<gh_stars>10-100
# coding: utf-8
import numpy as np
from numpy import pi, sqrt, sin, cos, deg2rad, rad2deg, arctan2

##### Constants ###############################################
G0 = 9.80665

### WGS84 ###
A = 6378137.0           # Equatorial radius [m]
ONE_F = 298.257223563   # Inverse flattening [-]
GM = 3.986004418e14     # Gravitational constant [m3/s2]
OMEGA = 7.292115e-5     # Angular velocity of the Earth [rad/s]

###############################################################

# lat: geodetic latitude
# latc: geocentric latitude

def posECEFfromLLH(posLLH_):
    """
    Args:
        posLLH_ (np.array 3x1) : position in LLH coordinate [deg, deg, m]
    Return:
        (np.array 3x1) : position in ECEF coordinate [m, m, m]
    """
    lat = deg2rad(posLLH_[0])
    lon = deg2rad(posLLH_[1])
    alt = posLLH_[2]
    a = A                           # Equatorial radius [m]
    f = 1.0 / ONE_F                 # Flattening [-]
    e2 = 2.0 * f - f * f            # Square of eccentricity e
    W = sqrt(1.0 - e2 * sin(lat) * sin(lat))
    N = a / W                       # Radius of prime vertical circle [m]

    posECEF_ = np.empty(3)
    posECEF_[0] = (N + alt) * cos(lat) * cos(lon)
    posECEF_[1] = (N + alt) * cos(lat) * sin(lon)
    posECEF_[2] = (N * (1 - e2) + alt) * sin(lat)

    return posECEF_


def posLLHfromECEF(posECEF_):
    """
    This function is an approximation.
    Please refer https://www.enri.go.jp/~fks442/K_MUSEN/1st/1st060428rev2.pdf.

    Args:
        posECEF_ (np.array 3x1) : [deg, deg, m]
    Return:
        (np.array 3x1) : position in LLH coordinate [deg, deg, m]
    """
    a = A                           # Equatorial radius [m]
    f = 1.0 / ONE_F                 # Flattening [-]
    e2 = 2.0 * f - f * f            # Square of eccentricity e
    b = a * (1.0 - f)               # Polar radius [m]
    ed2 = e2 / (1.0 - e2)           # Square of second eccentricity e'
    p = sqrt(posECEF_[0]**2 + posECEF_[1]**2)    # Distance from the rotation axis of the Earth [m]
    theta = arctan2(posECEF_[2] * a, p * b)      # [rad]

    posLLH = np.empty(3)
    posLLH[0] = rad2deg(arctan2((posECEF_[2] + ed2 * b * sin(theta)**3), p - e2 * a * cos(theta)**3))
    posLLH[1] = rad2deg(arctan2(posECEF_[1], posECEF_[0]))
    posLLH[2] = p / cos(deg2rad(posLLH[0])) - a / sqrt(1.0 - e2 * sin(deg2rad(posLLH[0]))**2)

    return posLLH  # deg, deg, m


def dcmECEF2NEDfromLLH(posLLH_):  # deg, deg, m
    """
    Args:
        posLLH_ (np.array 3x1) : [deg, deg, m]
    Return:
        dcm (np.array 3x3) : DCM from ECEF to NED
    """
    lat = deg2rad(posLLH_[0])
    lon = deg2rad(posLLH_[1])

    dcm = np.array([[-sin(lat) * cos(lon), -sin(lat)*sin(lon),  cos(lat)],
                    [-sin(lon),             cos(lon),           0.      ],
                    [-cos(lat) * cos(lon), -cos(lat)*sin(lon), -sin(lat)]])
    return dcm


def dcmNED2ECEFfromLLH(posLLH_):
    """
    Args:
        posLLH_ (np.array 3x1) : [deg, deg, m]
    Return:
        dcm (np.array 3x3) : DCM from NED to ECEF
    """
    return dcmECEF2NEDfromLLH(posLLH_).T


def dcmECI2ECEF(second):
    """
    Args:
        second (double) : time from reference time[s]
    Return:
        dcm (np.array 3x3) : DCM from ECI to ECEF
    """
    omega = OMEGA
    theta = omega * second

    dcm = np.array([[ cos(theta), sin(theta), 0.],
                    [-sin(theta), cos(theta), 0.],
                    [0.,          0.,         1.]])
    return dcm


