Coverage for pygeodesy/ltp.py: 96%
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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 _args_kwds_names, issubclassof, map1, map2 # .datums
17from pygeodesy.constants import EPS, INT0, _umod_360, _0_0, _0_01, _0_5, _1_0, \
18 _2_0, _60_0, _90_0, _100_0, _180_0, _3600_0, \
19 _N_1_0 # PYCHOK used!
20from pygeodesy.datums import _WGS84, _xinstanceof
21from pygeodesy.ecef import _EcefBase, EcefKarney, _llhn4, _xyzn4
22from pygeodesy.errors import _NotImplementedError, _TypesError, _ValueError, \
23 _xattr, _xkwds, _xkwds_get
24from pygeodesy.fmath import fabs, fdot, Fhorner
25from pygeodesy.fsums import _floor, _Fsumf_, fsumf_, fsum1f_
26from pygeodesy.interns import NN, _0_, _COMMASPACE_, _DOT_, _ecef_, _height_, \
27 _invalid_, _lat0_, _lon0_, _ltp_, _M_, _name_, _too_
28# from pygeodesy.lazily import _ALL_LAZY # from vector3d
29from pygeodesy.ltpTuples import Attitude4Tuple, ChLVEN2Tuple, ChLV9Tuple, \
30 ChLVYX2Tuple, Footprint5Tuple, Local9Tuple, \
31 ChLVyx2Tuple, _XyzLocals4, _XyzLocals5, Xyz4Tuple
32from pygeodesy.named import _NamedBase, notOverloaded
33from pygeodesy.namedTuples import LatLon3Tuple, LatLon4Tuple, Vector3Tuple
34from pygeodesy.props import Property, Property_RO, property_doc_, property_RO, \
35 _update_all
36from pygeodesy.streprs import Fmt, strs, unstr
37from pygeodesy.units import Bearing, Degrees, _isHeight, Meter
38from pygeodesy.utily import cotd, _loneg, sincos2d, sincos2d_, tand, tand_, \
39 wrap180, wrap360
40from pygeodesy.vector3d import _ALL_LAZY, Vector3d
42# from math import fabs, floor as _floor # from .fmath, .fsums
44__all__ = _ALL_LAZY.ltp
45__version__ = '24.04.14'
47_height0_ = _height_ + _0_
48_narrow_ = 'narrow'
49_wide_ = 'wide'
50_Xyz_ = 'Xyz'
53def _fov_2(**fov):
54 # Half a field-of-view angle in C{degrees}.
55 f = Degrees(Error=LocalError, **fov) * _0_5
56 if EPS < f < _90_0:
57 return f
58 t = _invalid_ if f < 0 else _too_(_wide_ if f > EPS else _narrow_)
59 raise LocalError(txt=t, **fov)
62class Attitude(_NamedBase):
63 '''The orientation of a plane or camera in space.
64 '''
65 _alt = Meter( alt =_0_0)
66 _roll = Degrees(roll=_0_0)
67 _tilt = Degrees(tilt=_0_0)
68 _yaw = Bearing(yaw =_0_0)
70 def __init__(self, alt_attitude=INT0, tilt=INT0, yaw=INT0, roll=INT0, name=NN):
71 '''New L{Attitude}.
73 @kwarg alt_attitude: An altitude (C{meter}) above earth or an attitude
74 (L{Attitude} or L{Attitude4Tuple}) with the
75 C{B{alt}itude}, B{C{tilt}}, B{C{yaw}} and B{C{roll}}.
76 @kwarg tilt: Pitch, elevation from horizontal (C{degrees180}), negative down
77 (clockwise rotation along and around the x- or East axis).
78 @kwarg yaw: Bearing, heading (compass C{degrees360}), clockwise from North
79 (counter-clockwise rotation along and around the z- or Up axis).
80 @kwarg roll: Roll, bank (C{degrees180}), positive to the right and down
81 (clockwise rotation along and around the y- or North axis).
82 @kwarg name: Optional name C{str}).
84 @raise AttitudeError: Invalid B{C{alt_attitude}}, B{C{tilt}}, B{C{yaw}} or
85 B{C{roll}}.
87 @see: U{Principal axes<https://WikiPedia.org/wiki/Aircraft_principal_axes>} and
88 U{Yaw, pitch, and roll rotations<http://MSL.CS.UIUC.edu/planning/node102.html>}.
89 '''
90 if _isHeight(alt_attitude):
91 t = Attitude4Tuple(alt_attitude, tilt, yaw, roll)
92 else:
93 try:
94 t = alt_attitude.atyr
95 except AttributeError:
96 raise AttitudeError(alt=alt_attitude, tilt=tilt, yaw=yaw, rol=roll)
97 for n, v in t.items():
98 if v:
99 setattr(self, n, v)
100 n = name or t.name
101 if n:
102 self.name = n
104 @property_doc_(' altitude above earth in C{meter}.')
105 def alt(self):
106 return self._alt
108 @alt.setter # PYCHOK setter!
109 def alt(self, alt): # PYCHOK no cover
110 a = Meter(alt=alt, Error=AttitudeError)
111 if self._alt != a:
112 _update_all(self)
113 self._alt = a
115 altitude = alt
117 @Property_RO
118 def atyr(self):
119 '''Return this attitude's alt[itude], tilt, yaw and roll as an L{Attitude4Tuple}.
120 '''
121 return Attitude4Tuple(self.alt, self.tilt, self.yaw, self.roll, name=self.name)
123 @Property_RO
124 def matrix(self):
125 '''Get the 3x3 rotation matrix C{R(yaw)·R(tilt)·R(roll)}, aka I{ZYX} (C{float}, row-order).
127 @see: Matrix M of case 10 in U{Appendix A
128 <https://ntrs.NASA.gov/api/citations/19770019231/downloads/19770019231.pdf>}.
129 '''
130 _f = fsum1f_
131 # to follow the definitions of rotation angles alpha, beta and gamma:
132 # negate yaw since yaw is counter-clockwise around the z-axis, swap
133 # tilt and roll since tilt is around the x- and roll around the y-axis
134 sa, ca, sb, cb, sg, cg = sincos2d_(-self.yaw, self.roll, self.tilt)
135 return ((ca * cb, _f(ca * sb * sg, -sa * cg), _f(ca * sb * cg, sa * sg)),
136 (sa * cb, _f(sa * sb * sg, ca * cg), _f(sa * sb * cg, -ca * sg)),
137 ( -sb, cb * sg, cb * cg))
139 @property_doc_(' roll/bank in C{degrees180}, positive to the right and down.')
140 def roll(self):
141 return self._roll
143 @roll.setter # PYCHOK setter!
144 def roll(self, roll):
145 r = Degrees(roll=roll, wrap=wrap180, Error=AttitudeError)
146 if self._roll != r:
147 _update_all(self)
148 self._roll = r
150 bank = roll
152 def rotate(self, x_xyz, y=None, z=None, Vector=None, **Vector_kwds):
153 '''Transform a (local) cartesian by this attitude's matrix.
