"""Helper functions for generating Perlin noise."""
# Original Code
# Copyright (c) 2021 VitjanZ
# https://github.com/VitjanZ/DRAEM.
# SPDX-License-Identifier: MIT
#
# Modified
# Copyright (C) 2022 Intel Corporation
# SPDX-License-Identifier: Apache-2.0
# pylint: disable=invalid-name
import math
from typing import Tuple, Union
import numpy as np
import torch
from torch import Tensor
[docs]def lerp_np(x, y, w):
"""Helper function."""
fin_out = (y - x) * w + x
return fin_out
[docs]def rand_perlin_2d_octaves_np(shape, res, octaves=1, persistence=0.5):
"""Generate Perlin noise parameterized by the octaves method. Numpy version."""
noise = np.zeros(shape)
frequency = 1
amplitude = 1
for _ in range(octaves):
noise += amplitude * generate_perlin_noise_2d(shape, (frequency * res[0], frequency * res[1]))
frequency *= 2
amplitude *= persistence
return noise
[docs]def generate_perlin_noise_2d(shape, res):
"""Fractal perlin noise."""
def f(t):
return 6 * t**5 - 15 * t**4 + 10 * t**3
delta = (res[0] / shape[0], res[1] / shape[1])
d = (shape[0] // res[0], shape[1] // res[1])
grid = np.mgrid[0 : res[0] : delta[0], 0 : res[1] : delta[1]].transpose(1, 2, 0) % 1
# Gradients
angles = 2 * np.pi * np.random.rand(res[0] + 1, res[1] + 1)
gradients = np.dstack((np.cos(angles), np.sin(angles)))
g00 = gradients[0:-1, 0:-1].repeat(d[0], 0).repeat(d[1], 1)
g10 = gradients[1:, 0:-1].repeat(d[0], 0).repeat(d[1], 1)
g01 = gradients[0:-1, 1:].repeat(d[0], 0).repeat(d[1], 1)
g11 = gradients[1:, 1:].repeat(d[0], 0).repeat(d[1], 1)
# Ramps
n00 = np.sum(grid * g00, 2)
n10 = np.sum(np.dstack((grid[:, :, 0] - 1, grid[:, :, 1])) * g10, 2)
n01 = np.sum(np.dstack((grid[:, :, 0], grid[:, :, 1] - 1)) * g01, 2)
n11 = np.sum(np.dstack((grid[:, :, 0] - 1, grid[:, :, 1] - 1)) * g11, 2)
# Interpolation
t = f(grid)
n0 = n00 * (1 - t[:, :, 0]) + t[:, :, 0] * n10
n1 = n01 * (1 - t[:, :, 0]) + t[:, :, 0] * n11
return np.sqrt(2) * ((1 - t[:, :, 1]) * n0 + t[:, :, 1] * n1)
[docs]def random_2d_perlin(
shape: Tuple,
res: Tuple[Union[int, Tensor], Union[int, Tensor]],
fade=lambda t: 6 * t**5 - 15 * t**4 + 10 * t**3,
) -> Union[np.ndarray, Tensor]:
"""Returns a random 2d perlin noise array.
Args:
shape (Tuple): Shape of the 2d map.
res (Tuple[Union[int, Tensor]]): Tuple of scales for perlin noise for height and width dimension.
fade (_type_, optional): Function used for fading the resulting 2d map.
Defaults to equation 6*t**5-15*t**4+10*t**3.
Returns:
Union[np.ndarray, Tensor]: Random 2d-array/tensor generated using perlin noise.
"""
if isinstance(res[0], int):
result = _rand_perlin_2d_np(shape, res, fade)
elif isinstance(res[0], Tensor):
result = _rand_perlin_2d(shape, res, fade)
else:
raise TypeError(f"got scales of type {type(res[0])}")
return result
[docs]def _rand_perlin_2d_np(shape, res, fade=lambda t: 6 * t**5 - 15 * t**4 + 10 * t**3):
"""Generate a random image containing Perlin noise. Numpy version."""
delta = (res[0] / shape[0], res[1] / shape[1])
d = (shape[0] // res[0], shape[1] // res[1])
grid = np.mgrid[0 : res[0] : delta[0], 0 : res[1] : delta[1]].transpose(1, 2, 0) % 1
angles = 2 * math.pi * np.random.rand(res[0] + 1, res[1] + 1)
gradients = np.stack((np.cos(angles), np.sin(angles)), axis=-1)
def tile_grads(slice1, slice2):
return np.repeat(np.repeat(gradients[slice1[0] : slice1[1], slice2[0] : slice2[1]], d[0], axis=0), d[1], axis=1)
def dot(grad, shift):
return (
np.stack((grid[: shape[0], : shape[1], 0] + shift[0], grid[: shape[0], : shape[1], 1] + shift[1]), axis=-1)
* grad[: shape[0], : shape[1]]
).sum(axis=-1)
n00 = dot(tile_grads([0, -1], [0, -1]), [0, 0])
n10 = dot(tile_grads([1, None], [0, -1]), [-1, 0])
n01 = dot(tile_grads([0, -1], [1, None]), [0, -1])
n11 = dot(tile_grads([1, None], [1, None]), [-1, -1])
t = fade(grid[: shape[0], : shape[1]])
return math.sqrt(2) * lerp_np(lerp_np(n00, n10, t[..., 0]), lerp_np(n01, n11, t[..., 0]), t[..., 1])
[docs]def _rand_perlin_2d(shape, res, fade=lambda t: 6 * t**5 - 15 * t**4 + 10 * t**3):
"""Generate a random image containing Perlin noise. PyTorch version."""
delta = (res[0] / shape[0], res[1] / shape[1])
d = (shape[0] // res[0], shape[1] // res[1])
grid = torch.stack(torch.meshgrid(torch.arange(0, res[0], delta[0]), torch.arange(0, res[1], delta[1])), dim=-1) % 1
angles = 2 * math.pi * torch.rand(res[0] + 1, res[1] + 1)
gradients = torch.stack((torch.cos(angles), torch.sin(angles)), dim=-1)
def tile_grads(slice1, slice2):
return (
gradients[slice1[0] : slice1[1], slice2[0] : slice2[1]]
.repeat_interleave(d[0], 0)
.repeat_interleave(d[1], 1)
)
def dot(grad, shift):
return (
torch.stack(
(grid[: shape[0], : shape[1], 0] + shift[0], grid[: shape[0], : shape[1], 1] + shift[1]), dim=-1
)
* grad[: shape[0], : shape[1]]
).sum(dim=-1)
n00 = dot(tile_grads([0, -1], [0, -1]), [0, 0])
n10 = dot(tile_grads([1, None], [0, -1]), [-1, 0])
n01 = dot(tile_grads([0, -1], [1, None]), [0, -1])
n11 = dot(tile_grads([1, None], [1, None]), [-1, -1])
t = fade(grid[: shape[0], : shape[1]])
return math.sqrt(2) * torch.lerp(torch.lerp(n00, n10, t[..., 0]), torch.lerp(n01, n11, t[..., 0]), t[..., 1])
[docs]def rand_perlin_2d_octaves(shape, res, octaves=1, persistence=0.5):
"""Generate Perlin noise parameterized by the octaves method. PyTorch version."""
noise = torch.zeros(shape)
frequency = 1
amplitude = 1
for _ in range(octaves):
noise += amplitude * _rand_perlin_2d(shape, (frequency * res[0], frequency * res[1]))
frequency *= 2
amplitude *= persistence
return noise