def dcmECEF2ECI(second):
    """
    Args:
        second (double) : time from reference time[s]
    Return:
        dcm (np.array 3x3) : DCM from ECEF to ECI
    """
    return dcmECI2ECEF(second).T


def dcmNED2BODY(azimuth_deg, elevation_deg, roll_deg):
    """
    Args:
        azimuth_deg (double) : azimuth of attitude [deg]
        elevation_deg (double) : elevation of attitude [deg]
        roll_deg (double) : roll of attitude [deg]
    Return:
        dcm (np.array 3x3) : DCM from NED to Body
    """
    az = deg2rad(azimuth_deg)
    el = deg2rad(elevation_deg)
    ro = deg2rad(roll_deg)

    dcm = np.array([
        [cos(el)*cos(az), cos(el)*sin(az), -sin(el)],
        [-cos(ro)*sin(az)+sin(ro)*sin(el)*cos(az), cos(ro)*cos(az)+sin(ro)*sin(el)*sin(az), sin(ro)*cos(el)],
        [sin(ro)*sin(az)+cos(ro)*sin(el)*cos(az),  -sin(ro)*cos(az)+cos(ro)*sin(el)*sin(az),  cos(ro)*cos(el)]
        ])
    return dcm


def dcmBODY2NED(azimuth_deg, elevation_deg, roll_deg):
    """
    Args:
        azimuth_deg (double) : azimuth of attitude [deg]
        elevation_deg (double) : elevation of attitude [deg]
        roll_deg (double) : roll of attitude [deg]
    Return:
        dcm (np.array 3x3) : DCM from Body to NED
    """
    dcm_inv = dcmNED2BODY(azimuth_deg, elevation_deg, roll_deg)
    return dcm_inv.T


def posECIfromECEF(posECEF_, second):
    """
    Args:
        posECEF_ (np.array 3x1) : position in ECEF coordinate [m, m, m]
        second (double) : time from reference time [s]
    Return:
        (np.array 3x1) : position in ECI coordinate [m, m, m]
    """
    return np.matmul(dcmECEF2ECI(second), posECEF_)


def posECEFfromECI(posECI_, second):
    return np.matmul(dcmECI2ECEF(second), posECI_)


def velECEFfromECI(posECI_, velECI_, second):
    omega = OMEGA
    omegaECI2ECEF_ = np.array([[0.,   -omega, 0.],
                               [omega, 0.,    0.],
                               [0.,    0.,    0.]])
    dcmECI2ECEF_ = dcmECI2ECEF(second)

    return np.matmul(dcmECI2ECEF_, velECI_ - np.matmul(omegaECI2ECEF_, posECI_))


def velECIfromECEF(posECEF_, velECEF_, second):
    omega = OMEGA
    omegaECI2ECEF_ = np.array([[0.,   -omega, 0.],
                               [omega, 0.,    0.],
                               [0.,    0.,    0.]])
    dcmECEF2ECI_ = dcmECEF2ECI(second)

    return np.matmul(dcmECEF2ECI_, velECEF_ + np.matmul(omegaECI2ECEF_, posECEF_))


def velECEFfromNED(posLLH_, velNED_):
    dcmNED2ECEF_ = dcmNED2ECEFfromLLH(posLLH_)
    return np.matmul(dcmNED2ECEF_, velNED_)


def velNEDfromECEF(posECEF_, velECEF_):
    posLLH_ = posLLHfromECEF(posECEF_)
    dcmECEF2NED_ = dcmECEF2NEDfromLLH(posLLH_)
    return np.matmul(dcmECEF2NED_, velECEF_)


def posLLHfromECI(posECI_, second):
    posECEF_ = posECEFfromECI(posECI_, second)
    posLLH_ = posLLHfromECEF(posECEF_)
    return posLLH_


def posECIfromLLH(posLLH_, second):
    posECEF_ = posECEFfromLLH(posLLH_)
    posECI_ = posECIfromECEF(posECEF_, second)
    return posECI_


