"""
Created on 29. des. 2015
@author: pab
"""
from __future__ import division, print_function
import numpy as np
from numpy import pi, arccos, cross, dot
from numpy.linalg import norm
from geographiclib.geodesic import Geodesic as _Geodesic
from nvector._core import (select_ellipsoid, rad, deg, zyx2R,
lat_lon2n_E, n_E2lat_lon, n_E2R_EN, n_E_and_wa2R_EL,
n_EB_E2p_EB_E, p_EB_E2n_EB_E, unit,
great_circle_distance, mean_horizontal_position,
E_rotation)
from nvector import _examples
from nvector._examples import use_docstring_from
import warnings
__all__ = ['FrameE', 'FrameB', 'FrameL', 'FrameN', 'GeoPoint', 'GeoPath',
'Nvector', 'ECEFvector', 'Pvector', 'diff_positions']
[docs]class GeoPoint(object):
"""
Geographical position given as latitude, longitude, depth in frame E
Parameters
----------
latitude, longitude: real scalars or vectors of length n.
Geodetic latitude and longitude given in [rad or deg]
z: real scalar or vector of length n.
Depth(s) [m] relative to the ellipsoid (depth = -height)
frame: FrameE object
reference ellipsoid. The default ellipsoid model used is WGS84, but
other ellipsoids/spheres might be specified.
degrees: bool
True if input are given in degrees otherwise radians are assumed.
Examples
--------
Solve geodesic problems.
The following illustrates its use
>>> import nvector as nv
>>> wgs84 = nv.FrameE(name='WGS84')
The geodesic inverse problem
>>> positionA = wgs84.GeoPoint(-41.32, 174.81, degrees=True))
>>> positionB = wgs84.GeoPoint(40.96, -5.50, degrees=True)
>>> s12, az1, az2 = positionA.distance_and_azimuth(positionB, degrees=True)
>>> 's12 = {:5.2f}, az1 = {:5.2f}, az2 = {:5.2f}'.format(s12, az1, az2)
's12 = 19959679.27, az1 = 161.07, az2 = 18.83'
The geodesic direct problem
>>> positionA = wgs84.GeoPoint(40.6, -73.8, degrees=True)
>>> az1, distance = 45, 10000e3
>>> positionB, az2 = positionA.geo_point(distance, az1, degrees=True)
>>> lat2, lon2 = positionB.latitude_deg, positionB.longitude_deg
>>> msg = 'lat2 = {:5.2f}, lon2 = {:5.2f}, az2 = {:5.2f}'
>>> msg.format(lat2, lon2, az2)
'lat2 = 32.64, lon2 = 49.01, az2 = 140.37'
"""
[docs] def __init__(self, latitude, longitude, z=0, frame=None, degrees=False):
if degrees:
latitude, longitude = rad(latitude), rad(longitude)
self.latitude = latitude
self.longitude = longitude
self.z = z
self.frame = _default_frame(frame)
@property
def latitude_deg(self):
return deg(self.latitude)
@property
def longitude_deg(self):
return deg(self.longitude)
def to_nvector(self):
"""
Converts latitude and longitude to n-vector.
Parameters
----------
latitude, longitude: real scalars or vectors of length n.
Geodetic latitude and longitude given in [rad]
Returns
-------
n_E: 3 x n array
n-vector(s) [no unit] decomposed in E.
See also
--------
n_E2lat_lon.
"""
latitude, longitude = self.latitude, self.longitude
n_E = lat_lon2n_E(latitude, longitude, self.frame.R_Ee)
return Nvector(n_E, self.z, self.frame)
def to_ecef_vector(self):
"""
Converts latitude and longitude to ECEF-vector.
"""
return self.to_nvector().to_ecef_vector()
def geo_point(self, distance, azimuth, long_unroll=False, degrees=False):
"""
Return position B computed from current position, distance and azimuth.
Parameters
----------
distance: real scalar
ellipsoidal distance [m] between position A and B.
azimuth_a:
azimuth [rad or deg] of line at position A.
degrees: bool
azimuths are given in degrees if True otherwise in radians.
