def fitGC(self):
""" Fits great circle to observations. """
self.cartesian_points = []
self.ra_array = np.array(self.ra_array)
self.dec_array = np.array(self.dec_array)
for ra, dec in zip(self.ra_array, self.dec_array):
vect = vectNorm(raDec2Vector(ra, dec))
self.cartesian_points.append(vect)
self.cartesian_points = np.array(self.cartesian_points)
# Set begin and end pointing vectors
self.beg_vect = self.cartesian_points[0]
self.end_vect = self.cartesian_points[-1]
# Compute alt of the begining and the last point
self.beg_azim, self.beg_alt = raDec2AltAz(self.ra_array[0], self.dec_array[0], self.jd_array[0], \
self.lat, self.lon)
self.end_azim, self.end_alt = raDec2AltAz(self.ra_array[-1], self.dec_array[-1], self.jd_array[-1], \
self.lat, self.lon)
# Fit a great circle through observations
x_arr, y_arr, z_arr = self.cartesian_points.T
coeffs, self.theta0, self.phi0 = fitGreatCircle(x_arr, y_arr, z_arr)
# Calculate the plane normal
self.normal = np.array([coeffs[0], coeffs[1], -1.0])
# Norm the normal vector to unit length
self.normal = vectNorm(self.normal)
# Compute RA/Dec of the normal direction
self.normal_ra, self.normal_dec = vector2RaDec(self.normal)
# Take pointing directions of the beginning and the end of the meteor
self.meteor_begin_cartesian = vectNorm(self.cartesian_points[0])
self.meteor_end_cartesian = vectNorm(self.cartesian_points[-1])
# Compute angular distance between begin and end (radians)
self.ang_be = angularSeparationVect(self.beg_vect, self.end_vect)
# Compute meteor duration in seconds
self.duration = (self.jd_array[-1] - self.jd_array[0])*86400.0
# Set the reference JD as the JD of the beginning
self.jdt_ref = self.jd_array[0]
# Compute the solar longitude of the beginning (degrees)
self.lasun = np.degrees(jd2SolLonSteyaert(self.jdt_ref))
def findGCPhase(self, ra, dec):
""" Finds the phase of the great circle that is closest to the given RA/Dec.
Arguments;
ra: [float] RA (deg).
dec: [float] Declination (deg).
Return:
phase: [float] Phase (deg).
"""
x, y, z = raDec2Vector(ra, dec)
theta, phi = cartesianToPolar(x, y, z)
# Find the corresponding phase
phase = np.degrees(greatCirclePhase(theta, phi, self.theta0,
self.phi0))
return phase
def showerAssociation(config, ftpdetectinfo_list, shower_code=None, show_plot=False, save_plot=False, \
plot_activity=False):
""" Do single station shower association based on radiant direction and height.
Arguments:
config: [Config instance]
ftpdetectinfo_list: [list] A list of paths to FTPdetectinfo files.
Keyword arguments:
shower_code: [str] Only use this one shower for association (e.g. ETA, PER, SDA). None by default,
in which case all active showers will be associated.
show_plot: [bool] Show the plot on the screen. False by default.
save_plot: [bool] Save the plot in the folder with FTPdetectinfos. False by default.
plot_activity: [bool] Whether to plot the shower activity plot of not. False by default.
Return:
associations, shower_counts: [tuple]
- associations: [dict] A dictionary where the FF name and the meteor ordinal number on the FF
file are keys, and the associated Shower object are values.
- shower_counts: [list] A list of shower code and shower count pairs.
