def apply_impulse(vf: ti.types.ndarray(field_dim=2),
dyef: ti.types.ndarray(field_dim=2),
imp_data: ti.types.ndarray(field_dim=1)):
g_dir = -ti.Vector([0, 9.8]) * 300
for i, j in vf:
omx, omy = imp_data[2], imp_data[3]
mdir = ti.Vector([imp_data[0], imp_data[1]])
dx, dy = (i + 0.5 - omx), (j + 0.5 - omy)
d2 = dx * dx + dy * dy
# dv = F * dt
factor = ti.exp(-d2 / force_radius)
dc = dyef[i, j]
a = dc.norm()
momentum = (mdir * f_strength * factor + g_dir * a / (1 + a)) * dt
v = vf[i, j]
vf[i, j] = v + momentum
# add dye
if mdir.norm() > 0.5:
dc += ti.exp(-d2 * (4 / (res / 15)**2)) * ti.Vector(
[imp_data[4], imp_data[5], imp_data[6]])
dyef[i, j] = dc
def mainImage(iMouse: ti.Vector, iTime: ti.f32, i: ti.i32,
j: ti.i32) -> ti.Vector:
fragCoord = ti.Vector([i, j])
p = -1.0 + 2.0 * fragCoord / iResolution
m = -1.0 + 2.0 * iMouse # iMouse 已经归一化
a1 = ti.atan2(p[1] - m[1], p[0] - m[0])
a2 = ti.atan2(p[1] + m[1], p[0] + m[0])
r1 = ti.sqrt((p - m).dot(p - m))
r2 = ti.sqrt((p + m).dot(p + m))
uv = ti.Vector(
[0.2 * iTime + (r1 - r2) * 0.25,
ti.asin(ti.sin(a1 - a2)) / 3.1416])
w = ti.exp(-15.0 * r1 * r1) + ti.exp(-15.0 * r2 * r2)
w += 0.25 * smoothstep(0.93, 1.0, ti.sin(128.0 * uv[0]))
w += 0.25 * smoothstep(0.93, 1.0, ti.sin(128.0 * uv[1]))
# 可以使用纹理
# vec3 col = texture( iChannel0, 0.125*uv ).zyx;
col = ti.Vector([0.0, 0.0, 0.0])
fragColor = col + w
return fragColor
def apply_mouse_input_and_render(self, vf: ti.template(),
dyef: ti.template(),
imp_data: ti.ext_arr(),
dt: ti.template()):
for i, j in vf:
mdir = ti.Vector([imp_data[0], imp_data[1]])
omx, omy = imp_data[2], imp_data[3]
# move to cell center
dx, dy = (i + 0.5 - omx), (j + 0.5 - omy)
d2 = dx * dx + dy * dy
# ref: https://developer.download.nvidia.cn/books/HTML/gpugems/gpugems_ch38.html
# apply the force
factor = ti.exp(-d2 * self.cfg.inv_force_radius)
momentum = mdir * self.cfg.f_strength * dt * factor
vf[i, j] += momentum
# add dye
dc = dyef[i, j]
