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+import numpy as np
+
+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