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mpm128_ggui_jelly_only.py
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mpm128_ggui_jelly_only.py
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import numpy as np
import taichi as ti
ti.init(arch=ti.gpu) # Try to run on GPU
quality = 1 # Use a larger value for higher-res simulations
n_particles = 3000 * quality ** 2
n_grid = 128 * quality
dx = 1 / n_grid
inv_dx = float(n_grid)
dt = 1e-4 / quality
p_vol = (dx * 0.5) ** 2
p_rho = 1
p_mass = p_vol * p_rho
E = 5e3 # Young's modulus
nu = 0.2 # Poisson's ratio
mu_0 = E / (2 * (1 + nu))
lambda_0 = E * nu / ((1 + nu) * (1 - 2 * nu)) # Lame parameters
x = ti.Vector.field(2, dtype=float, shape=n_particles) # position
v = ti.Vector.field(2, dtype=float, shape=n_particles) # velocity
C = ti.Matrix.field(2, 2, dtype=float, shape=n_particles) # affine velocity field
F = ti.Matrix.field(2, 2, dtype=float, shape=n_particles) # deformation gradient
material = ti.field(dtype=int, shape=n_particles) # material id
Jp = ti.field(dtype=float, shape=n_particles) # plastic deformation
grid_v = ti.Vector.field(
2, dtype=float, shape=(n_grid, n_grid)
) # grid node momentum/velocity
grid_m = ti.field(dtype=float, shape=(n_grid, n_grid)) # grid node mass
gravity = ti.Vector.field(2, dtype=float, shape=())
gravity[None] = [0, -1]
attractor_strength = ti.field(dtype=float, shape=())
attractor_pos = ti.Vector.field(2, dtype=float, shape=())
# group_size = n_particles // 3
group_size = n_particles
# water = ti.Vector.field(2, dtype=float, shape=group_size) # position
jelly = ti.Vector.field(2, dtype=float, shape=group_size) # position
# snow = ti.Vector.field(2, dtype=float, shape=group_size) # position
mouse_circle = ti.Vector.field(2, dtype=float, shape=(1,))
max_nodal_mass = ti.field(dtype=float, shape=())
@ti.kernel
def substep():
# clear grid
for i, j in grid_m:
grid_v[i, j] = [0, 0]
grid_m[i, j] = 0
# Particle state update and scatter to grid (P2G)
for p in x:
base = (x[p] * inv_dx - 0.5).cast(int)
fx = x[p] * inv_dx - base.cast(float)
# Quadratic kernels [http://mpm.graphics Eqn. 123, with x=fx, fx-1,fx-2]
w = [0.5 * (1.5 - fx) ** 2, 0.75 - (fx - 1) ** 2, 0.5 * (fx - 0.5) ** 2]
F[p] = (ti.Matrix.identity(float, 2) + dt * C[p]) @ F[
p
] # deformation gradient update
h = 1
mu, la = mu_0 * h, lambda_0 * h
U, sig, V = ti.svd(F[p])
J = 1.0
for d in ti.static(range(2)):
new_sig = sig[d, d]
Jp[p] *= sig[d, d] / new_sig
sig[d, d] = new_sig
J *= new_sig
stress = 2 * mu * (F[p] - U @ V.transpose()) @ F[
p
].transpose() + ti.Matrix.identity(float, 2) * la * J * (J - 1)
stress = (-dt * p_vol * 4 * inv_dx * inv_dx) * stress
affine = stress + p_mass * C[p]
for i, j in ti.static(ti.ndrange(3, 3)): # Loop over 3x3 grid node neighborhood
offset = ti.Vector([i, j])
dpos = (offset.cast(float) - fx) * dx
weight = w[i][0] * w[j][1]
grid_v[base + offset] += weight * (p_mass * v[p] + affine @ dpos)
grid_m[base + offset] += weight * p_mass
for i, j in grid_m:
ti.atomic_max(max_nodal_mass[None], grid_m[i, j])
# update grid
for i, j in grid_m:
if grid_m[i, j] > 0: # No need for epsilon here
grid_v[i, j] = (1 / grid_m[i, j]) * grid_v[i, j] # Momentum to velocity
grid_v[i, j] += dt * gravity[None] * 30 # gravity
dist = attractor_pos[None] - dx * ti.Vector([i, j])
grid_v[i, j] += (
dist / (0.01 + dist.norm()) * attractor_strength[None] * dt * 100
)
if i < 3 and grid_v[i, j][0] < 0:
grid_v[i, j][0] = 0 # Boundary conditions
if i > n_grid - 3 and grid_v[i, j][0] > 0:
grid_v[i, j][0] = 0
if j < 3 and grid_v[i, j][1] < 0:
grid_v[i, j][1] = 0
if j > n_grid - 3 and grid_v[i, j][1] > 0:
grid_v[i, j][1] = 0
# grid to particle (G2P)
for p in x:
base = (x[p] * inv_dx - 0.5).cast(int)
fx = x[p] * inv_dx - base.cast(float)
w = [0.5 * (1.5 - fx) ** 2, 0.75 - (fx - 1.0) ** 2, 0.5 * (fx - 0.5) ** 2]
new_v = ti.Vector.zero(float, 2)
new_C = ti.Matrix.zero(float, 2, 2)
for i, j in ti.static(ti.ndrange(3, 3)): # loop over 3x3 grid node neighborhood
dpos = ti.Vector([i, j]).cast(float) - fx
g_v = grid_v[base + ti.Vector([i, j])]
weight = w[i][0] * w[j][1]
new_v += weight * g_v
new_C += 4 * inv_dx * weight * g_v.outer_product(dpos)
v[p], C[p] = new_v, new_C
x[p] += dt * v[p] # advection
@ti.kernel
def reset():
for i in range(n_particles):
x[i] = [
ti.random() * 0.2 + 0.3 + 0.10 * (i // group_size),
ti.random() * 0.2 + 0.5 + 0.32 * (i // group_size),
]
# material[i] = i // group_size # 0: fluid, 1: jelly, 2: snow
material[i] = 1 # 0: fluid, 1: jelly, 2: snow
v[i] = [0, 0]
F[i] = ti.Matrix([[1, 0], [0, 1]])
Jp[i] = 1
C[i] = ti.Matrix.zero(float, 2, 2)
@ti.kernel
def render():
for i in range(group_size):
jelly[i] = x[i]
# water[i] = x[i]
# jelly[i] = x[i + group_size]
# snow[i] = x[i + 2 * group_size]
print(
"[Hint] Use WSAD/arrow keys to control gravity. Use left/right mouse bottons to attract/repel. Press R to reset."
)
res = (512, 512)
window = ti.ui.Window("Taichi MLS-MPM-128", res=res, vsync=True)
canvas = window.get_canvas()
radius = 0.003
reset()
gravity[None] = [0, -1]
while window.running:
if window.get_event(ti.ui.PRESS):
if window.event.key == "r":
reset()
elif window.event.key in [ti.ui.ESCAPE]:
break
# if window.event is not None:
# gravity[None] = [0, 0] # if had any event
# if window.is_pressed(ti.ui.LEFT, "a"):
# gravity[None][0] = -1
# if window.is_pressed(ti.ui.RIGHT, "d"):
# gravity[None][0] = 1
# if window.is_pressed(ti.ui.UP, "w"):
# gravity[None][1] = 1
# if window.is_pressed(ti.ui.DOWN, "s"):
# gravity[None][1] = -1
mouse = window.get_cursor_pos()
mouse_circle[0] = ti.Vector([mouse[0], mouse[1]])
canvas.circles(mouse_circle, color=(0.2, 0.4, 0.6), radius=0.05)
attractor_pos[None] = [mouse[0], mouse[1]]
attractor_strength[None] = 0
if window.is_pressed(ti.ui.LMB):
attractor_strength[None] = 1
if window.is_pressed(ti.ui.RMB):
attractor_strength[None] = -1
for s in range(int(2e-3 // dt)):
substep()
render()
canvas.set_background_color((0.067, 0.184, 0.255))
# canvas.circles(water, radius=radius, color=(0, 0.5, 0.5))
canvas.circles(jelly, radius=radius, color=(0.93, 0.33, 0.23))
# canvas.circles(snow, radius=radius, color=(1, 1, 1))
window.show()
print(max_nodal_mass[None])