# TODO what the hell is this?
if mdir.norm() > 0.5:
dc += ti.exp(-d2 * self.cfg.inv_dye_denom) * ti.Vector(
[imp_data[4], imp_data[5], imp_data[6]])
dc *= self.cfg.dye_decay
dyef[i, j] = dc
def initialize_vortices():
for i, j in ux:
s = 0.16
x = xCoord(i) * 2.0
y = yCoord(j) * 2.0
x0 = x - s
x1 = x + s
ux_ = 0.0
uy_ = 0.0
# add vortex
rr1 = sq(x0) + sq(y)
ux_ += -y * ti.exp(-rr1 / (2.0 * sq(0.12))) * 25.0
uy_ += x0 * ti.exp(-rr1 / (2.0 * sq(0.12))) * 25.0
# add vortex
rr2 = sq(x1) + sq(y)
ux_ += -y * ti.exp(-rr2 / (2.0 * sq(0.12))) * 25.0
uy_ += x1 * ti.exp(-rr2 / (2.0 * sq(0.12))) * 25.0
ux[i, j] = ux_
uy[i, j] = uy_
for i, j in omega:
i_p = mod(i + 1, Nx)
i_n = mod(i - 1 + Nx, Nx)
j_p = mod(j + 1, Ny)
j_n = mod(j - 1 + Ny, Ny)
omega[i, j] = \
(uy[i_p, j] - uy[i_n, j]) / (2.0 * dx) \
- (ux[i, j_p] - ux[i, j_n]) / (2.0 * dx)
def apply_force(velocities:ti.template(), colors:ti.template(), collisons:ti.template(), imp_data: ti.ext_arr()): f_strength = 10000.0 force_radius = n / 3.0 for i, j in velocities: omx, omy = imp_data[2], imp_data[3] mdir = ti.Vector([imp_data[0], imp_data[1]]) dx, dy = (i + 0.5 - omx), (j + 0.5 - omy) d2 = dx * dx + dy * dy # dv = F * dt factor = ti.exp(-d2 / force_radius) momentum = mdir * f_strength * dt * factor v = velocities[i, j] velocities[i, j] = v + momentum # add dye color = ti.Vector([1.0, 1.0, 1.0]) dc = colors[i, j] if mdir.norm() > 0.5: # dc += ti.exp(-d2 * (4 / (n / 15)**2)) * ti.Vector([imp_data[4], imp_data[5], imp_data[6]]) dc += ti.exp(-d2 * (4 / (n / 15)**2)) * color dc *= dye_decay colors[i, j] = dc if mdir.norm() > 0.5 and d2 < 50: collisons[i, j] = 1
def substep():
# 计算力和新的速度
# Compute force and new velocity
n = num_particles[None]
for i in range(n-1, -1, -1):
v[i] *= ti.exp(-dt * damping[None]) # damping
total_force = ti.Vector(gravity) * particle_mass # 初始受力只有重力
for j in range(n):
# 对于互相连接的粒子用胡克定律计算力
if rest_length[i, j] != 0:
x_ij = x[i] - x[j]
total_force += -spring_stiffness[None] * (
x_ij.norm() -
rest_length[i, j]) * x_ij.normalized() # 加上弹簧之间的力
v[i] += dt * total_force / particle_mass # 牛顿第二定律
# 碰撞地面
# Collide with ground
for i in range(n):
if x[i].y < bottom_y:
x[i].y = bottom_y
v[i].y = 0
# 计算新的位置
# Compute new position
for i in range(num_particles[None]):
x[i] += v[i] * dt
def init_level_set(self):
sdf = ti.static(self.sign_dis.curr)
inv_r = ti.static(4.0 / (self.resolution / 20.0)**2)
for i, j in sdf:
dx, dy = self.resolution / 2 - i, j
d2 = dx * dx + dy * dy
sdf[i, 0] = ti.exp(-d2 * inv_r) * 10.0
def collide(self, f, grid_pos, v_out, dt):
dist = self.sdf(f, grid_pos)
influence = min(ti.exp(-dist * self.softness[None]), 1)
if (self.softness[None] > 0 and influence > 0.1) or dist <= 0:
D = self.normal(f, grid_pos)
collider_v_at_grid = self.collider_v(f, grid_pos, dt)
input_v = v_out - collider_v_at_grid
normal_component = input_v.dot(D)
grid_v_t = input_v - min(normal_component, 0) * D
grid_v_t_norm = length(grid_v_t)
grid_v_t_friction = grid_v_t / grid_v_t_norm * max(
0, grid_v_t_norm + normal_component * self.friction[None])
flag = ti.cast(
normal_component < 0
and ti.sqrt(grid_v_t.dot(grid_v_t)) > 1e-30, self.dtype)
grid_v_t = grid_v_t_friction * flag + grid_v_t * (1 - flag)
v_out = collider_v_at_grid + input_v * (
