ChLV.unfalse2(Y, X) # PYCHOK ChLVYX2Tuple
817 return Y, X, h_, name
820class ChLV(_ChLV, Ltp):
821 '''Conversion between I{WGS84 geodetic} and I{Swiss} projection coordinates using
822 L{pygeodesy.EcefKarney}'s Earth-Centered, Earth-Fixed (ECEF) methods.
824 @see: U{Swiss projection formulas<https://www.SwissTopo.admin.CH/en/maps-data-online/
825 calculation-services.html>}, page 7ff, U{NAVREF<https://www.SwissTopo.admin.CH/en/
826 maps-data-online/calculation-services/navref.html>}, U{REFRAME<https://www.SwissTopo.admin.CH/
827 en/maps-data-online/calculation-services/reframe.html>} and U{SwissTopo Scripts GPS WGS84
828 <-> LV03<https://GitHub.com/ValentinMinder/Swisstopo-WGS84-LV03>}.
829 '''
830 _9Tuple = ChLV9Tuple
832 _ab_d = 0.36 # a, b units per degree, ...
833 _ab_m = 1.0e-6 # ... per meter and ...
834 _ab_M = _1_0 # ... per 1,000 Km or 1 Mm
835 _s_d = _3600_0 # arc-seconds per degree ...
836 _s_ab = _s_d / _ab_d # ... and per a, b unit
837 _sLat = 169028.66 # Bern, Ch in ...
838 _sLon = 26782.5 # ... arc-seconds ...
839 # lat, lon, height == 46°57'08.66", 7°26'22.50", 49.55m ("new" 46°57'07.89", 7°26'22.335")
840 Bern = LatLon4Tuple(_sLat / _s_d, _sLon / _s_d, 49.55, _WGS84, name='Bern')
842 def __init__(self, latlonh0=Bern, **other_Ltp_kwds):
843 '''New ECEF-based I{WGS84-Swiss} L{ChLV} converter, centered at I{Bern, Ch}.
845 @kwarg latlonh0: The I{geodetic} origin and height, overriding C{Bern, Ch}.
846 @kwarg other_Ltp_kwds: Optional, other L{Ltp.__init__} keyword arguments.
848 @see: L{Ltp.__init__} for more information.
849 '''
850 Ltp.__init__(self, latlonh0, **_xkwds(other_Ltp_kwds, ecef=None, name=ChLV.Bern.name))
852 def forward(self, latlonh, lon=None, height=0, M=None, name=NN): # PYCHOK unused M
853 # overloaded for the _ChLV.forward.__doc__
854 return Ltp.forward(self, latlonh, lon=lon, height=height, M=M, name=name)
856 def reverse(self, enh_, n=None, h_=0, M=None, **name): # PYCHOK signature
857 # overloaded for the _ChLV.reverse.__doc__
858 Y, X, h_, name = self._YXh_n4(enh_, n, h_, **name)
859 return Ltp.reverse(self, Y, X, h_, M=M, name=name)
861 @staticmethod
862 def false2(Y, X, LV95=True, name=NN):
863 '''Add the I{Swiss LV95} or I{LV03} falsing.
865 @arg Y: Unfalsed I{Swiss Y} easting (C{meter}).
866 @arg X: Unfalsed I{Swiss X} northing (C{meter}).
867 @kwarg LV95: If C{True} add C{LV95} falsing, if C{False} add
868 C{LV03} falsing, otherwise leave unfalsed.
869 @kwarg name: Optional name (C{str}).
871 @return: A L{ChLVEN2Tuple}C{(E_LV95, N_LV95)} or a
872 L{ChLVyx2Tuple}C{(y_LV03, x_LV03)} with falsed B{C{Y}}
873 and B{C{X}}, otherwise a L{ChLVYX2Tuple}C{(Y, X)}
874 with B{C{Y}} and B{C{X}} as-is.
875 '''
876 e, n = t = _ChLV._falsing2(LV95)
877 return t.classof(e + Y, n + X, name=name)
879 @staticmethod
880 def isLV03(e, n):
881 '''Is C{(B{e}, B{n})} a valid I{Swiss LV03} projection?
883 @arg e: Falsed (or unfalsed) I{Swiss} easting (C{meter}).
884 @arg n: Falsed (or unfalsed) I{Swiss} northing (C{meter}).
