def test_Ex8_position_A_and_azimuth_and_distance_to_B(): # Position A is given as n_EA_E: # Enter elements as lat/long in deg: lat, lon = rad(80), rad(-90) n_EA_E = lat_lon2n_E(lat, lon) # The initial azimuth and great circle distance (s_AB), and Earth # radius (r_Earth) are also given: azimuth = rad(200) s_AB = 1000 # m r_Earth = 6371e3 # m, mean Earth radius # Find the destination point B, as n_EB_E ("The direct/first geodetic # problem" for a sphere) # SOLUTION: # Step1: Convert distance in meter into distance in [rad]: distance_rad = s_AB / r_Earth # Step2: Find n_EB_E: n_EB_E = n_EA_E_distance_and_azimuth2n_EB_E(n_EA_E, distance_rad, azimuth) # When displaying the resulting position for humans, it is more # convenient to see lat, long: lat_EB, long_EB = n_E2lat_lon(n_EB_E) print('Ex8, Destination: lat, long = {0} {1} deg'.format( deg(lat_EB), deg(long_EB))) assert_array_almost_equal(deg(lat_EB), 79.99154867) assert_array_almost_equal(deg(long_EB), -90.01769837) azimuth1 = n_EA_E_and_n_EB_E2azimuth(n_EA_E, n_EB_E, a=r_Earth, f=0) assert_array_almost_equal(azimuth, azimuth1 + 2 * np.pi)
def test_Ex9_intersect(): # Two paths A and B are given by two pairs of positions: # Enter elements as lat/long in deg: n_EA1_E = lat_lon2n_E(rad(10), rad(20)) n_EA2_E = lat_lon2n_E(rad(30), rad(40)) n_EB1_E = lat_lon2n_E(rad(50), rad(60)) n_EB2_E = lat_lon2n_E(rad(70), rad(80)) # Find the intersection between the two paths, n_EC_E: n_EC_E_tmp = unit( np.cross(np.cross(n_EA1_E, n_EA2_E, axis=0), np.cross(n_EB1_E, n_EB2_E, axis=0), axis=0)) # 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(np.dot(n_EC_E_tmp.T, n_EA1_E)) * n_EC_E_tmp # When displaying the resulting position for humans, it is more # convenient to see lat, long: lat_EC, long_EC = n_E2lat_lon(n_EC_E) msg = 'Ex9, Intersection: lat, long = {} {} deg' print(msg.format(deg(lat_EC), deg(long_EC))) assert_array_almost_equal(deg(lat_EC), 40.31864307) assert_array_almost_equal(deg(long_EC), 55.90186788)
def test_Ex6_interpolated_position(): # Position B at time t0 and t2 is given as n_EB_E_t0 and n_EB_E_t1: # Enter elements as lat/long in deg: n_EB_E_t0 = lat_lon2n_E(rad(89), rad(0)) n_EB_E_t1 = lat_lon2n_E(rad(89), rad(180)) # The times are given as: t0 = 10 t1 = 20 ti = 16 # time of interpolation # Find the interpolated position at time ti, n_EB_E_ti # SOLUTION: # Using standard interpolation: n_EB_E_ti = unit(n_EB_E_t0 + (ti - t0) * (n_EB_E_t1 - n_EB_E_t0) / (t1 - t0)) # When displaying the resulting position for humans, it is more # convenient to see lat, long: lat_EB_ti, long_EB_ti = n_E2lat_lon(n_EB_E_ti) msg = 'Ex6, Interpolated position: lat, long = {} {} deg' print(msg.format(deg(lat_EB_ti), deg(long_EB_ti))) assert_array_almost_equal(deg(lat_EB_ti), 89.7999805) assert_array_almost_equal(deg(long_EB_ti), 180.)
def plot_mean_position(): """ Example ------- >>> plot_mean_position() Ex7, Average lat=[ 67.23615295], lon=[-6.91751117] """ positions = np.array([ (90, 0), (60, 10), (50, -20), ]) lats, lons = positions.T nvecs = lat_lon2n_E(rad(lats), rad(lons)) # Find the horizontal mean position: n_EM_E = unit(np.sum(nvecs, axis=1).reshape((3, 1))) lat, lon = n_E2lat_lon(n_EM_E) lat, lon = deg(lat), deg(lon) print(('Ex7, Average lat={0}, lon={1}'.format(lat, lon))) map1 = Basemap(projection='ortho', lat_0=int(lat), lon_0=int(lon), resolution='l') plot_world(map1) x, y = map1(lon, lat) map1.scatter(x, y, linewidth=5, marker='o', color='r') x1, y1 = map1(lons, lats) # print(len(lons), x1, y1) map1.scatter(x1, y1, linewidth=5, marker='o', color='k') plt.title('Figure of mean position (red dot) compared to positions ' 'A, B, and C (black dots).')
