OpenDroneMap-ODM/opendm/photo.py

776 wiersze
29 KiB
Python

import logging
import re
import os
import math
import exifread
import numpy as np
from six import string_types
from datetime import datetime, timedelta, timezone
import pytz
from opendm import io
from opendm import log
from opendm import system
import xmltodict as x2d
from opendm import get_image_size
from xml.parsers.expat import ExpatError
from opensfm.sensors import sensor_data
from opensfm.geo import ecef_from_lla
projections = ['perspective', 'fisheye', 'brown', 'dual', 'equirectangular', 'spherical']
def find_largest_photo_dim(photos):
max_dim = 0
for p in photos:
if p.width is None:
continue
max_dim = max(max_dim, max(p.width, p.height))
return max_dim
def find_largest_photo(photos):
max_p = None
max_area = 0
for p in photos:
if p.width is None:
continue
area = p.width * p.height
if area > max_area:
max_area = area
max_p = p
return max_p
def get_mm_per_unit(resolution_unit):
"""Length of a resolution unit in millimeters.
Uses the values from the EXIF specs in
https://www.sno.phy.queensu.ca/~phil/exiftool/TagNames/EXIF.html
Args:
resolution_unit: the resolution unit value given in the EXIF
"""
if resolution_unit == 2: # inch
return 25.4
elif resolution_unit == 3: # cm
return 10
elif resolution_unit == 4: # mm
return 1
elif resolution_unit == 5: # um
return 0.001
else:
log.ODM_WARNING("Unknown EXIF resolution unit value: {}".format(resolution_unit))
return None
class PhotoCorruptedException(Exception):
pass
class ODM_Photo:
"""ODMPhoto - a class for ODMPhotos"""
def __init__(self, path_file):
self.filename = os.path.basename(path_file)
self.mask = None
# Standard tags (virtually all photos have these)
self.width = None
self.height = None
self.camera_make = ''
self.camera_model = ''
self.orientation = 1
# Geo tags
self.latitude = None
self.longitude = None
self.altitude = None
# Multi-band fields
self.band_name = 'RGB'
self.band_index = 0
self.capture_uuid = None # DJI only
# Multi-spectral fields
self.fnumber = None
self.radiometric_calibration = None
self.black_level = None
# Capture info
self.exposure_time = None
self.iso_speed = None
self.bits_per_sample = None
self.vignetting_center = None
self.vignetting_polynomial = None
self.spectral_irradiance = None
self.horizontal_irradiance = None
self.irradiance_scale_to_si = None
self.utc_time = None
# OPK angles
self.yaw = None
self.pitch = None
self.roll = None
self.omega = None
self.phi = None
self.kappa = None
# DLS
self.sun_sensor = None
self.dls_yaw = None
self.dls_pitch = None
self.dls_roll = None
# self.center_wavelength = None
# self.bandwidth = None
# RTK
self.gps_xy_stddev = None # Dilution of Precision X/Y
self.gps_z_stddev = None # Dilution of Precision Z
# Misc SFM
self.camera_projection = 'brown'
self.focal_ratio = 0.85
# parse values from metadata
self.parse_exif_values(path_file)
# print log message
log.ODM_DEBUG('Loaded {}'.format(self))
def __str__(self):
return '{} | camera: {} {} | dimensions: {} x {} | lat: {} | lon: {} | alt: {} | band: {} ({})'.format(
self.filename, self.camera_make, self.camera_model, self.width, self.height,
self.latitude, self.longitude, self.altitude, self.band_name, self.band_index)
def set_mask(self, mask):
self.mask = mask
def update_with_geo_entry(self, geo_entry):
self.latitude = geo_entry.y
self.longitude = geo_entry.x
self.altitude = geo_entry.z
self.omega = geo_entry.omega
self.phi = geo_entry.phi
self.kappa = geo_entry.kappa
self.dls_yaw = geo_entry.omega
self.dls_pitch = geo_entry.phi
self.dls_roll = geo_entry.kappa
self.gps_xy_stddev = geo_entry.horizontal_accuracy
