def paint():
for i, j in ti.ndrange(n, n):
t = x[i, j]
block1_index = ti.rescale_index(x, block1, [i, j])
block2_index = ti.rescale_index(x, block2, [i, j])
block3_index = ti.rescale_index(x, block3, [i, j])
t += ti.is_active(block1, block1_index)
t += ti.is_active(block2, block2_index)
t += ti.is_active(block3, block3_index)
img[scatter(i), scatter(j)] = 1 - t / 4
def g2p(self, dt: ti.f32):
ti.block_dim(256)
if ti.static(self.use_bls):
for d in ti.static(range(self.dim)):
ti.block_local(self.grid_v.get_scalar_field(d))
ti.no_activate(self.particle)
for I in ti.grouped(self.pid):
p = self.pid[I]
base = ti.floor(self.x[p] * self.inv_dx - 0.5).cast(int)
Im = ti.rescale_index(self.pid, self.grid_m, I)
for D in ti.static(range(self.dim)):
base[D] = ti.assume_in_range(base[D], Im[D], 0, 1)
fx = self.x[p] * self.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(ti.f32, self.dim)
new_C = ti.Matrix.zero(ti.f32, self.dim, self.dim)
# Loop over 3x3 grid node neighborhood
for offset in ti.static(ti.grouped(self.stencil_range())):
dpos = offset.cast(float) - fx
g_v = self.grid_v[base + offset]
weight = 1.0
for d in ti.static(range(self.dim)):
weight *= w[offset[d]][d]
new_v += weight * g_v
new_C += 4 * self.inv_dx * weight * g_v.outer_product(dpos)
if self.material[p] != self.material_stationary:
self.v[p], self.C[p] = new_v, new_C
self.x[p] += dt * self.v[p] # advection
def sparse_api_demo():
ti.activate(block1, [0, 1])
ti.activate(block2, [1, 2])
for i, j in x:
print('field x[{}, {}] = {}'.format(i, j, x[i, j]))
# outputs:
# field x[2, 4] = 0
# field x[2, 5] = 0
# field x[3, 4] = 0
# field x[3, 5] = 0
for i, j in block2:
print('Active block2: [{}, {}]'.format(i, j))
# output: Active block2: [1, 2]
for i, j in block1:
print('Active block1: [{}, {}]'.format(i, j))
# output: Active block1: [0, 1]
for j in range(4):
print('Activity of block2[2, {}] = {}'.format(
j, ti.is_active(block2, [1, j])))
ti.deactivate(block2, [1, 2])
for i, j in block2:
print('Active block2: [{}, {}]'.format(i, j))
# output: nothing
for i, j in block1:
print('Active block1: [{}, {}]'.format(i, j))
# output: Active block1: [0, 1]
print(ti.rescale_index(x, block1, ti.Vector([9, 17])))
# output = [2, 4]
# Note: ti.Vector is optional in ti.rescale_index.
print(ti.rescale_index(x, block1, [9, 17]))
# output = [2, 4]
ti.activate(block2, [1, 2])
def insert():
ti.block_dim(256)
for i in x:
# It is important to ensure insert and p2g uses the exact same way to compute the base
# coordinates. Otherwise there might be coordinate mismatch due to float-point errors.
base = ti.Vector([
int(ti.floor(x[i][0] * N) - grid_offset[0]),
int(ti.floor(x[i][1] * N) - grid_offset[1])
])
base_p = ti.rescale_index(m1, pid, base)
ti.append(pid.parent(), base_p, i)
def build_pid(self, pid: ti.template(), grid_m: ti.template(), offset: ti.template()):
"""
grid has blocking (e.g. 4x4x4), we wish to put the particles from each block into a GPU block,
then used shared memory (ti.block_local) to accelerate
:param pid:
:param grid_m:
:param offset:
:return:
"""
ti.block_dim(64)
for p in self.x:
base = int(ti.floor(self.x[p] * self.inv_dx - 0.5)) \
- ti.Vector(list(self.offset))
# pid grandparent is `block`
base_pid = ti.rescale_index(grid_m, pid.parent(2), base)
ti.append(pid.parent(), base_pid, p)
def p2g(use_shared: ti.template(), m: ti.template()):
ti.block_dim(256)
if ti.static(use_shared):
ti.block_local(m)
for I in ti.grouped(pid):
p = pid[I]
u_ = ti.floor(x[p] * N).cast(ti.i32)
Im = ti.rescale_index(pid, m, I)
u0 = ti.assume_in_range(u_[0], Im[0], 0, 1)
u1 = ti.assume_in_range(u_[1], Im[1], 0, 1)
u = ti.Vector([u0, u1])
for offset in ti.static(ti.grouped(ti.ndrange(extend, extend))):
m[u + offset] += scatter_weight
def g2p(use_shared: ti.template(), s: ti.template()):
ti.block_dim(256)
if ti.static(use_shared):
ti.block_local(m1)
for I in ti.grouped(pid):
p = pid[I]
u_ = ti.floor(x[p] * N).cast(ti.i32)
Im = ti.rescale_index(pid, m1, I)
u0 = ti.assume_in_range(u_[0], Im[0], 0, 1)
u1 = ti.assume_in_range(u_[1], Im[1], 0, 1)
u = ti.Vector([u0, u1])
tot = 0.0
for offset in ti.static(ti.grouped(ti.ndrange(extend, extend))):
tot += m1[u + offset]
s[p] = tot
def p2g(self, dt: ti.f32):
ti.no_activate(self.particle)
ti.block_dim(256)
if ti.static(self.use_bls):
for d in ti.static(range(self.dim)):
ti.block_local(self.grid_v.get_scalar_field(d))
ti.block_local(self.grid_m)
for I in ti.grouped(self.pid):
p = self.pid[I]
base = ti.floor(self.x[p] * self.inv_dx - 0.5).cast(int)
Im = ti.rescale_index(self.pid, self.grid_m, I)
for D in ti.static(range(self.dim)):
# For block shared memory: hint compiler that there is a connection between `base` and loop index `I`
base[D] = ti.assume_in_range(base[D], Im[D], 0, 1)
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 * (1.5 - fx)**2, 0.75 - (fx - 1)**2, 0.5 * (fx - 0.5)**2]
# Deformation gradient update
F = self.F[p]
if self.material[p] == self.material_water: # liquid
F = ti.Matrix.identity(ti.f32, self.dim)
if ti.static(self.support_plasticity):
F[0, 0] = self.Jp[p]
F = (ti.Matrix.identity(ti.f32, self.dim) + dt * self.C[p]) @ F
# Hardening coefficient: snow gets harder when compressed
h = 1.0
if ti.static(self.support_plasticity):
if self.material[p] != self.material_water:
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(F)
J = 1.0
if self.material[p] != self.material_sand:
for d in ti.static(range(self.dim)):
new_sig = sig[d, d]
if self.material[p] == self.material_snow: # Snow
new_sig = min(max(sig[d, d], 1 - 2.5e-2),
1 + 4.5e-3) # Plasticity
if ti.static(self.support_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
F = ti.Matrix.identity(ti.f32, self.dim)
F[0, 0] = J
if ti.static(self.support_plasticity):
self.Jp[p] = J
elif self.material[p] == self.material_snow:
# Reconstruct elastic deformation gradient after plasticity
F = U @ sig @ V.transpose()
stress = ti.Matrix.zero(ti.f32, self.dim, self.dim)
if self.material[p] != self.material_sand:
stress = 2 * mu * (F - U @ V.transpose()) @ F.transpose(
) + ti.Matrix.identity(ti.f32, self.dim) * la * J * (J - 1)
else:
if ti.static(self.support_plasticity):
sig = self.sand_projection(sig, p)
F = U @ sig @ V.transpose()
log_sig_sum = 0.0
center = ti.Matrix.zero(ti.f32, self.dim, self.dim)
for i in ti.static(range(self.dim)):
log_sig_sum += ti.log(sig[i, i])
center[i, i] = 2.0 * self.mu_0 * ti.log(
sig[i, i]) * (1 / sig[i, i])
for i in ti.static(range(self.dim)):
center[i,
i] += self.lambda_0 * log_sig_sum * (1 /
sig[i, i])
stress = U @ center @ V.transpose() @ F.transpose()
self.F[p] = F
stress = (-dt * self.p_vol * 4 * self.inv_dx**2) * stress
# TODO: implement g2p2g pmass
mass = self.p_mass
if self.material[p] == self.material_water:
mass *= self.water_density
affine = stress + 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 * (mass * self.v[p] +
affine @ dpos)
self.grid_m[base + offset] += weight * mass
def g2p2g(self, dt: ti.f32, pid: ti.template(), grid_v_in: ti.template(),
grid_v_out: ti.template(), grid_m_out: ti.template()):
ti.block_dim(256)
ti.no_activate(self.particle)
if ti.static(self.use_bls):
ti.block_local(grid_m_out)
for d in ti.static(range(self.dim)):
ti.block_local(grid_v_in.get_scalar_field(d))
ti.block_local(grid_v_out.get_scalar_field(d))
for I in ti.grouped(pid):
p = pid[I]
# G2P
base = ti.floor(self.x[p] * self.inv_dx - 0.5).cast(int)
Im = ti.rescale_index(pid, grid_m_out, I)
for D in ti.static(range(self.dim)):
base[D] = ti.assume_in_range(base[D], Im[D], 0, 1)
fx = self.x[p] * self.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(ti.f32, self.dim)
C = ti.Matrix.zero(ti.f32, self.dim, self.dim)
# Loop over 3x3 grid node neighborhood
for offset in ti.static(ti.grouped(self.stencil_range())):
dpos = offset.cast(float) - fx
g_v = grid_v_in[base + offset]
weight = 1.0
for d in ti.static(range(self.dim)):
weight *= w[offset[d]][d]
new_v += weight * g_v
C += 4 * self.inv_dx * weight * g_v.outer_product(dpos)
if p >= self.last_time_final_particles[None]:
