e0 = np.deg2rad(10) # Solar elevation angle
F0 = 1365 # Solar constant
albedo = 0.3
emiss = 0.95
dir_sun = np.array([0, -np.cos(e0), np.sin(e0)]) # Direction of sun
# Compute the direct irradiance and find the elements which are in shadow.
tic()
E = shape_model.get_direct_irradiance(F0, dir_sun)
t_E = toc()
I_shadow = E == 0
print('Number of elements in E =', E.shape[0])
# Make plot of direct irradiance
fig, ax = tripcolor_vector(V, F, E, cmap=cmap['gray'])
fig.savefig('E.png')
plt.close(fig)
print('- wrote E.png')
tic()
B, niter_B = solve_radiosity(FF, E, rho=albedo)
t_B = toc()
print('- computed radiosity [%1.2f s]' % (t_B, ))
fig, ax = tripcolor_vector(V, F, B, cmap=cc.cm.gray)
fig.savefig('B.png')
plt.close(fig)
print('- wrote B.png')
tic()
print('- Number of vertices', V.shape[0], 'Number of facets', F.shape[0])
# Define constants used in the simulation:
e0 = np.deg2rad(10) # Solar elevation angle
F0 = 1365 # Solar constant
albedo = 0.3
emiss = 0.95
dir_sun = np.array([0, -np.cos(e0), np.sin(e0)]) # Direction of sun
# Compute the direct irradiance and find the elements which are in shadow.
E = shape_model.get_direct_irradiance(F0, dir_sun)
print('Number of elements in E =', E.shape[0])
# Make plot of direct irradiance
fig, ax = tripcolor_vector(V, F, E, cmap='gray')
fig.savefig('E.png')
plt.close(fig)
print('- wrote E.png')
# calculate analytical solution for bowl-shaped crater
Texact = exact_solution_ingersoll(F0, e0, albedo, emiss, 5., P, N, E,
dir_sun)
fig, ax = tripcolor_vector(V, F, Texact, cmap='inferno')
fig.savefig('Texact.png')
plt.close(fig)
print('- wrote Texact.png')
# set provisional values
Qabs = (1 - albedo) * E
def illuminate_form_factor(FF_path = 'lsp_compressed_form_factors.bin', compressed=True, plot_fluxes=False, use_svd=False):
"""
Compute Sun position, illuminate FF and compute irradiance and temperature
Args:
FF_path: input form factor matrix
compressed: bool, is the input FF compressed
Returns:
dict
"""
# clktol = '10:000'
spice.kclear()
spice.furnsh('simple.furnsh')
# Define time window
et0 = spice.str2et('2011 MAR 01 00:00:00.00')
et1 = spice.str2et('2011 APR 01 00:00:00.00')
et = np.linspace(et0, et1, 10, endpoint=False)
stepet = et[1]-et[0]
# Sun positions over time period
possun = spice.spkpos('SUN', et, 'MOON_ME', 'LT+S', 'MOON')[0]
lonsun = np.arctan2(possun[:, 1], possun[:, 0])
lonsun = np.mod(lonsun, 2*np.pi)
radsun = np.sqrt(np.sum(possun[:, :2]**2, axis=1))
latsun = np.arctan2(possun[:, 2], radsun)
sun_dirs = np.array([
np.cos(lonsun)*np.cos(latsun),
np.sin(lonsun)*np.cos(latsun),
np.sin(latsun)
]).T
# Load compressed form factor matrix, including shape model, from disk
if use_svd:
V = np.load('lsp_V.npy')
F = np.load('lsp_F.npy')
N = np.load('lsp_N.npy')
shape_model = TrimeshShapeModel(V, F, N)
elif compressed:
logging.warning("Retrieving compressed FF block and shape_model...")
FF = cff.CompressedFormFactorMatrix.from_file(FF_path)
shape_model = FF.shape_model
V = FF.shape_model.V
F = FF.shape_model.F
else:
logging.warning("Retrieving full FF block and shape_model...")