"""
# Load the list of meteor showers
shower_list = loadShowers(config.shower_path, config.shower_file_name)
# Load FTPdetectinfos
meteor_data = []
for ftpdetectinfo_path in ftpdetectinfo_list:
if not os.path.isfile(ftpdetectinfo_path):
print('No such file:', ftpdetectinfo_path)
continue
meteor_data += readFTPdetectinfo(*os.path.split(ftpdetectinfo_path))
if not len(meteor_data):
return {}, []
# Dictionary which holds FF names as keys and meteor measurements + associated showers as values
associations = {}
for meteor in meteor_data:
ff_name, cam_code, meteor_No, n_segments, fps, hnr, mle, binn, px_fm, rho, phi, meteor_meas = meteor
# Skip very short meteors
if len(meteor_meas) < 4:
continue
# Check if the data is calibrated
if not meteor_meas[0][0]:
print(
'Data is not calibrated! Meteors cannot be associated to showers!'
)
break
# Init container for meteor observation
meteor_obj = MeteorSingleStation(cam_code, config.latitude,
config.longitude, ff_name)
# Infill the meteor structure
for entry in meteor_meas:
calib_status, frame_n, x, y, ra, dec, azim, elev, inten, mag = entry
# Compute the Julian data of every point
jd = datetime2JD(
filenameToDatetime(ff_name) +
datetime.timedelta(seconds=float(frame_n) / fps))
meteor_obj.addPoint(jd, ra, dec, mag)
# Fit the great circle and compute the geometrical parameters
meteor_obj.fitGC()
# Skip all meteors with beginning heights below 15 deg
if meteor_obj.beg_alt < 15:
continue
# Go through all showers in the list and find the best match
best_match_shower = None
best_match_dist = np.inf
for shower_entry in shower_list:
# Extract shower parameters
shower = Shower(shower_entry)
# If the shower code was given, only check this one shower
if shower_code is not None:
if shower.name.lower() != shower_code.lower():
continue
### Solar longitude filter
# If the shower doesn't have a stated beginning or end, check if the meteor is within a preset
# threshold solar longitude difference
if np.any(np.isnan([shower.lasun_beg, shower.lasun_end])):
shower.lasun_beg = (shower.lasun_max -
config.shower_lasun_threshold) % 360
shower.lasun_end = (shower.lasun_max +
config.shower_lasun_threshold) % 360
# Filter out all showers which are not active
if not isAngleBetween(np.radians(shower.lasun_beg),
np.radians(meteor_obj.lasun),
np.radians(shower.lasun_end)):
continue
### ###
### Radiant filter ###
# Assume a fixed meteor height for an approximate apparent radiant
meteor_fixed_ht = 100000 # 100 km
shower.computeApparentRadiant(config.latitude, config.longitude, meteor_obj.jdt_ref, \
meteor_fixed_ht=meteor_fixed_ht)
# Compute the angle between the meteor radiant and the great circle normal
radiant_separation = meteor_obj.angularSeparationFromGC(
shower.ra, shower.dec)
# Make sure the meteor is within the radiant distance threshold
if radiant_separation > config.shower_max_radiant_separation:
continue
# Compute angle between the meteor's beginning and end, and the shower radiant
shower.radiant_vector = vectNorm(
raDec2Vector(shower.ra, shower.dec))
begin_separation = np.degrees(angularSeparationVect(shower.radiant_vector, \
meteor_obj.meteor_begin_cartesian))
end_separation = np.degrees(angularSeparationVect(shower.radiant_vector, \
meteor_obj.meteor_end_cartesian))
# Make sure the beginning of the meteor is closer to the radiant than it's end
if begin_separation > end_separation:
continue
### ###
### Height filter ###
# Estimate the limiting meteor height from the velocity (meters)
filter_beg_ht = heightModel(shower.v_init, ht_type='beg')
filter_end_ht = heightModel(shower.v_init, ht_type='end')
### Estimate the meteor beginning height with +/- 1 frame, otherwise some short meteor may get
### rejected
meteor_obj_orig = copy.deepcopy(meteor_obj)