self.gps_z_stddev = geo_entry.vertical_accuracy
def parse_exif_values(self, _path_file):
# Disable exifread log
logging.getLogger('exifread').setLevel(logging.CRITICAL)
try:
self.width, self.height = get_image_size.get_image_size(_path_file)
except Exception as e:
raise PhotoCorruptedException(str(e))
tags = {}
xtags = {}
with open(_path_file, 'rb') as f:
tags = exifread.process_file(f, details=False)
try:
if 'Image Make' in tags:
try:
self.camera_make = tags['Image Make'].values
self.camera_make = self.camera_make.strip()
except UnicodeDecodeError:
log.ODM_WARNING("EXIF Image Make might be corrupted")
self.camera_make = "unknown"
if 'Image Model' in tags:
try:
self.camera_model = tags['Image Model'].values
self.camera_model = self.camera_model.strip()
except UnicodeDecodeError:
log.ODM_WARNING("EXIF Image Model might be corrupted")
self.camera_model = "unknown"
if 'GPS GPSAltitude' in tags:
self.altitude = self.float_value(tags['GPS GPSAltitude'])
if 'GPS GPSAltitudeRef' in tags and self.int_value(tags['GPS GPSAltitudeRef']) > 0:
self.altitude *= -1
if 'GPS GPSLatitude' in tags and 'GPS GPSLatitudeRef' in tags:
self.latitude = self.dms_to_decimal(tags['GPS GPSLatitude'], tags['GPS GPSLatitudeRef'])
if 'GPS GPSLongitude' in tags and 'GPS GPSLongitudeRef' in tags:
self.longitude = self.dms_to_decimal(tags['GPS GPSLongitude'], tags['GPS GPSLongitudeRef'])
if 'Image Orientation' in tags:
self.orientation = self.int_value(tags['Image Orientation'])
except (IndexError, ValueError) as e:
log.ODM_WARNING("Cannot read basic EXIF tags for %s: %s" % (_path_file, str(e)))
try:
if 'Image Tag 0xC61A' in tags:
self.black_level = self.list_values(tags['Image Tag 0xC61A'])
elif 'BlackLevel' in tags:
self.black_level = self.list_values(tags['BlackLevel'])
if 'EXIF ExposureTime' in tags:
self.exposure_time = self.float_value(tags['EXIF ExposureTime'])
if 'EXIF FNumber' in tags:
self.fnumber = self.float_value(tags['EXIF FNumber'])
if 'EXIF ISOSpeed' in tags:
self.iso_speed = self.int_value(tags['EXIF ISOSpeed'])
elif 'EXIF PhotographicSensitivity' in tags:
self.iso_speed = self.int_value(tags['EXIF PhotographicSensitivity'])
elif 'EXIF ISOSpeedRatings' in tags:
self.iso_speed = self.int_value(tags['EXIF ISOSpeedRatings'])
if 'Image BitsPerSample' in tags:
self.bits_per_sample = self.int_value(tags['Image BitsPerSample'])
if 'EXIF DateTimeOriginal' in tags:
str_time = tags['EXIF DateTimeOriginal'].values
utc_time = datetime.strptime(str_time, "%Y:%m:%d %H:%M:%S")
subsec = 0
if 'EXIF SubSecTime' in tags:
subsec = self.int_value(tags['EXIF SubSecTime'])
negative = 1.0
if subsec < 0:
negative = -1.0
subsec *= -1.0
subsec = float('0.{}'.format(int(subsec)))
subsec *= negative
ms = subsec * 1e3
utc_time += timedelta(milliseconds = ms)
timezone = pytz.timezone('UTC')
epoch = timezone.localize(datetime.utcfromtimestamp(0))
self.utc_time = (timezone.localize(utc_time) - epoch).total_seconds() * 1000.0
except Exception as e:
log.ODM_WARNING("Cannot read extended EXIF tags for %s: %s" % (_path_file, str(e)))
# Extract XMP tags
f.seek(0)
xmp = self.get_xmp(f)
for xtags in xmp:
try:
band_name = self.get_xmp_tag(xtags, ['Camera:BandName', '@Camera:BandName'])
if band_name is not None:
self.band_name = band_name.replace(" ", "")
self.set_attr_from_xmp_tag('band_index', xtags, [
'DLS:SensorId', # Micasense RedEdge
'@Camera:RigCameraIndex', # Parrot Sequoia, Sentera 21244-00_3.2MP-GS-0001
'Camera:RigCameraIndex', # MicaSense Altum
])
self.set_attr_from_xmp_tag('radiometric_calibration', xtags, [
'MicaSense:RadiometricCalibration',
])
self.set_attr_from_xmp_tag('vignetting_center', xtags, [