FF = ff.FormFactorMatrix.from_file(FF_path)
V = np.load('lsp_V.npy')
F = np.load('lsp_F.npy')
N = np.load('lsp_N.npy')
shape_model = TrimeshShapeModel(V, F, N)
# illuminate FF
E_arr = []
for i, sun_dir in enumerate(sun_dirs[:]):
E_arr.append(shape_model.get_direct_irradiance(F0, sun_dir))
E = np.vstack(E_arr).T
Qrefl = []
QIR = []
T = []
if steady_state:
# Compute steady state temperature
T_arr = compute_steady_state_temp(FF, E, albedo, emiss)
T = np.vstack(T_arr).T
elif False:
# spin-up model until equilibrium is reached
# generate 1D grid
nz = 60
zfac = 1.05
zmax = 2.5
z = setgrid(nz=nz, zfac=zfac, zmax=zmax)
# compute provisional Tsurf and Q from direct illumination only
Qabs0 = (1 - albedo) * E[:, 0] + Fgeoth
Tsurf0 = (Qabs0 / (sigSB * emiss)) ** 0.25
# set up model (with Qprev = Qabs0)
model = PccThermalModel1D(nfaces=E.shape[0], z=z, T0=210, ti=120., rhoc=960000., # we have rho, but how do we get c?
emissivity=emiss, Fgeotherm=Fgeoth, Qprev=Qabs0.astype(np.double), bcond='Q')
# loop over time-steps/sun angles
T = [model.T[:,0]]
for i in range(len(sun_dirs) - 1):
# get Q(np1) as in Eq. 17-19
if i == 0:
Qrefl_np1, QIR_np1 = update_incoming_radiances(FF, E[:, i + 1], albedo, emiss,
Qrefl=0, QIR=0, Tsurf=Tsurf0)
else:
Qrefl_np1, QIR_np1 = update_incoming_radiances(FF, E[:, i + 1], albedo, emiss,
Qrefl=Qrefl_np1, QIR=QIR_np1, Tsurf=model.T[:, 0])
# compute Qabs, eq 19 radiosity paper
Qnp1 = (1 - albedo) * (E[:, i + 1] + Qrefl_np1) + emiss * QIR_np1
# extrapolate model at t_{i+1}, get model.T(i+1)
model.step(stepet, Qnp1)
# add check for steady-state (model.T(i) - model.T(i-1) < eps) to break loop
T.append(model.T[:,0])
# adapt shapes for plotting
T = np.vstack(T).T
else:
# loop over time-steps/sun angles
for i in range(len(sun_dirs) - 1):
Qabs0 = (1 - albedo) * E[:, i] + Fgeoth
Tsurf0 = (Qabs0 / (sigSB * emiss)) ** 0.25
if not use_svd:
# get Q(np1) as in Eq. 17-19
if i == 0:
Qrefl_np1, QIR_np1 = update_incoming_radiances(FF, E[:, i + 1], albedo, emiss,
Qrefl=0., QIR=0., Tsurf=Tsurf0)
else:
Qrefl_np1, QIR_np1 = update_incoming_radiances(FF, E[:, i + 1], albedo, emiss,
Qrefl=Qrefl_np1, QIR=0., Tsurf=Tsurf0)
else:
# read outputs of xSVDcomputation
U = np.loadtxt('svd_U.dat');
sigma = np.loadtxt('svd_sigma.dat')
Vt = np.loadtxt('svd_V.dat')
if i == 0:
Qrefl_np1, QIR = update_incoming_radiances_wsvd(E[:, i + 1], albedo, emiss, 0, 0,
Tsurf0, Vt, sigma, U)
else:
Qrefl_np1, QIR = update_incoming_radiances_wsvd(E[:, i + 1], albedo, emiss, Qrefl_np1, 0,
Tsurf0, Vt, sigma, U)
# save Qrefl
Qrefl.append(Qrefl_np1)
T.append(Tsurf0)
# adapt shapes for plotting
Qrefl = np.vstack(Qrefl).T
T = np.vstack(T).T
Path(f"./frames").mkdir(parents=True, exist_ok=True)
if plot_fluxes:
for i, sun_dir in enumerate(sun_dirs[:]):
print('frame = %d' % i)
fig, ax = tripcolor_vector(V, F, E[:,i], cmap=cc.cm.gray)
fig.savefig(f"./frames/lsp_E1_%03d.png" % i)
plt.close(fig)
fig, ax = tripcolor_vector(V, F, T[:,i], cmap=cc.cm.fire)
fig.savefig(f"./frames/lsp_T1_%03d.png" % i)
plt.close(fig)
I_shadow = E[:,i] == 0
fig, ax = tripcolor_vector(V, F, T[:,i], I=I_shadow, cmap=cc.cm.rainbow, vmax=100)
fig.savefig(f"./frames/lsp_T1_shadow_%03d.png" % i)
plt.close(fig)
# starting E from second element, to have same number of elements on all arrays
return {"V":V,"F":F,"E":E[:,1:],'Qrefl':Qrefl,"QIR":QIR,"T":T}
if args.blocks and args.tol:
tic()
fig, ax = plot_blocks(FF._root)
fig.savefig(os.path.join(args.outdir, 'blocks.png'))
plt.close(fig)
print('- wrote blocks.png [%1.2f s]' % (toc(),))
dir_sun = np.array([np.cos(e0), 0, np.sin(e0)])
tic()
E = shape_model.get_direct_irradiance(args.F0, dir_sun, eps=1e-6)
t_E = toc()
print('- computed direct irradiance [%1.2f s]' % (t_E,))
fig, ax = tripcolor_vector(V, F, E, cmap=cc.cm.gray)
fig.savefig(os.path.join(args.outdir, 'E.png'))
plt.close(fig)
print('- wrote E.png to disk')
tic()
B, niter_B = solve_radiosity(FF, E, rho=args.rho)
t_B = toc()
print('- computed radiosity [%1.2f s]' % (t_B,))
fig, ax = tripcolor_vector(V, F, B, cmap=cc.cm.gray)
fig.savefig(os.path.join(args.outdir, 'B.png'))
plt.close(fig)
print('- wrote B.png')
tic()
V = d['full']['V']
F = d['full']['F']
if test_svd:
residuals = np.abs(d['full']['Qrefl'] - d['svd']['Qrefl']) # #
else:
residuals = np.abs(d['full']['Qrefl'] - d['compressed']['Qrefl']) # #
print(len(residuals))
step2_res = residuals[:, 8]
print(np.where(step2_res > 1.e14))
# exit()
# plot residuals
for i in range(residuals.shape[1]):
# print('frame = %d' % i)
fig, ax = tripcolor_vector(V, F, residuals[:, i], vmax=1.e14)
fig.savefig(f"./frames/lsp_dfc32_%03d.png" % i)
plt.close(fig)
fig, ax = tripcolor_vector(V, F, d['full']['Qrefl'][:, i], vmax=1.e16)
fig.savefig(f"./frames/lsp_fd32_%03d.png" % i)
plt.close(fig)
fig, ax = tripcolor_vector(V,
F,
d['compressed']['Qrefl'][:, i],
vmax=1.e16)
fig.savefig(f"./frames/lsp_cd32_%03d.png" % i)
plt.close(fig)
if test_svd:
I_shadow = E == 0
# Compute the steady state temperature. This function is at the
# top of this file.
T = compute_steady_state_temp(FF, E, rho, emiss)
print('computed T')
# Finally, we make some plots showing what we just did, and write
# them to disk:
fig, ax = plot_blocks(FF._root)
fig.savefig('haworth_blocks.png')
plt.close(fig)
print('wrote haworth_blocks.png to disk')
fig, ax = tripcolor_vector(V, F, E, cmap=cmap['gray'])
fig.savefig('haworth_E.png')
plt.close(fig)
print('wrote haworth_E.png to disk')
fig, ax = tripcolor_vector(V, F, T, vmin=0, vmax=400, cmap=cmap['fire'])
fig.savefig('haworth_T.png')
plt.close(fig)
print('wrote haworth_T.png to disk')
fig, ax = tripcolor_vector(V, F, T, I=I_shadow, cmap=cmap['jet'])
fig.savefig('haworth_T_shadow.png')
plt.close(fig)
print('wrote haworth_T_shadow.png to disk')
# Use pyvista to make a nice 3D plot of the temperature.
V = np.row_stack([V.T, np.array([z(*v)[0] for v in V])]).T
num_faces = F.shape[0]
print('created mesh with %d triangles' % num_faces)
# Let's use another Python library (meshio) to save the triangle
# mesh as an OBJ file (optional).
points = V
cells = [('triangle', F)]
mesh = meshio.Mesh(points, cells)
mesh_path = 'mesh%d.obj' % num_faces
mesh.write(mesh_path)
print('wrote %s to disk' % mesh_path)
# Make plot of topography
fig, ax = tripcolor_vector(V, F, V[:, 2], cmap=cmap['jet'])
fig.savefig('topo2.png')
plt.close(fig)
print('wrote topo2.png')
# Since Embree runs in single precision, there's no reason to use
# double precision here.
V = V.astype(np.float32)
# Create a triangle mesh shape model using the vertices (V) and
# face indices (F).
shape_model = TrimeshShapeModel(V, F)
# Build the compressed form factor matrix. All of the code related
# to this can be found in the "form_factors.py" file in this
# directory.
