| 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] |