1 - influence) + grid_v_t * influence
#print(self.position[f], f)
#print(grid_pos, collider_v, v_out, dist, self.friction, D)
#if v_out[1] > 1000:
#print(input_v, collider_v_at_grid, normal_component, D)
return v_out
def affine(self, i):
self.system.F[i] = (ti.Matrix.identity(ti.f32, DIM) + self.system.dt *
self.system.C[i]) @ self.system.F[i]
h = 0.3 if self.system.type[i] == 1 else ti.exp(
10 * (1.0 - self.system.Jp[i]))
la = self.lambda_0 * h
U, sig, V = ti.svd(self.system.F[i])
J = 1.0
for d in ti.static(range(DIM)):
new_sig = min(max(sig[d, d], 1 - 2.5e-2), 1 +
4.5e-3) if self.system.type[i] == 2 else sig[d, d]
self.system.Jp[i] *= sig[d, d] / new_sig
sig[d, d] = new_sig
J *= new_sig
if self.system.type[
i] == 0: # Reset deformation gradient to avoid numerical instability
self.system.F[i] = ti.Matrix.identity(ti.f32, DIM)
self.system.F[i][0, 0] = J
elif self.system.type[i] == 2:
self.system.F[i] = U @ sig @ V.transpose(
) # Reconstruct elastic deformation gradient after plasticity
stress = ti.Matrix.identity(ti.f32, DIM) * la * J * (J - 1)
if self.system.type[i] != 0:
stress += 2 * self.mu_0 * h * (
self.system.F[i] -
U @ V.transpose()) @ self.system.F[i].transpose()
stress = (-self.system.dt * self.vol * 4 * self.inv_dx *
self.inv_dx) * stress
return stress + self.mass * self.system.C[i]
def substep(cur_x: ti.f32, cur_y: ti.f32, mag: ti.f32):
# Compute force and new velocity
n = num_particles[None]
for i in range(n):
v[i] *= ti.exp(-dt * damping[None]) # damping
i2cur = [cur_x, cur_y] - x[i]
total_force = i2cur.normalized() * mag * particle_mass
for j in range(n):
if rest_length[i, j] != 0:
x_ij = x[i] - x[j]
total_force += -spring_stiffness[None] * (
x_ij.norm() - rest_length[i, j]) * x_ij.normalized()
v[i] += dt * total_force / particle_mass
# Collide with boundary
for i in range(n):
if x[i].y < bottom:
x[i].y = bottom
v[i].y = -v[i].y
if x[i].y > top:
x[i].y = top
v[i].y = -v[i].y
if x[i].x < bottom:
x[i].x = bottom
v[i].x = -v[i].x
if x[i].x > top:
x[i].x = top
v[i].x = -v[i].x
# Compute new position
for i in range(num_particles[None]):
x[i] += v[i] * dt
def P2G(): # Particle to grid (P2G)
for p in x:
base = (x[p] * inv_dx - 0.5).cast(int)
fx = x[p] * inv_dx - base.cast(float)
# Bspline
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 = max(0.1, min(5, ti.exp(10 * (1.0 - Jp[p])))) # Hardening coefficient
mu, la = mu_0 * h, lambda_0 * h
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
F[p] = ti.Matrix.identity(float, 2) * ti.sqrt(J) # Reset deformation gradient
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
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
def implicit():
n = num_particles[None]
for i, j in ti.ndrange(n, n):
M[i, j].fill(0)
K[i, j].fill(0)
A[i, j].fill(0)
b[i].fill(0)
for i in range(n):
M[i, i][0, 0] = particle_mass
M[i, i][1, 1] = particle_mass
v[i] *= ti.exp(-dt * damping[None]) # damping
for i, j in ti.ndrange(n, n):
if rest_length[i, j] != 0:
x_ij = x[j] - x[i]
I = ti.Matrix([[1, 0], [0, 1]])
l = x_ij.norm()
t = spring_stiffness[None] * (-I + rest_length[i, j] / l *
(I - (x_ij @ x_ij.transpose() /
(l * l))))
K[i, i] += t
K[i, j] += -t
for i, j in ti.ndrange(n, n):
A[i, j] = (M[i, j] - dt * dt * K[i, j])
for i in range(n):
