def locdir_at(self, phi, theta, psi, row, col, alt=0, geo=True):
"""
Given the satellite attitude, computes lon, lat of point row, col, alt.
Args:
phi, theta, psi: attitude angles of the satellite camera
row, col: pixel coordinates in the image plane
alt: altitude of the 3d point above the Earth surface
geo: boolean flag telling whether to return geographic
coordinates or Cartesian coordinates.
Returns:
geographic coordinates (lon, lat), or Cartesian coordinates
(x, y, z). Cartesian coordinates are computed with respect to the
orbital frame.
"""
# first compute coordinates of the 3-space point in the orbital frame
orbital_to_camera = utils.rotation_3d('xyz', phi, theta, psi)
v = np.dot(orbital_to_camera, self.instrument.sight_vector(col))
c = np.array([0, 0, self.orbit.radius])
r = PhysicalConstants.earth_radius + alt
p = utils.intersect_line_and_sphere(v, c, r)
if not geo:
return p
# then convert them to lon, lat, using t to get the satellite position
if p is None:
return p
else:
t = row * self.instrument.dwell_time
mat_t_ol = self.rotational_to_orbital(t)
return utils.lon_lat(np.dot(mat_t_ol, -c + p))
def target_point_orbital_frame(self, a, b, alt=0):
"""
Computes orbital coordinates of the ground point targeted by the
satellite.
Args:
a: sight direction angle about the x axis of orbital frame, degrees
b: angle about the y axis of orbital frame, degrees
alt: altitude of the ground above the sphere
Returns:
numpy 1x3 array with the coordinates in the orbital frame
"""
# Earth center position in the orbital frame
c = np.array([0, 0, self.radius])
# coordinates of the vector defined by angles a, b and coordinate z=1
# in the orbital frame
a_rad = a * np.pi/180
b_rad = b * np.pi/180
v = np.array([np.tan(b_rad), -np.tan(a_rad), 1])
# intersection of the line directed by v with the Earth
r = PhysicalConstants.earth_radius + alt
return utils.intersect_line_and_sphere(v, c, r)
def locdir_at(self, phi, theta, psi, row, col, alt=0, geo=True):
"""
Given the satellite attitude, computes lon, lat of point row, col, alt.
Args:
phi, theta, psi: attitude angles of the satellite camera
row, col: pixel coordinates in the image plane
alt: altitude of the 3d point above the Earth surface
geo: boolean flag telling whether to return geographic
coordinates or Cartesian coordinates.
Returns:
geographic coordinates (lon, lat), or Cartesian coordinates
(x, y, z). Cartesian coordinates are computed with respect to the
orbital frame.
"""
# first compute coordinates of the 3-space point in the orbital frame
orbital_to_camera = utils.rotation_3d('xyz', phi, theta, psi)
v = np.dot(orbital_to_camera, self.instrument.sight_vector(col))
c = np.array([0, 0, self.orbit.radius])
r = PhysicalConstants.earth_radius + alt
p = utils.intersect_line_and_sphere(v, c, r)
if not geo:
return p
# then convert them to lon, lat, using t to get the satellite position
if p is None:
return p
else:
t = row * self.instrument.dwell_time
mat_t_ol = self.rotational_to_orbital(t)
return utils.lon_lat(np.dot(mat_t_ol, -c + p))
def target_point_orbital_frame(self, a, b, alt=0):
"""
Computes orbital coordinates of the ground point targeted by the
satellite.
Args:
a: sight direction angle about the x axis of orbital frame, degrees
b: angle about the y axis of orbital frame, degrees
alt: altitude of the ground above the sphere
Returns:
numpy 1x3 array with the coordinates in the orbital frame
"""
# Earth center position in the orbital frame
c = np.array([0, 0, self.radius])
# coordinates of the vector defined by angles a, b and coordinate z=1
# in the orbital frame
a_rad = a * np.pi / 180
b_rad = b * np.pi / 180
v = np.array([np.tan(b_rad), -np.tan(a_rad), 1])
# intersection of the line directed by v with the Earth
r = PhysicalConstants.earth_radius + alt
return utils.intersect_line_and_sphere(v, c, r)
def pixel_projection_width(self, m, x=0, y=0):
"""
Computes the width of the projection of a pixel on the ground.
Args:
m: numpy 3x3 array representing the change of
coordinates matrix between orbital frame and camera frame
x, y (optional, default is 0, 0): coordinates of the pixel in the
image plane
Returns:
width, in meters, of the projection of the pixel on the ground, in
the pushbroom direction (orthogonal to the pushbroom movement)
"""
# pixel width and focal length in mm
w = self.instrument.w_pix * 0.001
f = self.instrument.focal * 1000
# direction of the camera, expressed in the orbital frame
v = np.dot(m, np.array([-x, -y, f]))
# intersection of the line directed by v with the Earth
c = np.array([0, 0, self.orbit.radius])
r = PhysicalConstants.earth_radius
p = utils.intersect_line_and_sphere(v, c, r)
# normal to the tangent plane to the Earth at the intersection point p
n = p - c
# projection of the left and right borders of the pixel on the ground
v1 = np.dot(m, np.array([-(x + .5*w), -y, f]))
v2 = np.dot(m, np.array([-(x - .5*w), -y, f]))
p1 = utils.intersect_line_and_plane(v1, p, n)
p2 = utils.intersect_line_and_plane(v2, p, n)
return np.linalg.norm(p1 - p2)
def pixel_projection_width(self, m, x=0, y=0):
"""
Computes the width of the projection of a pixel on the ground.
Args:
m: numpy 3x3 array representing the change of
coordinates matrix between orbital frame and camera frame
x, y (optional, default is 0, 0): coordinates of the pixel in the
image plane
Returns:
width, in meters, of the projection of the pixel on the ground, in
the pushbroom direction (orthogonal to the pushbroom movement)
"""
# pixel width and focal length in mm
w = self.instrument.w_pix * 0.001
f = self.instrument.focal * 1000
# direction of the camera, expressed in the orbital frame
v = np.dot(m, np.array([-x, -y, f]))
# intersection of the line directed by v with the Earth
c = np.array([0, 0, self.orbit.radius])
r = PhysicalConstants.earth_radius
p = utils.intersect_line_and_sphere(v, c, r)
# normal to the tangent plane to the Earth at the intersection point p
n = p - c
# projection of the left and right borders of the pixel on the ground
v1 = np.dot(m, np.array([-(x + .5 * w), -y, f]))
v2 = np.dot(m, np.array([-(x - .5 * w), -y, f]))
p1 = utils.intersect_line_and_plane(v1, p, n)
p2 = utils.intersect_line_and_plane(v2, p, n)
return np.linalg.norm(p1 - p2)