def copy(bls: ti.template(), w: ti.template()):
if ti.static(bls):
ti.cache_shared(x, y, z)
for i, j in x:
w[i,
j] = x[i, j - 2] + y[i + 2, j -
1] + y[i - 1, j] + z[i - 1, j] + z[i + 1, j]
def g2p(self, dt: ti.f32):
ti.block_dim(256)
ti.cache_shared(*self.grid_v.entries)
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)
for D in ti.static(range(self.dim)):
base[D] = ti.assume_in_range(base[D], I[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)
self.v[p], self.C[p] = new_v, new_C
self.x[p] += dt * self.v[p] # advection
def p2g(use_shared: ti.template(), m: ti.template()):
ti.block_dim(256)
if ti.static(use_shared):
ti.cache_shared(m)
for i, j, l in pid:
p = pid[i, j, l]
u_ = ti.floor(x[p] * N).cast(ti.i32)
u0 = ti.assume_in_range(u_[0], i, 0, 1)
u1 = ti.assume_in_range(u_[1], j, 0, 1)
u = ti.Vector([u0, u1])
for offset in ti.static(ti.grouped(ti.ndrange(extend, extend))):
m[u + offset] += scatter_weight
def apply(use_bls: ti.template(), y: ti.template()):
if ti.static(use_bls and not scatter):
ti.cache_shared(x)
if ti.static(use_bls and scatter):
ti.cache_shared(y)
ti.block_dim(block_dim)
for I in ti.grouped(x):
if ti.static(scatter):
for offset in ti.static(stencil):
y[I + ti.Vector(offset)] += x[I]
else:
# gather
s = 0
for offset in ti.static(stencil):
s = s + x[I + ti.Vector(offset)]
y[I] = s
def g2p(use_shared: ti.template(), s: ti.template()):
ti.block_dim(256)
if ti.static(use_shared):
ti.cache_shared(m1)
for i, j, l in pid:
p = pid[i, j, l]
u_ = ti.floor(x[p] * N).cast(ti.i32)
u0 = ti.assume_in_range(u_[0], i, 0, 1)
u1 = ti.assume_in_range(u_[1], j, 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 copy():
ti.cache_shared(x)
for i, j in x:
y[i, j] = x[i, j]
def copy():
ti.cache_shared(x)
for i in x:
y[i] = x[i]
def p2g(self, dt: ti.f32):
ti.no_activate(self.particle)
ti.block_dim(256)
ti.cache_shared(*self.grid_v.entries)
ti.cache_shared(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)
for D in ti.static(range(self.dim)):
base[D] = ti.assume_in_range(base[D], I[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
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
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
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 = ti.Matrix.zero(ti.f32, self.dim, self.dim)
if self.material[p] != self.material_sand:
stress = 2 * mu * (self.F[p] - U @ V.T()) @ self.F[p].T(
) + ti.Matrix.identity(ti.f32, self.dim) * la * J * (J - 1)
else:
sig = self.sand_projection(sig, p)
self.F[p] = U @ sig @ V.T()
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.T() @ self.F[p].T()
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