def plot_mean_position(): positions = np.array([(90, 0), (60, 10), (50, -20), ]) lats, lons = positions.T nvecs = lat_lon2n_E(rad(lats), rad(lons)) # Find the horizontal mean position: n_EM_E = unit(np.sum(nvecs, axis=1).reshape((3, 1))) lat, lon = n_E2lat_lon(n_EM_E) lat, lon = deg(lat), deg(lon) print('Ex7, Average lat={0}, lon={1}'.format(lat, lon)) map1 = Basemap(projection='ortho', lat_0=int(lat), lon_0=int(lon), resolution='l') plot_world(map1) x, y = map1(lon, lat) map1.scatter(x, y, linewidth=5, marker='o', color='r') x1, y1 = map1(lons, lats) print(len(lons), x1, y1) map1.scatter(x1, y1, linewidth=5, marker='o', color='k') plt.title('Figure of mean position (red dot) compared to positions ' 'A, B, and C (black dots).')
def plot_mean_position(): """ Example ------- >>> plot_mean_position() Ex7, Average lat=67.2, lon=-6.9 >>> plt.show() # doctest: +SKIP >>> plt.close() """ positions = np.array([ (90, 0), (60, 10), (50, -20), ]) lats, lons = np.transpose(positions) nvecs = lat_lon2n_E(rad(lats), rad(lons)) # Find the horizontal mean position: n_EM_E = unit(np.sum(nvecs, axis=1).reshape((3, 1))) lat, lon = n_E2lat_lon(n_EM_E) lat, lon = deg(lat), deg(lon) print('Ex7, Average lat={0:2.1f}, lon={1:2.1f}'.format(lat[0], lon[0])) plotter = _init_plotter(lat, lon) plotter(lon, lat, linewidth=5, marker='o', color='r') plotter(lons, lats, linewidth=5, marker='o', color='k') plt.title('Figure of mean position (red dot) compared to \npositions ' 'A, B, and C (black dots).')
def find_c_point_from_precalc(to_point, point1, point2, c12, p1h, p2h, dp1p2): tpn = to_point.nv ctp = cross(tpn, c12, axis=0) try: c = unit(cross(ctp, c12, axis=0)) except Exception: print((to_point, point1, point2)) raise sutable_c = None for co in (c, 0 - c): co_rs = co.reshape((3, )) dp1co = arccos(arccos_limit(dot(p1h, co_rs))) dp2co = arccos(arccos_limit(dot(p2h, co_rs))) if abs(dp1co + dp2co - dp1p2) < 0.000001: sutable_c = co break if sutable_c is not None: c_point_lat, c_point_lng = n_E2lat_lon(sutable_c) c_point = Point(lat=rad2deg(c_point_lat[0]), lng=rad2deg(c_point_lng[0])) c_dist = distance(to_point, c_point) else: c_dist, c_point = min( ((distance(to_point, p), p) for p in (point1, point2)), key=itemgetter(0)) return find_c_point_result(c_dist, c_point)
def test_Ex9_intersection(): # Two paths A and B are given by two pairs of positions: # Enter elements as lat/long in deg: n_EA1_E = lat_lon2n_E(rad(10), rad(20)) n_EA2_E = lat_lon2n_E(rad(30), rad(40)) n_EB1_E = lat_lon2n_E(rad(50), rad(60)) n_EB2_E = lat_lon2n_E(rad(70), rad(80)) # Find the intersection between the two paths, n_EC_E: n_EC_E_tmp = unit(np.cross(np.cross(n_EA1_E, n_EA2_E, axis=0), np.cross(n_EB1_E, n_EB2_E, axis=0), axis=0)) # 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(np.dot(n_EC_E_tmp.T, n_EA1_E)) * n_EC_E_tmp # When displaying the resulting position for humans, it is more # convenient to see lat, long: lat_EC, long_EC = n_E2lat_lon(n_EC_E) msg = 'Ex9, Intersection: lat, long = {} {} deg' print(msg.format(deg(lat_EC), deg(long_EC))) assert_array_almost_equal(deg(lat_EC), 40.31864307) assert_array_almost_equal(deg(long_EC), 55.90186788)