155 @arg x_xyz: X component of vector (C{scalar}) or (3-D) vector
156 (C{Cartesian}, L{Vector3d} or L{Vector3Tuple}).
157 @kwarg y: Y component of vector (C{scalar}), same units as B{C{x}}.
158 @kwarg z: Z component of vector (C{scalar}), same units as B{C{x}}.
159 @kwarg Vector: Class to return transformed point (C{Cartesian},
160 L{Vector3d} or C{Vector3Tuple}) or C{None}.
161 @kwarg Vector_kwds: Optional, additional B{C{Vector}} keyword arguments,
162 ignored if C{B{Vector} is None}.
164 @return: A B{C{Vector}} instance or a L{Vector3Tuple}C{(x, y, z)} if
165 C{B{Vector}=None}.
167 @raise AttitudeError: Invalid B{C{x_xyz}}, B{C{y}} or B{C{z}}.
169 @see: U{Yaw, pitch, and roll rotations<http://MSL.CS.UIUC.edu/planning/node102.html>}.
170 '''
171 try:
172 try:
173 xyz = map2(float, x_xyz.xyz)
174 except AttributeError:
175 xyz = map1(float, x_xyz, y, z)
176 except (TypeError, ValueError) as x:
177 raise AttitudeError(x_xyz=x_xyz, y=y, z=z, cause=x)
179 x, y, z = (fdot(r, *xyz) for r in self.matrix)
180 return Vector3Tuple(x, y, z, name=self.name) if Vector is None else \
181 Vector(x, y, z, **_xkwds(Vector_kwds, name=self.name))
183 @property_doc_(' tilt/pitch/elevation from horizontal in C{degrees180}, negative down.')
184 def tilt(self):
185 return self._tilt
187 @tilt.setter # PYCHOK setter!
188 def tilt(self, tilt):
189 t = Degrees(tilt=tilt, wrap=wrap180, Error=AttitudeError)
190 if self._tilt != t:
191 _update_all(self)
192 self._tilt = t
194 elevation = pitch = tilt
196 def toStr(self, prec=6, sep=_COMMASPACE_, **unused): # PYCHOK signature
197 '''Format this attitude as string.
199 @kwarg prec: The C{float} precision, number of decimal digits (0..9).
200 Trailing zero decimals are stripped for B{C{prec}} values
201 of 1 and above, but kept for negative B{C{prec}} values.
202 @kwarg sep: Separator to join (C{str}).
204 @return: This attitude (C{str}).
205 '''
206 return self.atyr.toStr(prec=prec, sep=sep)
208 @Property_RO
209 def tyr3d(self):
210 '''Get this attitude's (3-D) directional vector (L{Vector3d}).
212 @see: U{Yaw, pitch, and roll rotations<http://MSL.CS.UIUC.edu/planning/node102.html>}.
213 '''
214 def _r2d(r):
215 return fsumf_(_N_1_0, *r)
217 return Vector3d(*map(_r2d, self.matrix), name=tyr3d.__name__)
219 @property_doc_(' yaw/bearing/heading in compass C{degrees360}, clockwise from North.')
220 def yaw(self):
221 return self._yaw
223 @yaw.setter # PYCHOK setter!
224 def yaw(self, yaw):
225 y = Bearing(yaw=yaw, Error=AttitudeError)
226 if self._yaw != y:
227 _update_all(self)
228 self._yaw = y
230 bearing = heading = yaw
233class AttitudeError(_ValueError):
234 '''An L{Attitude} or L{Attitude4Tuple} issue.
235 '''
236 pass
239class Frustum(_NamedBase):
240 '''A rectangular pyramid, typically representing a camera's I{field-of-view}
241 (fov) and the intersection with (or projection to) a I{local tangent plane}.
243 @see: U{Viewing frustum<https://WikiPedia.org/wiki/Viewing_frustum>}.
244 '''
245 _h_2 = _0_0 # half hfov in degrees
246 _ltp = None # local tangent plane
247 _tan_h_2 = _0_0 # tan(_h_2)
248 _v_2 = _0_0 # half vfov in degrees
250 def __init__(self, hfov, vfov, ltp=None):
251 '''New L{Frustum}.
253 @arg hfov: Horizontal field-of-view (C{degrees180}).
254 @arg vfov: Vertical field-of-view (C{degrees180}).
255 @kwarg ltp: Optional I{local tangent plane} (L{Ltp}).
257 @raise LocalError: Invalid B{C{hfov}} or B{C{vfov}}.
258 '''
259 self._h_2 = h = _fov_2(hfov=hfov)
260 self._v_2 = _fov_2(vfov=vfov)
262 self._tan_h_2 = tand(h, hfov_2=h)
264 if ltp:
265 self._ltp = _xLtp(ltp)
267 def footprint5(self, alt_attitude, tilt=0, yaw=0, roll=0, z=_0_0, ltp=None): # MCCABE 15
268 '''Compute the center and corners of the intersection with (or projection
269 to) the I{local tangent plane} (LTP).
271 @arg alt_attitude: An altitude (C{meter}) above I{local tangent plane} or
272 an attitude (L{Attitude} or L{Attitude4Tuple}) with the
273 C{B{alt}itude}, B{C{tilt}}, B{C{yaw}} and B{C{roll}}.
274 @kwarg tilt: Pitch, elevation from horizontal (C{degrees}), negative down
275 (clockwise rotation along and around the x- or East axis).
276 @kwarg yaw: Bearing, heading (compass C{degrees}), clockwise from North
277 (counter-clockwise rotation along and around the z- or Up axis).
278 @kwarg roll: Roll, bank (C{degrees}), positive to the right and down
279 (clockwise rotation along and around the y- or North axis).
280 @kwarg z: Optional height of the footprint (C{meter}) above I{local tangent plane}.
281 @kwarg ltp: The I{local tangent plane} (L{Ltp}), overriding this
282 frustum's C{ltp}.
284 @return: A L{Footprint5Tuple}C{(center, upperleft, upperight, loweright,
285 lowerleft)} with the C{center} and 4 corners, each an L{Xyz4Tuple}.
287 @raise TypeError: Invalid B{C{ltp}}.
289 @raise UnitError: Invalid B{C{altitude}}, B{C{tilt}}, B{C{roll}} or B{C{z}}.
291 @raise ValueError: If B{C{altitude}} too low, B{C{z}} too high or B{C{tilt}}
292 or B{C{roll}} -including B{C{vfov}} respectively B{C{hfov}}-
293 over the horizon.
295 @see: U{Principal axes<https://WikiPedia.org/wiki/Aircraft_principal_axes>}.
