def caps_all_anodes(tempdatetime):
et = spice.datetime2et(tempdatetime)
sclkdp = spice.sce2c(
-82, et) # converts an et to a continuous encoded sc clock (ticks)
caps_els_anode_vecs = []
for anodenumber, x in enumerate(np.arange(70, -90, -20)):
# print(anodenumber, x)
rotationmatrix_anode = spice.spiceypy.axisar(np.array(
[1, 0, 0]), x * spice.rpd()) # Get angles for different anodes
# print("rotationmatrix_anode", rotationmatrix_anode)
postanode_rotation = spice.vhat(
spice.mxv(rotationmatrix_anode, -spice.spiceypy.getfov(
-82821, 20)[2])) # Apply rotation for anodes
# print("postanode_rotation", postanode_rotation)
# print("caps_els_boresight", caps_els_boresight)
cassini_caps_mat = spice.ckgp(
-82821, sclkdp, 0, 'CASSINI_CAPS_BASE')[0] # Get actuation angle
# print("cassini_caps_mat", cassini_caps_mat)
cassini_caps_act_vec = spice.mxv(
cassini_caps_mat, postanode_rotation) # Rotate with actuator
# print("Actuating frame", cassini_caps_act_vec)
CAPS_act_2_titan_cmat = spice.ckgp(
-82000, sclkdp, 0,
'IAU_TITAN')[0] # Find matrix to transform to IAU_TITAN frame
CAPS_act_2_titan_cmat_transpose = spice.xpose(
CAPS_act_2_titan_cmat) # Tranpose matrix
rotated_vec = spice.mxv(CAPS_act_2_titan_cmat_transpose,
cassini_caps_act_vec) # Apply Matrix
# print("rotated_vec ", rotated_vec)
caps_els_anode_vecs.append(rotated_vec)
return caps_els_anode_vecs
def cassini_surfintercerpt(utc, output=False):
target = 'TITAN'
fixref = 'IAU_TITAN'
dref = 'IAU_TITAN'
method = 'ELLIPSOID'
abcorr = 'NONE'
obsrvr = 'CASSINI'
state = cassini_phase(utc)
dvec = spice.vhat(-state[:3])
et = spice.str2et(utc)
[point, trgepc, srfvec] = spice.sincpt(method, target, et, fixref, abcorr,
obsrvr, dref, dvec)
temp = spice.reclat(point)
radius = temp[0]
colat = 90 + spice.convrt(temp[1], "RADIANS", "DEGREES")
lon = np.mod(spice.convrt(temp[2], "RADIANS", "DEGREES"), 360)
if output:
print("Distance to Intercept Point", spice.vnorm(srfvec))
print("Radius", radius)
print("Colatitude", colat)
print("Longtitude", lon)
return point, [radius, colat, lon], spice.vnorm(srfvec)
def get_geometry_info(obs2refmtx, fov, width, height):
cvec = spice.vhat(fov.bounds_rect.center_vec)
cvec_ref = spice.mxv(obs2refmtx, cvec)
# Azimuth in the upward direction of the screen
mvec = spice.vhat(fov.bounds_rect.top_vec)
mvec_ref = spice.mxv(obs2refmtx, mvec)
pa, dist = vec_padist(cvec_ref, mvec_ref)
pos_angle = pa * spice.dpr()
# Pixel resolution up to the center of the screen top edge
vp = viewport_frustum(fov.bounds_rect, width, height, mvec)
angle_res = dist / (height / 2.0 - vp[1]) * spice.dpr()
_, ra, dec = spice.recrad(cvec_ref)
return pos_angle, angle_res, ra * spice.dpr(), dec * spice.dpr()
def point_towards_sun(self, pixel_res=0.5):
"""
Compute the solar azimuth.
Pixel resolution is required to stay within one pixel of the origin
point
"""
# Check if surface point spoint was set
if not self.spoint_set:
raise SPointNotSetError
# Get the difference vector poB=subsolar-origin with its tail at origin
# and its head at the subsolar point
poB = spice.vsub(self.subsolar, self.spoint)
# get pixel scale in km/pixel and then divide by 2 to insure to stay
# within a pixel of the origin point
scale = (pixel_res / 1000.0) / 2.0
# the difference vector cuts through the body,
# we need the tangent vector
# to the surface at the origin point. vperp receives the perpendicular
# component of the poB towards the spoint vector
hpoB = spice.vperp(poB, self.spoint)
# unitize the tangent vector and then scale it to within a pixel of the
# origin point
upoB = spice.vhat(hpoB)
spoB = spice.vscl(scale, upoB)
# Compute the new point in body fixed. This point will be within a
# pixel of the origin but in the same direction as the requested la/lon
# of the point of interest, i.e. the subsolar point
nB = spice.vadd(self.spoint, spoB)
coords = Coords.fromtuple(spice.reclat(nB))
return coords.dlon, coords.dlat
def point_towards_sun(self, pixel_res=0.5):
"""
Compute the solar azimuth.
Pixel resolution is required to stay within one pixel of the origin
point
"""
# Check if surface point spoint was set
if not self.spoint_set:
raise SPointNotSetError
# Get the difference vector poB=subsolar-origin with its tail at origin
# and its head at the subsolar point
poB = spice.vsub(self.subsolar, self.spoint)
# get pixel scale in km/pixel and then divide by 2 to insure to stay
# within a pixel of the origin point
scale = (pixel_res / 1000.0) / 2.0
# the difference vector cuts through the body,
# we need the tangent vector
# to the surface at the origin point. vperp receives the perpendicular
# component of the poB towards the spoint vector
hpoB = spice.vperp(poB, self.spoint)
# unitize the tangent vector and then scale it to within a pixel of the
# origin point
upoB = spice.vhat(hpoB)
spoB = spice.vscl(scale, upoB)
# Compute the new point in body fixed. This point will be within a
# pixel of the origin but in the same direction as the requested la/lon
# of the point of interest, i.e. the subsolar point
nB = spice.vadd(self.spoint, spoB)
coords = SurfaceCoords.fromtuple(spice.reclat(nB))
return coords.dlon, coords.dlat
def subsolar(self):
# normalize surface point vector:
uuB = spice.vhat(self.center_to_sun)
# receive subsolar point in IAU_MARS rectangular coords
# the *self.radii unpacks the Radii object into 3 arguments.
v_subsolar = spice.surfpt((0, 0, 0), uuB, *self.radii)
return v_subsolar
def _get_subsolar(self):
# normalize surface point vector:
uuB = spice.vhat(self.center_to_sun)