def test_Ex8_position_A_and_azimuth_and_distance_to_B(): # Position A is given as n_EA_E: # Enter elements as lat/long in deg: lat, lon = rad(80), rad(-90) n_EA_E = lat_lon2n_E(lat, lon) # The initial azimuth and great circle distance (s_AB), and Earth # radius (r_Earth) are also given: azimuth = rad(200) s_AB = 1000 # m r_Earth = 6371e3 # m, mean Earth radius # Find the destination point B, as n_EB_E ("The direct/first geodetic # problem" for a sphere) # SOLUTION: # Step1: Convert distance in meter into distance in [rad]: distance_rad = s_AB / r_Earth # Step2: Find n_EB_E: n_EB_E = n_EA_E_distance_and_azimuth2n_EB_E(n_EA_E, distance_rad, azimuth) # When displaying the resulting position for humans, it is more # convenient to see lat, long: lat_EB, long_EB = n_E2lat_lon(n_EB_E) print('Ex8, Destination: lat, long = {0} {1} deg'.format(deg(lat_EB), deg(long_EB))) assert_array_almost_equal(deg(lat_EB), 79.99154867) assert_array_almost_equal(deg(long_EB), -90.01769837) azimuth1 = n_EA_E_and_n_EB_E2azimuth(n_EA_E, n_EB_E, a=r_Earth, f=0) assert_array_almost_equal(azimuth, azimuth1+2*np.pi)
def find_closest_point_pair(points, to_point, req_min_dist=20, stop_after_dist=50): tpn = to_point.nv min_distance = None min_point_pair = None min_c_point = None for point1, point2 in pairs(points): p1 = point1.nv p2 = point2.nv c12 = cross(p1, p2, axis=0) ctp = cross(tpn, c12, axis=0) c = unit(cross(ctp, c12, axis=0)) p1h = p1.reshape((3, )) p2h = p2.reshape((3, )) dp1p2 = arccos(dot(p1h, p2h)) sutable_c = None for co in (c, 0 - c): co_rs = co.reshape((3, )) dp1co = arccos(dot(p1h, co_rs)) dp2co = arccos(dot(p2h, co_rs)) if abs(dp1co + dp2co - dp1p2) < 0.000001: sutable_c = co break if sutable_c is not None: c_point_lat, c_point_lng = n_E2lat_lon(sutable_c) c_point = Point(lat=rad2deg(c_point_lat[0]), lng=rad2deg(c_point_lng[0])) c_dist = distance(to_point, c_point) else: c_dist, c_point = min( ((distance(to_point, p), p) for p in (point1, point2))) if min_distance is None or c_dist < min_distance: min_distance = c_dist min_point_pair = (point1, point2) min_c_point = c_point if min_distance < req_min_dist and c_dist > stop_after_dist: break return min_point_pair, min_c_point, min_distance
def test_Ex3_ECEF_vector_to_geodetic_latitude(): # Position B is given as p_EB_E ("ECEF-vector") p_EB_E = 6371e3 * np.vstack((0.9, -1, 1.1)) # m # Find position B as geodetic latitude, longitude and height # SOLUTION: # Find n-vector from the p-vector: n_EB_E, z_EB = p_EB_E2n_EB_E(p_EB_E) # Convert to lat, long and height: lat_EB, long_EB = n_E2lat_lon(n_EB_E) h_EB = -z_EB msg = 'Ex3, Pos B: lat, long = {} {} deg, height = {} m' print(msg.format(deg(lat_EB), deg(long_EB), h_EB)) assert_array_almost_equal(deg(lat_EB), 39.37874867) assert_array_almost_equal(deg(long_EB), -48.0127875) assert_array_almost_equal(h_EB, 4702059.83429485)
def test_Ex2_B_and_delta_in_frame_B_to_C_in_frame_E(): # delta vector from B to C, decomposed in B is given: p_BC_B = np.r_[3000, 2000, 100].reshape((-1, 1)) # Position and orientation of B is given: n_EB_E = unit([[1], [2], [3]]) # unit to get unit length of vector z_EB = -400 R_NB = zyx2R(rad(10), rad(20), rad(30)) # the three angles are yaw, pitch, and roll # A custom reference ellipsoid is given (replacing WGS-84): a, f = 6378135, 1.0 / 298.26 # (WGS-72) # Find the position of C. # SOLUTION: # Step1: Find R_EN: R_EN = n_E2R_EN(n_EB_E) # Step2: Find R_EB, from R_EN and R_NB: R_EB = np.dot(R_EN, R_NB) # Note: closest frames cancel # Step3: Decompose the delta vector in E: p_BC_E = np.dot(R_EB, p_BC_B) # no transpose of R_EB, since the vector is in B # Step4: Find the position of C, using the functions that goes from one # position and a delta, to a new position: n_EC_E, z_EC = n_EA_E_and_p_AB_E2n_EB_E(n_EB_E, p_BC_E, z_EB, a, f) # When displaying the resulting position for humans, it is more # convenient to see lat, long: lat_EC, long_EC = n_E2lat_lon(n_EC_E) # Here we also assume that the user wants output height (= - depth): msg = 'Ex2, Pos C: lat, long = {},{} deg, height = {} m' print(msg.format(deg(lat_EC), deg(long_EC), -z_EC)) assert_array_almost_equal(deg(lat_EC), 53.32637826) assert_array_almost_equal(deg(long_EC), 63.46812344) assert_array_almost_equal(z_EC, -406.00719607)
def from_nv(cls, nv, round_digits=6): lat, lng = n_E2lat_lon(nv) point = cls(round(rad2deg(lat[0]), round_digits), round(rad2deg(lng[0]), round_digits)) point._nv = nv return point
def to_lla(self): lat, lon = nv.n_E2lat_lon(self.n_EB_E) return Lla(np.rad2deg(lat[0]), np.rad2deg(lon[0]), -self.depth)
def pvec_b_to_lla(forward, right, down, roll, pitch, yaw, lat, lon, alt): """ returns the lat lon and alt corresponding to a p-vec in the UAV's body frame Parameters ---------- forward: float The number of meters forward of the UAV right: float The number of meters to the right of the UAV down: float The number of meters below the UAV roll: float The UAV's roll angle in degrees pitch: float The UAV's pitch angle in degrees yaw: float The UAV's yaw angle in degrees lat: float The UAV's latitude in degrees lon: float The UAV's longitude in degrees alt: float The UAV's altitude in meters Returns ------- list This list holds three floats representing the latitude in degrees, longitude in degrees and altitude in meters (in that order). """ # create a p-vector with the forward, right and down values p_B = np.array([forward, right, down]) # this matrix can transform a pvec in the body frame to a pvec in the NED frame rot_NB = nv.zyx2R(radians(yaw), radians(pitch), radians(roll)) # calculate the pvec in the NED frame p_N = rot_NB.dot(p_B) # create an n-vector for the UAV n_UAV = nv.lat_lon2n_E(radians(lat), radians(lon)) # this creates a matrix that rotates pvecs from NED to ECEF rot_EN = nv.n_E2R_EN(n_UAV) # find the offset vector from the UAV to the point of interest in the ECEF frame p_delta_E = rot_EN.dot(p_N) # find the p-vector for the UAV in the ECEF frame p_EUAV_E = nv.n_EB_E2p_EB_E(n_UAV, -alt).reshape(1, 3)[0] # find the p-vector for the point of interest. This is the UAV + the offset in the ECEF frame. p_E = p_EUAV_E + p_delta_E # find the n-vector for the point of interest given the p-vector in the ECEF frame. n_result, z_result = nv.p_EB_E2n_EB_E(p_E.reshape(3, 1)) # convert the n-vector to a lat and lon lat_result, lon_result = nv.n_E2lat_lon(n_result) lat_result, lon_result = degrees(lat_result), degrees(lon_result) # convert depth to alt alt_result = -z_result[0] return [lat_result, lon_result, alt_result]
def getMiddlePointFromList(positions): n_EM_E = nv.unit(sum(positions)) lat, lon = nv.n_E2lat_lon(n_EM_E) lat, lon = degrees(lat[0]), degrees(lon[0]) return lat, lon