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Level4.py
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Level4.py
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import taichi as ti
import numpy as np
import time
from taichi.ui.gui import rgb_to_hex
ti.init(arch=ti.gpu)
## determine whether the player succeed passing the game
intersect_ratio=0.5
n_particles_base=9000
quality = 2 # Use a larger value for higher-res simulations
n_particles, n_grid = n_particles_base * quality**2, 128 * quality
dx, inv_dx = 1 / n_grid, float(n_grid)
dt = 1e-4 / quality
p_vol,p_rho = (dx * 0.5)**2,1
p_mass = p_vol * p_rho
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=())
attractor_strength = ti.field(dtype=float, shape=())
attractor_pos = ti.Vector.field(2, dtype=float, shape=())
drag_damping = ti.field(dtype=ti.f32, shape=())
E_np = np.array([5e3,5e3,5e3]), # Young's modulus and Poisson's ratio
nu_np = np.array([0.2,0.3,0.4])
mu_0_np = (E_np / (2 * (1 + nu_np))).flatten()
lambda_0_np = (E_np * nu_np / ((1 + nu_np) * (1 - 2 * nu_np))).flatten() # Lame parameters
mu_0_0,mu_0_1,mu_0_2 = mu_0_np
lambda_0_0,lambda_0_1,lambda_0_2 = lambda_0_np
colors = [0x068587, 0xED553B, 0xEEEEF0]
#set Target Shape------------------------------------------------------------
target_polys_np_list = [
np.array([[0.2,0.4],[0.5,0.1],[0.8,0.4],[0.5,0.7]]).astype(np.float32),
]
target_bounds_material = [2]
target_polys_vec_list,target_bound_xs,target_bound_ys = [],[],[]
for i in range(len(target_polys_np_list)):
target_poly_temp = ti.Vector.field(2, dtype=float,shape=(target_polys_np_list[i].shape[0],))
target_poly_temp.from_numpy(target_polys_np_list[i])
target_polys_vec_list.append(target_poly_temp)
target_bound_xs.append(target_polys_np_list[i])
target_bound_ys.append(np.concatenate([target_polys_np_list[i][1:],target_polys_np_list[i][0].reshape(1,-1)]))
target_bound_width = 2
is_in = ti.field(dtype=ti.int32,shape=x.shape[0])
wall_polys_np_list = [
np.array([[0.1,0.9],[0.2,0.9],[0.3,0.7],[0.1,0.6]]).astype(np.float32),
]
wall_polys_vec_list,wall_bound_xs,wall_bound_ys = [],[],[]
for i in range(len(wall_polys_np_list)):
wall_poly_temp = ti.Vector.field(2, dtype=float,shape=(wall_polys_np_list[i].shape[0],))
wall_poly_temp.from_numpy(wall_polys_np_list[i])
wall_polys_vec_list.append(wall_poly_temp)
wall_bound_xs.append(wall_polys_np_list[i])
wall_bound_ys.append(np.concatenate([wall_polys_np_list[i][1:],wall_polys_np_list[i][0].reshape(1,-1)]))
wall_bound_width = 2
@ti.kernel
def substep():
for i, j in grid_m:
grid_v[i, j] = [0, 0]
grid_m[i, j] = 0
for p in x: # Particle state update and scatter to grid (P2G)
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]
# deformation gradient update
F[p] = (ti.Matrix.identity(float, 2) + dt * C[p]) @ F[p]
# Hardening coefficient: snow gets harder when compressed
h = max(0.1, min(5, ti.exp(10 * (1.0 - Jp[p]))))
if material[p] == 1: # jelly, make it softer
h = 0.3
mu_0,lambda_0 = mu_0_0,lambda_0_0
if material[p] == 1:
mu_0,lambda_0 = mu_0_1,lambda_0_1
elif material[p] == 2:
mu_0,lambda_0 = mu_0_2,lambda_0_2
mu, la = mu_0 * h, lambda_0 * h
if material[p] == 0: # liquid
mu = 0.0
U, sig, V = ti.svd(F[p])
J = 1.0
for d in ti.static(range(2)):
new_sig = sig[d, d]
if material[p] == 2: # Snow
new_sig = min(max(sig[d, d], 1 - 2.5e-2),
1 + 4.5e-3) # Plasticity
Jp[p] *= sig[d, d] / new_sig
sig[d, d] = new_sig
J *= new_sig
if material[p] == 0:
# Reset deformation gradient to avoid numerical instability
F[p] = ti.Matrix.identity(float, 2) * ti.sqrt(J)
elif material[p] == 2:
# Reconstruct elastic deformation gradient after plasticity
F[p] = U @ sig @ V.transpose()
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:
if grid_m[i, j] > 0: # No need for epsilon here
# Momentum to velocity
grid_v[i, j] = (1 / grid_m[i, j]) * grid_v[i, j]
# 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
if is_pt_in_poly(pt=(i/n_grid,j/n_grid),poly=wall_polys_vec_list[0]) == 1:
grid_v[i, j][0] = 0