# receive subsolar point in IAU_MARS rectangular coords
# the *self.radii unpacks the Radii object into 3 arguments.
v_subsolar = spice.surfpt((0, 0, 0), uuB, *self.radii)
return v_subsolar
def parse_inertial(input_vertex, return_radec=True):
"""Parse input vertex as either RA,Dec or XYZ;
Return RA,DEC (optional) and unit vector
"""
if 2==len(input_vertex):
### Vertex has two items: assume they are RA and Dec
ra,dec = map(float,input_vertex)
assert ra<=360.0 and ra>=0.0,'RA ({0}) is out of range [0,360)'.format(ra)
assert dec<=90.0 and dec>=-90.0,'RA ({0}) is out of range [-90,+90]'.format(dec)
uvxyz = sp.radrec(1.0,ra*rpd,dec*rpd)
else:
### Vertex has three items: assume they are XYZ
assert 3==len(input_vertex),'XYZ input vector [{0}] for vertex does not have 3 elements'.format(str(input_vertex))
uvxyz = sp.vhat(sp.vpack(*map(float,input_vertex)))
if return_radec: ra,dec = sp.vsclg(dpr,sp.recrad(uvxyz)[1:],2)
if return_radec: return ra,dec,uvxyz
return uvxyz
def cassini_ramdirection_SCframe(tempdatetime, target='CASSINI', frame='J2000', observ='titan', corrtn='NONE',
output=False):
et = spice.datetime2et(tempdatetime)
state, ltime = spice.spkezr(target, et, frame, corrtn, observ)
ramdir = spice.vhat(state[3:6])
# Gets Attitude
sclkdp = spice.sce2c(-82, et) # converts an et to a continuous encoded sc clock (ticks)
ckgp_output = spice.ckgp(-82000, sclkdp, 0, frame)
cmat = ckgp_output[0]
ram_unit = spice.mxv(cmat, ramdir)
if output:
print('ET = {:20.6f}'.format(et))
print('VX = {:20.6f}'.format(ram_unit[0]))
print('VY = {:20.6f}'.format(ram_unit[1]))
print('VZ = {:20.6f}'.format(ram_unit[2]))
return ram_unit
def caps_crosstrack(tempdatetime, windspeed):
et = spice.datetime2et(tempdatetime)
state, ltime = spice.spkezr("CASSINI", et, "IAU_TITAN", "NONE", "titan")
ramdir = spice.vhat(state[3:6])
# print("ramdir",ramdir)
# Gets Attitude
sclkdp = spice.sce2c(
-82, et) # converts an et to a continuous encoded sc clock (ticks)
ckgp_output = spice.ckgp(-82000, sclkdp, 0, "IAU_TITAN")
cmat = ckgp_output[0]
spacecraft_axis = np.array([0, 0, 1])
rotated_spacecraft_axis = spice.mxv(cmat, spacecraft_axis)
# print("cmat", cmat)
# print("rotated spacecraft axis",rotated_spacecraft_axis)
ram_unit = spice.mxv(cmat, -ramdir) # Ram Unit in SC coords
# print("ram_unit",ram_unit)
if windspeed < 0:
rotationmatrix = spice.axisar(np.array([0, 0, -1]), 90 * spice.rpd())
if windspeed > 0:
rotationmatrix = spice.axisar(np.array([0, 0, -1]), -90 * spice.rpd())
# print(rotationmatrix)
crossvec = spice.mxv(
rotationmatrix,
ram_unit) # Rotate ram unit to find crosstrack velocity vector
# print("temp crossvec",crossvec)
# print("vsep SC Frame",spice.vsep(ram_unit,crossvec)*spice.dpr())
cmat_t = spice.xpose(cmat)
crossvec_titan = spice.mxv(cmat_t,
crossvec) # Transform back to IAU Titan Frame
# print("crossvec", crossvec)
# print("crossvec_titan", crossvec_titan, spice.unorm(crossvec_titan))
# print("vsep titan frame", spice.vsep(ramdir, crossvec_titan) * spice.dpr())
return crossvec_titan
def dooneRandom():
### Random normal unit vector
unitNormal = sp.vhat([r.uniform(-1, 1) for i in xrange(3)])
### Random positive semi-axes' lengths
semi_axes = [abs(r.uniform(.5, 100)) for i in xrange(3)]
### Solve for surface point with that surface normal
xyz = norm2surfpt(semi_axes, unitNormal)
### Use spiceypy.surfnm() to calculate surface unit normal vector, at
### solved-for surface point vector xyz, to compare to input unit normal
### vector, and calculate error magnitude, errMag
surfnm = sp.surfnm(semi_axes[0], semi_axes[1], semi_axes[2], xyz)
errVec = sp.vsub(surfnm, unitNormal)
errMag = sp.vnorm(errVec)
if doLog:
pprint.pprint(dict(errVec=errVec, errMag=errMag))
###return error magnitude
return errMag
def caps_crosstrack_latlon(time, negwindspeed, poswindspeed, anodes=False):
anode_vecs = []
anode_seps = [[], [], [], [], [], [], [], []]
beamanodes = []
# print(time)
beamanodes.append(np.mean(ELS_ramanodes(time)) + 1)
state = cassini_phase(time.strftime('%Y-%m-%dT%H:%M:%S'))
# crossvec = caps_crosstrack(time, windspeed) * abs(windspeed) * 1e-3 #Old Method
crossvec, anode1, anode8 = caps_crosstrack_spice(
time, np.mean([negwindspeed, poswindspeed])) # SPICE Plane method
crossvec_neg = crossvec * 1e-3
crossvec_pos = crossvec * 1e-3
print("crossvec", crossvec_neg, crossvec_pos)
newstate_neg = list(state[:3]) + list(crossvec_neg)
newstate_pos = list(state[:3]) + list(crossvec_pos)
transformed_state_neg = spice.xfmsta(newstate_neg, 'RECTANGULAR',
'Latitudinal', "TITAN")
transformed_state_pos = spice.xfmsta(newstate_pos, 'RECTANGULAR',
'Latitudinal', "TITAN")
print("test state", newstate_neg, newstate_pos)
print("test xfmsta", transformed_state_neg, transformed_state_pos)