# def velNEDfromECI(posECI_, velECI_, dcmECI2NED_):
#     omega = OMEGA
#     omegaECI2ECEF_ = np.array([[0.,   -omega, 0.],
#                                [omega, 0.,    0.],
#                                [0.,    0.,    0.]])
# 
#     return np.matmul(dcmECI2NED_, (velECI_ - np.matmul(omegaECI2ECEF_, posECI_)))


def velNEDfromECI(posECI_, velECI_, second):
    posECEF_ = posECEFfromECI(posECI_, second)
    velECEF_ = velECEFfromECI(posECI_, velECI_, second)
    velNED_ = velNEDfromECEF(posECEF_, velECEF_)
    return velNED_


def velECIfromNED(posLLH_, velNED_, second):
    posECEF_ = posECEFfromLLH(posLLH_)
    velECEF_ = velECEFfromNED(posLLH_, velNED_)
    velECI_ = velECIfromECEF(posECEF_, velECEF_, second)
    return velECI_


def posLLH_IIP(posLLH_, velNED_):
    g0 = G0
    vel_north_ = velNED_[0]
    vel_east_ = velNED_[1]
    vel_up_ = - velNED_[2]
    h = posLLH_[2]
    if h > 0.0:
        tau = 1.0 / g0 * (vel_up_ + sqrt(vel_up_**2 + 2 * h * g0))
    else:
        tau = 0.0
    dist_IIP_from_now_NED = np.array([vel_north_ * tau, vel_east_ * tau, h])
    posECEF_ = posECEFfromLLH(posLLH_)
    dcmECEF2NED_ = dcmECEF2NEDfromLLH(posLLH_)
    dcmNED2ECEF_ = dcmECEF2NED_.T
    posECEF_IIP_ = posECEF_ + np.matmul(dcmNED2ECEF_, dist_IIP_from_now_NED)
    return posLLHfromECEF(posECEF_IIP_)


def posLLH_IIP_fromECEF(posECEF_, velECEF_):
    posLLH_ = posLLHfromECEF(posECEF_)
    velNED_ = velNEDfromECEF(posECEF_, velECEF_)
    return posLLH_IIP(posLLH_, velNED_)


### utility functions ###

def distance_surface(posLLH1, posLLH2):
    earth_radius = A            # Earth radius ~ Equatorial radius
    if len(posLLH1) == 2:
        posLLH1 = np.append(posLLH1, 0.)
    if len(posLLH2) == 2:
        posLLH2 = np.append(posLLH2, 0.)
    posECEF1 = posECEFfromLLH(posLLH1)
    posECEF2 = posECEFfromLLH(posLLH2)

    costheta = np.dot(posECEF1, posECEF2) / (np.linalg.norm(posECEF1) * np.linalg.norm(posECEF2))
    costheta = np.clip(costheta, -1., 1.)
    theta = np.arccos(costheta)     # Angle at the center of the Earth
    return earth_radius * theta


def posfromDistanceAndAzimuth(latlon, disaz):  # ([deg], [deg]), ([m], [deg])
    a = A                           # Equatorial radius [m]
    f = 1.0 / ONE_F                 # Flattening [-]
    e2 = 2.0 * f - f * f            # Square of eccentricity e

    lat, lon = latlon
    d, az = disaz

    theta_lat = deg2rad(lat)
    N = a / sqrt(1.0 - e2 * sin(theta_lat)**2)  # Prime vertical radius of curvature
    Re = N * sqrt(cos(theta_lat)**2 + ((1.0 - e2) * sin(theta_lat))**2)

    theta = d / Re
    phi = pi - deg2rad(az)

    x = sin(theta) * cos(phi)
    y = sin(theta) * sin(phi)
    z = cos(theta)

    alpha = pi * 0.5 - deg2rad(lat)

    X = x * cos(alpha) + z * sin(alpha)
    Y = y
    Z = -x * sin(alpha) + z * cos(alpha)

    theta_new = np.arccos(Z)
    phi_new = np.sign(Y) * np.arccos(X / sqrt(X**2 + Y**2))

    lat_ans = rad2deg(pi * 0.5 - theta_new)
    lon_ans = lon + rad2deg(phi_new)

    lat_ans = (lat_ans + 90) % 180 - 90
    lon_ans = (lon_ans + 180) % 360 - 180

    return (lat_ans, lon_ans)


def lonlat2xyratio(lat):  # [lon[deg], lat[deg]] to [x[m], y[m]] ratio
    a = A                           # Equatorial radius [m]
    f = 1.0 / ONE_F                 # Flattening [-]
    e2 = 2.0 * f - f * f            # Square of eccentricity e

    theta_lat = deg2rad(lat)
    N = a / sqrt(1.0 - e2 * sin(theta_lat)**2)  # Prime vertical radius of curvature

    dxdlon = N * cos(theta_lat)
    dydlat = N * (1.0 - e2) / (1.0 - e2 * sin(theta_lat)**2)

    return np.array([dxdlon, dydlat]).T * deg2rad(1.)