296 '''
297 def _xy2(a, e, h_2, tan_h_2, r):
298 # left and right corners, or swapped
299 if r < EPS: # no roll
300 r = a * tan_h_2
301 l = -r # PYCHOK l is ell
302 else: # roll
303 r, l = tand_(r - h_2, r + h_2, roll_hfov=r) # PYCHOK l is ell
304 r *= -a # negate right positive
305 l *= -a # PYCHOK l is ell
306 y = a * cotd(e, tilt_vfov=e)
307 return (l, y), (r, y)
309 def _xyz5(b, xy5, z, ltp):
310 # rotate (x, y)'s by bearing, clockwise
311 s, c = sincos2d(b)
312 _f = fsum1f_
313 for x, y in xy5:
314 yield Xyz4Tuple(_f(x * c, y * s),
315 _f(y * c, -x * s), z, ltp)
317 try:
318 a, t, y, r = alt_attitude.atyr
319 except AttributeError:
320 a, t, y, r = alt_attitude, tilt, yaw, roll
322 a = Meter(altitude=a)
323 if a < EPS: # too low
324 raise _ValueError(altitude=a)
325 if z: # PYCHOK no cover
326 z = Meter(z=z)
327 a -= z
328 if a < EPS: # z above a
329 raise _ValueError(altitude_z=a)
330 else:
331 z = _0_0
333 b = Degrees(yaw=y, wrap=wrap360) # bearing
334 e = -Degrees(tilt=t, wrap=wrap180) # elevation, pitch
335 if not EPS < e < _180_0:
336 raise _ValueError(tilt=t)
337 if e > _90_0:
338 e = _loneg(e)
339 b = _umod_360(b + _180_0)
341 r = Degrees(roll=r, wrap=wrap180) # roll center
342 x = (-a * tand(r, roll=r)) if r else _0_0
343 y = a * cotd(e, tilt=t) # ground range
344 if fabs(y) < EPS:
345 y = _0_0
347 v, h, t = self._v_2, self._h_2, self._tan_h_2
348 # center and corners, clockwise from upperleft, rolled
349 xy5 = ((x, y),) + _xy2(a, e - v, h, t, r) \
350 + _xy2(a, e + v, -h, -t, r) # swapped
351 # turn center and corners by yaw, clockwise
352 p = self.ltp if ltp is None else ltp # None OK
353 return Footprint5Tuple(_xyz5(b, xy5, z, p)) # *_xyz5
355 @Property_RO
356 def hfov(self):
357 '''Get the horizontal C{fov} (C{degrees}).
358 '''
359 return Degrees(hfov=self._h_2 * _2_0)
361 @Property_RO
362 def ltp(self):
363 '''Get the I{local tangent plane} (L{Ltp}) or C{None}.
364 '''
365 return self._ltp
367 def toStr(self, prec=3, fmt=Fmt.F, sep=_COMMASPACE_): # PYCHOK signature
368 '''Convert this frustum to a "hfov, vfov, ltp" string.
370 @kwarg prec: Number of (decimal) digits, unstripped (0..8 or C{None}).
371 @kwarg fmt: Optional, C{float} format (C{letter}).
372 @kwarg sep: Separator to join (C{str}).
374 @return: Frustum in the specified form (C{str}).
375 '''
376 t = self.hfov, self.vfov
377 if self.ltp:
378 t += self.ltp,
379 t = strs(t, prec=prec, fmt=fmt)
380 return sep.join(t) if sep else t
382 @Property_RO
383 def vfov(self):
384 '''Get the vertical C{fov} (C{degrees}).
385 '''
386 return Degrees(vfov=self._v_2 * _2_0)
389class LocalError(_ValueError):
390 '''A L{LocalCartesian} or L{Ltp} related issue.
391 '''
392 pass
395class LocalCartesian(_NamedBase):
396 '''Conversion between geodetic C{(lat, lon, height)} and I{local
397 cartesian} C{(x, y, z)} coordinates with I{geodetic} origin
398 C{(lat0, lon0, height0)}, transcoded from I{Karney}'s C++ class
399 U{LocalCartesian<https://GeographicLib.SourceForge.io/C++/doc/
400 classGeographicLib_1_1LocalCartesian.html>}.
402 The C{z} axis is normal to the ellipsoid, the C{y} axis points due
403 North. The plane C{z = -height0} is tangent to the ellipsoid.
405 The conversions all take place via geocentric coordinates using a
406 geocentric L{EcefKarney}, by default the WGS84 datum/ellipsoid.
408 @see: Class L{Ltp}.
409 '''
410 _ecef = EcefKarney(_WGS84)
411 _Ecef = EcefKarney
412 _lon00 = INT0 # self.lon0
413 _t0 = None # origin (..., lat0, lon0, height0, ...) L{Ecef9Tuple}
414 _9Tuple = Local9Tuple
416 def __init__(self, latlonh0=INT0, lon0=INT0, height0=INT0, ecef=None, name=NN, **lon00):
417 '''New L{LocalCartesian} converter.
419 @kwarg latlonh0: The (geodetic) origin (C{LatLon}, L{LatLon4Tuple}, L{Ltp}
420 L{LocalCartesian} or L{Ecef9Tuple}) or the C{scalar}
421 latitude of the (goedetic) origin (C{degrees}).
422 @kwarg lon0: Longitude of the (goedetic) origin (C{degrees}) for C{scalar}
423 B{C{latlonh0}}, ignored otherwise.
424 @kwarg height0: Optional height (C{meter}, conventionally) at the (goedetic)
425 origin perpendicular to and above (or below) the ellipsoid's
426 surface and for C{scalar} B{C{latlonh0}}, ignored otherwise.
427 @kwarg ecef: An ECEF converter (L{EcefKarney} I{only}) for C{scalar}
428 B{C{latlonh0}}, ignored otherwise.
429 @kwarg name: Optional name (C{str}).
430 @kwarg lon00: An arbitrary, I{polar} longitude (C{degrees}), overriding
431 the default C{B{lon00}=B{lon0}}, see method C{reverse}.
433 @raise LocalError: If B{C{latlonh0}} not C{LatLon}, L{LatLon4Tuple}, L{Ltp},
434 L{LocalCartesian} or L{Ecef9Tuple} or B{C{latlonh0}},
435 B{C{lon0}}, B{C{height0}} or B{C{lon00}} invalid.
437 @raise TypeError: Invalid B{C{ecef}} or not L{EcefKarney}.
439 @note: If BC{latlonh0} is an L{Ltp} or L{LocalCartesian}, only C{lat0}, C{lon0},
440 C{height0} and I{polar} C{lon00} are copied, I{not} the ECEF converter.
441 '''
442 self.reset(latlonh0, lon0=lon0, height0=height0, ecef=ecef, name=name, **lon00)
444 def __eq__(self, other):
445 '''Compare this and an other instance.
447 @arg other: The other ellipsoid (L{LocalCartesian} or L{Ltp}).
449 @return: C{True} if equal, C{False} otherwise.
450 '''
451 return other is self or (isinstance(other, self.__class__) and
452 other.ecef == self.ecef and
453 other._t0 == self._t0)
455 @Property_RO
456 def datum(self):
457 '''Get the ECEF converter's datum (L{Datum}).
458 '''
459 return self.ecef.datum
461 @Property_RO
462 def ecef(self):
463 '''Get the ECEF converter (L{EcefKarney}).
464 '''
465 return self._ecef
467 def _ecef2local(self, ecef, Xyz, Xyz_kwds):
468 '''(INTERNAL) Convert geocentric/geodetic to local, like I{forward}.
470 @arg ecef: Geocentric (and geodetic) (L{Ecef9Tuple}).
