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simulate_wave.py
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simulate_wave.py
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from distutils.log import WARN
import numpy as np
import torch
import torch.nn.functional as F
import math
class WaveTMA():
def __init__(self,
center,
normal,
vec_x,
plane_len:float,
ampl_const:float,
device='cpu'
):
self.device = device
self.center = center
self.normal = normal.to(device)
self.init_vec_xy(normal, vec_x)
self.plane_len = plane_len
self.u_resolution = 4096
self.u_size = 1000.0
self.u_wind = torch.tensor([-5.0, 5.0])
self.G = 9.81
self.KM = 370.0
self.CM = 0.23
self.Omega = 0.84
self.gamma = 1.7
self.sigma = 0.08 * (1.0 + 4.0 * math.pow(self.Omega, -3.0))
self.alphap = 0.006 * np.sqrt(self.Omega)
self.freq = 5.0 # how many timestamps per cycle
self.ampl_const = ampl_const # amplitude for the wave
self.choppiness = 1.0
self.init_K_k()
self.init_spectrum()
def init_vec_xy(self, normal, vec_x):
vec_y = torch.cross(normal, vec_x)
vec_y = vec_y / torch.norm(vec_y)
vec_x = torch.cross(vec_y, normal)
vec_x = vec_x / torch.norm(vec_x)
self.vec_x = vec_x.to(self.device)
self.vec_y = vec_y.to(self.device)
def omega_func(self, k):
return torch.sqrt(self.G*k*(1.0 + (k/self.KM)**2))
def init_K_k(self):
n, m = np.meshgrid(np.linspace(0.5, self.u_resolution+0.5, self.u_resolution), np.linspace(0.5, self.u_resolution+0.5, self.u_resolution))
n = torch.FloatTensor(n).to(self.device)
m = torch.FloatTensor(m).to(self.device)
mask_n = (n < self.u_resolution * 0.5)
n = mask_n * n + (~mask_n) * (self.u_resolution - n)
mask_m = (m < self.u_resolution * 0.5)
m = mask_m * m + (~mask_m) * (self.u_resolution - m)
K = torch.stack((n, m), dim=2) * 2.0 * np.pi / self.u_size
k = torch.norm(K, dim=2)
self.K = K
self.k = k
def init_spectrum(self):
K = self.K.cpu()
k = self.k.cpu()
l_wind = torch.norm(self.u_wind).item()
kp = self.G * np.square(self.Omega / l_wind)
c = self.omega_func(k) / k
cp = self.omega_func(torch.FloatTensor([kp])) / kp
Lpm = torch.exp(-1.25 * torch.square(kp / k))
Gamma = torch.exp(-torch.square(torch.sqrt(k / kp) - 1.0) / 2.0 * np.square(self.sigma))
Jp = self.gamma ** Gamma
Fp = Lpm * Jp * torch.exp(-self.Omega / np.sqrt(10.0) * (torch.sqrt(k / kp) - 1.0))
Bl = 0.5 * self.alphap * cp / c * Fp
z0 = 0.000037 * np.square(l_wind) / self.G * np.power(l_wind / cp, 0.9)
uStar = 0.41 * l_wind / np.log(10.0 / z0)
alpham = 0.01 * ((uStar < self.CM)*(1.0 + np.log(uStar / self.CM)) + (~(uStar < self.CM)) * (1.0 + 3.0 * np.log(uStar / self.CM)))
Fm = torch.exp(-0.25 * torch.square(k / self.KM - 1.0))
Bh = 0.5 * alpham * self.CM / c * Fm * Lpm
a0 = np.log(2.0) / 4.0
am = 0.13 * uStar / self.CM
Delta = np.tanh(a0 + 4.0 * np.power(c / cp, 2.5) + am * np.power(self.CM / c, 2.5))
u_wind_norm = self.u_wind / l_wind
K_norm = K / torch.unsqueeze(torch.norm(K, dim=2), dim=2)
cosPhi = K_norm@u_wind_norm
S = (1.0 / (2.0 * np.pi)) * (k**(-4.0)) * (Bl + Bh) * (1.0 + Delta * (2.0 * cosPhi * cosPhi - 1.0))
dk = 2.0 * np.pi / self.u_size
spec0 = torch.sqrt(S / 2.0) * dk