# points in hull must not be overlapping (hull[0] != hull[-1]), and ordered in anti-clockwise
def extend_lonlat_hull(lonlat_hull, distance, dlondlat=[0, 0], max_deg=30):  # [deg, deg], [m], [deg, deg]
    lonlat_ave = np.mean(lonlat_hull, axis=0)
    lola2xy = lonlat2xyratio(lonlat_ave[1])
    dxdy = dlondlat * lola2xy
    xy_hull = lonlat_hull * lola2xy
    xy_hull_new = extend_xy_hull(xy_hull, distance, dxdy, max_deg)
    lonlat_hull_new = xy_hull_new / lola2xy
    return lonlat_hull_new


def extend_xy_hull(xy_hull, distance, dxdy=[0, 0], max_deg=30):
    xy0 = xy_hull
    xy1 = np.roll(xy_hull, -1, axis=0)
    dxy = xy1 - xy0
    udxy = dxy / np.array([np.linalg.norm(dxy, axis=1)]).T
    ndxy = np.matmul(udxy, [[0, -1], [1, 0]])
    ddxy = distance * ndxy
    xy0n = xy0 + ddxy + dxdy
    xy1n = xy1 + ddxy + dxdy

    costheta = np.sum(ndxy * np.roll(ndxy, -1, axis=0), axis=1).clip(-1, 1)
    theta = np.arccos(costheta)
    xy_corners = []
    for theta_, ddxy_, xy1_ in zip(theta, ddxy, xy1):
        N_ = (theta_ // deg2rad(max_deg))
        n_ = np.arange(0, N_, 1)
        theta_n = theta_ * (n_ + 1) / (N_ + 1)
        An_T = np.array([[cos(theta_n), -sin(theta_n)], [sin(theta_n), cos(theta_n)]]).transpose(2, 1, 0)
        ddxy_n = np.matmul(ddxy_, An_T)
        xy1_nn = xy1_ + ddxy_n + dxdy
        xy_corners += [xy1_nn]

    xy_ans_list = []
    for xy0n_, xy1n_, xycs_ in zip(xy0n, xy1n, xy_corners):
        xy_ans_list += [xy0n_, xy1n_]
        xy_ans_list += list(xycs_)
    return np.array(xy_ans_list)


# coding: utf-8
import numpy as np
from numpy import pi, sqrt, sin, cos, deg2rad, rad2deg, arctan2

##### Constants ###############################################
G0 = 9.80665

### WGS84 ###
A = 6378137.0           # Equatorial radius [m]
ONE_F = 298.257223563   # Inverse flattening [-]
GM = 3.986004418e14     # Gravitational constant [m3/s2]
OMEGA = 7.292115e-5     # Angular velocity of the Earth [rad/s]

###############################################################

# lat: geodetic latitude
# latc: geocentric latitude

def posECEFfromLLH(posLLH_):
    """
    Args:
        posLLH_ (np.array 3x1) : position in LLH coordinate [deg, deg, m]
    Return:
        (np.array 3x1) : position in ECEF coordinate [m, m, m]
    """
    lat = deg2rad(posLLH_[0])
    lon = deg2rad(posLLH_[1])
    alt = posLLH_[2]
    a = A                           # Equatorial radius [m]
    f = 1.0 / ONE_F                 # Flattening [-]
    e2 = 2.0 * f - f * f            # Square of eccentricity e
    W = sqrt(1.0 - e2 * sin(lat) * sin(lat))
    N = a / W                       # Radius of prime vertical circle [m]

    posECEF_ = np.empty(3)
    posECEF_[0] = (N + alt) * cos(lat) * cos(lon)
    posECEF_[1] = (N + alt) * cos(lat) * sin(lon)
    posECEF_[2] = (N * (1 - e2) + alt) * sin(lat)

    return posECEF_


def posLLHfromECEF(posECEF_):
    """
    This function is an approximation.
    Please refer https://www.enri.go.jp/~fks442/K_MUSEN/1st/1st060428rev2.pdf.

