diff options
| -rw-r--r-- | contrib/cone-vector.py | 6 |
1 files changed, 6 insertions, 0 deletions
diff --git a/contrib/cone-vector.py b/contrib/cone-vector.py index 9501464..676750f 100644 --- a/contrib/cone-vector.py +++ b/contrib/cone-vector.py @@ -22,10 +22,12 @@ from numpy.linalg import norm from scipy.special import betainc, betaincinv, gamma def random_vector_on_sphere(dim): + """Return a random vector uniformly distributed on the unit sphere.""" x = randn(dim) return x / norm(x) def planar_angle2solid_angle_fraction(planar_angle, dim): + """Return the solid angle fraction for a given planar angle.""" alpha = (dim - 1) / 2 beta = 1/2 return where(planar_angle < pi/2, @@ -33,6 +35,7 @@ def planar_angle2solid_angle_fraction(planar_angle, dim): 1 - 0.5*betainc(alpha, beta, sin(planar_angle)**2)) def solid_angle_fraction2planar_angle(solid_angle_fraction, dim): + """Return the planar angle for a given solid angle fraction.""" alpha = (dim - 1) / 2 beta = 1/2 return where(solid_angle_fraction < 1/2, @@ -40,6 +43,8 @@ def solid_angle_fraction2planar_angle(solid_angle_fraction, dim): pi - arcsin(sqrt(betaincinv(alpha, beta, 2*(1-solid_angle_fraction))))) def rotate_from_nth_canonical(x, axis): + """Rotate vector from around the nth canonical axis to the given axis. + """ xn = x[-1] axisn = axis[-1] if axisn != 1: @@ -52,6 +57,7 @@ def rotate_from_nth_canonical(x, axis): return x def random_vector_on_spherical_cap(axis, maximum_planar_angle): + """Return a random vector uniformly distributed on a spherical cap.""" dim = axis.size maximum_solid_angle_fraction = planar_angle2solid_angle_fraction(maximum_planar_angle, dim) solid_angle_fraction = maximum_solid_angle_fraction*random() |