alt = transformed_state_neg[0]
lon = transformed_state_neg[1] * spice.dpr()
lat = transformed_state_neg[2] * spice.dpr()
if anodes:
anode_vecs.append(caps_all_anodes(time))
for anodecounter, i in enumerate(anode_vecs[-1]):
anode_seps[anodecounter].append(
spice.vsep(spice.vhat(state[3:]),
spice.vhat(anode_vecs[-1][anodecounter])) *
spice.dpr())
print("anode_vecs", anode_vecs)
print("anode_seps", anode_seps)
dvec_neg = [
transformed_state_neg[4], transformed_state_neg[5],
transformed_state_neg[3]
]
dvec_pos = [
transformed_state_pos[4], transformed_state_pos[5],
transformed_state_pos[3]
]
print("dvec xfmsta", dvec_neg, dvec_pos)
print(lon, lat, alt)
titanrad = spice.bodvrd('TITAN', 'RADII', 3)[1][0] # Get Titan Radius
mag_test_neg = spice.unorm([
dvec_neg[0] * (alt + titanrad) * 1e3,
dvec_neg[1] * (alt + titanrad) * 1e3, dvec_neg[2] * 1e3
])
mag_test_pos = spice.unorm([
dvec_pos[0] * (alt + titanrad) * 1e3,
dvec_pos[1] * (alt + titanrad) * 1e3, dvec_pos[2] * 1e3
])
# Convert Lat/Lon from rad/s to m/s, convert Alt from km/s to m/s. Forms Unit Vector here
print("mag test", mag_test_pos)
dlon_neg = mag_test_neg[0][0] * abs(negwindspeed)
dlat_neg = mag_test_neg[0][1] * abs(negwindspeed)
dalt_neg = mag_test_neg[0][2] * abs(negwindspeed)
dlon_pos = mag_test_pos[0][0] * abs(poswindspeed)
dlat_pos = mag_test_pos[0][1] * abs(poswindspeed)
dalt_pos = mag_test_pos[0][2] * abs(poswindspeed)
return lon, lat, alt, dlon_neg, dlat_neg, dalt_neg, dlon_pos, dlat_pos, dalt_pos
def cassini_titan_test(flyby, anodes=False):
times = []
states = []
lons, lats, alts = [], [], []
crossvecs_lonlatalts = []
crossvecs_lonlatalts_spicenormal = []
cmats = []
vecs = []
anode_vecs = []
anode_seps = [[], [], [], [], [], [], [], []]
anodes1, anodes8 = [], []
crossvecs = []
angularseparations = []
beamanodes = []
spiceplanenormals = []
windsdf = pd.read_csv("crosswinds_full.csv", index_col=0, parse_dates=True)
tempdf = windsdf[windsdf['Flyby'] == flyby]
for tempdatetime, negwindspeed, poswindspeed in zip(
pd.to_datetime(tempdf['Bulk Time']),
tempdf["Negative crosstrack velocity"],
tempdf["Positive crosstrack velocity"]):
print("---------")
print(tempdatetime)
times.append(tempdatetime)
beamanodes.append(np.mean(ELS_ramanodes(tempdatetime)) + 1)
states.append(cassini_phase(
tempdatetime.strftime('%Y-%m-%dT%H:%M:%S')))
# print(states[-1])
lon, lat, alt = spice.recpgr("TITAN", states[-1][:3],
spice.bodvrd("TITAN", 'RADII', 3)[1][0],
1.44e-4)
lons.append(lon * spice.dpr())
lats.append(lat * spice.dpr())
alts.append(alt)
# vecs.append(cassini_act_2_titan(tempdatetime))
crossvec = caps_crosstrack(tempdatetime,
np.mean([negwindspeed, poswindspeed]))
print("crossvec", crossvec)
testspicenormal, anode1, anode8 = caps_crosstrack_spice(
tempdatetime, np.mean([negwindspeed, poswindspeed]))
anodes1.append(anode1)
anodes8.append(anode8)
spiceplanenormals.append(testspicenormal)
print("test spice normal", testspicenormal)
jacobian = spice.dpgrdr("TITAN", states[-1][0], states[-1][1],
states[-1][2],
spice.bodvrd('TITAN', 'RADII',
3)[1][0], 1.44e-4)
# print("jacobian", jacobian)
crossvec_lonlatalt = spice.mxv(jacobian, spice.vhat(crossvec))
crossvec_lonlatalt_spicenormal = spice.mxv(jacobian, testspicenormal)
# print("recpgr", lon, lat, alt)
# print("crossvec latlon", crossvec_lonlatalt)
# print("crossvec latlon vhat", spice.vhat(crossvec_latlon))
crossvecs.append(crossvec)
crossvecs_lonlatalts.append(crossvec_lonlatalt)
crossvecs_lonlatalts_spicenormal.append(crossvec_lonlatalt_spicenormal)
# print("Time", tempdatetime)
# print("position", states[-1][:3])
# print("velocity", spice.vhat(states[-1][3:]))
# print("direction", spice.vhat(vecs[-1]))
# if anodes:
# anode_vecs.append(caps_all_anodes(tempdatetime))
# print("anode vecs 1 & 8", anode_vecs[-1][0], anode_vecs[-1][7])
# # spiceplanenormal = spice.psv2pl(states[-1][:3],anode_vecs[-1][0],anode_vecs[-1][7])
# # print("SPICE NORMAL", spice.pl2nvp(spiceplanenormal))
# #
# # spiceplanenormals.append(-1*spice.pl2nvp(spiceplanenormal)[0])
# # print("Crossvec", crossvec)
# for anodecounter, i in enumerate(anode_vecs[-1]):
# # print(anodecounter,anode_vecs[-1][anodecounter])
# anode_seps[anodecounter].append(
# spice.vsep(spice.vhat(states[-1][3:]), spice.vhat(anode_vecs[-1][anodecounter])) * spice.dpr())
# print("anodeseps",anode_seps)
# print("Angular Separation", spice.vsep(spice.vhat(states[-1][3:]), spice.vhat(vecs[-1])) * spice.dpr())
x, y, z, u, v, w = [], [], [], [], [], []
for i in states:
x.append(i[0])
y.append(i[1])
z.append(i[2])
# CAPS direction
for i in vecs:
u.append(i[0])
v.append(i[1])
w.append(i[2])
# Crosstrack
u2, v2, w2 = [], [], []
for j in crossvecs:
u2.append(j[0])
v2.append(j[1])
w2.append(j[2])
# SPICE plane normal
u3, v3, w3 = [], [], []