grid_v[i, j][1] = 0
for p in x: # grid to particle (G2P)
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
v[p] *= ti.exp(-dt * drag_damping[None])
x[p] += dt * v[p] # advection
@ti.kernel
def reset():
group_size = n_particles // 3
for i in range(n_particles):
## initial positions-------------------------------------------------
group_n=i // group_size
if group_n==0:
x[i] = [
ti.random() * 0.98 + 0.01,
ti.random() * 0.05+0.01
]
elif group_n==1:
x[i] = [
ti.random() * 0.98+0.01,
ti.random() * 0.05+0.94
]
elif group_n==2:
x[i] = [
ti.random() * 0.05,
ti.random() * 0.9+0.05
]
else:
x[i] = [
ti.random() * 0.2 + 0.3 + 0.10 * (i // group_size),
ti.random() * 0.2 + 0.05 + 0.32 * (i // group_size)
]
## initial positions-------------------------------------------------
# material[i] = i // group_size # 0: fluid 1: jelly 2: snow
material[i] = 2
v[i] = [0, 0]
F[i] = ti.Matrix([[1, 0], [0, 1]])
Jp[i] = 1
C[i] = ti.Matrix.zero(float, 2, 2)
@ti.func
def is_pt_in_poly(pt,poly):
nvert = poly.shape[0]
j = nvert - 1
res = -1
for i in range(poly.shape[0]):
if (poly[j][1] - poly[i][0]) == 0:
j = i
continue
xx = (poly[j][0] - poly[i][0]) * \
(pt[1] - poly[i][1]) / (poly[j][1] - poly[i][1]) + \
poly[i][0]
if ((poly[i][1] > pt[1]) != (poly[j][1] > pt[1])) and (pt[0] < xx):
res = - res
j = i
return res
@ti.kernel
def update_isin():
for pt in x:
in_target_bound_0 = is_pt_in_poly(x[pt],target_polys_vec_list[0])
# in_target_bound_1 = is_pt_in_poly(x[pt],target_polys_vec_list[1])
is_in[pt] = 0
if in_target_bound_0 == 1 and target_bounds_material[0] == material[pt]:
is_in[pt] = 1
# elif in_target_bound_1 == 1 and target_bounds_material[1] == material[pt]:
# is_in[pt] = 1
def level4_main():
gui = ti.GUI("Level1", res=720, background_color=0x112F41)
# Show the score and time -----------------------------------------------------
score = gui.label('Score')
time_record = gui.label('Time(s)')
attract_scale = gui.slider('attaction_scale', 0, 100, step=5)
damping_scale = gui.slider('damping scale', 0, 100, step=5)
score.value=0
time_record.value=0
start_time=time.time()
X_border,Y_border=0.605,0.835
reset()
win_flag = False
frame=0
while gui.running:
## Target Shape
for taregt_bound_x,taregt_bound_y,material_id in zip(target_bound_xs,target_bound_ys,target_bounds_material):
gui.lines(begin=taregt_bound_x, end=taregt_bound_y, radius=target_bound_width, color=colors[material_id])
for wall_bound_x,wall_bound_y in zip(wall_bound_xs,wall_bound_ys):
gui.lines(begin=wall_bound_x, end=wall_bound_y, radius=wall_bound_width, color=0xFFFFFF)
if gui.get_event(ti.GUI.PRESS):
if gui.event.key == 'r':
reset()
start_time=time.time()
score.value=0
frame=0
elif gui.event.key in [ti.GUI.ESCAPE, ti.GUI.EXIT]:
break
mouse = gui.get_cursor_pos()
gui.circle((mouse[0], mouse[1]), color=0x336699, radius=15)
attractor_pos[None] = [mouse[0], mouse[1]]
attractor_strength[None]=0
if gui.is_pressed(ti.GUI.LMB):
if mouse[0]<X_border or mouse[1]<Y_border:
attractor_strength[None] = (14/(np.e-1)*np.exp(attract_scale.value/100) + 2-14/(np.e-1))
if gui.is_pressed(ti.GUI.RMB):
if mouse[0]<X_border or mouse[1]<Y_border:
attractor_strength[None] = -(14/(np.e-1)*np.exp(attract_scale.value/100) + 2-14/(np.e-1))
drag_damping[None] = damping_scale.value
for s in range(int(2e-3 // dt)):
substep()
gui.circles(x.to_numpy(),
radius=1.5,
palette=colors,
palette_indices=material)
# update time--------------------------------------------------------------
end_time = time.time()
current_time = end_time-start_time
time_record.value = current_time
# update time--------------------------------------------------------------
update_isin()
score.value = is_in.to_numpy().sum() / is_in.to_numpy().shape[0] / intersect_ratio
if score.value >= 1.0:
win_flag = True
gui.text("Congratulations!",pos=np.array([0.14,0.5]),font_size=60,color=rgb_to_hex([100,100,100]))
gui.text("You pass the game!",pos=np.array([0.18,0.35]),font_size=45,color=rgb_to_hex([100,100,100]))
frame+=1
gui.show()
return True