Returns
-------
point_b: GeoPoint object
latitude and longitude of position B.
azimuth_b
azimuth [rad or deg] of line at position B.
"""
E = self.frame
z = self.z
if not degrees:
azimuth = deg(azimuth)
lat_a, lon_a = self.latitude_deg, self.longitude_deg
latb, lonb, azimuth_b = E.direct(lat_a, lon_a, azimuth, distance, z=z,
long_unroll=long_unroll, degrees=True)
if not degrees:
azimuth_b = rad(azimuth_b)
point_b = GeoPoint(latitude=latb, longitude=lonb, z=z,
frame=E, degrees=True)
return point_b, azimuth_b
def distance_and_azimuth(self, point, long_unroll=False, degrees=False):
"""
Return ellipsoidal distance between positions as well as the direction.
Parameters
----------
point: GeoPoint object
Latitude and longitude of position B.
degrees: bool
azimuths are returned in degrees if True otherwise in radians.
Returns
-------
s_ab: real scalar
ellipsoidal distance [m] between position A and B.
azimuth_a, azimuth_b
direction [rad or deg] of line at position A and B relative to
North, respectively.
"""
_check_frames(self, point)
lat_a, lon_a = self.latitude, self.longitude
lat_b, lon_b = point.latitude, point.longitude
if degrees:
lat_a, lon_a, lat_b, lon_b = deg((lat_a, lon_a, lat_b, lon_b))
return self.frame.inverse(lat_a, lon_a, lat_b, lon_b, z=self.z,
long_unroll=long_unroll, degrees=degrees)
[docs]class Nvector(object):
"""
Geographical position given as n-vector and depth in frame E
Parameters
----------
normal: 3 x n array
n-vector(s) [no unit] decomposed in E.
z: real scalar or vector of length n.
Depth(s) [m] relative to the ellipsoid (depth = -height)
frame: FrameE object
reference ellipsoid. The default ellipsoid model used is WGS84, but
other ellipsoids/spheres might be specified.
Notes
-----
The position of B (typically body) relative to E (typically Earth) is
given into this function as n-vector, n_EB_E and a depth, z relative to the
ellipsiod.
See also
--------
GeoPoint, ECEFvector, Pvector
"""
[docs] def __init__(self, normal, z=0, frame=None):
self.normal = normal
self.z = z
self.frame = _default_frame(frame)
def to_geo_point(self):
"""
Converts n-vector to geo-point.
See also
--------
n_E2lat_lon, GeoPoint, ECEFvector, Pvector
"""
n_E = self.normal
latitude, longitude = n_E2lat_lon(n_E, R_Ee=self.frame.R_Ee)
return GeoPoint(latitude, longitude, self.z, self.frame)
def to_ecef_vector(self):
"""
Converts n-vector to Cartesian position vector ("ECEF-vector")
Returns
-------
p_EB_E: ECEFvector object
Cartesian position vector(s) from E to B, decomposed in E.
The calculation is excact, taking the ellipsity of the Earth into
account. It is also non-singular as both n-vector and p-vector are
non-singular (except for the center of the Earth).
See also
--------
n_EB_E2p_EB_E, ECEFvector, Pvector, GeoPoint
"""
frame = self.frame
n_EB_E = self.normal
a, f, R_Ee = frame.a, frame.f, frame.R_Ee
p_EB_E = n_EB_E2p_EB_E(n_EB_E, depth=self.z, a=a, f=f, R_Ee=R_Ee)
return ECEFvector(p_EB_E, self.frame)
def to_nvector(self):
return self
def mean_horizontal_position(self):
"""
Return horizontal mean position of the n-vectors.
Returns
-------
p_EM_E: 3 x 1 array
n-vector [no unit] of the mean position, decomposed in E.