# Shorter
meteor_obj_m1 = copy.deepcopy(meteor_obj_orig)
meteor_obj_m1.duration -= 1.0 / config.fps
meteor_beg_ht_m1 = estimateMeteorHeight(config, meteor_obj_m1,
shower)
# Nominal
meteor_beg_ht = estimateMeteorHeight(config, meteor_obj_orig,
shower)
# Longer
meteor_obj_p1 = copy.deepcopy(meteor_obj_orig)
meteor_obj_p1.duration += 1.0 / config.fps
meteor_beg_ht_p1 = estimateMeteorHeight(config, meteor_obj_p1,
shower)
meteor_obj = meteor_obj_orig
### ###
# If all heights (even those with +/- 1 frame) are outside the height range, reject the meteor
if ((meteor_beg_ht_p1 < filter_end_ht) or (meteor_beg_ht_p1 > filter_beg_ht)) and \
((meteor_beg_ht < filter_end_ht) or (meteor_beg_ht > filter_beg_ht)) and \
((meteor_beg_ht_m1 < filter_end_ht) or (meteor_beg_ht_m1 > filter_beg_ht)):
continue
### ###
# Compute the radiant elevation above the horizon
shower.azim, shower.elev = raDec2AltAz(shower.ra, shower.dec, meteor_obj.jdt_ref, \
config.latitude, config.longitude)
# Take the shower that's closest to the great circle if there are multiple candidates
if radiant_separation < best_match_dist:
best_match_dist = radiant_separation
best_match_shower = copy.deepcopy(shower)
# If a shower is given and the match is not this shower, skip adding the meteor to the list
# If no specific shower is give for association, add all meteors
if ((shower_code is not None) and
(best_match_shower is not None)) or (shower_code is None):
# Store the associated shower
associations[(ff_name,
meteor_No)] = [meteor_obj, best_match_shower]
# Find shower frequency and sort by count
shower_name_list_temp = []
shower_list_temp = []
for key in associations:
_, shower = associations[key]
if shower is None:
shower_name = '...'
else:
shower_name = shower.name
shower_name_list_temp.append(shower_name)
shower_list_temp.append(shower)
_, unique_showers_indices = np.unique(shower_name_list_temp,
return_index=True)
unique_shower_names = np.array(
shower_name_list_temp)[unique_showers_indices]
unique_showers = np.array(shower_list_temp)[unique_showers_indices]
shower_counts = [[shower_obj, shower_name_list_temp.count(shower_name)] for shower_obj, \
shower_name in zip(unique_showers, unique_shower_names)]
shower_counts = sorted(shower_counts, key=lambda x: x[1], reverse=True)
# Create a plot of showers
if show_plot or save_plot:
# Generate consistent colours
colors_by_name = makeShowerColors(shower_list)
def get_shower_color(shower):
try:
return colors_by_name[shower.name] if shower else "0.4"
except KeyError:
return 'gray'
# Init the figure
plt.figure()
# Init subplots depending on if the activity plot is done as well
if plot_activity:
gs = gridspec.GridSpec(2, 1, height_ratios=[3, 1])
ax_allsky = plt.subplot(gs[0], facecolor='black')
ax_activity = plt.subplot(gs[1], facecolor='black')
else:
ax_allsky = plt.subplot(111, facecolor='black')
# Init the all-sky plot
allsky_plot = AllSkyPlot(ax_handle=ax_allsky)
# Plot all meteors
for key in associations:
meteor_obj, shower = associations[key]
### Plot the observed meteor points ###
color = get_shower_color(shower)
allsky_plot.plot(meteor_obj.ra_array,
meteor_obj.dec_array,
color=color,
linewidth=1,
zorder=4)
# Plot the peak of shower meteors a different color
peak_color = 'blue'
if shower is not None:
peak_color = 'tomato'
allsky_plot.scatter(meteor_obj.ra_array[-1], meteor_obj.dec_array[-1], c=peak_color, marker='+', \
s=5, zorder=5)
### ###
### Plot fitted great circle points ###
# Find the GC phase angle of the beginning of the meteor
gc_beg_phase = meteor_obj.findGCPhase(
meteor_obj.ra_array[0], meteor_obj.dec_array[0])[0] % 360
# If the meteor belongs to a shower, find the GC phase which ends at the shower
if shower is not None:
gc_end_phase = meteor_obj.findGCPhase(shower.ra,
shower.dec)[0] % 360