'Camera:VignettingCenter',
'Sentera:VignettingCenter',
])
self.set_attr_from_xmp_tag('vignetting_polynomial', xtags, [
'Camera:VignettingPolynomial',
'Sentera:VignettingPolynomial',
])
self.set_attr_from_xmp_tag('horizontal_irradiance', xtags, [
'Camera:HorizontalIrradiance'
], float)
self.set_attr_from_xmp_tag('irradiance_scale_to_si', xtags, [
'Camera:IrradianceScaleToSIUnits'
], float)
self.set_attr_from_xmp_tag('sun_sensor', xtags, [
'Camera:SunSensor',
], float)
self.set_attr_from_xmp_tag('spectral_irradiance', xtags, [
'Camera:SpectralIrradiance',
'Camera:Irradiance',
], float)
self.set_attr_from_xmp_tag('capture_uuid', xtags, [
'@drone-dji:CaptureUUID', # DJI
'@Camera:ImageUniqueID', # sentera 6x
])
# Camera make / model for some cameras is stored in the XMP
if self.camera_make == '':
self.set_attr_from_xmp_tag('camera_make', xtags, [
'@tiff:Make'
])
if self.camera_model == '':
self.set_attr_from_xmp_tag('camera_model', xtags, [
'@tiff:Model'
])
# DJI GPS tags
self.set_attr_from_xmp_tag('longitude', xtags, [
'@drone-dji:Longitude'
], float)
self.set_attr_from_xmp_tag('latitude', xtags, [
'@drone-dji:Latitude'
], float)
self.set_attr_from_xmp_tag('altitude', xtags, [
'@drone-dji:AbsoluteAltitude'
], float)
# Phantom 4 RTK
if '@drone-dji:RtkStdLon' in xtags:
y = float(self.get_xmp_tag(xtags, '@drone-dji:RtkStdLon'))
x = float(self.get_xmp_tag(xtags, '@drone-dji:RtkStdLat'))
self.gps_xy_stddev = max(x, y)
if '@drone-dji:RtkStdHgt' in xtags:
self.gps_z_stddev = float(self.get_xmp_tag(xtags, '@drone-dji:RtkStdHgt'))
else:
self.set_attr_from_xmp_tag('gps_xy_stddev', xtags, [
'@Camera:GPSXYAccuracy',
'GPSXYAccuracy'
], float)
self.set_attr_from_xmp_tag('gps_z_stddev', xtags, [
'@Camera:GPSZAccuracy',
'GPSZAccuracy'
], float)
if 'DLS:Yaw' in xtags:
self.set_attr_from_xmp_tag('dls_yaw', xtags, ['DLS:Yaw'], float)
self.set_attr_from_xmp_tag('dls_pitch', xtags, ['DLS:Pitch'], float)
self.set_attr_from_xmp_tag('dls_roll', xtags, ['DLS:Roll'], float)
camera_projection = self.get_xmp_tag(xtags, ['@Camera:ModelType', 'Camera:ModelType'])
if camera_projection is not None:
camera_projection = camera_projection.lower()
if camera_projection in projections:
self.camera_projection = camera_projection
# OPK
self.set_attr_from_xmp_tag('yaw', xtags, ['@drone-dji:FlightYawDegree', '@Camera:Yaw', 'Camera:Yaw'], float)
self.set_attr_from_xmp_tag('pitch', xtags, ['@drone-dji:GimbalPitchDegree', '@Camera:Pitch', 'Camera:Pitch'], float)
self.set_attr_from_xmp_tag('roll', xtags, ['@drone-dji:GimbalRollDegree', '@Camera:Roll', 'Camera:Roll'], float)
# Normalize YPR conventions (assuming nadir camera)
# Yaw: 0 --> top of image points north
# Yaw: 90 --> top of image points east
# Yaw: 270 --> top of image points west
# Pitch: 0 --> nadir camera
# Pitch: 90 --> camera is looking forward
# Roll: 0 (assuming gimbal)
if self.has_ypr():
if self.camera_make.lower() in ['dji', 'hasselblad']:
self.pitch = 90 + self.pitch
if self.camera_make.lower() == 'sensefly':
self.roll *= -1
except Exception as e:
log.ODM_WARNING("Cannot read XMP tags for %s: %s" % (_path_file, str(e)))
# self.set_attr_from_xmp_tag('center_wavelength', xtags, [
# 'Camera:CentralWavelength'
# ], float)
# self.set_attr_from_xmp_tag('bandwidth', xtags, [
# 'Camera:WavelengthFWHM'
# ], float)
# Sanitize band name since we use it in folder paths
self.band_name = re.sub('[^A-Za-z0-9]+', '', self.band_name)
self.compute_focal(tags, xtags)
self.compute_opk()
def compute_focal(self, tags, xtags):
try:
self.focal_ratio = self.extract_focal(self.camera_make, self.camera_model, tags, xtags)
except (IndexError, ValueError) as e:
log.ODM_WARNING("Cannot extract focal ratio for %s: %s" % (self.filename, str(e)))
def extract_focal(self, make, model, tags, xtags):
if make != "unknown":
# remove duplicate 'make' information in 'model'
model = model.replace(make, "")
sensor_string = (make.strip() + " " + model.strip()).strip().lower()
sensor_width = None
if ("EXIF FocalPlaneResolutionUnit" in tags and "EXIF FocalPlaneXResolution" in tags):
resolution_unit = self.float_value(tags["EXIF FocalPlaneResolutionUnit"])
mm_per_unit = get_mm_per_unit(resolution_unit)
if mm_per_unit:
pixels_per_unit = self.float_value(tags["EXIF FocalPlaneXResolution"])
if pixels_per_unit <= 0 and "EXIF FocalPlaneYResolution" in tags:
pixels_per_unit = self.float_value(tags["EXIF FocalPlaneYResolution"])
if pixels_per_unit > 0 and self.width is not None:
units_per_pixel = 1 / pixels_per_unit
sensor_width = self.width * units_per_pixel * mm_per_unit
focal_35 = None
focal = None
if "EXIF FocalLengthIn35mmFilm" in tags:
focal_35 = self.float_value(tags["EXIF FocalLengthIn35mmFilm"])
if "EXIF FocalLength" in tags:
focal = self.float_value(tags["EXIF FocalLength"])
if focal is None and "@aux:Lens" in xtags:
lens = self.get_xmp_tag(xtags, ["@aux:Lens"])
matches = re.search('([\d\.]+)mm', str(lens))
if matches:
focal = float(matches.group(1))
if focal_35 is not None and focal_35 > 0:
focal_ratio = focal_35 / 36.0 # 35mm film produces 36x24mm pictures.
else:
if not sensor_width:
sensor_width = sensor_data().get(sensor_string, None)
if sensor_width and focal:
focal_ratio = focal / sensor_width
else:
focal_ratio = 0.85
return focal_ratio
def set_attr_from_xmp_tag(self, attr, xmp_tags, tags, cast=None):
v = self.get_xmp_tag(xmp_tags, tags)
if v is not None:
if cast is None:
setattr(self, attr, v)
else:
# Handle fractions
if (cast == float or cast == int) and "/" in v:
v = self.try_parse_fraction(v)
setattr(self, attr, cast(v))
def get_xmp_tag(self, xmp_tags, tags):
if isinstance(tags, str):
tags = [tags]
for tag in tags:
if tag in xmp_tags:
t = xmp_tags[tag]
if isinstance(t, string_types):
return str(t)
elif isinstance(t, dict):
items = t.get('rdf:Seq', {}).get('rdf:li', {})
if items:
if isinstance(items, string_types):
return items
return " ".join(items)
elif isinstance(t, int) or isinstance(t, float):
return t
# From https://github.com/mapillary/OpenSfM/blob/master/opensfm/exif.py
def get_xmp(self, file):
img_bytes = file.read()
xmp_start = img_bytes.find(b'<x:xmpmeta')
xmp_end = img_bytes.find(b'</x:xmpmeta')
if xmp_start < xmp_end:
xmp_str = img_bytes[xmp_start:xmp_end + 12].decode('utf8')
try:
xdict = x2d.parse(xmp_str)
except ExpatError as e:
from bs4 import BeautifulSoup
xmp_str = str(BeautifulSoup(xmp_str, 'xml'))
xdict = x2d.parse(xmp_str)
log.ODM_WARNING("%s has malformed XMP XML (but we fixed it)" % self.filename)
xdict = xdict.get('x:xmpmeta', {})
xdict = xdict.get('rdf:RDF', {})
xdict = xdict.get('rdf:Description', {})
if isinstance(xdict, list):
return xdict
else:
return [xdict]
else:
return []
def dms_to_decimal(self, dms, sign):
"""Converts dms coords to decimal degrees"""
degrees, minutes, seconds = self.float_values(dms)
if degrees is not None and minutes is not None and seconds is not None:
return (-1 if sign.values[0] in 'SWsw' else 1) * (
degrees +
minutes / 60 +
seconds / 3600
)
def float_values(self, tag):
if isinstance(tag.values, list):
result = []
for v in tag.values:
if isinstance(v, int):
result.append(float(v))
elif v.den != 0:
result.append(float(v.num) / float(v.den))
else:
result.append(None)
return result
else:
return [float(tag.values.num) / float(tag.values.den) if tag.values.den != 0 else None]
