def center_G2P(self, grid_v: ti.template(), dx: ti.f32, dt: ti.f32):
inv_dx = 1 / dx
for p in self.px:
xp = self.px[p]
base = (xp * inv_dx - 0.5).cast(ti.i32)
fx = xp * inv_dx - base.cast(ti.f32)
w = [0.5 * (1.5 - fx)**2, 0.75 - (fx - 1)**2,
0.5 * (fx - 0.5)**2] # Bspline
new_v = ti.Vector.zero(ti.f32, 3)
new_C = ti.Matrix.zero(ti.f32, 3, 3)
for i in ti.static(range(3)):
for j in ti.static(range(3)):
for k in ti.static(range(3)):
dpos = vec3(i, j, k) - fx
g_v = grid_v[base + vec3(i, j, k)]
weight = w[i][0] * w[j][1] * w[k][2]
new_v += weight * g_v
new_C += 4 * weight * g_v.outer_product(dpos) * inv_dx
self.pv[p] = new_v
self.px[p] += dt * self.pv[p]
self.J[p] *= 1 + dt * new_C.trace()
self.C[p] = new_C
def init_properties(self):
# init particles
for p in self.px:
self.pv[p] = vec3(0.0, 0.0, 0.0)
if ti.static(self.sim_algo == 'MPM'):
self.C[p] = ti.Matrix.zero(ti.f32, 3, 3)
self.J[p] = 1.0
elif ti.static(self.sim_algo == 'APIC'):
self.c_x[p] = vec3(0.0, 0.0, 0.0)
self.c_y[p] = vec3(0.0, 0.0, 0.0)
self.c_z[p] = vec3(0.0, 0.0, 0.0)
# init field
if ti.static(self.sim_algo != 'MPM'):
for i, j, k in self.u:
self.u[i, j, k] = 0.0
self.u_weight[i, j, k] = 0.0
for i, j, k in self.v:
self.v[i, j, k] = 0.0
self.v_weight[i, j, k] = 0.0
for i, j, k in self.w:
self.w[i, j, k] = 0.0
self.w_weight[i, j, k] = 0.0
for i, j, k in self.p:
self.p[i, j, k] = 0.0
def voxelize(self, px: ti.template(), world: ti.f32, n_grid: ti.i32,
bound_grid: ti.i32, npar: ti.i32):
dx = world / n_grid
bound = bound_grid * dx
space_x = dx / npar
for i, j, k in ti.ndrange(n_grid, n_grid, n_grid):
x = (i + 0.5) * dx
y = (j + 0.5) * dx
z = (k + 0.5) * dx
if (x - self.c_x)**2 + (y - self.c_y)**2 + (
z - self.c_z)**2 - self.r**2 < 0:
for ix in range(npar):
for jx in range(npar):
for kx in range(npar):
xp = clamp(
i * dx + (ix + random.random()) * space_x,
bound + 1e-4, world - bound - 1e-4)
yp = clamp(
j * dx + (jx + random.random()) * space_x,
bound + 1e-4, world - bound - 1e-4)
zp = clamp(
k * dx + (kx + random.random()) * space_x,
bound + 1e-4, world - bound - 1e-4)
px[particle_idx(i, j, k, ix, jx, kx, n_grid,
npar)] = vec3(xp, yp, zp)
def voxelize(self, px: ti.template(), world: ti.f32, n_grid: ti.i32,
bound_grid: ti.i32, npar: ti.i32):
dx = world / n_grid
bound = bound_grid * dx
space_x = dx / npar
for i, j, k in ti.ndrange(n_grid, n_grid, n_grid):
x = (i + 0.5) * dx
y = (j + 0.5) * dx
z = (k + 0.5) * dx
if self.x_start < x < self.x_end and self.y_start < y < self.y_end and self.z_start < z < self.z_end:
for ix in range(npar):
for jx in range(npar):
for kx in range(npar):
xp = clamp(
i * dx + (ix + random.random()) * space_x,
bound + 1e-4, world - bound - 1e-4)
yp = clamp(
j * dx + (jx + random.random()) * space_x,
bound + 1e-4, world - bound - 1e-4)
zp = clamp(
k * dx + (kx + random.random()) * space_x,
bound + 1e-4, world - bound - 1e-4)
px[particle_idx(i, j, k, ix, jx, kx, n_grid,
npar)] = vec3(xp, yp, zp)
def map_color(c):
return vec3(bwrR.map(c), bwrG.map(c), bwrB.map(c))