for j in spiceplanenormals:
u3.append(j[0])
v3.append(j[1])
w3.append(j[2])
# Ram Direction
u1, v1, w1 = [], [], []
for i in states:
u1.append(i[3])
v1.append(i[4])
w1.append(i[5])
fig = plt.figure()
u = np.linspace(0, 2 * np.pi, 50)
v = np.linspace(0, np.pi, 50)
x_sphere = 2574.7 * np.outer(np.cos(u), np.sin(v))
y_sphere = 2574.7 * np.outer(np.sin(u), np.sin(v))
z_sphere = 2574.7 * np.outer(np.ones(np.size(u)), np.cos(v))
ax = fig.add_subplot(111, projection='3d')
# Plot the surface
# ax.plot_wireframe(x_sphere, y_sphere, z_sphere, color='b')
# ax.plot(x, y, z, alpha=0.5, color='k')
if anodes:
for timecounter, (i, j) in enumerate(zip(anodes1, anodes8)):
X = x[timecounter]
Y = y[timecounter]
Z = z[timecounter]
# print(i)
# for anodecounter, j in enumerate(i):
# if anodecounter in [0, 7]:
# ax.quiver(X, Y, Z, j[0], j[1], j[2], length=20, color='C' + str(anodecounter))
# print(timecounter, i, j)
ax.quiver(X, Y, Z, i[0], i[1], i[2], length=30, color='C1')
ax.quiver(X, Y, Z, j[0], j[1], j[2], length=30, color='C2')
ax.quiver(x, y, z, u2, v2, w2, length=30, color='m')
ax.quiver(x, y, z, u1, v1, w1, length=5, color='k')
ax.quiver(x, y, z, u3, v3, w3, length=30, color='r')
ax.set_xlabel("X")
ax.set_ylabel("Y")
ax.set_zlabel("Z")
ax.set_xlim(min(x), max(x))
ax.set_ylim(min(y), max(y))
ax.set_zlim(min(z), max(z))
dlat, dlon = [], []
for i in crossvecs_lonlatalts:
dlat.append(i[1])
dlon.append(i[0])
dlat_spicenormal, dlon_spicenormal = [], []
for i in crossvecs_lonlatalts_spicenormal:
dlat_spicenormal.append(i[1])
dlon_spicenormal.append(i[0])
fig2, ax2 = plt.subplots()
ax2.plot(lons, lats)
ax2.quiver(lons, lats, dlon, dlat)
ax2.quiver(lons, lats, dlon_spicenormal, dlat_spicenormal, color='r')
ax2.set_xlabel("Longitude")
ax2.set_ylabel("Latitude")
ax2.grid()
def caps_crosstrack_spice(tempdatetime, windspeed):
et = spice.datetime2et(tempdatetime)
sclkdp = spice.sce2c(
-82, et) # converts an et to a continuous encoded sc clock (ticks)
state, ltime = spice.spkezr("CASSINI", et, "IAU_TITAN", "NONE", "titan")
ramdir = spice.vhat(state[3:6])
# print("ramdir",ramdir)
# Gets Attitude
sclkdp = spice.sce2c(
-82, et) # converts an et to a continuous encoded sc clock (ticks)
ckgp_output = spice.ckgp(-82000, sclkdp, 0, "IAU_TITAN")
cmat = ckgp_output[0]
print("cmat", cmat)
ram_unit = spice.mxv(cmat, ramdir) # Ram Unit in SC coords
# print("ram_unit", ram_unit)
anglediff = spice.vsepg(
ram_unit[:2], np.array([0, 1, 0]),
2) # Find azimuthal angle between normal boresight and ram direction
# print("anglediff", anglediff * spice.dpr())
cassini_ram_mat = spice.rotate(-anglediff, 3)
# print("cassini_ram_mat", cassini_ram_mat)
# Rotates rotational axis with actuation
# cassini_caps_mat = spice.ckgp(-82821, sclkdp, 0, 'CASSINI_CAPS_BASE')[0] # Rotation matrix of actuation
# print("cassini_caps_mat", cassini_caps_mat)
anode_rotational_axis = spice.mxv(cassini_ram_mat,
np.array([1, 0,
0])) # Rotate with actuator
print("Rotational Axis", anode_rotational_axis)
rotationmatrix_1 = spice.spiceypy.axisar(anode_rotational_axis,
-70 * spice.rpd())
rotationmatrix_2 = spice.spiceypy.axisar(anode_rotational_axis,
70 * spice.rpd())
ram_unit_rotated1 = spice.mxv(rotationmatrix_1, ram_unit)
ram_unit_rotated2 = spice.mxv(rotationmatrix_2, ram_unit)
scframe_spiceplane = spice.psv2pl([0, 0, 0], ram_unit_rotated1,
ram_unit_rotated2)
print("ram_unit", ram_unit, ram_unit_rotated1, ram_unit_rotated2)
print("SC frame spice normal",
spice.psv2pl([0, 0, 0], ram_unit_rotated1, ram_unit_rotated2))
cmat_t = spice.xpose(cmat)
ram_unit_rotated1_titan = spice.mxv(
cmat_t, ram_unit_rotated1) # Transform back to IAU Titan Frame
ram_unit_rotated2_titan = spice.mxv(
cmat_t, ram_unit_rotated2) # Transform back to IAU Titan Frame
spiceplanenormal = spice.mxv(cmat_t, spice.pl2nvp(scframe_spiceplane)[0])
# Old method finding normal in titan frame
# spiceplane = spice.psv2pl(state[:3], ram_unit_rotated1_titan, ram_unit_rotated2_titan)
# spiceplanenormal = spice.pl2nvp(spiceplane)[0]
print("SPICE NORMAL", spiceplanenormal)
# print("Spice normal, sc frame", scframe_spicenormal_titan)
if windspeed > 0:
spiceplanenormal = -1 * spiceplanenormal
print("spice plane fipped", windspeed, spiceplanenormal)
print("vsep titan frame",
spice.vsep(ramdir, spiceplanenormal) * spice.dpr())
return spiceplanenormal, ram_unit_rotated1_titan, ram_unit_rotated2_titan
def norm2surfpt(semi_axes, inputNormal):
### Ellipsoid semi-axes' lengths, per the ellipsoid formula:
###
### 2 2 2
### / x \ / y \ / z \
### ( --- ) + ( --- ) + ( --- ) = 1
### \ a / \ b / \ c /
### Ensure abc components are positive
abc = sp.vequ([abs(semi_axis) for semi_axis in semi_axes[:3]])
### Get unit vector, n, parallel to input normal
n = sp.vhat(inputNormal)