471 @arg Xyz: An L{XyzLocal}, L{Enu} or L{Ned} I{class} or C{None}.
472 @arg Xyz_kwds: B{C{Xyz}} keyword arguments, ignored if C{B{Xyz} is None}.
474 @return: An C{B{Xyz}(x, y, z, ltp, **B{Xyz_kwds}} instance or if
475 C{B{Xyz} is None}, a L{Local9Tuple}C{(x, y, z, lat, lon,
476 height, ltp, ecef, M)} with this C{ltp}, B{C{ecef}}
477 (L{Ecef9Tuple}) converted to this C{datum} and C{M=None},
478 always.
479 '''
480 ltp = self
481 if ecef.datum != ltp.datum:
482 ecef = ecef.toDatum(ltp.datum)
483 x, y, z = self.M.rotate(ecef.xyz, *ltp._t0_xyz)
484 r = Local9Tuple(x, y, z, ecef.lat, ecef.lon, ecef.height,
485 ltp, ecef, None, name=ecef.name)
486 if Xyz:
487 if not issubclassof(Xyz, *_XyzLocals4): # Vector3d
488 raise _TypesError(_Xyz_, Xyz, *_XyzLocals4)
489 r = r.toXyz(Xyz=Xyz, **Xyz_kwds)
490 return r
492 @Property_RO
493 def ellipsoid(self):
494 '''Get the ECEF converter's ellipsoid (L{Ellipsoid}).
495 '''
496 return self.ecef.datum.ellipsoid
498 def forward(self, latlonh, lon=None, height=0, M=False, name=NN):
499 '''Convert I{geodetic} C{(lat, lon, height)} to I{local} cartesian
500 C{(x, y, z)}.
502 @arg latlonh: Either a C{LatLon}, L{Ltp}, L{Ecef9Tuple} or C{scalar}
503 (geodetic) latitude (C{degrees}).
504 @kwarg lon: Optional C{scalar} (geodetic) longitude for C{scalar}
505 B{C{latlonh}} (C{degrees}).
506 @kwarg height: Optional height (C{meter}, conventionally) perpendicular
507 to and above (or below) the ellipsoid's surface.
508 @kwarg M: Optionally, return the I{concatenated} rotation L{EcefMatrix},
509 iff available (C{bool}).
510 @kwarg name: Optional name (C{str}).
512 @return: A L{Local9Tuple}C{(x, y, z, lat, lon, height, ltp, ecef, M)}
513 with I{local} C{x}, C{y}, C{z}, I{geodetic} C{(lat}, C{lon},
514 C{height}, this C{ltp}, C{ecef} (L{Ecef9Tuple}) with
515 I{geocentric} C{x}, C{y}, C{z} (and I{geodetic} C{lat},
516 C{lon}, C{height}) and the I{concatenated} rotation matrix
517 C{M} (L{EcefMatrix}) if requested.
519 @raise LocalError: If B{C{latlonh}} not C{scalar}, C{LatLon}, L{Ltp},
520 L{Ecef9Tuple} or invalid or if B{C{lon}} not
521 C{scalar} for C{scalar} B{C{latlonh}} or invalid
522 or if B{C{height}} invalid.
523 '''
524 lat, lon, h, n = _llhn4(latlonh, lon, height, Error=LocalError, name=name)
525 t = self.ecef._forward(lat, lon, h, n, M=M)
526 x, y, z = self.M.rotate(t.xyz, *self._t0_xyz)
527 m = self.M.multiply(t.M) if M else None
528 return self._9Tuple(x, y, z, lat, lon, h, self, t, m, name=n or self.name)
530 @Property_RO
531 def height0(self):
532 '''Get the origin's height (C{meter}).
533 '''
534 return self._t0.height
536 @Property_RO
537 def lat0(self):
538 '''Get the origin's latitude (C{degrees}).
539 '''
540 return self._t0.lat
542 @Property_RO
543 def latlonheight0(self):
544 '''Get the origin's lat-, longitude and height (L{LatLon3Tuple}C{(lat, lon, height)}).
545 '''
546 return LatLon3Tuple(self.lat0, self.lon0, self.height0, name=self.name)
548 def _local2ecef(self, local, nine=False, M=False):
549 '''(INTERNAL) Convert I{local} to geocentric/geodetic, like I{.reverse}.
551 @arg local: Local (L{XyzLocal}, L{Enu}, L{Ned}, L{Aer} or L{Local9Tuple}).
552 @kwarg nine: Return 3- or 9-tuple (C{bool}).
553 @kwarg M: Include the rotation matrix (C{bool}).
555 @return: A I{geocentric} 3-tuple C{(x, y, z)} or if C{B{nine}=True},
556 an L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)},
557 optionally including rotation matrix C{M} or C{None}.
558 '''
559 t = self.M.unrotate(local.xyz, *self._t0_xyz)
560 if nine:
561 t = self.ecef.reverse(*t, M=M)
562 return t
564 @Property_RO
565 def lon0(self):
566 '''Get the origin's longitude (C{degrees}).
567 '''
568 return self._t0.lon
570 @Property
571 def lon00(self):
572 '''Get the arbitrary, I{polar} longitude (C{degrees}).
573 '''
574 return self._lon00
576 @lon00.setter # PYCHOK setter!
577 def lon00(self, lon00):
578 '''Set the arbitrary, I{polar} longitude (C{degrees}).
579 '''
580 # lon00 <https://GitHub.com/mrJean1/PyGeodesy/issues/77>
581 self._lon00 = Degrees(lon00=lon00)
583 @Property_RO
584 def M(self):
585 '''Get the rotation matrix (C{EcefMatrix}).
586 '''
587 return self._t0.M
589 def reset(self, latlonh0=INT0, lon0=INT0, height0=INT0, ecef=None, name=NN, **lon00):
590 '''Reset this converter, see L{LocalCartesian.__init__} and L{Ltp.__init__} for more details.
591 '''
592 if isinstance(latlonh0, LocalCartesian):
593 if self._t0:
594 _update_all(self)
595 self._ecef = latlonh0.ecef
596 self._lon00 = latlonh0.lon00
597 self._t0 = latlonh0._t0
598 n = name or latlonh0.name
599 else:
600 lat0, lon0, height0, n = _llhn4(latlonh0, lon0, height0, suffix=_0_,
601 Error=LocalError, name=name or self.name)
602 if ecef: # PYCHOK no cover
603 _xinstanceof(self._Ecef, ecef=ecef)
604 _update_all(self)
605 self._ecef = ecef
606 elif self._t0:
607 _update_all(self)
608 self._t0 = self.ecef._forward(lat0, lon0, height0, n, M=True)
609 self.lon00 = _xattr(latlonh0, lon00=_xkwds_get(lon00, lon00=lon0))
610 if n:
611 self.rename(n)
613 def reverse(self, xyz, y=None, z=None, M=False, name=NN, **lon00):
614 '''Convert I{local} C{(x, y, z)} to I{geodetic} C{(lat, lon, height)}.