def float_value(self, tag):
v = self.float_values(tag)
if len(v) > 0:
return v[0]
def int_values(self, tag):
if isinstance(tag.values, list):
return [int(v) for v in tag.values]
else:
return [int(tag.values)]
def int_value(self, tag):
v = self.int_values(tag)
if len(v) > 0:
return v[0]
def list_values(self, tag):
return " ".join(map(str, tag.values))
def try_parse_fraction(self, val):
parts = val.split("/")
if len(parts) == 2:
try:
num, den = map(float, parts)
return num / den if den != 0 else val
except ValueError:
pass
return val
def get_radiometric_calibration(self):
if isinstance(self.radiometric_calibration, str):
parts = self.radiometric_calibration.split(" ")
if len(parts) == 3:
return list(map(float, parts))
return [None, None, None]
def get_dark_level(self):
if self.black_level:
levels = np.array([float(v) for v in self.black_level.split(" ")])
return levels.mean()
def get_gain(self):
#(gain = ISO/100)
if self.iso_speed:
return self.iso_speed / 100.0
def get_vignetting_center(self):
if self.vignetting_center:
parts = self.vignetting_center.split(" ")
if len(parts) == 2:
return list(map(float, parts))
return [None, None]
def get_vignetting_polynomial(self):
if self.vignetting_polynomial:
parts = self.vignetting_polynomial.split(" ")
if len(parts) > 0:
coeffs = list(map(float, parts))
# Different camera vendors seem to use different ordering for the coefficients
if self.camera_make != "Sentera":
coeffs.reverse()
return coeffs
def get_utc_time(self):
if self.utc_time:
return datetime.fromtimestamp(self.utc_time / 1000, timezone.utc)
def get_photometric_exposure(self):
# H ~= (exposure_time) / (f_number^2)
if self.fnumber is not None and self.exposure_time is not None and self.exposure_time > 0 and self.fnumber > 0:
return self.exposure_time / (self.fnumber * self.fnumber)
def get_horizontal_irradiance(self):
if self.horizontal_irradiance is not None:
scale = 1.0 # Assumed
if self.irradiance_scale_to_si is not None:
scale = self.irradiance_scale_to_si
return self.horizontal_irradiance * scale
def get_sun_sensor(self):
if self.sun_sensor is not None:
# TODO: Presence of XMP:SunSensorExposureTime
# and XMP:SunSensorSensitivity might
# require additional logic. If these two tags are present,
# then sun_sensor is not in physical units?
return self.sun_sensor / 65535.0 # normalize uint16 (is this correct?)
elif self.spectral_irradiance is not None:
scale = 1.0 # Assumed
if self.irradiance_scale_to_si is not None:
scale = self.irradiance_scale_to_si
return self.spectral_irradiance * scale
def get_dls_pose(self):
if self.dls_yaw is not None:
return [self.dls_yaw, self.dls_pitch, self.dls_roll]
return [0.0, 0.0, 0.0]
def get_bit_depth_max(self):
if self.bits_per_sample:
return float(2 ** self.bits_per_sample)
return None
def get_capture_id(self):
# Use capture UUID first, capture time as fallback
if self.capture_uuid is not None:
return self.capture_uuid
return self.get_utc_time()
def get_gps_dop(self):
val = -9999
if self.gps_xy_stddev is not None:
val = self.gps_xy_stddev
if self.gps_z_stddev is not None:
val = max(val, self.gps_z_stddev)
if val > 0:
return val
return None
def override_gps_dop(self, dop):
self.gps_xy_stddev = self.gps_z_stddev = dop
def override_camera_projection(self, camera_projection):
if camera_projection in projections:
self.camera_projection = camera_projection
def is_thermal(self):
#Added for support M2EA camera sensor
if(self.camera_make == "DJI"):
return self.camera_model == "MAVIC2-ENTERPRISE-ADVANCED" and self.width == 640 and self.height == 512
return self.band_name.upper() in ["LWIR"] # TODO: more?