### Direction of normal, N, at [x,y,z] is [ x/(a*a), y/(b*b), z/(c*c)]
### - Vector N is unknown, and is not necessarily a unit vector
### - Argument inputNormal is parallel to N, and of arbitrary length
### - Unit vector parallel to N is n, calculated above from inputNormal
### - Assume length of N is scalar 1/k; k is initially unknown
### - Scaling unit normal, n, by k yields N:
###
### n/k = N = [x/(a*a), y/(b*b), z/(c*c)] Eqn. 1
###
### so
###
### nx/k = x/(a*a) Eqn. 2x
### ny/k = y/(b*b) Eqn. 2y
### nz/k = z/(c*c) Eqn. 2z
###
### and, solving for surface point components, [x,y,z]:
###
### x = nx*a*a/k Eqn. 3x
### y = ny*b*b/k Eqn. 3y
### z = nz*c*c/k Eqn. 3z
###
### Substituting Eqns. 3x, 3y, and 3z for x, y, and z
### back into the ellipsoid formula (x^2/a^2 + ... = 1):
###
### (nx*a*a/k)^2/(a*a)
### + (ny*b*b/k)^2/(b*b)
### + (nz*c*c/k)^2/(c*c) = 1 Eqn. 4
###
### and solving for k:
###
### (nx*a)^2 + (ny*b)^2 + (nz*c)^2 = k^2 Eqn. 5
###
### Since nx, a, ny, b, nz, and c are all known, k
### can be calculated directly using Eqn. 5, and the
### surface point components, x, y, and z, can then
### be calculated using Eqns. 3x, 3y, and 3z.
### Calculate two vectors:
### - [a*a, b*b, c*c]
### - [nx*nx, ny*ny, nz*nz]
abcXabc = vXv(abc, abc)
nXn = vXv(n, n)
### Solve for k using abcXabc, nXn, and Eqn. 5:
k2 = sp.vdot(abcXabc, nXn)
k = math.sqrt(k2)
### Use k, abcXabc, n, and Eqns. 3x, 3y, and
### 3z to calculate surface point vector xyz
xyz = sp.vscl(1. / k, vXv(abcXabc, n))
### Debug logging:
if doLog:
### Calculate (x/a)^2 + (y/b)^2 + (z/c)^2; it should be = 1
one = sp.vdot(vXv(xyz, xyz), 1 / abcXabc)
pprint.pprint(
dict(n=n,
abc=abc,
abcXabc=abcXabc,
nXn=nXn,
nMag=sp.vnorm(n),
k=k,
k2=k2,
xyz=xyz,
one=one))
### Return surface point
return xyz
for iet in range(-400,401):
### ET (TDB)
et = float(iet) / 10
ets.append(et)
### Position of Bennu (2101955) wrt instrument
storxinstr,ltorxinstr = sp.spkezr('2101955',et,'J2000','none','-64999')
storx,ltorx = sp.spkezr('2101955',et,'J2000','none','-64')
### Position of Bennu (2101955) wrt S/C COM
porxinstr,vorxinstr = storxinstr[:3],storxinstr[3:]
porx,vorx = storx[:3],storx[3:]
### Delta dRange/dt
dvs.append( sp.vdot(vorxinstr,sp.vhat(porx))
- sp.vdot(vorx,sp.vhat(porx))
)
porxinstrs.append(list(porxinstr))
vorxinstrs.append(list(vorxinstr))
porxs.append(list(porx))
vorxs.append(list(vorx))
with open('relvel.json','w') as fjson:
sj.dump(dict(porxinstrs=porxinstrs
,vorxinstrs=vorxinstrs
,porxs=porxs
,vorxs=vorxs
,dvs=dvs
,ets=ets
degPerHour = 2.0 * dpr * twopi / hpd
xTolerance = lambda xDiff: xDiff < 1e-10
xDiffTolerance = lambda x, xExpect: xTolerance(abs(x - xExpect))
et, iPass = et0, 0
while et < (et0 + spd + 1):
### Get the state of the MINUTE and HOUR bodies every half hour
stMinute, lt = sp.spkezr(sMinute, et, 'J2000', 'NONE', sClock)
stHour, lt = sp.spkezr(sHour, et, 'J2000', 'NONE', sClock)
if (iPass % 2):
### On the half hour, the minute hand will be at RA=180, along [-1,0,0]
assert xTolerance(
sp.vnorm(sp.vsub([-1.0, 0., 0.], sp.vhat(stMinute[:3]))))
else:
### On the hour, the minute hand will be at RA=0, at [+1,0,0]
assert xTolerance(
sp.vnorm(sp.vsub([1.0, 0., 0.], sp.vhat(stMinute[:3]))))
vsepDeg = dpr * sp.vsep(stHour[:3], stMinute[:3])
vsepExpectDeg = (degPerHour * (iPass >> 1)) % 360
### On the hour, the houre hand will be (30 * iPass) degrees clockwise
### from +X, and therefor also the same from the minute hand
assert xDiffTolerance(vsepDeg, vsepExpectDeg) or xDiffTolerance(
(360 - vsepDeg), vsepExpectDeg)
### Step to next half hour and pass
et += halfHour
iPass += 1
def __init__(self,fovraws,ralohi=(),declohi=()
,obs_pos=None,obs_vel=None,obs_year=None
):
"""Convert FOV definition in external inertial reference frame to an
FOV definition in a local reference frame; also determine RA,Dec limits
of FOV for use in star catalog lookup.
For polygonal FOVs, set up FOV as vectors in a local reference frame,
with a matrix to rotate vectors from the external to the local frame.
The local reference frame (reffrm) will have +Z along the average
vertices' direction, and will be rotated such the the +X axis is not
parallel to any of the edges of the polygon from the FOV projected onto
the Z=+1 plane.