886 @return: C{True} if C{(B{e}, B{n})} is a valid, falsed I{Swiss
887 LV03}, projection C{False} otherwise.
888 '''
889 # @see: U{Map<https://www.SwissTopo.admin.CH/en/knowledge-facts/
890 # surveying-geodesy/reference-frames/local/lv95.html>}
891 return 400.0e3 < e < 900.0e3 and 40.0e3 < n < 400.0e3
893 @staticmethod
894 def isLV95(e, n, raiser=True):
895 '''Is C{(B{e}, B{n})} a valid I{Swiss LV95} or I{LV03} projection?
897 @arg e: Falsed (or unfalsed) I{Swiss} easting (C{meter}).
898 @arg n: Falsed (or unfalsed) I{Swiss} northing (C{meter}).
899 @kwarg raiser: If C{True}, throw a L{LocalError} if B{C{e}} and
900 B{C{n}} are invalid I{Swiss LV95} nor I{LV03}.
902 @return: C{True} or C{False} if C{(B{e}, B{n})} is a valid I{Swiss
903 LV95} respectively I{LV03} projection, C{None} otherwise.
904 '''
905 if ChLV.isLV03(e, n):
906 return False
907 elif ChLV.isLV03(e - 2.0e6, n - 1.0e6): # _92_falsing = _95_ - _03_
908 return True
909 elif raiser: # PYCHOK no cover
910 raise LocalError(unstr(ChLV.isLV95, e=e, n=n))
911 return None
913 @staticmethod
914 def unfalse2(e, n, LV95=None, name=NN):
915 '''Remove the I{Swiss LV95} or I{LV03} falsing.
917 @arg e: Falsed I{Swiss E_LV95} or I{y_LV03} easting (C{meter}).
918 @arg n: Falsed I{Swiss N_LV95} or I{x_LV03} northing (C{meter}).
919 @kwarg LV95: If C{True} remove I{LV95} falsing, if C{False} remove
920 I{LV03} falsing, otherwise use method C{isLV95(B{e},
921 B{n})}.
922 @kwarg name: Optional name (C{str}).
924 @return: A L{ChLVYX2Tuple}C{(Y, X)} with the unfalsed B{C{e}}
925 respectively B{C{n}}.
926 '''
927 Y, X = _ChLV._falsing2(ChLV.isLV95(e, n) if LV95 is None else LV95)
928 return ChLVYX2Tuple(e - Y, n - X, name=name)
931class ChLVa(_ChLV, LocalCartesian):
932 '''Conversion between I{WGS84 geodetic} and I{Swiss} projection coordinates
933 using the U{Approximate<https://www.SwissTopo.admin.CH/en/maps-data-online/
934 calculation-services.html>} formulas, page 13.
936 @see: Older U{references<https://GitHub.com/alphasldiallo/Swisstopo-WGS84-LV03>}.
937 '''
938 def __init__(self, name=ChLV.Bern.name):
939 '''New I{Approximate WGS84-Swiss} L{ChLVa} converter, centered at I{Bern, Ch}.
941 @kwarg name: Optional name (C{str}), overriding C{Bern.name}.