616 @arg xyz: A I{local} (L{XyzLocal}, L{Enu}, L{Ned}, L{Aer}, L{Local9Tuple}) or
617 local C{x} coordinate (C{scalar}).
618 @kwarg y: Local C{y} coordinate for C{scalar} B{C{xyz}} and B{C{z}} (C{meter}).
619 @kwarg z: Local C{z} coordinate for C{scalar} B{C{xyz}} and B{C{y}} (C{meter}).
620 @kwarg M: Optionally, return the I{concatenated} rotation L{EcefMatrix}, iff
621 available (C{bool}).
622 @kwarg name: Optional name (C{str}).
623 @kwarg lon00: An arbitrary, I{polar} longitude (C{degrees}), returned for local
624 C{B{x}=0} and C{B{y}=0} at I{polar} latitudes C{abs(B{lat0}) == 90},
625 overriding property C{lon00} and default C{B{lon00}=B{lon0}}.
627 @return: An L{Local9Tuple}C{(x, y, z, lat, lon, height, ltp, ecef, M)} with
628 I{local} C{x}, C{y}, C{z}, I{geodetic} C{lat}, C{lon}, C{height},
629 this C{ltp}, an C{ecef} (L{Ecef9Tuple}) with the I{geocentric} C{x},
630 C{y}, C{z} (and I{geodetic} C{lat}, C{lon}, C{height}) and the
631 I{concatenated} rotation matrix C{M} (L{EcefMatrix}) if requested.
633 @raise LocalError: Invalid B{C{xyz}} or C{scalar} C{x} or B{C{y}} and/or B{C{z}}
634 not C{scalar} for C{scalar} B{C{xyz}}.
635 '''
636 x, y, z, n = _xyzn4(xyz, y, z, _XyzLocals5, Error=LocalError, name=name)
637 c = self.M.unrotate((x, y, z), *self._t0_xyz)
638 t = self.ecef.reverse(*c, M=M, lon00=_xkwds_get(lon00, lon00=self.lon00))
639 m = self.M.multiply(t.M) if M else None
640 return self._9Tuple(x, y, z, t.lat, t.lon, t.height, self, t, m, name=n or self.name)
642 @Property_RO
643 def _t0_xyz(self):
644 '''(INTERNAL) Get C{(x0, y0, z0)} as L{Vector3Tuple}.
645 '''
646 return self._t0.xyz
648 def toStr(self, prec=9, **unused): # PYCHOK signature
649 '''Return this L{LocalCartesian} as a string.
651 @kwarg prec: Precision, number of (decimal) digits (0..9).
653 @return: This L{LocalCartesian} representation (C{str}).
654 '''
655 return self.attrs(_lat0_, _lon0_, _height0_, _M_, _ecef_, _name_, prec=prec)
658class Ltp(LocalCartesian):
659 '''A I{local tangent plan} (LTP), a sub-class of C{LocalCartesian} with
660 (re-)configurable ECEF converter.
661 '''
662 _Ecef = _EcefBase
664 def __init__(self, latlonh0=INT0, lon0=INT0, height0=INT0, ecef=None, name=NN, **lon00):
665 '''New C{Ltp}, see L{LocalCartesian.__init__} for more details.
667 @kwarg ecef: Optional ECEF converter (L{EcefKarney}, L{EcefFarrell21},
668 L{EcefFarrell22}, L{EcefSudano}, L{EcefVeness} or
669 L{EcefYou} I{instance}), overriding the default
670 L{EcefKarney}C{(datum=Datums.WGS84)} for C{scalar}.
672 @raise TypeError: Invalid B{C{ecef}}.
673 '''
674 LocalCartesian.reset(self, latlonh0, lon0=lon0, height0=height0,
675 ecef=ecef, name=name, **lon00)
677 @Property
678 def ecef(self):
679 '''Get this LTP's ECEF converter (C{Ecef...} I{instance}).
680 '''
681 return self._ecef
683 @ecef.setter # PYCHOK setter!
684 def ecef(self, ecef):
685 '''Set this LTP's ECEF converter (C{Ecef...} I{instance}).
687 @raise TypeError: Invalid B{C{ecef}}.
688 '''
689 _xinstanceof(_EcefBase, ecef=ecef)
690 if self._ecef != ecef: # PYCHOK no cover
691 self.reset(self._t0)
692 self._ecef = ecef
695class _ChLV(object):
696 '''(INTERNAL) Base class for C{ChLV*} classes.
697 '''
698 _03_falsing = ChLVyx2Tuple(0.6e6, 0.2e6)
699# _92_falsing = ChLVYX2Tuple(2.0e6, 1.0e6) # _95_ - _03_
700 _95_falsing = ChLVEN2Tuple(2.6e6, 1.2e6)
702 def _ChLV9Tuple(self, fw, M, name, *Y_X_h_lat_lon_h):
703 '''(INTERNAL) Helper for C{ChLVa/e.forward} and C{.reverse}.
704 '''
705 if bool(M): # PYCHOK no cover
706 m = self.forward if fw else self.reverse # PYCHOK attr
707 n = _DOT_(self.__class__.__name__, m.__name__)
708 raise _NotImplementedError(unstr(n, M=M), txt=None)
709 t = Y_X_h_lat_lon_h + (self, self._t0, None) # PYCHOK _t0
710 return ChLV9Tuple(t, name=name)
712 @property_RO
713 def _enh_n_h(self):
714 '''(INTERNAL) Get C{ChLV*.reverse} args[1:4] names, I{once}.
715 '''
716 _ChLV._enh_n_h = t = _args_kwds_names(_ChLV.reverse)[1:4] # overwrite property_RO
717 # assert _args_kwds_names( ChLV.reverse)[1:4] == t
718 # assert _args_kwds_names(ChLVa.reverse)[1:4] == t
719 # assert _args_kwds_names(ChLVe.reverse)[1:4] == t
720 return t
722 def forward(self, latlonh, lon=None, height=0, M=None, name=NN): # PYCHOK no cover
723 '''Convert WGS84 geodetic to I{Swiss} projection coordinates. I{Must be overloaded}.
725 @arg latlonh: Either a C{LatLon}, L{Ltp} or C{scalar} (geodetic) latitude (C{degrees}).
726 @kwarg lon: Optional, C{scalar} (geodetic) longitude for C{scalar} B{C{latlonh}} (C{degrees}).
727 @kwarg height: Optional, height, vertically above (or below) the surface of the ellipsoid
728 (C{meter}) for C{scalar} B{C{latlonh}} and B{C{lon}}.
729 @kwarg M: If C{True}, return the I{concatenated} rotation L{EcefMatrix} iff available
730 for C{ChLV} only, C{None} otherwise (C{bool}).
731 @kwarg name: Optional name (C{str}).
733 @return: A L{ChLV9Tuple}C{(Y, X, h_, lat, lon, height, ltp, ecef, M)} with the unfalsed
734 I{Swiss Y, X} coordinates, I{Swiss h_} height, the given I{geodetic} C{lat},
735 C{lon} and C{height}, this C{ChLV*} instance and C{ecef} (L{Ecef9Tuple}) at
736 I{Bern, Ch} and rotation matrix C{M}. The returned C{ltp} is this C{ChLV},
737 C{ChLVa} or C{ChLVe} instance.
739 @raise LocalError: Invalid or non-C{scalar} B{C{latlonh}}, B{C{lon}} or B{C{height}}.
