def random_directions_bounded_density_3d(center, radius, N):
S = random_directions_bounded(3, radius, N, center=center)
distances = distances_from(S, center)
if not (distances <= radius).all():
invalid = np.nonzero(distances > radius)[0]
msg = 'Invalid distances: %s > %f' % (distances[invalid], radius)
raise Exception(msg)
subs = 6
A = spherical_cap_area(cap_radius=radius)
da = A / subs
dist = np.zeros(subs, dtype='int')
for s in range(subs):
lower = s * da
upper = lower + da
r1 = spherical_cap_with_area(lower)
r2 = spherical_cap_with_area(upper)
num_here = np.logical_and(distances >= r1, distances < r2).sum()
dist[s] = num_here
assert dist.sum() == N
return DiscreteUniformDistribution(dist,
'Distribution of distances from center')
def random_directions_bounded_density_3d(center, radius, N):
S = random_directions_bounded(3, radius, N, center=center)
distances = distances_from(S, center)
if not (distances <= radius).all():
invalid = np.nonzero(distances > radius)[0]
msg = 'Invalid distances: %s > %f' % (distances[invalid], radius)
raise Exception(msg)
subs = 6
A = spherical_cap_area(cap_radius=radius)
da = A / subs
dist = np.zeros(subs, dtype='int')
for s in range(subs):
lower = s * da
upper = lower + da
r1 = spherical_cap_with_area(lower)
r2 = spherical_cap_with_area(upper)
num_here = np.logical_and(distances >= r1, distances < r2).sum()
dist[s] = num_here
assert dist.sum() == N
return DiscreteUniformDistribution(dist,
'Distribution of distances from center')
def spherical_cap_area_test():
for radius, area in couples:
yield assert_allclose, spherical_cap_area(radius), area
def spherical_cap_area_test():
for radius, area in couples:
yield assert_allclose, spherical_cap_area(radius), area