Arguments
fovraws - sequence either of vector and cone and half-angle for
circular FOV, or of a pair of vectors for RA,Dec box, or
of three or more vectors for a polygonal FOV. A vector is
a sequence either of two values, RA,Dec, or of three values,
X,Y,Z.
obs_pos - Observer position, solar system barycentric, 3-vector, km
- For parallax correction
obs_vel - Observer velocity, solar system barycentric, 3-vector, km/s
- For proper motion correction
obs_year - Observer time, y past 2015.5 (Gaia DR2 epoch)
- For stellar aberration correction
"""
### Get count of items in FOV sequence; ensure it is 2 or more
### and ralohi and declohi are empty, or that fovraws is empty
### and ralohi and declohi have 2 values each
(self.fovraws
,self.ralohi
,self.declohi
,self.obs_pos
,self.obs_vel
,self.obs_year
,)= fovraws,list(ralohi),list(declohi),obs_pos,obs_vel,obs_year
self.L = len(fovraws)
assert (1<self.L and not (self.ralohi+self.declohi)
) or (0==self.L and 2==len(self.ralohi) and 2==len(self.declohi)
), 'Invalid vertices in FOV'
################################
### Initialize: FOV RA,Dec pairs; FOV type (assume polygon); FOV
### vector triples; list of RA,Dec boxes
self.radecdegs = list()
self.fovtype = 1<self.L and FOV.POLYGONTYPE or FOV.RADECBOXTYPE
self.uvfovxyzs,fovsum = list(),sp.vpack(0.,0.,0.)
self.radec_boxes = list()
rdba = self.radec_boxes.append ### Shorthand to append box to list
################################
### Parse list of vertices:
### - [list,float] => Circle (cone)
### - [list,list] => RA,Dec box
### - [list,list,list,...] => Polygon
for vertex in fovraws:
### For second of two vertices ...
if 1==len(self.radecdegs) and 2==self.L:
### Two-vertex items are either a conic FOV, or an [RA,Dec] box
try:
### If second item in list is a float, then it's a half-angle
### of the cone
self.hangdeg = float(vertex)
assert self.hangdeg < 90.0,'Cone half-angle is not less than 90degrees'
assert self.hangdeg > 0.0,'Cone half-angle is not greater than 0degrees'
self.hangrad = self.hangdeg * rpd
self.min_cosine = math.cos(self.hangrad)
self.uv_cone_axis = self.uvfovxyzs[0]
self.fovtype = FOV.CIRCLETYPE
break
except AssertionError as e:
raise
except:
### If the above fails, then it's the second corner of the box
self.fovtype = FOV.RADECBOXTYPE
### Parse one vertex
ra,dec,uvxyz = parse_inertial(vertex)
### Append RA,Dec and unit vector XYZ onto their resepective lists
self.radecdegs.append((ra,dec,))
self.uvfovxyzs.append(uvxyz)
fovsum = sp.vadd(fovsum,uvxyz)
################################
### Calculate RA,DEC limits as list of [ralo,rahi,declo,dechi] boxes
### - .radec_boxes is a list; rdba is .radec_boxes.append
### - List will have multiple RA,Dec boxes if FOV crosses the Prime
### Meridian (PM) an even number of times.
if self.fovtype == FOV.RADECBOXTYPE:
### RA,DEC box FOV: calculate limits; handle PM crossing
if 2==self.L:
ras,decs = zip(*self.radecdegs)
ralo,rahi = sorted(ras)
declo,dechi = sorted(decs)
if 180 > (rahi-ralo):
rdba([ralo,rahi,declo,dechi])
else:
rdba([0.0,ralo,declo,dechi])
rdba([rahi,360.0,declo,dechi])
else:
if self.ralohi[1] > self.ralohi[0]:
rdba(self.ralohi+self.declohi)
else:
rdba([self.ralohi[0],360.0]+self.declohi)
rdba([0.0,self.ralohi[1]]+self.declohi)
elif self.fovtype == FOV.CIRCLETYPE:
### Circular FOV: DEC limits determine RA limits; handle PM Xing
ra,dec = self.radecdegs[0]
fovdeclo = dec - self.hangdeg
fovdechi = dec + self.hangdeg
if fovdeclo < -90.0 or fovdechi > 90.0:
### A pole is in the FOV; use full RA range
fovralo,fovrahi = 0.0,360.0
fovdeclo,fovdechi = max([fovdeclo,-90.0]),min([fovdechi,+90.0])
elif fovdeclo == -90.0 or fovdechi == 90.0:
### A pole is on the FOV circumference; RA range is 180 degrees
fovralo,fovrahi = ra-90.0,ra+90.0
else:
### The FOV excludes the poles; calculate the RA range, using
### the formula validated in script validate_delta_ra_formula.py
tanhang,tandec = math.tan(self.hangrad),math.tan(dec*rpd)
sinhang,cosdec = math.sin(self.hangrad),math.cos(dec*rpd)
coshang = math.cos(self.hangrad)
T = sinhang / math.sqrt(1.0 - ((tanhang*tandec)**2))
deltara = dpr * math.atan(T / (cosdec * coshang))
fovralo,fovrahi = ra-deltara,ra+deltara
### Ensure RA limits are within range [0:360] (N.B. inclusive)
if fovralo < 0.0: fovralo += 360.0
if fovrahi > 360.0: fovrahi -= 360.0
if fovralo <= fovrahi:
### RA lo <= RA hi: no PM crosssing
rdba([fovralo,fovrahi,fovdeclo,fovdechi])
else:
### RA hi < RA hi: there is a PM crosssing
rdba([0.0,fovrahi,fovdeclo,fovdechi])
rdba([fovralo,360.,fovdeclo,fovdechi])
else:
assert self.fovtype == FOV.POLYGONTYPE
### Polygonal FOV: build frame where all vertices will be
### projected onto the plane Z=1
### .uvavg: unit vector = mean of all vertices, will be +Z
self.uvavg = sp.vhat(fovsum)
### Create rotation matrix to FOV frame: +Z is mean of vertices'
### directions (.uvavg); +X will be a direction that is not
### parallel to any side of the polygon
### - Start with temporary matrix with +Z as defined above; +X
### toward vertex at largest angle from .uvavg
vother = min([(sp.vdot(self.uvavg,v),list(v),) for v in self.uvfovxyzs])[1]
tmpmtx = sp.twovec(self.uvavg,3,vother,1)
### - Rotate all vectors to that frame; scale Z components to 1.0
vtmps = list()
for v in self.uvfovxyzs:
### - Ensure all vertices are in the same hemisphere
assert 0.0 < sp.vdot(self.uvavg,v),'All vertices are not in the same hemisphere'
vtmp = sp.mxv(tmpmtx,v)
vtmps.append(sp.vscl(1.0/vtmp[2],vtmp))
### Find largest azimuth gap between any two sides: that azimuth
### will be direction of +X in the final rotation matrix
### - Get azimuths of all sides of polygon, in range [-PI:PI]
azimuths,vlast = list(),vtmps[-1]
for v in self.uvfovxyzs:
azimuths.append(numpy.arctan((v[1]-vlast[1])/(v[0]-vlast[0])))
vlast = v
### - Sort angles and add [least angle plus PI] to end of list
azimuths.sort()
azimuths.append(azimuths[0]+sp.pi())
### - Find largest delta-azimuth and its index
dazimuths = [hi-lo for hi,lo in zip(azimuths[1:],azimuths[:-1])]
maxdaz = max(dazimuths)
imaxdaz = dazimuths.index(maxdaz)
### - Calculate azimuth from to mean of that delta-azimuth,
meanaz = azimuths[imaxdaz] + (maxdaz / 2.0)
### Final matrix: add rotation of tmpmtx around +Z by that angle
self.mtxtofov = sp.mxm(sp.rotate(meanaz,3),tmpmtx)