740 '''
741 notOverloaded(self, latlonh, lon=lon, height=height, M=M, name=name)
743 def reverse(self, enh_, n=None, h_=0, M=None, **name): # PYCHOK no cover
744 '''Convert I{Swiss} projection to WGS84 geodetic coordinates.
746 @arg enh_: A Swiss projection (L{ChLV9Tuple}) or the C{scalar}, falsed I{Swiss E_LV95}
747 or I{y_LV03} easting (C{meter}).
748 @kwarg n: Falsed I{Swiss N_LV85} or I{x_LV03} northing for C{scalar} B{C{enh_}} and
749 B{C{h_}} (C{meter}).
750 @kwarg h_: I{Swiss h'} height for C{scalar} B{C{enh_}} and B{C{n}} (C{meter}).
751 @kwarg M: If C{True}, return the I{concatenated} rotation L{EcefMatrix} iff available
752 for C{ChLV} only, C{None} otherwise (C{bool}).
753 @kwarg name: Optional name (C{str}).
755 @return: A L{ChLV9Tuple}C{(Y, X, h_, lat, lon, height, ltp, ecef, M)} with the unfalsed
756 I{Swiss Y, X} coordinates, I{Swiss h_} height, the given I{geodetic} C{lat},
757 C{lon} and C{height}, this C{ChLV*} instance and C{ecef} (L{Ecef9Tuple}) at
758 I{Bern, Ch} and rotation matrix C{M}. The returned C{ltp} is this C{ChLV},
759 C{ChLVa} or C{ChLVe} instance.
761 @raise LocalError: Invalid or non-C{scalar} B{C{enh_}}, B{C{n}} or B{C{h_}}.
762 '''
763 notOverloaded(self, enh_, n=n, h_=h_, M=M, **name)
765 @staticmethod
766 def _falsing2(LV95):
767 '''(INTERNAL) Get the C{LV95} or C{LV03} falsing.
768 '''
769 return _ChLV._95_falsing if LV95 in (True, 95) else (
770 _ChLV._03_falsing if LV95 in (False, 3) else ChLVYX2Tuple(0, 0))
772 @staticmethod
773 def _llh2abh_3(lat, lon, h):
774 '''(INTERNAL) Helper for C{ChLVa/e.forward}.
775 '''
776 def _deg2ab(deg, sLL):
777 # convert degrees to arc-seconds
778 def _dms(ds, p, q, swap):
779 d = _floor(ds)
780 t = (ds - d) * p
781 m = _floor(t)
782 s = (t - m) * p
783 if swap:
784 d, s = s, d
785 return d + (m + s * q) * q
787 s = _dms(deg, _60_0, _0_01, False) # deg2sexag
788 s = _dms( s, _100_0, _60_0, True) # sexag2asec
789 return (s - sLL) / ChLV._s_ab
791 a = _deg2ab(lat, ChLV._sLat) # phi', lat_aux
792 b = _deg2ab(lon, ChLV._sLon) # lam', lng_aux
793 h_ = fsumf_(h, -ChLV.Bern.height, 2.73 * b, 6.94 * a)
794 return a, b, h_
796 @staticmethod
797 def _YXh_2abh3(Y, X, h_):
798 '''(INTERNAL) Helper for C{ChLVa/e.reverse}.
799 '''
800 def _YX2ab(YX):
801 return YX * ChLV._ab_m
803 a, b = map1(_YX2ab, Y, X)
804 h = fsumf_(h_, ChLV.Bern.height, -12.6 * a, -22.64 * b)
805 return a, b, h
807 def _YXh_n4(self, enh_, n, h_, **name):
808 '''(INTERNAL) Helper for C{ChLV*.reverse}.
809 '''
810 Y, X, h_, name = _xyzn4(enh_, n, h_, ChLV9Tuple,
811 _xyz_y_z_names=self._enh_n_h, **name)
812 if isinstance(enh_, ChLV9Tuple):
813 Y, X = enh_.Y, enh_.X
814 else: # isscalar(enh_)
815 Y, X = ChLV.unfalse2(Y, X) # PYCHOK ChLVYX2Tuple
816 return Y, X, h_, name
819class ChLV(_ChLV, Ltp):
820 '''Conversion between I{WGS84 geodetic} and I{Swiss} projection coordinates using
821 L{pygeodesy.EcefKarney}'s Earth-Centered, Earth-Fixed (ECEF) methods.
823 @see: U{Swiss projection formulas<https://www.SwissTopo.admin.CH/en/maps-data-online/
824 calculation-services.html>}, page 7ff, U{NAVREF<https://www.SwissTopo.admin.CH/en/
825 maps-data-online/calculation-services/navref.html>}, U{REFRAME<https://www.SwissTopo.admin.CH/
826 en/maps-data-online/calculation-services/reframe.html>} and U{SwissTopo Scripts GPS WGS84
827 <-> LV03<https://GitHub.com/ValentinMinder/Swisstopo-WGS84-LV03>}.
828 '''
829 _9Tuple = ChLV9Tuple
831 _ab_d = 0.36 # a, b units per degree, ...
832 _ab_m = 1.0e-6 # ... per meter and ...
833 _ab_M = _1_0 # ... per 1,000 Km or 1 Mm
834 _s_d = _3600_0 # arc-seconds per degree ...
835 _s_ab = _s_d / _ab_d # ... and per a, b unit
836 _sLat = 169028.66 # Bern, Ch in ...
837 _sLon = 26782.5 # ... arc-seconds ...
838 # lat, lon, height == 46°57'08.66", 7°26'22.50", 49.55m ("new" 46°57'07.89", 7°26'22.335")
839 Bern = LatLon4Tuple(_sLat / _s_d, _sLon / _s_d, 49.55, _WGS84, name='Bern')
841 def __init__(self, latlonh0=Bern, **other_Ltp_kwds):
842 '''New ECEF-based I{WGS84-Swiss} L{ChLV} converter, centered at I{Bern, Ch}.
844 @kwarg latlonh0: The I{geodetic} origin and height, overriding C{Bern, Ch}.
845 @kwarg other_Ltp_kwds: Optional, other L{Ltp.__init__} keyword arguments.
847 @see: L{Ltp.__init__} for more information.
848 '''
849 Ltp.__init__(self, latlonh0, **_xkwds(other_Ltp_kwds, ecef=None, name=ChLV.Bern.name))
851 def forward(self, latlonh, lon=None, height=0, M=None, name=NN): # PYCHOK unused M
852 # overloaded for the _ChLV.forward.__doc__
853 return Ltp.forward(self, latlonh, lon=lon, height=height, M=M, name=name)
855 def reverse(self, enh_, n=None, h_=0, M=None, **name): # PYCHOK signature
856 # overloaded for the _ChLV.reverse.__doc__
857 Y, X, h_, name = self._YXh_n4(enh_, n, h_, **name)
858 return Ltp.reverse(self, Y, X, h_, M=M, name=name)
860 @staticmethod
861 def false2(Y, X, LV95=True, name=NN):
862 '''Add the I{Swiss LV95} or I{LV03} falsing.