942 '''
943 LocalCartesian.__init__(self, latlonh0=ChLV.Bern, name=name)
945 def forward(self, latlonh, lon=None, height=0, M=None, name=NN):
946 # overloaded for the _ChLV.forward.__doc__
947 lat, lon, h, name = _llhn4(latlonh, lon, height, name=name)
948 a, b, h_ = _ChLV._llh2abh_3(lat, lon, h)
949 a2, b2 = a**2, b**2
951 Y = fsumf_( 72.37, 211455.93 * b,
952 -10938.51 * b * a,
953 -0.36 * b * a2,
954 -44.54 * b * b2) # + 600_000
955 X = fsumf_(147.07, 308807.95 * a,
956 3745.25 * b2,
957 76.63 * a2,
958 -194.56 * b2 * a,
959 119.79 * a2 * a) # + 200_000
960 return self._ChLV9Tuple(True, M, name, Y, X, h_, lat, lon, h)
962 def reverse(self, enh_, n=None, h_=0, M=None, **name): # PYCHOK signature
963 # overloaded for the _ChLV.reverse.__doc__
964 Y, X, h_, name = self._YXh_n4(enh_, n, h_, **name)
965 a, b, h = _ChLV._YXh_2abh3(Y, X, h_)
966 ab_d, a2, b2 = ChLV._ab_d, a**2, b**2
968 lat = Fsum(16.9023892, 3.238272 * b,
969 -0.270978 * a2,
970 -0.002528 * b2,
971 -0.0447 * a2 * b,
972 -0.014 * b2 * b).fover(ab_d)
973 lon = Fsum( 2.6779094, 4.728982 * a,
974 0.791484 * a * b,
975 0.1306 * a * b2,
976 -0.0436 * a * a2).fover(ab_d)
977 return self._ChLV9Tuple(False, M, name, Y, X, h_, lat, lon, h)
980class ChLVe(_ChLV, LocalCartesian):
981 '''Conversion between I{WGS84 geodetic} and I{Swiss} projection coordinates
982 using the U{Ellipsoidal approximate<https://www.SwissTopo.admin.CH/en/
983 maps-data-online/calculation-services.html>} formulas, pp 10-11 and U{Bolliger,
984 J.<https://eMuseum.GGGS.CH/literatur-lv/liste-Dateien/1967_Bolliger_a.pdf>}
985 pp 148-151 (also U{GGGS<https://eMuseum.GGGS.CH/literatur-lv/liste.htm>}).
987 @note: Methods L{ChLVe.forward} and L{ChLVe.reverse} have an additional keyword
988 argument C{B{gamma}=False} to approximate the I{meridian convergence}.
989 If C{B{gamma}=True} a 2-tuple C{(t, gamma)} is returned with C{t} the
990 usual result (C{ChLV9Tuple}) and C{gamma}, the I{meridian convergence}
991 (decimal C{degrees}). To convert C{gamma} to C{grades} or C{gons},
992 use function L{pygeodesy.degrees2grades}.
994 @see: Older U{references<https://GitHub.com/alphasldiallo/Swisstopo-WGS84-LV03>}.
995 '''
996 def __init__(self, name=ChLV.Bern.name):
997 '''New I{Approximate WGS84-Swiss} L{ChLVe} converter, centered at I{Bern, Ch}.
999 @kwarg name: Optional name (C{str}), overriding C{Bern.name}.
1000 '''
1001 LocalCartesian.__init__(self, latlonh0=ChLV.Bern, name=name)
1003 def forward(self, latlonh, lon=None, height=0, M=None, name=NN, gamma=False): # PYCHOK gamma
1004 # overloaded for the _ChLV.forward.__doc__
1005 lat, lon, h, name = _llhn4(latlonh, lon, height, name=name)
1006 a, b, h_ = _ChLV._llh2abh_3(lat, lon, h)
1007 ab_M, z, _F = ChLV._ab_M, 0, Fhorner
1009 B1 = _F(a, 211428.533991, -10939.608605, -2.658213, -8.539078, -0.00345, -0.007992)
1010 B3 = _F(a, -44.232717, 4.291740, -0.309883, 0.013924)
1011 B5 = _F(a, 0.019784, -0.004277)
1012 Y = _F(b, z, B1, z, B3, z, B5).fover(ab_M) # 1,000 Km!
1014 B0 = _F(a, z, 308770.746371, 75.028131, 120.435227, 0.009488, 0.070332, -0.00001)
1015 B2 = _F(a, 3745.408911, -193.792705, 4.340858, -0.376174, 0.004053)
1016 B4 = _F(a, -0.734684, 0.144466, -0.011842)
1017 B6 = 0.000488
1018 X = _F(b, B0, z, B2, z, B4, z, B6).fover(ab_M) # 1,000 Km!
1020 t = self._ChLV9Tuple(True, M, name, Y, X, h_, lat, lon, h)
1021 if gamma:
1022 U1 = _F(a, 2255515.207166, 2642.456961, 1.284180, 2.577486, 0.001165)
1023 U3 = _F(a, -412.991934, 64.106344, -2.679566, 0.123833)
1024 U5 = _F(a, 0.204129, -0.037725)
1025 g = _F(b, z, U1, z, U3, z, U5).fover(ChLV._ab_m) # * ChLV._ab_d degrees?