# Fix 0/360 wrap
if abs(gc_end_phase - gc_beg_phase) > 180:
if gc_end_phase > gc_beg_phase:
gc_end_phase -= 360
else:
gc_beg_phase -= 360
gc_alpha = 1.0
else:
# If it's a sporadic, find the direction to which the meteor should extend
gc_end_phase = meteor_obj.findGCPhase(meteor_obj.ra_array[-1], \
meteor_obj.dec_array[-1])[0]%360
# Find the correct direction
if (gc_beg_phase - gc_end_phase) % 360 > (gc_end_phase -
gc_beg_phase) % 360:
gc_end_phase = gc_beg_phase - 170
else:
gc_end_phase = gc_beg_phase + 170
gc_alpha = 0.7
# Store great circle beginning and end phase
meteor_obj.gc_beg_phase = gc_beg_phase
meteor_obj.gc_end_phase = gc_end_phase
# Get phases 180 deg before the meteor
phase_angles = np.linspace(gc_end_phase, gc_beg_phase, 100) % 360
# Compute RA/Dec of points on the great circle
ra_gc, dec_gc = meteor_obj.sampleGC(phase_angles)
# Cull all points below the horizon
azim_gc, elev_gc = raDec2AltAz(ra_gc, dec_gc, meteor_obj.jdt_ref, config.latitude, \
config.longitude)
temp_arr = np.c_[ra_gc, dec_gc]
temp_arr = temp_arr[elev_gc > 0]
ra_gc, dec_gc = temp_arr.T
# Plot the great circle fitted on the radiant
gc_color = get_shower_color(shower)
allsky_plot.plot(ra_gc,
dec_gc,
linestyle='dotted',
color=gc_color,
alpha=gc_alpha,
linewidth=1)
# Plot the point closest to the shower radiant
if shower is not None:
allsky_plot.plot(ra_gc[0],
dec_gc[0],
color='r',
marker='+',
ms=5,
mew=1)
# Store shower radiant point
meteor_obj.radiant_ra = ra_gc[0]
meteor_obj.radiant_dec = dec_gc[0]
### ###
### Plot all showers ###
# Find unique showers and their apparent radiants computed at highest radiant elevation
# (otherwise the apparent radiants can be quite off)
shower_dict = {}
for key in associations:
meteor_obj, shower = associations[key]
if shower is None:
continue
# If the shower name is in dict, find the shower with the highest radiant elevation
if shower.name in shower_dict:
if shower.elev > shower_dict[shower.name].elev:
shower_dict[shower.name] = shower
else:
shower_dict[shower.name] = shower
# Plot the location of shower radiants
for shower_name in shower_dict:
shower = shower_dict[shower_name]
heading_arr = np.linspace(0, 360, 50)
# Compute coordinates on a circle around the given RA, Dec
ra_circle, dec_circle = sphericalPointFromHeadingAndDistance(shower.ra, shower.dec, \
heading_arr, config.shower_max_radiant_separation)
# Plot the shower circle
allsky_plot.plot(ra_circle,
dec_circle,
color=colors_by_name[shower_name])
# Plot the shower name
x_text, y_text = allsky_plot.raDec2XY(shower.ra, shower.dec)
allsky_plot.ax.text(x_text, y_text, shower.name, color='w', size=8, va='center', \
ha='center', zorder=6)
# Plot station name and solar longiutde range
allsky_plot.ax.text(-180,
89,
"{:s}".format(cam_code),
color='w',
family='monospace')
# Get a list of JDs of meteors
jd_list = [associations[key][0].jdt_ref for key in associations]
if len(jd_list):
# Get the range of solar longitudes
jd_min = min(jd_list)
sol_min = np.degrees(jd2SolLonSteyaert(jd_min))
jd_max = max(jd_list)
sol_max = np.degrees(jd2SolLonSteyaert(jd_max))
# Plot the date and solar longitude range
date_sol_beg = u"Beg: {:s} (sol = {:.2f}\u00b0)".format(
jd2Date(jd_min, dt_obj=True).strftime("%Y%m%d %H:%M:%S"),
sol_min)
date_sol_end = u"End: {:s} (sol = {:.2f}\u00b0)".format(
jd2Date(jd_max, dt_obj=True).strftime("%Y%m%d %H:%M:%S"),
sol_max)
allsky_plot.ax.text(-180,
85,
date_sol_beg,
color='w',
family='monospace')
allsky_plot.ax.text(-180,
81,
date_sol_end,
color='w',
family='monospace')
allsky_plot.ax.text(-180,
77,
"-" * len(date_sol_end),
color='w',
family='monospace')
# Plot shower counts
for i, (shower, count) in enumerate(shower_counts):
if shower is not None:
shower_name = shower.name
else:
shower_name = "..."