b[i] = M[i, i] @ v[i] + dt * ti.Vector(gravity) * particle_mass
for j in range(n):
if rest_length[i, j] != 0:
x_ij = x[i] - x[j]
b[i] += -dt * spring_stiffness[None] * (
x_ij.norm() - rest_length[i, j]) * x_ij.normalized()
for i in range(n):
solve_v[i] = v[i]
def addRandomForce(dt: ti.f32):
pos_p = ti.Vector([ti.random(), ti.random()])
F = ti.Vector([ti.random(), ti.random()]) * ti.random() * 1000.0
# if ti.random() > 0.01:
# F.fill(0)
for I in ti.grouped(u_old):
u_old[I] += F * dt * ti.exp(-(I - pos_p).norm() / 0.1)
def substep():
# Compute force and new velocity
n = num_particles[None]
for i in range(n):
v[i] *= ti.exp(-dt * damping[None]) # damping
total_force = ti.Vector(gravity) * particle_mass
for j in range(n):
if rest_length[i, j] != 0:
x_ij = x[i] - x[j]
total_force += -spring_stiffness[None] * (x_ij.norm() - rest_length[i, j]) * x_ij.normalized()
v[i] += dt * total_force / particle_mass
# Collide with ground
for i in range(n):
if x[i].y < bottom_y:
x[i].y = bottom_y
v[i].y = 0
# Compute new position
for i in range(num_particles[None]):
x[i] += v[i] * dt
df_ij(0,0)
f_ij(0,0)
def electric_field(t: ti.f64):
t_eff = t - t_h
a = parameters[0] / (ti.sqrt(2 * np.pi) * parameters[1])
w = ti.sqr(parameters[1])
e = a * ti.exp(-ti.sqr(t_eff) /
(2 * w)) * (ti.sin(parameters[2] * t_eff) +
parameters[3] * ti.sin(parameters[4] * t_eff))
e_field[None] = e
grad[0] = e / parameters[0]
grad[1] = -e / parameters[1] + e * ti.sqr(t_eff) / (parameters[1]**3)
grad[2] = a * ti.exp(-ti.sqr(t_eff) /
(2 * w)) * ti.cos(parameters[2] * t_eff) * t_eff
grad[3] = a * ti.exp(-ti.sqr(t_eff) /
(2 * w)) * ti.sin(parameters[4] * t_eff)
grad[4] = a * ti.exp(-ti.sqr(t_eff) / (2 * w)) * parameters[3] * ti.cos(
parameters[4] * t_eff) * t_eff
def paint(t:ti.f32) :
for i, j in pixels:
p = ti.Vector([2*i-Width, 2*j-Height])/min(Width,Height)
#background-color
bcol = ti.Vector([1.0,0.8,0.7-0.07*p[1]]) * (1.0-0.25*p.norm())
#animate
tt = mod(t, 1.5)/1.5
ss = pow(tt, 0.2)*0.5+0.5
ss = 1.0 + ss*0.5*ti.sin(tt*6.2831*3.0+p[1]*0.5)*ti.exp(-4.0*tt)
p *= ti.Vector([0.5, 1.5]) + ss*ti.Vector([0.5, -0.5])
#shape
p[1] -= 0.25
a = ti.atan2(p[0], p[1]) / 3.141593
r = p.norm()
h = abs(a)
d = (13.0*h - 22.0*h*h + 10.0*h*h*h)/(6.0-5.0*h)
#color
s = 0.75 + 0.75*p[0]
s *= 1.0 - 0.4*r
s = 0.3 + 0.7*s
s *= 0.5 + 0.5*pow(1.0-clamp(r/d, 0.0, 1.0), 1.0)
hcol = ti.Vector([1.0, 0.5*r, 0.3])*s
pixels[i,j] = mix(bcol , hcol ,smoothstep(-0.01, 0.01, d-r))
def substep():
for i in ti.grouped(x):
v[i] += gravity * dt
for i in ti.grouped(x):
force = ti.Vector([0.0, 0.0, 0.0])
for spring_offset in ti.static(spring_offsets):
j = i + spring_offset
if 0 <= j[0] < n and 0 <= j[1] < n:
x_ij = x[i] - x[j]
v_ij = v[i] - v[j]
d = x_ij.normalized()
current_dist = x_ij.norm()
original_dist = quad_size * float(i - j).norm() # pylint: disable=no-member
# Spring force
force += -spring_Y * d * (current_dist / original_dist - 1)
# Dashpot damping
force += -v_ij.dot(d) * d * dashpot_damping * quad_size
v[i] += force * dt
for i in ti.grouped(x):
v[i] *= ti.exp(-drag_damping * dt)
offset_to_center = x[i] - ball_center[0]
if offset_to_center.norm() <= ball_radius:
# Velocity projection
normal = offset_to_center.normalized()
v[i] -= min(v[i].dot(normal), 0) * normal