self.spec0 = spec0
h0 = torch.randn(self.u_resolution, self.u_resolution) + \
1.j * torch.randn(self.u_resolution, self.u_resolution)
self.h0 = (h0*spec0).to(self.device)
self.h0_star = torch.flip(self.h0, dims=[0, 1])
self.phase0 = torch.randn(self.u_resolution, self.u_resolution, device=self.device)
def compute_phase(self, t):
deltaPhase = self.omega_func(self.k) * t/self.freq
phase = torch.remainder(self.phase0 + deltaPhase, 2.0*np.pi)
return phase
def get_wave_points(self, t):
X, Y = np.meshgrid(np.linspace(-1, 1, self.u_resolution), np.linspace(-1, 1, self.u_resolution))
X = torch.FloatTensor(X).to(self.device)
Y = torch.FloatTensor(Y).to(self.device)
phase = self.compute_phase(t)
phase_complex = torch.cos(phase) + 1.j * torch.sin(phase)
phase_complex_star = torch.cos(phase) - 1.j * torch.sin(phase)
ht = self.h0 * phase_complex + self.h0_star * phase_complex_star # this seems correct as ifft is not real number
waveVector_normalized = self.K / self.k.unsqueeze(2)
wave_x = waveVector_normalized[:, :, 0]
wave_y = waveVector_normalized[:, :, 1]
dZ = torch.real(torch.fft.ifft2(ht)) * self.ampl_const
dX = torch.real(torch.fft.ifft2(ht*(1.j) * wave_x)) * self.ampl_const * self.choppiness
dY = torch.real(torch.fft.ifft2(ht*(1.j) * wave_y)) * self.ampl_const * self.choppiness
dZ_x = torch.real(torch.fft.ifft2(ht*(1.j) * wave_x)) * self.ampl_const * self.choppiness
dX_x = torch.real(torch.fft.ifft2(ht*(-1) * wave_x * wave_x)) * self.ampl_const * self.choppiness
# dY_x = torch.real(torch.fft.ifft2(ht*(-1) * wave_y * wave_x)) * self.ampl_const * self.choppiness
dZ_y = torch.real(torch.fft.ifft2(ht*(1.j) * wave_y)) * self.ampl_const * self.choppiness
# dX_y = torch.real(torch.fft.ifft2(ht*(-1) * wave_x * wave_y)) * self.ampl_const * self.choppiness
dY_y = torch.real(torch.fft.ifft2(ht*(-1) * wave_y * wave_y)) * self.ampl_const * self.choppiness
# grad_x = torch.stack([dX_x, dY_x, dZ_x], dim=-1)
# grad_y = torch.stack([dX_y, dY_y, dZ_y], dim=-1)
# normal = torch.cross(grad_x, grad_y, dim=-1)
# basis = torch.stack([self.vec_x, self.vec_y, self.normal], dim=0) # (3, 3)
# normal = torch.matmul(normal, basis)
# normal = F.normalize(normal, dim=-1)
sx = dZ_x / (1+dX_x)
sy = dZ_y / (1+dY_y)
ones = torch.ones_like(sx)
normal = torch.stack([-sx, -sy, ones], dim=-1)
basis = torch.stack([self.vec_x, self.vec_y, self.normal], dim=0) # (3, 3)
normal = torch.matmul(normal, basis)
normal = F.normalize(normal, dim=-1)
# grad_x = torch.ones_like(dZ_x).unsqueeze(-1)*self.vec_x[None] + dZ_x.unsqueeze(-1)*self.normal[None]
# grad_y = torch.ones_like(dZ_y).unsqueeze(-1)*self.vec_y[None] + dZ_y.unsqueeze(-1)*self.normal[None]
# normal = torch.cross(grad_x, grad_y, dim=-1)
# normal = F.normalize(normal, dim=-1)
return X+dX, Y+dY, dZ, normal
def sample_normals(self, t, points):
'''
Inputs
points: (n, 3)
'''
device = points.device
vec_xy = torch.stack([self.vec_x, self.vec_y], dim=-1).to(device) #(3, 2)
center = self.center.to(device)
plane_coord = torch.matmul(points - center.unsqueeze(0), vec_xy) #(n, 2)
grid = plane_coord / (self.plane_len/2)
x, y, z, normal = self.get_wave_points(t)