allsky_plot.ax.text(-180, 73 - i*4, "{:s}: {:d}".format(shower_name, count), color='w', \
family='monospace')
### ###
# Plot yearly meteor shower activity
if plot_activity:
# Plot the activity diagram
generateActivityDiagram(config, shower_list, ax_handle=ax_activity, \
sol_marker=[sol_min, sol_max], colors=colors_by_name)
# Save plot and text file
if save_plot:
dir_path, ftpdetectinfo_name = os.path.split(ftpdetectinfo_path)
ftpdetectinfo_base_name = ftpdetectinfo_name.replace(
'FTPdetectinfo_', '').replace('.txt', '')
plot_name = ftpdetectinfo_base_name + '_radiants.png'
# Increase figure size
allsky_plot.fig.set_size_inches(18, 9, forward=True)
allsky_plot.beautify()
plt.savefig(os.path.join(dir_path, plot_name),
dpi=100,
facecolor='k')
# Save the text file with shower info
if len(jd_list):
with open(
os.path.join(dir_path, ftpdetectinfo_base_name +
"_radiants.txt"), 'w') as f:
# Print station code
f.write("# RMS single station association\n")
f.write("# \n")
f.write("# Station: {:s}\n".format(cam_code))
# Print date range
f.write(
"# Beg | End \n"
)
f.write(
"# -----------------------------------------------------\n"
)
f.write("# Date | {:24s} | {:24s} \n".format(jd2Date(jd_min, \
dt_obj=True).strftime("%Y%m%d %H:%M:%S.%f"), jd2Date(jd_max, \
dt_obj=True).strftime("%Y%m%d %H:%M:%S.%f")))
f.write("# Sol | {:>24.2f} | {:>24.2f} \n".format(
sol_min, sol_max))
# Write shower counts
f.write("# \n")
f.write("# Shower counts:\n")
f.write("# --------------\n")
f.write("# Code, Count, IAU link\n")
for i, (shower, count) in enumerate(shower_counts):
if shower is not None:
shower_name = shower.name
# Create link to the IAU database of showers
iau_link = "https://www.ta3.sk/IAUC22DB/MDC2007/Roje/pojedynczy_obiekt.php?kodstrumienia={:05d}".format(
shower.iau_code)
else:
shower_name = "..."