### Apply final rotation matrix, store results in .uvlclxyzs
tmpmtx = sp.twovec(self.uvavg,3,vother,1)
self.uvlclxyzs = [self.rotate_to_local(v) for v in self.uvfovxyzs]
### Calculate upper and lower RA and Dec limits, with PM crossings
los,his = list(),list()
### - Create [[RA,Dec],[X,Y,Z]] pairs list; ensure last is off PM
pairs = list(zip(self.radecdegs,self.uvfovxyzs))
pop_count = 0
while pairs[-1][0][0] == 0.0:
pop_count += 1
assert pop_count < self.L,'All vertices are on the Prime Meridian'
pairs.append(pairs.pop(0))
### Count PM crossings
self.crossing_count = 0
lastra = pairs[-1][0][0]
zero_count = 0
for (ra,dec,),xyz in pairs:
if ra == 0.0:
zero_count += 1
if lastra > 180.0: ra = 360.0
if 180 < abs(ra-lastra): self.crossing_count += 1
lastra = ra
if 0==self.crossing_count or 1==(1&self.crossing_count):
### If there are either no, or an odd number, of PM crossings,
### then use the pairs as-is for a single FOV
subfovs = [pairs]
if self.crossing_count:
### - For odd crossing count, one pole or the other must be
### in the FOV; init full RA range, that pole for Dec ranges
ralo,rahi = 0.0,360.0
if sp.vdot(self.uvavg,[0,0,1]) > 0.0: declo = dechi = +90.0
else : declo = dechi = -90.0
else:
### - For zero crossing count, initialize inverted ranges
ralo,rahi = 360.0,0.0
declo,dechi = +90.0,-90.0
subranges = [[ralo,rahi,declo,dechi]]
else:
### If there are an even, non-zero number of PM crossings, break
### them into two sub-FOVs, one on either side of the PM
eastfov,westfov = list(),list()
if zero_count:
### If there are any zero RA values, rotate the pairs to
### ensure a zero-RA pair is the first, so it and the non-zero
### last pair will be assigned to the correct side of the PM
while pairs[0][0][0]!=0.0: pairs.append(pairs.pop(0))
else:
### If there are no zero RA values, rotate the pairs to ensure
### a crossing occurs between the last and first pair, so the
### corresponding zero crossing will be assigned to the
### correct side of the PM
while abs(pairs[0][0][0]-pairs[-1][0][0])<180:
pairs.append(pairs.pop(0))
### Write vertices into the two sub-FOVs
### - Set last-vertex values for first item in pairs
(lastra,lastdec,),lastxyz = pairs[-1]
for pair in pairs:
### - Loop over vertex pairs ((RA,DEC,),Cartesian_Vector)
(ra,dec,),xyz = pair
if ra == 0.0:
### - When RA=0, the previous RA determines if it's 0 ar 360
if lastra >= 180.0:
ra = 360.0
westfov.append([(ra,dec,),xyz])
iswest = True
else:
eastfov.append(pair)
iswest = False
elif abs(lastra-ra) >= 180.0:
### - When the change in RA>=180, the PM is being crossed
### - Find the mid-vector where the PM is crossed
k1 = -xyz[1] / (lastxyz[1]-xyz[1])
midxyz = sp.vhat(sp.vlcom(1.0-k1,xyz,k1,lastxyz))
middec = dpr * sp.recrad(midxyz)[2]
### - Add that mid-vector, with RA=360, to the west FOV
westfov.append([(360.0,middec,),midxyz])
### - Determine if vector is west
iswest = ra >= 180.0
### - Add that mid-vector, with RA=0, to the east FOV ...
if (ra > 0.0) and (not iswest):
### - ... only if the ra is not already 0, as it will be
### added in the next step
eastfov.append([(0.0,middec,),midxyz])
### Add the vector to either east or west FOV
if iswest: westfov.append(pair)
else : eastfov.append(pair)
else:
### PM was not crossed, add vector to same FOV, as last time
if iswest: westfov.append(pair)
else : eastfov.append(pair)
### - Set last-vertex values for next item in pairs
(lastra,lastdec,),lastxyz = (ra,dec,),xyz
### - Create subfovs list of east and west FOVs; set subranges
subfovs = [eastfov,westfov]
subranges = [[360.0,0.0,90.0,-90.0],[360.0,0.0,90.0,-90.0]]
### To here, we have list of FOV(s) and list of range(s); use them
### to determine RA,DEC box(es) to use for database query
while subfovs:
### Get sub-FOV, sub-range; set last vertex's XYZ
subfov,(ralo,rahi,declo,dechi,) = subfovs.pop(),subranges.pop()
lastxyz = subfov[-1][-1]
for pair in subfov:
### Each element of subfov comprises (RA,Dec) and vertex XYZ
### - xyz is a unit vector
(ra,dec,),xyz = pair
### - Adjust RA limits as needed from RA of vertex
if ra > rahi: rahi = ra
elif ra < ralo: ralo = ra
### - Set Dec extrema from DEC of vertex
maxdec = mindec = dec
### - Calculate Dec extrema from lastxyz to xyz
### -- Normal to plane of lastxyz and syz
sidenormal = sp.vcrss(lastxyz,xyz)
### -- Z-rates along great circle at lastxyz and at xyz
lastdz = sp.vcrss(sidenormal,lastxyz)[2]
dz = sp.vcrss(sidenormal,xyz)[2]
if 0.0 > (lastdz*dz):
### -- If sign of Z-rates differs, there should be an
### extreme value between lastxyz and xyz
### --- Get vector perpendicular to side normal on equator
### --- Use that to calculate the unit vector at Dec extreme
equinox = sp.vcrss([0,0,1],sidenormal)
vtoextremez = sp.ucrss(sidenormal,equinox)
### --- Cosine of angle between lastxyz and xyz
mindot = sp.vdot(lastxyz,xyz)
for none in [None,None]:
### --- Two cases: vtoextremez and -vtoextremez
### - Angles from vtoextremez to lastxyz and to xyz
### must be less than angle between lastxyz and xyz
### so cosines of those angles must be greater
lastxyzdot = sp.vdot(lastxyz,vtoextremez)
xyzdot = sp.vdot(xyz,vtoextremez)
if lastxyzdot>mindot and xyzdot>mindot:
### --- Adjust maxdec and mindec as needed
try : extremedec = dpr * math.asin(vtoextremez[2])
except: extremedec = dpr * sp.recrad(vtoextremez)[2]
if extremedec > maxdec: maxdec = extremedec
elif extremedec < mindec: mindec = extremedec
break
### --- Invert vtoextremez for next pass
vtoextremez = sp.vminus(vtoextremez)
### - Adjust Dec limits as needed from Dec extrema of side
if maxdec > dechi: dechi = maxdec
if mindec < declo: declo = mindec
lastxyz = xyz
### Append calculated RA,Dec box(es)
rdba((ralo,rahi,declo,dechi,))
### Put None in .localxyzs, in .v_for_stellar_aberr, and in
### .v_for_parallax; if no stellar aberration or parallax is
### explicitly applied to define it later, then .localxyzs will be
### calculated on the fly
self.localxyzs = None
self.v_for_stellar_aberr = None
self.v_for_parallax = None
"earth")[0]
if do_debug:
### Ensure that light-time correction is zero for earth->star vector
### for star at fixed positon relative to SSB
earth2star_lt = sp.spkcpt(vstar, ssb, j2000, et, j2000, "observer", LT,
"earth")[0]
assert 0.0 == sp.vnormg(sp.vsubg(earth2star_none, earth2star_lt, 6), 6)