"""
n_EB_E = self.normal
n_EM_E = mean_horizontal_position(n_EB_E)
return self.frame.Nvector(n_EM_E)
def __eq__(self, other):
try:
if self is other:
return True
return self._is_equal_to(other)
except AttributeError:
return False
def _is_equal_to(self, other):
return (np.allclose(self.normal, other.normal) and
self.frame == other.frame)
def __add__(self, other):
_check_frames(self, other)
return self.frame.Nvector(self.normal + other.normal,
self.z + other.z)
def __sub__(self, other):
_check_frames(self, other)
return self.frame.Nvector(self.normal - other.normal,
self.z - other.z)
def __neg__(self):
return self.frame.Nvector(-self.normal, -self.z)
def __mul__(self, scalar):
"""elementwise multiplication"""
if not isinstance(scalar, Nvector):
return self.frame.Nvector(self.normal*scalar, self.z*scalar)
raise NotImplementedError('Only scalar multiplication is implemented')
def __div__(self, scalar):
"""elementwise division"""
if not isinstance(scalar, Nvector):
return self.frame.Nvector(self.normal/scalar, self.z/scalar)
raise NotImplementedError('Only scalar division is implemented')
__truediv__ = __div__
__radd__ = __add__
__rmul__ = __mul__
class _DiffPos(object):
__doc__ = """
Return delta vector from positions A to B.
Parameters
----------
positionA, positionB: Nvector, GeoPoint or ECEFvector objects
position A and B, decomposed in E.
Returns
-------
p_AB_E: ECEFvector
Cartesian position vector(s) from A to B, decomposed in E.
Notes
-----
The calculation is excact, taking the ellipsity of the Earth into account.
It is also non-singular as both n-vector and p-vector are non-singular
(except for the center of the Earth).
Examples
--------
{}
See also
--------
n_EA_E_and_p_AB_E2n_EB_E, p_EB_E2n_EB_E, n_EB_E2p_EB_E.
""".format(_examples.get_examples([1]))
pass
@use_docstring_from(_DiffPos)
[docs]def diff_positions(positionA, positionB):
# Function 1. in Section 5.4 in Gade (2010):
p_EA_E = positionA.to_ecef_vector()
p_EB_E = positionB.to_ecef_vector()
p_AB_E = -p_EA_E + p_EB_E
return p_AB_E
[docs]class Pvector(object):
[docs] def __init__(self, pvector, frame):
self.pvector = pvector
self.frame = frame
def to_ecef_vector(self):
frame_B = self.frame
p_AB_N = self.pvector
p_AB_E = np.dot(frame_B.R_EN, p_AB_N)
return ECEFvector(p_AB_E, frame=frame_B.nvector.frame)
def to_nvector(self):
self.to_ecef_vector().to_nvector()
def to_geo_point(self):
self.to_ecef_vector().to_geo_point()
[docs]class ECEFvector(object):
__doc__ = """
Geographical position given as Cartesian position vector in frame E
Parameters
----------
pvector: 3 x n array
Cartesian position vector(s) [m] from E to B, decomposed in E.
frame: FrameE object
reference ellipsoid. The default ellipsoid model used is WGS84, but
other ellipsoids/spheres might be specified.
Notes
-----
The position of B (typically body) relative to E (typically Earth) is
given into this function as p-vector, p_EB_E relative to the center of the
frame.
Examples
--------
See also
--------
GeoPoint, ECEFvector, Pvector
""".format(_examples.get_examples([3, 4]))
[docs] def __init__(self, pvector, frame=None):
self.pvector = pvector
self.frame = _default_frame(frame)
def change_frame(self, frame):
"""
Converts to Cartesian position vector in another frame
Parameters
----------
frame: FrameB, FrameN or frameL object
Frame N used to convert p_AB_E (position vector from A to B,
decomposed in E) to p_AB_N.
Returns
-------
p_AB_N: Pvector object
position vector from A to B, decomposed in frame N.
See also
--------
n_EB_E2p_EB_E, n_EA_E_and_p_AB_E2n_EB_E, n_EA_E_and_n_EB_E2p_AB_E.
"""
_check_frames(self, frame.nvector)
p_AB_E = self.pvector
p_AB_N = np.dot(frame.R_EN.T, p_AB_E)
return Pvector(p_AB_N, frame=frame)
def to_geo_point(self):
"""
Converts ECEF-vector to geo-point.