    Args:
        posECEF_ (np.array 3x1) : [deg, deg, m]
    Return:
        (np.array 3x1) : position in LLH coordinate [deg, deg, m]
    """
    a = A                           # Equatorial radius [m]
    f = 1.0 / ONE_F                 # Flattening [-]
    e2 = 2.0 * f - f * f            # Square of eccentricity e
    b = a * (1.0 - f)               # Polar radius [m]
    ed2 = e2 / (1.0 - e2)           # Square of second eccentricity e'
    p = sqrt(posECEF_[0]**2 + posECEF_[1]**2)    # Distance from the rotation axis of the Earth [m]
    theta = arctan2(posECEF_[2] * a, p * b)      # [rad]

    posLLH = np.empty(3)
    posLLH[0] = rad2deg(arctan2((posECEF_[2] + ed2 * b * sin(theta)**3), p - e2 * a * cos(theta)**3))
    posLLH[1] = rad2deg(arctan2(posECEF_[1], posECEF_[0]))
    posLLH[2] = p / cos(deg2rad(posLLH[0])) - a / sqrt(1.0 - e2 * sin(deg2rad(posLLH[0]))**2)

    return posLLH  # deg, deg, m


def dcmECEF2NEDfromLLH(posLLH_):  # deg, deg, m
    """
    Args:
        posLLH_ (np.array 3x1) : [deg, deg, m]
    Return:
        dcm (np.array 3x3) : DCM from ECEF to NED
    """
    lat = deg2rad(posLLH_[0])
    lon = deg2rad(posLLH_[1])

    dcm = np.array([[-sin(lat) * cos(lon), -sin(lat)*sin(lon),  cos(lat)],
                    [-sin(lon),             cos(lon),           0.      ],
                    [-cos(lat) * cos(lon), -cos(lat)*sin(lon), -sin(lat)]])
    return dcm


def dcmNED2ECEFfromLLH(posLLH_):
    """
    Args:
        posLLH_ (np.array 3x1) : [deg, deg, m]
    Return:
        dcm (np.array 3x3) : DCM from NED to ECEF
    """
    return dcmECEF2NEDfromLLH(posLLH_).T


def dcmECI2ECEF(second):
    """
    Args:
        second (double) : time from reference time[s]
    Return:
        dcm (np.array 3x3) : DCM from ECI to ECEF
    """
    omega = OMEGA
    theta = omega * second

    dcm = np.array([[ cos(theta), sin(theta), 0.],
                    [-sin(theta), cos(theta), 0.],
                    [0.,          0.,         1.]])
    return dcm


def dcmECEF2ECI(second):
    """
    Args:
        second (double) : time from reference time[s]
    Return:
        dcm (np.array 3x3) : DCM from ECEF to ECI
    """
    return dcmECI2ECEF(second).T


def dcmNED2BODY(azimuth_deg, elevation_deg, roll_deg):
    """
    Args:
        azimuth_deg (double) : azimuth of attitude [deg]
        elevation_deg (double) : elevation of attitude [deg]
        roll_deg (double) : roll of attitude [deg]
    Return:
        dcm (np.array 3x3) : DCM from NED to Body
    """
    az = deg2rad(azimuth_deg)
    el = deg2rad(elevation_deg)
    ro = deg2rad(roll_deg)

    dcm = np.array([
        [cos(el)*cos(az), cos(el)*sin(az), -sin(el)],
        [-cos(ro)*sin(az)+sin(ro)*sin(el)*cos(az), cos(ro)*cos(az)+sin(ro)*sin(el)*sin(az), sin(ro)*cos(el)],
        [sin(ro)*sin(az)+cos(ro)*sin(el)*cos(az),  -sin(ro)*cos(az)+cos(ro)*sin(el)*sin(az),  cos(ro)*cos(el)]
        ])
    return dcm


def dcmBODY2NED(azimuth_deg, elevation_deg, roll_deg):
    """
    Args:
        azimuth_deg (double) : azimuth of attitude [deg]
        elevation_deg (double) : elevation of attitude [deg]
        roll_deg (double) : roll of attitude [deg]
    Return:
        dcm (np.array 3x3) : DCM from Body to NED
    """
    dcm_inv = dcmNED2BODY(azimuth_deg, elevation_deg, roll_deg)
    return dcm_inv.T