iau_link = "None"
f.write("# {:>4s}, {:>5d}, {:s}\n".format(
shower_name, count, iau_link))
f.write("# \n")
f.write("# Meteor parameters:\n")
f.write("# ------------------\n")
f.write(
"# Date And Time, Beg Julian date, La Sun, Shower, RA beg, Dec beg, RA end, Dec end, RA rad, Dec rad, GC theta0, GC phi0, GC beg phase, GC end phase, Mag\n"
)
# Create a sorted list of meteor associations by time
associations_list = [
associations[key] for key in associations
]
associations_list = sorted(associations_list,
key=lambda x: x[0].jdt_ref)
# Write out meteor parameters
for meteor_obj, shower in associations_list:
# Find peak magnitude
if np.any(meteor_obj.mag_array):
peak_mag = "{:+.1f}".format(
np.min(meteor_obj.mag_array))
else:
peak_mag = "None"
if shower is not None:
f.write("{:24s}, {:20.12f}, {:>10.6f}, {:>6s}, {:6.2f}, {:+7.2f}, {:6.2f}, {:+7.2f}, {:6.2f}, {:+7.2f}, {:9.3f}, {:8.3f}, {:12.3f}, {:12.3f}, {:4s}\n".format(jd2Date(meteor_obj.jdt_ref, dt_obj=True).strftime("%Y%m%d %H:%M:%S.%f"), \
meteor_obj.jdt_ref, meteor_obj.lasun, shower.name, \
meteor_obj.ra_array[0]%360, meteor_obj.dec_array[0], \
meteor_obj.ra_array[-1]%360, meteor_obj.dec_array[-1], \
meteor_obj.radiant_ra%360, meteor_obj.radiant_dec, \
np.degrees(meteor_obj.theta0), np.degrees(meteor_obj.phi0), \
meteor_obj.gc_beg_phase, meteor_obj.gc_end_phase, peak_mag))
else:
f.write("{:24s}, {:20.12f}, {:>10.6f}, {:>6s}, {:6.2f}, {:+7.2f}, {:6.2f}, {:+7.2f}, {:>6s}, {:>7s}, {:9.3f}, {:8.3f}, {:12.3f}, {:12.3f}, {:4s}\n".format(jd2Date(meteor_obj.jdt_ref, dt_obj=True).strftime("%Y%m%d %H:%M:%S.%f"), \
meteor_obj.jdt_ref, meteor_obj.lasun, '...', meteor_obj.ra_array[0]%360, \
meteor_obj.dec_array[0], meteor_obj.ra_array[-1]%360, \
meteor_obj.dec_array[-1], "None", "None", np.degrees(meteor_obj.theta0), \
np.degrees(meteor_obj.phi0), meteor_obj.gc_beg_phase, \
meteor_obj.gc_end_phase, peak_mag))
if show_plot:
allsky_plot.show()
else:
plt.clf()
plt.close()
return associations, shower_counts
def estimateMeteorHeight(config, meteor_obj, shower):
""" Estimate the height of a meteor from single station give a candidate shower.
Arguments:
config: [Config instance]
meteor_obj: [MeteorSingleStation instance]
shower: [Shower instance]
Return:
ht: [float] Estimated height in meters.
"""
### Compute all needed values in alt/az coordinates ###
# Compute beginning point vector in alt/az
beg_ra, beg_dec = vector2RaDec(meteor_obj.beg_vect)
beg_azim, beg_alt = raDec2AltAz(beg_ra, beg_dec, meteor_obj.jdt_ref,
meteor_obj.lat, meteor_obj.lon)
beg_vect_horiz = raDec2Vector(beg_azim, beg_alt)
# Compute end point vector in alt/az
end_ra, end_dec = vector2RaDec(meteor_obj.end_vect)
end_azim, end_alt = raDec2AltAz(end_ra, end_dec, meteor_obj.jdt_ref,
meteor_obj.lat, meteor_obj.lon)
end_vect_horiz = raDec2Vector(end_azim, end_alt)
# Compute radiant vector in alt/az
radiant_azim, radiant_alt = raDec2AltAz(shower.ra, shower.dec, meteor_obj.jdt_ref, meteor_obj.lat, \
meteor_obj.lon)
radiant_vector_horiz = raDec2Vector(radiant_azim, radiant_alt)
# Reject the pairing if the radiant is below the horizon
if radiant_alt < 0:
return -1
# Get distance from Earth's centre to the position given by geographical coordinates for the
# observer's latitude
earth_radius = EARTH.EQUATORIAL_RADIUS / np.sqrt(
1.0 - (EARTH.E**2) * np.sin(np.radians(config.latitude))**2)
# Compute the distance from Earth's centre to the station (including the sea level height of the station)
re_dist = earth_radius + config.elevation
### ###
# Compute the distance the meteor traversed during its duration (meters)
dist = shower.v_init * meteor_obj.duration
# Compute the angle between the begin and the end point of the meteor (rad)
ang_beg_end = np.arccos(
np.dot(vectNorm(beg_vect_horiz), vectNorm(end_vect_horiz)))
# Compute the angle between the radiant vector and the begin point (rad)
ang_beg_rad = np.arccos(
np.dot(vectNorm(radiant_vector_horiz), -vectNorm(beg_vect_horiz)))
# Compute the distance from the station to the begin point (meters)
dist_beg = dist * np.sin(ang_beg_rad) / np.sin(ang_beg_end)
# Compute the height using the law of cosines
ht = np.sqrt(dist_beg**2 + re_dist**2 - 2 * dist_beg * re_dist *
np.cos(np.radians(90 + meteor_obj.beg_alt)))
ht -= earth_radius
ht = abs(ht)
return ht
def estimateMeteorHeight(meteor_obj, shower):
""" Estimate the height of a meteor from single station give a candidate shower.