### Calculate differences between gaiif_util.py and SPICE results ...
ab_vec_spice = sp.vsub(earth2star_lts[:3], earth2star_none[:3])
ab_vec_gaia = sp.vscl(range2star, sp.vsub(uvstar_ab, uvstar_noab))
ab_vec_diff = sp.vsub(ab_vec_spice, ab_vec_gaia)
ab_diff_frac = sp.vnorm(ab_vec_diff) / sp.vnorm(ab_vec_spice)
no_ab_diff = sp.vsep(uvstar_noab, sp.vhat(earth2star_none[:3]))
ab_diff = sp.vsep(uvstar_ab, sp.vhat(earth2star_lts[:3]))
ab_diff_frac = sp.vsep(uvstar_ab, sp.vhat(earth2star_lts[:3]))
try:
### ... Success
assert 1e-15 > no_ab_diff
assert 1e-8 > ab_diff
except:
### ... Failure
print(
dict(no_ab_diff=no_ab_diff,
ab_diff=ab_diff,
ab_diff_frac=ab_diff_frac,
ab_mag_spice=sp.vsep(earth2star_none[:3], earth2star_lts[:3]),
ab_mag_gaia=sp.vsep(uvstar_noab, uvstar_ab)))
def star_in_fov(self
,vstar
,parallax_maspau=None
,pmra_maspy=None
,pmdec_maspy=None
):
"""Return True if the star (RA,Dec or xyz) argument is in the FOV
Argument vstar is either an RA,Dec pair (degrees) or a 3-vector
"""
if self.fovtype == FOV.RADECBOXTYPE:
##################################################################
### Compare star vector to [RA,Dec] box
ra,dec = parse_inertial(vstar,return_radec=True)[:2]
for ralo,rahi,declo,dechi in self.radec_boxes:
if ra<ralo: continue
if ra>rahi: continue
if dec<declo: continue
if dec>dechi: continue
return True,sp.radrec(1.,rpd*ra,rpd*dec)
return False,None
### Get inertial star unit vector without RA,Dec
uvinertial = uvraw = parse_inertial(vstar,return_radec=False)
### Corrections for direction to star
### - Assume all corrections are small and can be applied in units
### of radians to a unit vector in a plane perpendicular to the
### vector to the star
### - Proper Motion (PM)
### - Uses PM in RA and Dec only, not radial velocity and parallax
if (not (None is self.obs_year)
) and (not (None in (pmra_maspy,pmdec_maspy,))
) and (pmra_maspy != 0.0 or pmdec_maspy != 0.0):
### - Unit vectors E and N in plane perpendicular to star vector
uveast = sp.ucrss([0,0,1],uvraw)
uvnorth = sp.ucrss(uvraw,uveast)
### - Scale unit vectors in radians, and add to nominal vector
### - pmra_maspy from Gaia includes factor of secant(Declination)
uvinertial = sp.vhat(sp.vlcom3(self.obs_year*rpmas*pmdec_maspy,uvnorth
,self.obs_year*rpmas*pmra_maspy,uveast
,1.0,uvinertial
)
)
### - Parallax
if (not (None is self.obs_pos)
) and (not (None is parallax_maspau)
) and (parallax_maspau != 0.0):
### - Scale observer position, by parallax in mas/AU, then scale
### to radians (since star vector is unit vector), make that the
### new origin of the vector
uvinertial = sp.vhat(sp.vsub(uvinertial
,sp.vscl(aupkm*parallax_maspau*rpmas,self.obs_pos)
)
)
### - Stellar Aberration
if not (None is self.obs_vel):
### - Scale observer velocity by reciprocal of the speed of light,
### add result to unit vector toward star.
uvinertial = sp.vhat(sp.vadd(uvinertial
,sp.vscl(recip_clight,self.obs_vel)
)
)
if self.fovtype == FOV.CIRCLETYPE:
##################################################################
### Compare inertial star vector to circular FOV
return sp.vdot(uvinertial,self.uv_cone_axis) >= self.min_cosine,uvinertial
assert FOV.POLYGONTYPE == self.fovtype,'Unknown FOV type [{0}]'.format(self.fovtype)
####################################################################
### Compare star vector to polygonal FOV
if self.is_convex():
### Convex FOV: a negative dot product with the inward-pointing
### normal to any side indicates star is outside FOV
for inwardnorm in self.inwardsidenorms:
if sp.vdot(uvinertial,inwardnorm) < 0.0: return False,uvinertial
### All dot products were non-negative: star is within FOV
return True,uvinertial
### Rotate inertial unit vector to local reference frame (reffrm)
uvlocalstar = self.rotate_to_local(uvinertial)
### Scale to Z=unity
if uvlocalstar[2] < 1e-15: return False,uvinertial
z1star = sp.vscl(1.0/uvlocalstar[2],uvlocalstar)
### Setup .localxyzs and .fovsides
if None is self.localxyzs: self.setup_localxyzs()
### Count number of crossings of FOV sides
count = len([None
for fovside in self.fovsides
if fovside.right_of(z1star)
])
return ((count&1) and True or False),uvinertial