x[i] += dt * v[i]
def substep():
for i, j in ti.ndrange(n_grid, n_grid):
grid_v[i, j] = [0, 0]
grid_m[i, j] = 0
for p in range(n_particles): # 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 * ti.sqr(1.5 - fx), 0.75 - ti.sqr(fx - 1), 0.5 * ti.sqr(fx - 0.5)]
F[p] = (ti.Matrix.identity(ti.f32, 2) + dt * C[p]) @ F[p] # deformation gradient update
h = ti.exp(10 * (1.0 - Jp[p])) # Hardening coefficient: snow gets harder when compressed
if material[p] == 1: # jelly, make it softer
h = 0.3
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(ti.f32, 2) * ti.sqrt(J)
elif material[p] == 2:
F[p] = U @ sig @ V.T() # Reconstruct elastic deformation gradient after plasticity
stress = 2 * mu * (F[p] - U @ V.T()) @ F[p].T() + ti.Matrix.identity(ti.f32, 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 ti.ndrange(n_grid, n_grid):
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][1] -= dt * 50 # gravity
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
for p in range(n_particles): # grid to particle (G2P)
base = (x[p] * inv_dx - 0.5).cast(int)
fx = x[p] * inv_dx - base.cast(float)
w = [0.5 * ti.sqr(1.5 - fx), 0.75 - ti.sqr(fx - 1.0), 0.5 * ti.sqr(fx - 0.5)]
new_v = ti.Vector.zero(ti.f32, 2)
new_C = ti.Matrix.zero(ti.f32, 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 * ti.outer_product(g_v, dpos)
v[p], C[p] = new_v, new_C
x[p] += dt * v[p] # advection
def sample(self, dir, N, t, i, j, mat_buf, mat_id):
next_dir = ti.Vector([0.0, 0.0, 0.0])
w_out = dir
cos_theta_i = w_out.dot(N)
ior = UF.get_material_ior(mat_buf, mat_id)
eta = ior
probability = ti.random()
f_or_b = 1.0
R = probability + 1.0
extinction = 1.0
if (cos_theta_i > 0.0):
N = -N
extinction = ti.exp(-0.1*t)
else:
cos_theta_i = -cos_theta_i
eta = 1.0 /ior
next_dir,suc = self.refract(w_out, N, eta)
if suc > 0.0:
R = self.schlick(cos_theta_i, ior)
if (probability < R):
next_dir = ts.reflect(w_out, N)
else:
f_or_b = -1.0
return next_dir, f_or_b*extinction
def hardening(
dq, p
): # The amount of hardening depends on the amount of correction that occurred due to plasticity
q_s[p] += dq
phi = h0 + (h1 * q_s[p] - h3) * ti.exp(-h2 * q_s[p])
phi = phi / 180 * pi # details in Table. 3: Friction angle phi_F and hardening parameters h0, h1, and h3 are listed in degrees for convenience
sin_phi = ti.sin(phi)
alpha_s[p] = ti.sqrt(2 / 3) * (2 * sin_phi) / (3 - sin_phi)
def test_unary():
import time
t = time.time()
grad_test(lambda x: ti.sqrt(x), lambda x: np.sqrt(x))
grad_test(lambda x: ti.exp(x), lambda x: np.exp(x))
grad_test(lambda x: ti.log(x), lambda x: np.log(x))
ti.core.print_profile_info()
print("Total time {:.3f}s".format(time.time() - t))
def init_gwei():
sum = -1.0
for i in self.gwei:
x = i / self.radius
y = ti.exp(-x**2)
self.gwei[i] = y
sum += y * 2
for i in self.gwei:
self.gwei[i] /= sum
def particle_to_grid():
for k in particle_position:
p = particle_position[k]
grid = p * inv_dx
base = int(grid - 0.5)
fx = grid - base
w = [0.5 * (1.5 - fx)**2, 0.75 - (fx - 1)**2,
0.5 * (fx - 0.5)**2] # B-spline
# stress = -dt * 4 * E * p_vol * (particle_J[k] - 1) * (inv_dx**2)
# affine = ti.Matrix([[stress, 0], [0, stress]]) + p_mass * particle_C[k]
particle_F[k] = (ti.Matrix.identity(float, 2) +