Arguments:
meteor_obj: [MeteorSingleStation instance]
shower: [Shower instance]
Return:
ht: [float] Estimated height in meters.
"""
### Compute all needed values in alt/az coordinates ###
# Compute beginning point vector in alt/az
beg_ra, beg_dec = vector2RaDec(meteor_obj.beg_vect)
beg_azim, beg_alt = raDec2AltAz(beg_ra, beg_dec, meteor_obj.jdt_ref,
meteor_obj.lat, meteor_obj.lon)
beg_vect_horiz = raDec2Vector(beg_azim, beg_alt)
# Compute end point vector in alt/az
end_ra, end_dec = vector2RaDec(meteor_obj.end_vect)
end_azim, end_alt = raDec2AltAz(end_ra, end_dec, meteor_obj.jdt_ref,
meteor_obj.lat, meteor_obj.lon)
end_vect_horiz = raDec2Vector(end_azim, end_alt)
# Compute normal vector in alt/az
normal_azim, normal_alt = raDec2AltAz(meteor_obj.normal_ra, meteor_obj.normal_dec, meteor_obj.jdt_ref, \
meteor_obj.lat, meteor_obj.lon)
normal_horiz = raDec2Vector(normal_azim, normal_alt)
# Compute radiant vector in alt/az
radiant_azim, radiant_alt = raDec2AltAz(shower.ra, shower.dec, meteor_obj.jdt_ref, meteor_obj.lat, \
meteor_obj.lon)
radiant_vector_horiz = raDec2Vector(radiant_azim, radiant_alt)
# Reject the pairing if the radiant is below the horizon
if radiant_alt < 0:
return -1
### ###
# Compute cartesian coordinates of the pointing at the beginning of the meteor
pt = vectNorm(beg_vect_horiz)
# Compute reference vector perpendicular to the plane normal and the radiant
vec = vectNorm(np.cross(normal_horiz, radiant_vector_horiz))
# Compute angles between the reference vector and the pointing
dot_vb = np.dot(vec, beg_vect_horiz)
dot_ve = np.dot(vec, end_vect_horiz)
dot_vp = np.dot(vec, pt)
# Compute distance to the radiant intersection line
r_mag = 1.0 / (dot_vb**2)
r_mag += 1.0 / (dot_ve**2)
r_mag += -2 * np.cos(meteor_obj.ang_be) / (dot_vb * dot_ve)
r_mag = np.sqrt(r_mag)
r_mag = shower.v_init * meteor_obj.duration / r_mag
pt_mag = r_mag / dot_vp
# Compute the height
ht = pt_mag**2 + EARTH.EQUATORIAL_RADIUS**2 \
- 2*pt_mag*EARTH.EQUATORIAL_RADIUS*np.cos(np.radians(90 - meteor_obj.beg_alt))
ht = np.sqrt(ht)
ht -= EARTH.EQUATORIAL_RADIUS
ht = abs(ht)
return ht