Returns
-------
point: GeoPoint object
containing geodetic latitude and longitude given in [rad or deg]
and depth, z, relative to the ellipsoid (depth = -height).
See also
--------
n_E2lat_lon, n_EB_E2p_EB_E, GeoPoint, Nvector, ECEFvector, Pvector
"""
return self.to_nvector().to_geo_point()
def to_nvector(self):
"""
Converts ECEF-vector to n-vector.
Returns
-------
n_EB_E: Nvector object
n-vector(s) [no unit] of position B, decomposed in E.
Notes
-----
The calculation is excact, taking the ellipsity of the Earth into
account. It is also non-singular as both n-vector and p-vector are
non-singular (except for the center of the Earth).
See also
--------
n_EB_E2p_EB_E, Nvector
"""
frame = self.frame
p_EB_E = self.pvector
R_Ee = frame.R_Ee
n_EB_E, depth = p_EB_E2n_EB_E(p_EB_E, a=frame.a, f=frame.f, R_Ee=R_Ee)
return Nvector(n_EB_E, z=depth, frame=frame)
def __add__(self, other):
_check_frames(self, other)
return ECEFvector(self.pvector + other.pvector, self.frame)
def __sub__(self, other):
_check_frames(self, other)
return ECEFvector(self.pvector - other.pvector, self.frame)
def __neg__(self):
return ECEFvector(-self.pvector, self.frame)
[docs]class GeoPath(object):
__doc__ = """
Geographical path between two positions in Frame E
Parameters
----------
positionA, positionB: Nvector, GeoPoint or ECEFvector objects
The path is defined by the line between position A and B, decomposed
in E.
Examples
--------
""" + _examples.get_examples([5, 6, 9, 10])
[docs] def __init__(self, positionA, positionB):
self.positionA = positionA
self.positionB = positionB
def _euclidean_cross_track_distance(self, cos_angle, radius=1):
return -cos_angle * radius
def _great_circle_cross_track_distance(self, cos_angle, radius=1):
return (arccos(cos_angle) - pi / 2) * radius
def nvectors(self):
""" Return positionA and positionB as n-vectors
"""
return self.positionA.to_nvector(), self.positionB.to_nvector()
def _nvectors(self):
n_EA_E, n_EB_E = self.nvectors()
return n_EA_E.normal, n_EB_E.normal
def _normal_to_great_circle(self):
n_EA1_E, n_EA2_E = self._nvectors()
return cross(n_EA1_E, n_EA2_E, axis=0)
def _get_average_radius(self):
# n1 = self.positionA.to_nvector()
# n2 = self.positionB.to_nvector()
# n_EM_E = mean_horizontal_position(np.hstack((n1.normal, n2.normal)))
# p_EM_E = n1.frame.Nvector(n_EM_E).to_ecef_vector()
# radius = norm(p_EM_E.pvector, axis=0)
p_E1_E = self.positionA.to_ecef_vector()
p_E2_E = self.positionB.to_ecef_vector()
radius = (norm(p_E1_E.pvector, axis=0) +
norm(p_E2_E.pvector, axis=0)) / 2
return radius
def cross_track_distance(self, point, method='greatcircle', radius=None):
"""
Return cross track distance from the path to a point.
Parameters
----------
point: GeoPoint, Nvector or ECEFvector object
position to measure the cross track distance to.
radius: real scalar
radius of sphere in [m]. Default mean Earth radius
method: string
defining distance calculated. Options are:
'greatcircle' or 'euclidean'
Returns
-------
distance: real scalar
distance in [m]
"""
if radius is None:
radius = self._get_average_radius()
c_E = unit(self._normal_to_great_circle())
n_EB_E = point.to_nvector()
cos_angle = dot(c_E.T, n_EB_E.normal)
if method[0].lower() == 'e':
return self._euclidean_cross_track_distance(cos_angle, radius)
return self._great_circle_cross_track_distance(cos_angle, radius)
def track_distance(self, method='greatcircle', radius=None):
"""
Return the distance of the path.