def camera_id(self):
return " ".join(
[
"v2",
self.camera_make.strip(),
self.camera_model.strip(),
str(int(self.width)),
str(int(self.height)),
self.camera_projection,
str(float(self.focal_ratio))[:6],
]
).lower()
def to_opensfm_exif(self):
capture_time = 0.0
if self.utc_time is not None:
capture_time = self.utc_time / 1000.0
gps = {}
if self.latitude is not None and self.longitude is not None:
gps['latitude'] = self.latitude
gps['longitude'] = self.longitude
if self.altitude is not None:
gps['altitude'] = self.altitude
else:
gps['altitude'] = 0.0
dop = self.get_gps_dop()
if dop is None:
dop = 10.0 # Default
gps['dop'] = dop
d = {
"make": self.camera_make,
"model": self.camera_model,
"width": self.width,
"height": self.height,
"projection_type": self.camera_projection,
"focal_ratio": self.focal_ratio,
"orientation": self.orientation,
"capture_time": capture_time,
"gps": gps,
"camera": self.camera_id()
}
if self.has_opk():
d['opk'] = {
'omega': self.omega,
'phi': self.phi,
'kappa': self.kappa
}
return d
def has_ypr(self):
return self.yaw is not None and \
self.pitch is not None and \
self.roll is not None
def has_opk(self):
return self.omega is not None and \
self.phi is not None and \
self.kappa is not None
def has_geo(self):
return self.latitude is not None and \
self.longitude is not None
def compute_opk(self):
if self.has_ypr() and self.has_geo():
y, p, r = math.radians(self.yaw), math.radians(self.pitch), math.radians(self.roll)
# Ref: New Calibration and Computing Method for Direct
# Georeferencing of Image and Scanner Data Using the
# Position and Angular Data of an Hybrid Inertial Navigation System
# by Manfred Bäumker
# YPR rotation matrix
cnb = np.array([[ math.cos(y) * math.cos(p), math.cos(y) * math.sin(p) * math.sin(r) - math.sin(y) * math.cos(r), math.cos(y) * math.sin(p) * math.cos(r) + math.sin(y) * math.sin(r)],
[ math.sin(y) * math.cos(p), math.sin(y) * math.sin(p) * math.sin(r) + math.cos(y) * math.cos(r), math.sin(y) * math.sin(p) * math.cos(r) - math.cos(y) * math.sin(r)],
[ -math.sin(p), math.cos(p) * math.sin(r), math.cos(p) * math.cos(r)],
])
# Convert between image and body coordinates
# Top of image pixels point to flying direction
# and camera is looking down.
# We might need to change this if we want different
# camera mount orientations (e.g. backward or sideways)
# (Swap X/Y, flip Z)
cbb = np.array([[0, 1, 0],
[1, 0, 0],
[0, 0, -1]])
delta = 1e-7
alt = self.altitude if self.altitude is not None else 0.0
p1 = np.array(ecef_from_lla(self.latitude + delta, self.longitude, alt))
p2 = np.array(ecef_from_lla(self.latitude - delta, self.longitude, alt))
xnp = p1 - p2
m = np.linalg.norm(xnp)
if m == 0:
log.ODM_WARNING("Cannot compute OPK angles, divider = 0")
return
# Unit vector pointing north
xnp /= m
znp = np.array([0, 0, -1]).T
ynp = np.cross(znp, xnp)
cen = np.array([xnp, ynp, znp]).T
# OPK rotation matrix
ceb = cen.dot(cnb).dot(cbb)
self.omega = math.degrees(math.atan2(-ceb[1][2], ceb[2][2]))
self.phi = math.degrees(math.asin(ceb[0][2]))
self.kappa = math.degrees(math.atan2(-ceb[0][1], ceb[0][0]))