import torch
import math

def rand_perlin_2d(shape, res, fade = lambda t: 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 = 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)
    
    tile_grads = lambda slice1, slice2: gradients[slice1[0]:slice1[1], slice2[0]:slice2[1]].repeat_interleave(d[0], 0).repeat_interleave(d[1], 1)
    dot = lambda grad, shift: (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])

def rand_perlin_2d_octaves(shape, res, octaves=1, persistence=0.5):
    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

def perlin_2d(shape, res, seed, fade=lambda t: 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 = torch.stack(torch.meshgrid(torch.arange(0, res[0], delta[0]), torch.arange(0, res[1], delta[1])), dim=-1) % 1
    base_seed = int(seed)
    frac_seed = seed - base_seed
    
    torch.manual_seed(base_seed)
    angles_base = 2 * math.pi * torch.rand(res[0] + 1, res[1] + 1)
    gradients_base = torch.stack((torch.cos(angles_base), torch.sin(angles_base)), dim=-1)
    
    torch.manual_seed(base_seed + 1)
    angles_next = 2 * math.pi * torch.rand(res[0] + 1, res[1] + 1)
    gradients_next = torch.stack((torch.cos(angles_next), torch.sin(angles_next)), dim=-1)
    
    gradients = (1 - frac_seed) * gradients_base + frac_seed * gradients_next
    
    tile_grads = lambda slice1, slice2: gradients[slice1[0]:slice1[1], slice2[0]:slice2[1]].repeat_interleave(d[0], 0).repeat_interleave(d[1], 1)
    dot = lambda grad, shift: (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])


def perlin_2d_octaves(shape, res, seed, octaves=1, persistence=0.5, fade=lambda t: 6*t**5 - 15*t**4 + 10*t**3):
    noise = torch.zeros(shape)
    frequency = 1
    amplitude = 1
    for i in range(octaves):
        noise += amplitude * perlin_2d(shape, (frequency * res[0], frequency * res[1]), seed + i, fade)
        frequency *= 2
        amplitude *= persistence
    return noise