def __init__(self, target, spots = [], resolution = 50):
# Constructor. Precomputes ray hits.
self.target = target
self.resolution = resolution
self.spots = spots
# make grid of rays
R = target.radius
res = resolution
grid = np.mgrid[ -R:R:res*1j, -R:R:res*1j ]
# collide rays with sphere
z2 = target.radius**2 - grid[0]**2 - grid[1]**2
hits = (z2 > 0)
z = np.sqrt( z2[hits] )
# save positions of hit pixels, and hit locations
self.pixels = np.nonzero(hits)
self.points = np.vstack([grid[0][hits], grid[1][hits], z]).transpose()
# get TV = AV x r, RV = -z . TV
angvels = target.angvel(self.points)
tangvels = np.cross(angvels, self.points)
self.radvels = -tangvels[:,2]
# get base luminosity mask from limb darkening
norms = np.apply_along_axis(np.linalg.norm, 1, self.points)
thetas = np.arccos( self.points[:,2] / norms )
self.base_mask = physics.default_limb_darkening( thetas )
def rv(self, t): # area => spot area
# Computes approximate mean RV time t.
rv_all = 0
for pos,fracarea in self.spots:
pos_t = self.target.evolve(pos, -t) / self.target.radius
if pos_t[2] < 0:
# behind star
continue
if hasattr(fracarea, '__call__'): # is fracarea a lambda?
theta = geometry.cap_half_angle( fracarea(t) )
else: # or a constant
theta = geometry.cap_half_angle( fracarea )
area = math.pi * math.sin(theta)**2
area *= math.sqrt(1 - pos_t[0]**2 - pos_t[1]**2 ) # perspective
R = self.target.radius
rv = self.max_rv * pos_t[0]
ld = physics.default_limb_darkening(math.acos( pos_t[2] ))
rv_all -= area * rv * ld
return rv_all