1026 t = t, g
1027 return t
1029 def reverse(self, enh_, n=None, h_=0, M=None, name=NN, gamma=False): # PYCHOK gamma
1030 # overloaded for the _ChLV.reverse.__doc__
1031 Y, X, h_, name = self._YXh_n4(enh_, n, h_, name=name)
1032 a, b, h = _ChLV._YXh_2abh3(Y, X, h_)
1033 s_d, _F, z = ChLV._s_d, Fhorner, 0
1035 A0 = _F(b, ChLV._sLat, 32386.4877666, -25.486822, -132.457771, 0.48747, 0.81305, -0.0069)
1036 A2 = _F(b, -2713.537919, -450.442705, -75.53194, -14.63049, -2.7604)
1037 A4 = _F(b, 24.42786, 13.20703, 4.7476)
1038 A6 = -0.4249
1039 lat = _F(a, A0, z, A2, z, A4, z, A6).fover(s_d)
1041 A1 = _F(b, 47297.3056722, 7925.714783, 1328.129667, 255.02202, 48.17474, 9.0243)
1042 A3 = _F(b, -442.709889, -255.02202, -96.34947, -30.0808)
1043 A5 = _F(b, 9.63495, 9.0243)
1044 lon = _F(a, ChLV._sLon, A1, z, A3, z, A5).fover(s_d)
1045 # == (ChLV._sLon + a * (A1 + a**2 * (A3 + a**2 * A5))) / s_d
1047 t = self._ChLV9Tuple(False, M, name, Y, X, h_, lat, lon, h)
1048 if gamma:
1049 U1 = _F(b, 106679.792202, 17876.57022, 4306.5241, 794.87772, 148.1545, 27.8725)
1050 U3 = _F(b, -1435.508, -794.8777, -296.309, -92.908)
1051 U5 = _F(b, 29.631, 27.873)
1052 g = _F(a, z, U1, z, U3, z, U5).fover(ChLV._s_ab) # degrees
1053 t = t, g
1054 return t
1057def tyr3d(tilt=INT0, yaw=INT0, roll=INT0, Vector=Vector3d, **Vector_kwds):
1058 '''Convert an attitude oriention into a (3-D) direction vector.
1060 @kwarg tilt: Pitch, elevation from horizontal (C{degrees}), negative down
1061 (clockwise rotation along and around the x-axis).
1062 @kwarg yaw: Bearing, heading (compass C{degrees360}), clockwise from North
1063 (counter-clockwise rotation along and around the z-axis).
1064 @kwarg roll: Roll, bank (C{degrees}), positive to the right and down
1065 (clockwise rotation along and around the y-axis).
1067 @return: A named B{C{Vector}} instance or if B{C{Vector}} is C{None},
1068 a named L{Vector3Tuple}C{(x, y, z)}.
1070 @see: U{Yaw, pitch, and roll rotations<http://MSL.CS.UIUC.edu/planning/node102.html>}
1071 and function L{pygeodesy.hartzell} argument C{los}.
1072 '''
1073 d = Attitude4Tuple(_0_0, tilt, yaw, roll).tyr3d
1074 return d if Vector is type(d) else (
1075 Vector3Tuple(d.x, d.y, d.z, name=d.name) if Vector is None else
1076 Vector(d.x, d.y, d.z, **_xkwds(Vector_kwds, name=d.name))) # PYCHOK indent
1079def _xLtp(ltp, *dflt):
1080 '''(INTERNAL) Validate B{C{ltp}}.
1081 '''
1082 if dflt and ltp is None:
1083 ltp = dflt[0]
1084 if isinstance(ltp, (LocalCartesian, Ltp)):
1085 return ltp
1086 raise _TypesError(_ltp_, ltp, Ltp, LocalCartesian)
1088# **) MIT License
1089#
1090# Copyright (C) 2016-2023 -- mrJean1 at Gmail -- All Rights Reserved.
1091#
1092# Permission is hereby granted, free of charge, to any person obtaining a
1093# copy of this software and associated documentation files (the "Software"),
1094# to deal in the Software without restriction, including without limitation
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1096# and/or sell copies of the Software, and to permit persons to whom the
1097# Software is furnished to do so, subject to the following conditions:
1098#
1099# The above copyright notice and this permission notice shall be included
1100# in all copies or substantial portions of the Software.
1101#
1102# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
1103# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
1104# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
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