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import numpy as np
from transform import rotate
def uniform_sphere(size=None, dtype=np.double):
"""
Generate random points isotropically distributed across the unit sphere.
Args:
- size: int, *optional*
Number of points to generate. If no size is specified, a single
point is returned.
Source: Weisstein, Eric W. "Sphere Point Picking." Mathworld.
"""
theta, u = np.random.uniform(0.0, 2*np.pi, size), \
np.random.uniform(-1.0, 1.0, size)
c = np.sqrt(1-u**2)
if size is None:
return np.array([c*np.cos(theta), c*np.sin(theta), u])
points = np.empty((size, 3), dtype)
points[:,0] = c*np.cos(theta)
points[:,1] = c*np.sin(theta)
points[:,2] = u
return points
def flashlight(phi=np.pi/4, direction=(0,0,1), size=None, dtype=np.double):
theta, u = np.random.uniform(0.0, 2*np.pi, size), \
np.random.uniform(np.cos(phi), 1, size)
c = np.sqrt(1-u**2)
if np.equal(direction, (0,0,1)).all():
rotation_axis = (0,0,1)
rotation_angle = 0.0
else:
rotation_axis = np.cross((0,0,1), direction)
rotation_angle = \
-np.arccos(np.dot(direction, (0,0,1))/np.linalg.norm(direction))
if size is None:
return rotate(np.array([c*np.cos(theta), c*np.sin(theta), u]),
rotation_angle, rotation_axis)
points = np.empty((size, 3), dtype)
points[:,0] = c*np.cos(theta)
points[:,1] = c*np.sin(theta)
points[:,2] = u
return rotate(points, rotation_angle, rotation_axis)
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