def posECIfromECEF(posECEF_, second):
    """
    Args:
        posECEF_ (np.array 3x1) : position in ECEF coordinate [m, m, m]
        second (double) : time from reference time [s]
    Return:
        (np.array 3x1) : position in ECI coordinate [m, m, m]
    """
    return np.matmul(dcmECEF2ECI(second), posECEF_)


def posECEFfromECI(posECI_, second):
    return np.matmul(dcmECI2ECEF(second), posECI_)


def velECEFfromECI(posECI_, velECI_, second):
    omega = OMEGA
    omegaECI2ECEF_ = np.array([[0.,   -omega, 0.],
                               [omega, 0.,    0.],
                               [0.,    0.,    0.]])
    dcmECI2ECEF_ = dcmECI2ECEF(second)

    return np.matmul(dcmECI2ECEF_, velECI_ - np.matmul(omegaECI2ECEF_, posECI_))


def velECIfromECEF(posECEF_, velECEF_, second):
    omega = OMEGA
    omegaECI2ECEF_ = np.array([[0.,   -omega, 0.],
                               [omega, 0.,    0.],
                               [0.,    0.,    0.]])
    dcmECEF2ECI_ = dcmECEF2ECI(second)

    return np.matmul(dcmECEF2ECI_, velECEF_ + np.matmul(omegaECI2ECEF_, posECEF_))


def velECEFfromNED(posLLH_, velNED_):
    dcmNED2ECEF_ = dcmNED2ECEFfromLLH(posLLH_)
    return np.matmul(dcmNED2ECEF_, velNED_)


def velNEDfromECEF(posECEF_, velECEF_):
    posLLH_ = posLLHfromECEF(posECEF_)
    dcmECEF2NED_ = dcmECEF2NEDfromLLH(posLLH_)
    return np.matmul(dcmECEF2NED_, velECEF_)


def posLLHfromECI(posECI_, second):
    posECEF_ = posECEFfromECI(posECI_, second)
    posLLH_ = posLLHfromECEF(posECEF_)
    return posLLH_


def posECIfromLLH(posLLH_, second):
    posECEF_ = posECEFfromLLH(posLLH_)
    posECI_ = posECIfromECEF(posECEF_, second)
    return posECI_


# def velNEDfromECI(posECI_, velECI_, dcmECI2NED_):
#     omega = OMEGA
#     omegaECI2ECEF_ = np.array([[0.,   -omega, 0.],
#                                [omega, 0.,    0.],
#                                [0.,    0.,    0.]])
# 
#     return np.matmul(dcmECI2NED_, (velECI_ - np.matmul(omegaECI2ECEF_, posECI_)))


def velNEDfromECI(posECI_, velECI_, second):
    posECEF_ = posECEFfromECI(posECI_, second)
    velECEF_ = velECEFfromECI(posECI_, velECI_, second)
    velNED_ = velNEDfromECEF(posECEF_, velECEF_)
    return velNED_


def velECIfromNED(posLLH_, velNED_, second):
    posECEF_ = posECEFfromLLH(posLLH_)
    velECEF_ = velECEFfromNED(posLLH_, velNED_)
    velECI_ = velECIfromECEF(posECEF_, velECEF_, second)
    return velECI_


def posLLH_IIP(posLLH_, velNED_):
    g0 = G0
    vel_north_ = velNED_[0]
    vel_east_ = velNED_[1]
    vel_up_ = - velNED_[2]
    h = posLLH_[2]
    if h > 0.0:
        tau = 1.0 / g0 * (vel_up_ + sqrt(vel_up_**2 + 2 * h * g0))
    else:
        tau = 0.0
    dist_IIP_from_now_NED = np.array([vel_north_ * tau, vel_east_ * tau, h])
    posECEF_ = posECEFfromLLH(posLLH_)
    dcmECEF2NED_ = dcmECEF2NEDfromLLH(posLLH_)
    dcmNED2ECEF_ = dcmECEF2NED_.T
    posECEF_IIP_ = posECEF_ + np.matmul(dcmNED2ECEF_, dist_IIP_from_now_NED)
    return posLLHfromECEF(posECEF_IIP_)


def posLLH_IIP_fromECEF(posECEF_, velECEF_):
    posLLH_ = posLLHfromECEF(posECEF_)
    velNED_ = velNEDfromECEF(posECEF_, velECEF_)
    return posLLH_IIP(posLLH_, velNED_)


