content: import numpy as np
  
  PRIMES = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53]
  
  def radical_inverse(base, n):
      val = 0
      inv_base = 1.0 / base
      inv_base_n = inv_base
      while n > 0:
          digit = n % base
          val += digit * inv_base_n
          n //= base
          inv_base_n *= inv_base
      return val
  
  def halton_sequence(dim, n):
      return [radical_inverse(PRIMES[dim], n) for dim in range(dim)]
  
  def hammersley_sequence(dim, n, num_samples):
      return [n / num_samples] + halton_sequence(dim - 1, n)
  
  def sphere_hammersley_sequence(n, num_samples, offset=(0, 0), remap=False):
      u, v = hammersley_sequence(2, n, num_samples)
      u += offset[0] / num_samples
      v += offset[1]
      if remap:
          u = 2 * u if u < 0.25 else 2 / 3 * u + 1 / 3
      theta = np.arccos(1 - 2 * u) - np.pi / 2
      phi = v * 2 * np.pi
      return [phi, theta]