864 @arg Y: Unfalsed I{Swiss Y} easting (C{meter}).
865 @arg X: Unfalsed I{Swiss X} northing (C{meter}).
866 @kwarg LV95: If C{True} add C{LV95} falsing, if C{False} add
867 C{LV03} falsing, otherwise leave unfalsed.
868 @kwarg name: Optional name (C{str}).
870 @return: A L{ChLVEN2Tuple}C{(E_LV95, N_LV95)} or a
871 L{ChLVyx2Tuple}C{(y_LV03, x_LV03)} with falsed B{C{Y}}
872 and B{C{X}}, otherwise a L{ChLVYX2Tuple}C{(Y, X)}
873 with B{C{Y}} and B{C{X}} as-is.
874 '''
875 e, n = t = _ChLV._falsing2(LV95)
876 return t.classof(e + Y, n + X, name=name)
878 @staticmethod
879 def isLV03(e, n):
880 '''Is C{(B{e}, B{n})} a valid I{Swiss LV03} projection?
882 @arg e: Falsed (or unfalsed) I{Swiss} easting (C{meter}).
883 @arg n: Falsed (or unfalsed) I{Swiss} northing (C{meter}).
885 @return: C{True} if C{(B{e}, B{n})} is a valid, falsed I{Swiss
886 LV03}, projection C{False} otherwise.
887 '''
888 # @see: U{Map<https://www.SwissTopo.admin.CH/en/knowledge-facts/
889 # surveying-geodesy/reference-frames/local/lv95.html>}
890 return 400.0e3 < e < 900.0e3 and 40.0e3 < n < 400.0e3
892 @staticmethod
893 def isLV95(e, n, raiser=True):
894 '''Is C{(B{e}, B{n})} a valid I{Swiss LV95} or I{LV03} projection?
896 @arg e: Falsed (or unfalsed) I{Swiss} easting (C{meter}).
897 @arg n: Falsed (or unfalsed) I{Swiss} northing (C{meter}).
898 @kwarg raiser: If C{True}, throw a L{LocalError} if B{C{e}} and
899 B{C{n}} are invalid I{Swiss LV95} nor I{LV03}.
901 @return: C{True} or C{False} if C{(B{e}, B{n})} is a valid I{Swiss
902 LV95} respectively I{LV03} projection, C{None} otherwise.
903 '''
904 if ChLV.isLV03(e, n):
905 return False
906 elif ChLV.isLV03(e - 2.0e6, n - 1.0e6): # _92_falsing = _95_ - _03_
907 return True
908 elif raiser: # PYCHOK no cover
909 raise LocalError(unstr(ChLV.isLV95, e=e, n=n))
910 return None
912 @staticmethod
913 def unfalse2(e, n, LV95=None, name=NN):
914 '''Remove the I{Swiss LV95} or I{LV03} falsing.
916 @arg e: Falsed I{Swiss E_LV95} or I{y_LV03} easting (C{meter}).
917 @arg n: Falsed I{Swiss N_LV95} or I{x_LV03} northing (C{meter}).
918 @kwarg LV95: If C{True} remove I{LV95} falsing, if C{False} remove
919 I{LV03} falsing, otherwise use method C{isLV95(B{e},
920 B{n})}.
921 @kwarg name: Optional name (C{str}).
923 @return: A L{ChLVYX2Tuple}C{(Y, X)} with the unfalsed B{C{e}}
924 respectively B{C{n}}.
925 '''
926 Y, X = _ChLV._falsing2(ChLV.isLV95(e, n) if LV95 is None else LV95)
927 return ChLVYX2Tuple(e - Y, n - X, name=name)
930class ChLVa(_ChLV, LocalCartesian):
931 '''Conversion between I{WGS84 geodetic} and I{Swiss} projection coordinates
932 using the U{Approximate<https://www.SwissTopo.admin.CH/en/maps-data-online/
933 calculation-services.html>} formulas, page 13.
935 @see: Older U{references<https://GitHub.com/alphasldiallo/Swisstopo-WGS84-LV03>}.
936 '''
937 def __init__(self, name=ChLV.Bern.name):
938 '''New I{Approximate WGS84-Swiss} L{ChLVa} converter, centered at I{Bern, Ch}.
940 @kwarg name: Optional name (C{str}), overriding C{Bern.name}.
941 '''
942 LocalCartesian.__init__(self, latlonh0=ChLV.Bern, name=name)
944 def forward(self, latlonh, lon=None, height=0, M=None, name=NN):
945 # overloaded for the _ChLV.forward.__doc__
946 lat, lon, h, name = _llhn4(latlonh, lon, height, name=name)
947 a, b, h_ = _ChLV._llh2abh_3(lat, lon, h)
948 a2, b2 = a**2, b**2
950 Y = fsumf_( 72.37, 211455.93 * b,
951 -10938.51 * b * a,
952 -0.36 * b * a2,
953 -44.54 * b * b2) # + 600_000
954 X = fsumf_(147.07, 308807.95 * a,
955 3745.25 * b2,
956 76.63 * a2,
957 -194.56 * b2 * a,
958 119.79 * a2 * a) # + 200_000
959 return self._ChLV9Tuple(True, M, name, Y, X, h_, lat, lon, h)
961 def reverse(self, enh_, n=None, h_=0, M=None, **name): # PYCHOK signature
962 # overloaded for the _ChLV.reverse.__doc__
963 Y, X, h_, name = self._YXh_n4(enh_, n, h_, **name)
964 a, b, h = _ChLV._YXh_2abh3(Y, X, h_)
965 ab_d, a2, b2 = ChLV._ab_d, a**2, b**2
967 lat = _Fsumf_(16.9023892, 3.238272 * b,
968 -0.270978 * a2,
969 -0.002528 * b2,
970 -0.0447 * a2 * b,
971 -0.014 * b2 * b).fover(ab_d)
972 lon = _Fsumf_( 2.6779094, 4.728982 * a,
973 0.791484 * a * b,
974 0.1306 * a * b2,
975 -0.0436 * a * a2).fover(ab_d)
976 return self._ChLV9Tuple(False, M, name, Y, X, h_, lat, lon, h)
979class ChLVe(_ChLV, LocalCartesian):
980 '''Conversion between I{WGS84 geodetic} and I{Swiss} projection coordinates
981 using the U{Ellipsoidal approximate<https://www.SwissTopo.admin.CH/en/
982 maps-data-online/calculation-services.html>} formulas, pp 10-11 and U{Bolliger,
983 J.<https://eMuseum.GGGS.CH/literatur-lv/liste-Dateien/1967_Bolliger_a.pdf>}
984 pp 148-151 (also U{GGGS<https://eMuseum.GGGS.CH/literatur-lv/liste.htm>}).