Parameters
----------
method: string
'greatcircle':
'euclidean'
radius: real scalar
radius of sphere
"""
if radius is None:
radius = self._get_average_radius()
n_EA_E, n_EB_E = self._nvectors()
if method[0] == "e": # Euclidean distance:
return norm(n_EB_E - n_EA_E, axis=0) * radius
return great_circle_distance(n_EA_E, n_EB_E, radius)
def intersection(self, path):
"""
Return the intersection between the paths
Parameters
----------
path: GeoPath object
path to intersect
Returns
-------
point: GeoPoint
point of intersection between paths
"""
frame = self.positionA.frame
n_EA1_E, n_EA2_E = self._nvectors()
n_EB1_E, n_EB2_E = path._nvectors()
# Find the intersection between the two paths, n_EC_E:
n_EC_E_tmp = unit(cross(cross(n_EA1_E, n_EA2_E, axis=0),
cross(n_EB1_E, n_EB2_E, axis=0), axis=0),
norm_zero_vector=np.nan)
# n_EC_E_tmp is one of two solutions, the other is -n_EC_E_tmp. Select
# the one that is closet to n_EA1_E, by selecting sign from the dot
# product between n_EC_E_tmp and n_EA1_E:
n_EC_E = np.sign(dot(n_EC_E_tmp.T, n_EA1_E)) * n_EC_E_tmp
if np.any(np.isnan(n_EC_E)):
warnings.warn('Paths are Equal. Intersection point undefined. '
'NaN returned.')
lat_EC, long_EC = n_E2lat_lon(n_EC_E, frame.R_Ee)
return GeoPoint(lat_EC, long_EC, frame=frame)
def interpolate(self, ti):
"""
Return the interpolated point along the path
Parameters
----------
ti: real scalar
interpolation time assuming position A and B is at t0=0 and t1=1,
respectively.
Returns
-------
point: Nvector
point of interpolation along path
"""
n_EB_E_t0, n_EB_E_t1 = self._nvectors()
n_EB_E_ti = unit(n_EB_E_t0 + ti * (n_EB_E_t1 - n_EB_E_t0))
zi = self.positionA.z + ti * (self.positionB.z-self.positionA.z)
frame = self.positionA.frame
return frame.Nvector(n_EB_E_ti, zi)
class _BaseFrame(object):
def __eq__(self, other):
try:
if self is other:
return True
return self._is_equal_to(other)
except AttributeError:
return False
[docs]class FrameE(_BaseFrame):
"""
Earth-fixed frame
Parameters
----------
a: real scalar, default WGS-84 ellipsoid.
Semi-major axis of the Earth ellipsoid given in [m].
f: real scalar, default WGS-84 ellipsoid.
Flattening [no unit] of the Earth ellipsoid. If f==0 then spherical
Earth with radius a is used in stead of WGS-84.
name: string
defining the default ellipsoid.
axes: 'e' or 'E'
defines axes orientation of E frame. Default is axes='e' which means
that the orientation of the axis is such that:
z-axis -> North Pole, x-axis -> Latitude=Longitude=0.
Notes
-----
The frame is Earth-fixed (rotates and moves with the Earth) where the
origin coincides with Earth's centre (geometrical centre of ellipsoid
model).
See also
--------
FrameN, FrameL, FrameB
"""
[docs] def __init__(self, a=None, f=None, name='WGS84', axes='e'):
if a is None or f is None:
a, f, _full_name = select_ellipsoid(name)
self.a = a
self.f = f
self.name = name
self.R_Ee = E_rotation(axes)
def _is_equal_to(self, other):
return (np.allclose(self.a, other.a) and
np.allclose(self.f, other.f) and
np.allclose(self.R_Ee, other.R_Ee))
def inverse(self, lat_a, lon_a, lat_b, lon_b, z=0, long_unroll=False,
degrees=False):
"""
Return ellipsoidal distance between positions as well as the direction.