### utility functions ###

def distance_surface(posLLH1, posLLH2):
    earth_radius = A            # Earth radius ~ Equatorial radius
    if len(posLLH1) == 2:
        posLLH1 = np.append(posLLH1, 0.)
    if len(posLLH2) == 2:
        posLLH2 = np.append(posLLH2, 0.)
    posECEF1 = posECEFfromLLH(posLLH1)
    posECEF2 = posECEFfromLLH(posLLH2)

    costheta = np.dot(posECEF1, posECEF2) / (np.linalg.norm(posECEF1) * np.linalg.norm(posECEF2))
    costheta = np.clip(costheta, -1., 1.)
    theta = np.arccos(costheta)     # Angle at the center of the Earth
    return earth_radius * theta


def posfromDistanceAndAzimuth(latlon, disaz):  # ([deg], [deg]), ([m], [deg])
    a = A                           # Equatorial radius [m]
    f = 1.0 / ONE_F                 # Flattening [-]
    e2 = 2.0 * f - f * f            # Square of eccentricity e

    lat, lon = latlon
    d, az = disaz

    theta_lat = deg2rad(lat)
    N = a / sqrt(1.0 - e2 * sin(theta_lat)**2)  # Prime vertical radius of curvature
    Re = N * sqrt(cos(theta_lat)**2 + ((1.0 - e2) * sin(theta_lat))**2)

    theta = d / Re
    phi = pi - deg2rad(az)

    x = sin(theta) * cos(phi)
    y = sin(theta) * sin(phi)
    z = cos(theta)

    alpha = pi * 0.5 - deg2rad(lat)

    X = x * cos(alpha) + z * sin(alpha)
    Y = y
    Z = -x * sin(alpha) + z * cos(alpha)

    theta_new = np.arccos(Z)
    phi_new = np.sign(Y) * np.arccos(X / sqrt(X**2 + Y**2))

    lat_ans = rad2deg(pi * 0.5 - theta_new)
    lon_ans = lon + rad2deg(phi_new)

    lat_ans = (lat_ans + 90) % 180 - 90
    lon_ans = (lon_ans + 180) % 360 - 180

    return (lat_ans, lon_ans)


def lonlat2xyratio(lat):  # [lon[deg], lat[deg]] to [x[m], y[m]] ratio
    a = A                           # Equatorial radius [m]
    f = 1.0 / ONE_F                 # Flattening [-]
    e2 = 2.0 * f - f * f            # Square of eccentricity e

    theta_lat = deg2rad(lat)
    N = a / sqrt(1.0 - e2 * sin(theta_lat)**2)  # Prime vertical radius of curvature

    dxdlon = N * cos(theta_lat)
    dydlat = N * (1.0 - e2) / (1.0 - e2 * sin(theta_lat)**2)

    return np.array([dxdlon, dydlat]).T * deg2rad(1.)


# points in hull must not be overlapping (hull[0] != hull[-1]), and ordered in anti-clockwise
def extend_lonlat_hull(lonlat_hull, distance, dlondlat=[0, 0], max_deg=30):  # [deg, deg], [m], [deg, deg]
    lonlat_ave = np.mean(lonlat_hull, axis=0)
    lola2xy = lonlat2xyratio(lonlat_ave[1])
    dxdy = dlondlat * lola2xy
    xy_hull = lonlat_hull * lola2xy
    xy_hull_new = extend_xy_hull(xy_hull, distance, dxdy, max_deg)
    lonlat_hull_new = xy_hull_new / lola2xy
    return lonlat_hull_new


def extend_xy_hull(xy_hull, distance, dxdy=[0, 0], max_deg=30):
    xy0 = xy_hull
    xy1 = np.roll(xy_hull, -1, axis=0)
    dxy = xy1 - xy0
    udxy = dxy / np.array([np.linalg.norm(dxy, axis=1)]).T
    ndxy = np.matmul(udxy, [[0, -1], [1, 0]])
    ddxy = distance * ndxy
    xy0n = xy0 + ddxy + dxdy
    xy1n = xy1 + ddxy + dxdy

