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| """ | |
| Simplex noise implementation by Alex Dodge, 2023 | |
| References: | |
| Simplex noise demystified, Stefan Gustavson (2005) | |
| http://staffwww.itn.liu.se/~stegu/simplexnoise/simplexnoise.pdf | |
| """ | |
| import itertools | |
| from typing import Optional | |
| import numpy as np | |
| # fmt: off | |
| PERMUTATION_TABLE_ARRAY = np.array([ | |
| 151, 160, 137, 91, 90, 15, 131, 13, 201, 95, 96, 53, 194, 233, 7, 225, 140, 36, 103, | |
| 30, 69, 142, 8, 99, 37, 240, 21, 10, 23, 190, 6, 148, 247, 120, 234, 75, 0, 26, 197, | |
| 62, 94, 252, 219, 203, 117, 35, 11, 32, 57, 177, 33, 88, 237, 149, 56, 87, 174, 20, | |
| 125, 136, 171, 168, 68, 175, 74, 165, 71, 134, 139, 48, 27, 166, 77, 146, 158, 231, | |
| 83, 111, 229, 122, 60, 211, 133, 230, 220, 105, 92, 41, 55, 46, 245, 40, 244, 102, 143, | |
| 54, 65, 25, 63, 161, 1, 216, 80, 73, 209, 76, 132, 187, 208, 89, 18, 169, 200, 196, | |
| 135, 130, 116, 188, 159, 86, 164, 100, 109, 198, 173, 186, 3, 64, 52, 217, 226, 250, | |
| 124, 123, 5, 202, 38, 147, 118, 126, 255, 82, 85, 212, 207, 206, 59, 227, 47, 16, 58, | |
| 17, 182, 189, 28, 42, 223, 183, 170, 213, 119, 248, 152, 2, 44, 154, 163, 70, 221, | |
| 153, 101, 155, 167, 43, 172, 9, 129, 22, 39, 253, 19, 98, 108, 110, 79, 113, 224, | |
| 232, 178, 185, 112, 104, 218, 246, 97, 228, 251, 34, 242, 193, 238, 210, 144, 12, 191, | |
| 179, 162, 241, 81, 51, 145, 235, 249, 14, 239, 107, 49, 192, 214, 31, 181, 199, 106, | |
| 157, 184, 84, 204, 176, 115, 121, 50, 45, 127, 4, 150, 254, 138, 236, 205, 93, 222, | |
| 114, 67, 29, 24, 72, 243, 141, 128, 195, 78, 66, 215, 61, 156, 180 | |
| ], dtype=np.int32) | |
| # fmt: on | |
| # Empirically determined scaling factor for different numbers of dimensions | |
| SCALE = { | |
| 2: 50, | |
| 3: 39, | |
| 4: 32, | |
| 5: 28, | |
| 6: 26, | |
| # It looks terrible at this many dimensions anyway | |
| } | |
| class SimplexNoise: | |
| def __init__(self, dimensions: int, seed: Optional[int], r2: float = 0.5): | |
| if dimensions <= 0: | |
| raise ValueError | |
| if dimensions == 1: | |
| raise RuntimeError("1D Simplex noise is not implemented here.") | |
| if dimensions > 6: | |
| raise RuntimeError("7D+ Simplex noise is not implemented here.") | |
| self.dimensions = dimensions | |
| self.r2 = r2 | |
| self.F = (np.sqrt(self.dimensions + 1) - 1) / self.dimensions | |
| self.G = (1 - 1 / np.sqrt(self.dimensions + 1)) / self.dimensions | |
| """ | |
| For 2D noise, we pick 16 gradients evenly distributed around the unit circle. | |
| For 3D and above, we pick gradients pointing at the midpoints of the edges of a hypercube centered on the origin | |
| """ | |
| if self.dimensions == 2: | |
| n_gradients = 16 | |
| self.gradients = np.array( | |
| [ | |
| ( | |
| np.cos(2 * np.pi * i / n_gradients), | |
| np.sin(2 * np.pi * i / n_gradients), | |
| ) | |
| for i in range(n_gradients) | |
| ] | |
| ) | |
| else: | |
| n_gradients = self.dimensions * 2 ** (self.dimensions - 1) | |
| self.gradients = np.zeros((n_gradients, self.dimensions)) | |
| for zero_dim in range(self.dimensions): | |
| for i, vec in enumerate( | |
| itertools.product([-1, 1], repeat=self.dimensions - 1) | |
| ): | |
| idx = zero_dim * 2 ** (self.dimensions - 1) + i | |
| self.gradients[idx, :zero_dim] = vec[:zero_dim] | |
| self.gradients[idx, zero_dim + 1 :] = vec[zero_dim:] | |
| if seed is None: | |
| # Use the canonical table from the reference implementation | |
| self.permutation_table = PERMUTATION_TABLE_ARRAY | |
| else: | |
| np.random.seed(seed) | |
| self.permutation_table = np.arange(self.gradients.shape[0] * 16) | |
| np.random.shuffle(self.permutation_table) | |
| def evaluate(self, points: np.ndarray): | |
| n_points = points.shape[0] | |
| assert points.shape == (n_points, self.dimensions) | |
| skewed_points = points + (points.sum(axis=1) * self.F).reshape((n_points, 1)) | |
| skewed_bases, skewed_points_remainder = np.divmod(skewed_points, 1) | |
| skewed_simplex_verts = np.full( | |
| (n_points, self.dimensions + 1, self.dimensions), | |
| fill_value=skewed_bases.reshape((n_points, 1, -1)), | |
| dtype="int32", | |
| ) | |
| skewed_simplex_verts[:, self.dimensions, :] += 1 | |
| for i in range(1, self.dimensions): | |
| largest_dimension = np.argmax(skewed_points_remainder, axis=1) | |
| for o in range(self.dimensions): | |
| skewed_simplex_verts[ | |
| (largest_dimension == o), i : self.dimensions, o | |
| ] += 1 | |
| if i != self.dimensions - 1: | |
| skewed_points_remainder[(largest_dimension == o), o] = -1 | |
| gradient_index = np.zeros(skewed_simplex_verts.shape[:2], dtype="int32") | |
| for i in range(skewed_simplex_verts.shape[2]): | |
| gradient_index = ( | |
| gradient_index + skewed_simplex_verts[:, :, i] | |
| ) % self.permutation_table.size | |
| gradient_index = self.permutation_table[gradient_index] | |
| gradients = self.gradients[gradient_index % self.gradients.shape[0]] | |
| simplex_verts = ( | |
| skewed_simplex_verts | |
| - skewed_simplex_verts.sum(axis=2).reshape((n_points, -1, 1)) * self.G | |
| ) | |
| displacement = np.power( | |
| points.reshape((n_points, 1, -1)) - simplex_verts, 2 | |
| ).sum(axis=2) | |
| dot_gradient = np.sum( | |
| (points.reshape((n_points, 1, -1)) - simplex_verts) * gradients, axis=2 | |
| ) | |
| contributions = ( | |
| np.power(np.maximum(0, self.r2 - displacement), 4) * dot_gradient | |
| ) | |
| return np.sum(contributions, axis=1) * SCALE[self.dimensions] + 0.5 | |