dt * particle_C[k]) @ particle_F[k]
# hardening coefficient
h = ti.exp(10 * (1.0 - particle_J[k]))
if particle_material[k] == 1: # jelly
h = 0.3
mu, la = mu_0 * h, lambda_0 * h
if particle_material[k] == 0: # fluid
mu = 0.0
U, sig, V = ti.svd(particle_F[k])
J = 1.0
for d in ti.static(range(2)):
new_sig = sig[d, d]
if particle_material[k] == 2: # snow
new_sig = min(max(sig[d, d], 1 - 2.5e-2),
1 + 4.5e-3) # plasticity
particle_J[k] *= sig[d, d] / new_sig
sig[d, d] = new_sig
J *= new_sig
if particle_material[
k] == 0: # Fluid: Reset deformation gradient to avoid numerical instability
particle_F[k] = ti.Matrix.identity(float, 2) * ti.sqrt(J)
elif particle_material[k] == 2:
particle_F[k] = U @ sig @ V.transpose(
) # Snow: Reconstruct elastic deformation gradient after plasticity
stress = 2 * mu * (particle_F[k] - U @ V.transpose()) @ particle_F[
k].transpose() + ti.Matrix.identity(float, 2) * la * J * (J - 1)
stress = (-dt * p_vol * 4 * inv_dx * inv_dx) * stress
affine = stress + p_mass * particle_C[k]
for i in ti.static(range(3)):
for j in ti.static(range(3)):
offset = ti.Vector([i, j])
weight = w[i][0] * w[j][1]
dpos = (offset - fx) * dx
grid_velocity[base + offset] += weight * (
p_mass * particle_velocity[k] + affine @ dpos)
grid_weight[base + offset] += weight * p_mass
def accel(v: ti.template(), x: ti.template(), dt):
for i in ti.grouped(x):
acc = x[i] * 0
for d in ti.static(links):
disp = x[tl.clamp(i + d, 0, tl.vec(*NN) - 1)] - x[i]
dis = disp.norm()
acc += disp * (dis - L) / L**2
v[i] += stiff * acc * dt
v[i] *= ti.exp(-damp * dt)
def init_wei():
total = -1.0
for i in self.wei:
x = i / self.radius
r = ti.exp(-x**2)
self.wei[i] = r
total += r * 2
for i in self.wei:
self.wei[i] /= total
def substep(n: ti.i32, t: ti.i32): # Compute force and new velocity
for i in range(n):
v[i] *= ti.exp(-dt * damping[None]) # damping
total_force = ti.Vector(
gravity) * particle_mass #gravity -> accelaration
if actuation_type[i] == 1:
#total_force = ti.Vector([9.8 * t, 0], real) * particle_mass
total_force = ti.Vector(H_force) * particle_mass
v[i] += dt * total_force / particle_mass
def p2g(f: ti.i32):
for p in range(0, n_particles):
new_Jp = Jp[f, p]
base = ti.cast(x[f, p] * inv_dx - 0.5, ti.i32)
fx = x[f, p] * inv_dx - ti.cast(base, ti.f32)
w = [
0.5 * ti.sqr(1.5 - fx), 0.75 - ti.sqr(fx - 1.0),
0.5 * ti.sqr(fx - 0.5)
] # quadratic kernels
new_F = (ti.Matrix.diag(dim=dim, val=1) +
dt * C[f, p]) @ F[f, p] # deformation gradient update
h = max(0.1, min(5, ti.exp(10 * (1.0 - new_Jp))))
if particle_type[p] == 1: # jelly, make it softer
h = 0.3
mu, la = mu_0 * h, lambda_0 * h
if particle_type[p] == 0: # liquid
mu = 0.0
U, sig, V = ti.svd(new_F)
J = 1.0
for d in ti.static(range(2)):
new_sig = sig[d, d]
if particle_type[p] == 2: # Snow
new_sig = min(max(sig[d, d], 1 - 2.5e-2),
1 + 4.5e-3) # Plasticity
new_Jp *= sig[d, d] / new_sig
sig[d, d] = new_sig
J *= new_sig
if particle_type[
p] == 0: # Reset deformation gradient to avoid numerical instability
new_F = ti.Matrix.diag(dim=dim, val=1) * ti.sqrt(J)
elif particle_type[p] == 2:
new_F = U @ sig @ ti.transposed(
V) # Reconstruct elastic deformation gradient after plasticity
F[f + 1, p] = new_F
Jp[f + 1, p] = new_Jp
stress = 2 * mu * (new_F - U @ ti.transposed(V)) @ ti.transposed(