986 @note: Methods L{ChLVe.forward} and L{ChLVe.reverse} have an additional keyword
987 argument C{B{gamma}=False} to approximate the I{meridian convergence}.
988 If C{B{gamma}=True} a 2-tuple C{(t, gamma)} is returned with C{t} the
989 usual result (C{ChLV9Tuple}) and C{gamma}, the I{meridian convergence}
990 (decimal C{degrees}). To convert C{gamma} to C{grades} or C{gons},
991 use function L{pygeodesy.degrees2grades}.
993 @see: Older U{references<https://GitHub.com/alphasldiallo/Swisstopo-WGS84-LV03>}.
994 '''
995 def __init__(self, name=ChLV.Bern.name):
996 '''New I{Approximate WGS84-Swiss} L{ChLVe} converter, centered at I{Bern, Ch}.
998 @kwarg name: Optional name (C{str}), overriding C{Bern.name}.
999 '''
1000 LocalCartesian.__init__(self, latlonh0=ChLV.Bern, name=name)
1002 def forward(self, latlonh, lon=None, height=0, M=None, name=NN, gamma=False): # PYCHOK gamma
1003 # overloaded for the _ChLV.forward.__doc__
1004 lat, lon, h, name = _llhn4(latlonh, lon, height, name=name)
1005 a, b, h_ = _ChLV._llh2abh_3(lat, lon, h)
1006 ab_M, z, _H = ChLV._ab_M, 0, Fhorner
1008 B1 = _H(a, 211428.533991, -10939.608605, -2.658213, -8.539078, -0.00345, -0.007992)
1009 B3 = _H(a, -44.232717, 4.291740, -0.309883, 0.013924)
1010 B5 = _H(a, 0.019784, -0.004277)
1011 Y = _H(b, z, B1, z, B3, z, B5).fover(ab_M) # 1,000 Km!
1013 B0 = _H(a, z, 308770.746371, 75.028131, 120.435227, 0.009488, 0.070332, -0.00001)
1014 B2 = _H(a, 3745.408911, -193.792705, 4.340858, -0.376174, 0.004053)
1015 B4 = _H(a, -0.734684, 0.144466, -0.011842)
1016 B6 = 0.000488
1017 X = _H(b, B0, z, B2, z, B4, z, B6).fover(ab_M) # 1,000 Km!
1019 t = self._ChLV9Tuple(True, M, name, Y, X, h_, lat, lon, h)
1020 if gamma:
1021 U1 = _H(a, 2255515.207166, 2642.456961, 1.284180, 2.577486, 0.001165)
1022 U3 = _H(a, -412.991934, 64.106344, -2.679566, 0.123833)
1023 U5 = _H(a, 0.204129, -0.037725)
1024 g = _H(b, z, U1, z, U3, z, U5).fover(ChLV._ab_m) # * ChLV._ab_d degrees?
1025 t = t, g
1026 return t
1028 def reverse(self, enh_, n=None, h_=0, M=None, name=NN, gamma=False): # PYCHOK gamma
1029 # overloaded for the _ChLV.reverse.__doc__
1030 Y, X, h_, name = self._YXh_n4(enh_, n, h_, name=name)
1031 a, b, h = _ChLV._YXh_2abh3(Y, X, h_)
1032 s_d, _H, z = ChLV._s_d, Fhorner, 0
1034 A0 = _H(b, ChLV._sLat, 32386.4877666, -25.486822, -132.457771, 0.48747, 0.81305, -0.0069)
1035 A2 = _H(b, -2713.537919, -450.442705, -75.53194, -14.63049, -2.7604)
1036 A4 = _H(b, 24.42786, 13.20703, 4.7476)
1037 A6 = -0.4249
1038 lat = _H(a, A0, z, A2, z, A4, z, A6).fover(s_d)
1040 A1 = _H(b, 47297.3056722, 7925.714783, 1328.129667, 255.02202, 48.17474, 9.0243)
1041 A3 = _H(b, -442.709889, -255.02202, -96.34947, -30.0808)
1042 A5 = _H(b, 9.63495, 9.0243)
1043 lon = _H(a, ChLV._sLon, A1, z, A3, z, A5).fover(s_d)
1044 # == (ChLV._sLon + a * (A1 + a**2 * (A3 + a**2 * A5))) / s_d
1046 t = self._ChLV9Tuple(False, M, name, Y, X, h_, lat, lon, h)
1047 if gamma:
1048 U1 = _H(b, 106679.792202, 17876.57022, 4306.5241, 794.87772, 148.1545, 27.8725)
1049 U3 = _H(b, -1435.508, -794.8777, -296.309, -92.908)
1050 U5 = _H(b, 29.631, 27.873)
1051 g = _H(a, z, U1, z, U3, z, U5).fover(ChLV._s_ab) # degrees
1052 t = t, g
1053 return t
1056def tyr3d(tilt=INT0, yaw=INT0, roll=INT0, Vector=Vector3d, **Vector_kwds):
1057 '''Convert an attitude oriention into a (3-D) direction vector.
1059 @kwarg tilt: Pitch, elevation from horizontal (C{degrees}), negative down
1060 (clockwise rotation along and around the x-axis).
1061 @kwarg yaw: Bearing, heading (compass C{degrees360}), clockwise from North
1062 (counter-clockwise rotation along and around the z-axis).
1063 @kwarg roll: Roll, bank (C{degrees}), positive to the right and down
1064 (clockwise rotation along and around the y-axis).
1066 @return: A named B{C{Vector}} instance or if B{C{Vector}} is C{None},
1067 a named L{Vector3Tuple}C{(x, y, z)}.
1069 @see: U{Yaw, pitch, and roll rotations<http://MSL.CS.UIUC.edu/planning/node102.html>}
1070 and function L{pygeodesy.hartzell} argument C{los}.
1071 '''
1072 d = Attitude4Tuple(_0_0, tilt, yaw, roll).tyr3d
1073 return d if Vector is type(d) else (
1074 Vector3Tuple(d.x, d.y, d.z, name=d.name) if Vector is None else
1075 Vector(d.x, d.y, d.z, **_xkwds(Vector_kwds, name=d.name))) # PYCHOK indent
1078def _xLtp(ltp, *dflt):
1079 '''(INTERNAL) Validate B{C{ltp}}.
1080 '''
1081 if dflt and ltp is None:
1082 ltp = dflt[0]
1083 if isinstance(ltp, (LocalCartesian, Ltp)):
1084 return ltp
1085 raise _TypesError(_ltp_, ltp, Ltp, LocalCartesian)
1087# **) MIT License
1088#
1089# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.
1090#
1091# Permission is hereby granted, free of charge, to any person obtaining a
1092# copy of this software and associated documentation files (the "Software"),
1093# to deal in the Software without restriction, including without limitation
1094# the rights to use, copy, modify, merge, publish, distribute, sublicense,
1095# and/or sell copies of the Software, and to permit persons to whom the
1096# Software is furnished to do so, subject to the following conditions:
1097#
1098# The above copyright notice and this permission notice shall be included
1099# in all copies or substantial portions of the Software.
1100#
1101# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
1102# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
1103# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
1104# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
1105# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
1106# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
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