Parameters
----------
lat_a, lon_a: real scalars
Latitude and longitude of position a.
lat_b, lon_b: real scalars
Latitude and longitude of position b.
z : real scalar
depth relative to Earth ellipsoid.
degrees: bool
angles are given in degrees if True otherwise in radians.
Returns
-------
s_ab: real scalar
ellipsoidal distance [m] between position A and B.
azimuth_a, azimuth_b
direction [rad or deg] of line at position A and B relative to
North, respectively.
References
----------
C. F. F. Karney, Algorithms for geodesics, J. Geodesy 87(1), 43-55
`geographiclib <https://pypi.python.org/pypi/geographiclib>`_
"""
outmask = _Geodesic.STANDARD
if long_unroll:
outmask = _Geodesic.STANDARD | _Geodesic.LONG_UNROLL
geo = _Geodesic(self.a-z, self.f)
if not degrees:
lat_a, lon_a, lat_b, lon_b = deg((lat_a, lon_a, lat_b, lon_b))
result = geo.Inverse(lat_a, lon_a, lat_b, lon_b, outmask=outmask)
azimuth_a = result['azi1'] if degrees else rad(result['azi1'])
azimuth_b = result['azi2'] if degrees else rad(result['azi2'])
return result['s12'], azimuth_a, azimuth_b
def direct(self, lat_a, lon_a, azimuth, distance, z=0, long_unroll=False,
degrees=False):
"""
Return position B computed from position A, distance and azimuth.
Parameters
----------
lat_a, lon_a: real scalars
Latitude and longitude [rad or deg] of position a.
azimuth_a:
azimuth [rad or deg] of line at position A.
distance: real scalar
ellipsoidal distance [m] between position A and B.
z : real scalar
depth relative to Earth ellipsoid.
degrees: bool
angles are given in degrees if True otherwise in radians.
Returns
-------
lat_b, lon_b: real scalars
Latitude and longitude of position b.
azimuth_b
azimuth [rad or deg] of line at position B.
References
----------
C. F. F. Karney, Algorithms for geodesics, J. Geodesy 87(1), 43-55
`geographiclib <https://pypi.python.org/pypi/geographiclib>`_
"""
geo = _Geodesic(self.a-z, self.f)
outmask = _Geodesic.STANDARD
if long_unroll:
outmask = _Geodesic.STANDARD | _Geodesic.LONG_UNROLL
if not degrees:
lat_a, lon_a, azimuth = deg((lat_a, lon_a, azimuth))
result = geo.Direct(lat_a, lon_a, azimuth, distance, outmask=outmask)
latb, lonb, azimuth_b = result['lat2'], result['lon2'], result['azi2']
if not degrees:
return rad(latb), rad(lonb), rad(azimuth_b)
return latb, lonb, azimuth_b
@use_docstring_from(GeoPoint)
def GeoPoint(self, *args, **kwds):
kwds.pop('frame', None)
return GeoPoint(*args, frame=self, **kwds)
@use_docstring_from(Nvector)
def Nvector(self, *args, **kwds):
kwds.pop('frame', None)
return Nvector(*args, frame=self, **kwds)
@use_docstring_from(ECEFvector)
def ECEFvector(self, *args, **kwds):
kwds.pop('frame', None)
return ECEFvector(*args, frame=self, **kwds)
[docs]class FrameN(_BaseFrame):
__doc__ = """
North-East-Down frame
Parameters
----------
position: ECEFvector, GeoPoint or Nvector object
position of the vehicle (B) which also defines the origin of the local
frame N. The origin is directly beneath or above the vehicle (B), at
Earth's surface (surface of ellipsoid model).
Notes
-----
The Cartesian frame is local and oriented North-East-Down, i.e.,
the x-axis points towards north, the y-axis points towards east (both are
horizontal), and the z-axis is pointing down.
When moving relative to the Earth, the frame rotates about its z-axis
to allow the x-axis to always point towards north. When getting close
to the poles this rotation rate will increase, being infinite at the
poles. The poles are thus singularities and the direction of the
x- and y-axes are not defined here. Hence, this coordinate frame is
NOT SUITABLE for general calculations.