new_F) + ti.Matrix.diag(dim=dim, val=1) * la * J * (J - 1)
stress = (-dt * p_vol * 4 * inv_dx * inv_dx) * stress
affine = stress + p_mass * C[f, p]
# loop over 3x3 node neighborhood
for i in ti.static(range(3)):
for j in ti.static(range(3)):
offset = ti.Vector([i, j])
dpos = (ti.cast(ti.Vector([i, j]), ti.f32) - fx) * dx
weight = w[i](0) * w[j](1)
ti.atomic_add(grid_v_in[base + offset],
weight * (p_mass * v[f, p] + affine @ dpos))
ti.atomic_add(grid_m[base + offset], weight * p_mass)
def sampleScattering(u: ti.f32, maxDistance: ti.f32):
# remap u to account for finite max distance
## f32
minU = ti.exp(-SIGMA * maxDistance)
a = u * (1.0 - minU) + minU
# sample with pdf proportional to exp(-sig*d)
dist = -ti.log(a) / SIGMA
pdf = SIGMA * a / (1.0 - minU)
return (dist, pdf)
def apply_impulse(vf: ti.template(), dyef: ti.template(),
imp_data: ti.ext_arr()):
for i, j in vf:
omx, omy = imp_data[2], imp_data[3]
mdir = ti.Vector([imp_data[0], imp_data[1]])
dx, dy = (i + 0.5 - omx), (j + 0.5 - omy)
d2 = dx * dx + dy * dy
# dv = F * dt
factor = ti.exp(-d2 / force_radius)
momentum = mdir * f_strength * dt * factor
v = vf[i, j]
vf[i, j] = v + momentum
# add dye
dc = dyef[i, j]
if mdir.norm() > 0.5:
dc += ti.exp(-d2 * (4 / (res / 15)**2)) * ti.Vector(
[imp_data[4], imp_data[5], imp_data[6]])
dc *= dye_decay
dyef[i, j] = dc
def p2g(self, dt: ti.f32):
for p in self.x:
base = (self.x[p] * self.inv_dx - 0.5).cast(int)
fx = self.x[p] * self.inv_dx - base.cast(float)
# Quadratic kernels [http://mpm.graphics Eqn. 123, with x=fx, fx-1,fx-2]
w = [
0.5 * ti.sqr(1.5 - fx), 0.75 - ti.sqr(fx - 1),
0.5 * ti.sqr(fx - 0.5)
]
# deformation gradient update
self.F[p] = (ti.Matrix.identity(ti.f32, self.dim) +
dt * self.C[p]) @ self.F[p]
# Hardening coefficient: snow gets harder when compressed
h = ti.exp(10 * (1.0 - self.Jp[p]))
if self.material[
p] == self.material_elastic: # jelly, make it softer
h = 0.3
mu, la = self.mu_0 * h, self.lambda_0 * h
if self.material[p] == self.material_water: # liquid
mu = 0.0
U, sig, V = ti.svd(self.F[p])
J = 1.0
for d in ti.static(range(self.dim)):
new_sig = sig[d, d]
#section 7 of snow paper ... dt being too big
if self.material[p] == self.material_snow: # Snow
new_sig = min(max(sig[d, d], 1 - 2.5e-2),
1 + 4.5e-3) # Plasticity
self.Jp[p] *= sig[d, d] / new_sig
sig[d, d] = new_sig
J *= new_sig
if self.material[p] == self.material_water:
# Reset deformation gradient to avoid numerical instability
new_F = ti.Matrix.identity(ti.f32, self.dim)
new_F[0, 0] = J
self.F[p] = new_F
elif self.material[p] == self.material_snow:
# Reconstruct elastic deformation gradient after plasticity
self.F[p] = U @ sig @ V.T()
stress = 2 * mu * (self.F[p] - U @ V.T()) @ self.F[p].T(
) + ti.Matrix.identity(ti.f32, self.dim) * la * J * (J - 1)
stress = (-dt * self.p_vol * 4 * self.inv_dx**2) * stress
affine = stress + self.p_mass * self.C[p]
# Loop over 3x3 grid node neighborhood
for offset in ti.static(ti.grouped(self.stencil_range())):
dpos = (offset.cast(float) - fx) * self.dx
weight = 1.0
for d in ti.static(range(self.dim)):
weight *= w[offset[d]][d]
self.grid_v[base +
offset] += weight * (self.p_mass * self.v[p] +
affine @ dpos)
self.grid_m[base + offset] += weight * self.p_mass