# New particles. No G2P.
new_v = self.v[p]
C = ti.Matrix.zero(ti.f32, self.dim, self.dim)
if self.material[p] != self.material_stationary:
self.v[p] = new_v
self.x[p] += dt * self.v[p] # advection
# P2G
base = ti.floor(self.x[p] * self.inv_dx - 0.5).cast(int)
for D in ti.static(range(self.dim)):
base[D] = ti.assume_in_range(base[D], Im[D], -1, 2)
fx = self.x[p] * self.inv_dx - base.cast(float)
# Quadratic kernels [http://mpm.graphics Eqn. 123, with x=fx, fx-1,fx-2]
w2 = [0.5 * (1.5 - fx)**2, 0.75 - (fx - 1)**2, 0.5 * (fx - 0.5)**2]
# Deformation gradient update
new_F = (ti.Matrix.identity(ti.f32, self.dim) + dt * C) @ self.F[p]
if ti.static(self.quant):
new_F = max(-self.F_bound, min(self.F_bound, new_F))
self.F[p] = new_F
# Hardening coefficient: snow gets harder when compressed
h = 1.0
if ti.static(self.support_plasticity):
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
if self.material[p] != self.material_sand:
for d in ti.static(range(self.dim)):
new_sig = sig[d, d]
if self.material[p] == self.material_snow: # Snow
new_sig = min(max(sig[d, d], 1 - 2.5e-2),
1 + 4.5e-3) # Plasticity
if ti.static(self.support_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.transpose()
stress = ti.Matrix.zero(ti.f32, self.dim, self.dim)
if self.material[p] != self.material_sand:
stress = 2 * mu * (
self.F[p] - U @ V.transpose()) @ self.F[p].transpose(
) + ti.Matrix.identity(ti.f32, self.dim) * la * J * (J - 1)
else:
if ti.static(self.support_plasticity):
sig = self.sand_projection(sig, p)
self.F[p] = U @ sig @ V.transpose()
log_sig_sum = 0.0
center = ti.Matrix.zero(ti.f32, self.dim, self.dim)
for i in ti.static(range(self.dim)):
log_sig_sum += ti.log(sig[i, i])
center[i, i] = 2.0 * self.mu_0 * ti.log(
sig[i, i]) * (1 / sig[i, i])
for i in ti.static(range(self.dim)):
center[i,
i] += self.lambda_0 * log_sig_sum * (1 /
sig[i, i])
stress = U @ center @ V.transpose() @ self.F[p].transpose()
stress = (-dt * self.p_vol * 4 * self.inv_dx**2) * stress
affine = stress + self.p_mass * C
# 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 *= w2[offset[d]][d]
grid_v_out[base +
offset] += weight * (self.p_mass * self.v[p] +
affine @ dpos)
grid_m_out[base + offset] += weight * self.p_mass
self.last_time_final_particles[None] = self.n_particles[None]
def set_a():
for I in ti.grouped(b):
Ia = ti.rescale_index(b, a, I)
a[Ia] = 1.0
def set_b():
for I in ti.grouped(a):
Ib = ti.rescale_index(a, b, I)
b[Ib] += 1.0