Examples
--------
{}
See also
--------
FrameE, FrameL, FrameB
""".format(_examples.get_examples([1]))
[docs] def __init__(self, position):
nvector = position.to_nvector()
n_EA_E = nvector.normal
self.nvector = Nvector(n_EA_E, z=0, frame=nvector.frame)
self.R_EN = n_E2R_EN(n_EA_E, nvector.frame.R_Ee)
def _is_equal_to(self, other):
return (np.allclose(self.R_EN, other.R_EN) and
self.nvector == other.nvector)
def Pvector(self, pvector):
return Pvector(pvector, frame=self)
[docs]class FrameL(FrameN):
"""
Local level, Wander azimuth frame
Parameters
----------
position: ECEFvector, GeoPoint or Nvector object
position of the vehicle (B) which also defines the origin of the local
frame L. The origin is directly beneath or above the vehicle (B), at
Earth's surface (surface of ellipsoid model).
wander_azimuth: real scalar
Angle between the x-axis of L and the north direction.
Notes
-----
The Cartesian frame is local and oriented Wander-azimuth-Down. This means
that the z-axis is pointing down. Initially, the x-axis points towards
north, and the y-axis points towards east, but as the vehicle moves they
are not rotating about the z-axis (their angular velocity relative to the
Earth has zero component along the z-axis).
(Note: Any initial horizontal direction of the x- and y-axes is valid
for L, but if the initial position is outside the poles, north and east
are usually chosen for convenience.)
The L-frame is equal to the N-frame except for the rotation about the
z-axis, which is always zero for this frame (relative to E). Hence, at
a given time, the only difference between the frames is an angle
between the x-axis of L and the north direction; this angle is called
the wander azimuth angle. The L-frame is well suited for general
calculations, as it is non-singular.
See also
--------
FrameE, FrameN, FrameB
"""
[docs] def __init__(self, position, wander_azimuth=0):
nvector = position.to_nvector()
n_EA_E = nvector.normal
R_Ee = nvector.frame.R_Ee
self.nvector = Nvector(n_EA_E, z=0, frame=nvector.frame)
self.R_EN = n_E_and_wa2R_EL(n_EA_E, wander_azimuth, R_Ee=R_Ee)
[docs]class FrameB(FrameN):
__doc__ = """
Body frame
Parameters
----------
position: ECEFvector, GeoPoint or Nvector object
position of the vehicle's reference point which also coincides with
the origin of the frame B.
yaw, pitch, roll: real scalars
defining the orientation of frame B in [deg] or [rad].
degrees : bool
if True yaw, pitch, roll are given in degrees otherwise in radians
Notes
-----
The frame is fixed to the vehicle where the x-axis points forward, the
y-axis to the right (starboard) and the z-axis in the vehicle's down
direction.
Examples
--------
{}
See also
--------
FrameE, FrameL, FrameN
""".format(_examples.get_examples([2]))
[docs] def __init__(self, position, yaw=0, pitch=0, roll=0, degrees=False):
nvector = position.to_nvector()
self.nvector = nvector
if degrees:
yaw, pitch, roll = rad(yaw), rad(pitch), rad(roll)
self.yaw = yaw
self.pitch = pitch
self.roll = roll
@property
def R_EN(self):
R_NB = zyx2R(self.yaw, self.pitch, self.roll)
n_EB_E = self.nvector.normal
R_EN = n_E2R_EN(n_EB_E, self.nvector.frame.R_Ee)
return np.dot(R_EN, R_NB) # rotation matrix
def _is_equal_to(self, other):
return (np.allclose(self.yaw, other.yaw) and
np.allclose(self.pitch, other.pitch) and
np.allclose(self.roll, other.roll) and
np.allclose(self.R_EN, other.R_EN) and
self.nvector == other.nvector)
def _check_frames(self, other):
if not self.frame == other.frame:
raise ValueError('Frames are unequal')
def _default_frame(frame):
if frame is None:
return FrameE()
return frame
if __name__ == '__main__':
pass