normal = normal.permute(2, 0, 1)[None].to(device)
grid = grid[None, None]
normal_samples = F.grid_sample(
normal,
grid,
mode='bilinear',
padding_mode='reflection',
align_corners=True
) #(1, 3, 1, n)
normal_samples = normal_samples.permute(0, 2, 3, 1)[0, 0] #(n, 3)
normal_samples = F.normalize(normal_samples, dim=-1)
return normal_samples
class WaveSimple():
def __init__(self,
center,
normal,
vec_x,
):
self.center = center
self.normal = normal
self.init_vec_xy(normal, vec_x)
# f(x, y, t) = k*sin(omega_x*t + phi_x*x)*sin(omega_y*t + phi_y*y)
self.k = 1e-3
self.omega_x = 1e-1
self.omega_y = 0 #5e-2
self.phi_x = 1e1
self.phi_y = 1e1
def init_vec_xy(self, normal, vec_x):
vec_y = torch.cross(normal, vec_x)
vec_y = vec_y / torch.norm(vec_y)
vec_x = torch.cross(vec_y, normal)
vec_x = vec_x / torch.norm(vec_x)
self.vec_x = vec_x
self.vec_y = vec_y
def get_wave_points(self, t):
res = 512
x, y = np.meshgrid(np.linspace(-1, 1, res), np.linspace(-1, 1, res))
z = self.k * np.sin(self.omega_x*t + self.phi_x*x) * np.sin(self.omega_y*t + self.phi_y*y)
return x, y, z
def test():
wave = WaveTMA(
center=torch.FloatTensor([0, 0, 0]),
normal=torch.FloatTensor([0, 0, 1]),
vec_x=torch.FloatTensor([1, 0, 0]),
plane_len=5,
device='cuda'
)
phase = wave.compute_phase(5)
x, y, z, n = wave.get_wave_points(5)
print('normal shape')
print(n.size())
print(n[:,:,-1])
print(torch.norm(n, dim=-1))
points = torch.randn(100, 3).to('cuda')
normal_samples = wave.sample_normals(5, points)
print('Normal samples')
print('size:', normal_samples.size())
print('device:', normal_samples.device)
def test_vis():
import matplotlib.pyplot as plt
from matplotlib import cm
from matplotlib.ticker import LinearLocator
from matplotlib.animation import FuncAnimation, PillowWriter
wave = WaveTMA(
center=torch.FloatTensor([0, 0, 0]),
normal=torch.FloatTensor([0, 0, 1]),
vec_x=torch.FloatTensor([1, 0, 0]),
plane_len=5
)
# wave = WaveSimple(
# center=torch.FloatTensor([0, 0, 0]),
# normal=torch.FloatTensor([0, 0, 1]),
# vec_x=torch.FloatTensor([1, 0, 0]),
# )
# fig, ax = plt.subplots(subplot_kw={"projection": "3d"}, figsize=(20, 20))
# def animate_surface(t):
# x, y, z, normal = wave.get_wave_points(t)
# ax.clear()
# surf = ax.plot_surface(x, y, z,
# rstride=1, cstride=1, linewidth=0, cmap=cm.coolwarm, antialiased=False)
# ax.set_zlim(-1.01, 1.01)
# ax.zaxis.set_major_locator(LinearLocator(10))
# ax.zaxis.set_major_formatter('{x:.02f}')
# print(t)
# return surf
# ani = FuncAnimation(fig, animate_surface, interval=1, blit=False, repeat=True, frames=100)
# ani.save("output/3D_wave_surface.gif", dpi=300, writer=PillowWriter(fps=10))
fig, ax = plt.subplots(figsize=(20, 20))
x, y, z, normal = wave.get_wave_points(0)
im = plt.imshow((normal + 1)/2, animated=True)
def animate_normal(t):
x, y, z, normal = wave.get_wave_points(t)
im.set_array((normal + 1)/2)
print(t)
return im
ani = FuncAnimation(fig, animate_normal, interval=1, blit=False, repeat=True, frames=100)
ani.save("output/1028_waves/wave_gif/3D_wave_normal.gif", dpi=300, writer=PillowWriter(fps=10))
if __name__ == '__main__':
test()