    costheta = np.sum(ndxy * np.roll(ndxy, -1, axis=0), axis=1).clip(-1, 1)
    theta = np.arccos(costheta)
    xy_corners = []
    for theta_, ddxy_, xy1_ in zip(theta, ddxy, xy1):
        N_ = (theta_ // deg2rad(max_deg))
        n_ = np.arange(0, N_, 1)
        theta_n = theta_ * (n_ + 1) / (N_ + 1)
        An_T = np.array([[cos(theta_n), -sin(theta_n)], [sin(theta_n), cos(theta_n)]]).transpose(2, 1, 0)
        ddxy_n = np.matmul(ddxy_, An_T)
        xy1_nn = xy1_ + ddxy_n + dxdy
        xy_corners += [xy1_nn]

    xy_ans_list = []
    for xy0n_, xy1n_, xycs_ in zip(xy0n, xy1n, xy_corners):
        xy_ans_list += [xy0n_, xy1n_]
        xy_ans_list += list(xycs_)
    return np.array(xy_ans_list)
# coding: utf-8 ##### Constants ############################################### ### WGS84 ### # Equatorial radius [m] # Inverse flattening [-] # Gravitational constant [m3/s2] # Angular velocity of the Earth [rad/s] ############################################################### # lat: geodetic latitude # latc: geocentric latitude Args:         posLLH_ (np.array 3x1) : position in LLH coordinate [deg, deg, m]     Return:         (np.array 3x1) : position in ECEF coordinate [m, m, m] # Equatorial radius [m] # Flattening [-] # Square of eccentricity e # Radius of prime vertical circle [m] This function is an approximation.     Please refer https://www.enri.go.jp/~fks442/K_MUSEN/1st/1st060428rev2.pdf.      Args:         posECEF_ (np.array 3x1) : [deg, deg, m]     Return:         (np.array 3x1) : position in LLH coordinate [deg, deg, m] # Equatorial radius [m] # Flattening [-] # Square of eccentricity e # Polar radius [m] # Square of second eccentricity e' # Distance from the rotation axis of the Earth [m] # [rad] # deg, deg, m # deg, deg, m Args:         posLLH_ (np.array 3x1) : [deg, deg, m]     Return:         dcm (np.array 3x3) : DCM from ECEF to NED Args:         posLLH_ (np.array 3x1) : [deg, deg, m]     Return:         dcm (np.array 3x3) : DCM from NED to ECEF Args:         second (double) : time from reference time[s]     Return:         dcm (np.array 3x3) : DCM from ECI to ECEF Args:         second (double) : time from reference time[s]     Return:         dcm (np.array 3x3) : DCM from ECEF to ECI Args:         azimuth_deg (double) : azimuth of attitude [deg]         elevation_deg (double) : elevation of attitude [deg]         roll_deg (double) : roll of attitude [deg]     Return:         dcm (np.array 3x3) : DCM from NED to Body Args:         azimuth_deg (double) : azimuth of attitude [deg]         elevation_deg (double) : elevation of attitude [deg]         roll_deg (double) : roll of attitude [deg]     Return:         dcm (np.array 3x3) : DCM from Body to NED Args:         posECEF_ (np.array 3x1) : position in ECEF coordinate [m, m, m]         second (double) : time from reference time [s]     Return:         (np.array 3x1) : position in ECI coordinate [m, m, m] # def velNEDfromECI(posECI_, velECI_, dcmECI2NED_): #     omega = OMEGA #     omegaECI2ECEF_ = np.array([[0.,   -omega, 0.], #                                [omega, 0.,    0.], #                                [0.,    0.,    0.]]) # #     return np.matmul(dcmECI2NED_, (velECI_ - np.matmul(omegaECI2ECEF_, posECI_))) ### utility functions ### # Earth radius ~ Equatorial radius # Angle at the center of the Earth # ([deg], [deg]), ([m], [deg]) # Equatorial radius [m] # Flattening [-] # Square of eccentricity e # Prime vertical radius of curvature # [lon[deg], lat[deg]] to [x[m], y[m]] ratio # Equatorial radius [m] # Flattening [-] # Square of eccentricity e # Prime vertical radius of curvature # points in hull must not be overlapping (hull[0] != hull[-1]), and ordered in anti-clockwise # [deg, deg], [m], [deg, deg]