def march(self) -> int:
r_n = 0
for I in ti.grouped(ti.ndrange(*[[1, self.N - 1]] * self.dim)):
id = 0
if ti.static(self.dim == 2):
i, j = I
if self.m[i, j] > 1: id |= 1
if self.m[i + 1, j] > 1: id |= 2
if self.m[i, j + 1] > 1: id |= 4
if self.m[i + 1, j + 1] > 1: id |= 8
else:
i, j, k = I
if self.m[i, j, k] > 1: id |= 1
if self.m[i + 1, j, k] > 1: id |= 2
if self.m[i + 1, j + 1, k] > 1: id |= 4
if self.m[i, j + 1, k] > 1: id |= 8
if self.m[i, j, k + 1] > 1: id |= 16
if self.m[i + 1, j, k + 1] > 1: id |= 32
if self.m[i + 1, j + 1, k + 1] > 1: id |= 64
if self.m[i, j + 1, k + 1] > 1: id |= 128
for m in range(self.et.shape[1]):
if self.et[id, m][0] == -1:
break
n = ti.atomic_add(r_n, 1)
for l in ti.static(range(self.dim)):
e = self.et[id, m][l]
R = float(I)
if ti.static(self.dim == 2):
i, j = I
# (.5, 0), (0, .5), (1, .5), (.5, 1)
if e == 0:
p = (1 - self.m[i, j]) / (self.m[i + 1, j] -
self.m[i, j])
R = [i + p, j]
elif e == 1:
p = (1 - self.m[i, j]) / (self.m[i, j + 1] -
self.m[i, j])
R = [i, j + p]
elif e == 2:
p = (1 - self.m[i + 1, j]) / (
self.m[i + 1, j + 1] - self.m[i + 1, j])
R = [i + 1, j + p]
elif e == 3:
p = (1 - self.m[i, j + 1]) / (
self.m[i + 1, j + 1] - self.m[i, j + 1])
R = [i + p, j + 1]
else:
i, j, k = I
# (.5, 0, 0), (1, .5, 0), (.5, 1, 0), (0, .5, 0)
# (.5, 0, 1), (1, .5, 1), (.5, 1, 1), (0, .5, 1)
# (0, 0, .5), (1, 0, .5), (1, 1, .5), (0, 1, .5)
if e == 0:
p = (1 - self.m[i, j, k]) / (self.m[i + 1, j, k] -
self.m[i, j, k])
R = [i + p, j, k]
elif e == 1:
p = (1 - self.m[i + 1, j, k]) / (
self.m[i + 1, j + 1, k] - self.m[i + 1, j, k])
R = [i + 1, j + p, k]
elif e == 2:
p = (1 - self.m[i, j + 1, k]) / (
self.m[i + 1, j + 1, k] - self.m[i, j + 1, k])
R = [i + p, j + 1, k]
elif e == 3:
p = (1 - self.m[i, j, k]) / (self.m[i, j + 1, k] -
self.m[i, j, k])
R = [i, j + p, k]
elif e == 4:
p = (1 - self.m[i, j, k + 1]) / (
self.m[i + 1, j, k + 1] - self.m[i, j, k + 1])
R = [i + p, j, k + 1]
elif e == 5:
p = (1 - self.m[i + 1, j, k + 1]) / (
self.m[i + 1, j + 1, k + 1] -
self.m[i + 1, j, k + 1])
R = [i + 1, j + p, k + 1]
elif e == 6:
p = (1 - self.m[i, j + 1, k + 1]) / (
self.m[i + 1, j + 1, k + 1] -
self.m[i, j + 1, k + 1])
R = [i + p, j + 1, k + 1]
elif e == 7:
p = (1 - self.m[i, j, k + 1]) / (
self.m[i, j + 1, k + 1] - self.m[i, j, k + 1])
R = [i, j + p, k + 1]
elif e == 8:
p = (1 - self.m[i, j, k]) / (self.m[i, j, k + 1] -
self.m[i, j, k])
R = [i, j, k + p]
elif e == 9:
p = (1 - self.m[i + 1, j, k]) / (
self.m[i + 1, j, k + 1] - self.m[i + 1, j, k])
R = [i + 1, j, k + p]
elif e == 10:
p = (1 - self.m[i + 1, j + 1, k]) / (
self.m[i + 1, j + 1, k + 1] -
self.m[i + 1, j + 1, k])
R = [i + 1, j + 1, k + p]
elif e == 11:
p = (1 - self.m[i, j + 1, k]) / (
self.m[i, j + 1, k + 1] - self.m[i, j + 1, k])
R = [i, j + 1, k + p]
self.r[n, l] = R
return r_n
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 * 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 = max(0.1, min(5, 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 grid_m:
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] += 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
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 * 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 func():
for i in x:
for j in ti.static(range(3)):
y[i] += x[i]
y[i] += x[i] * 42
def test():
for i, v in ti.static(enumerate(range(8))):
pass
print(i)
def static():
if ti.static(x[0]):
x[0] = 1
else:
x[0] = 0
def run(self):
for I in ti.static(self.dst):
self.dst[I] += self.src[I]
def point_aabb_distance2(box_min, box_max, o):
p = ti.Vector([0.0, 0.0, 0.0])
for i in ti.static(range(3)):
p[i] = ti.max(ti.min(o[i], box_max[i]), box_min[i])
return ti.Matrix.norm_sqr(p - o)
def compute_center(t: ti.i32):
for _ in range(1):
c = ti.Vector([0.0, 0.0])
for i in ti.static(range(n_objects)):
c += x[t, i]
center[t] = (1.0 / n_objects) * c
def p2g(self, dt: ti.f32):
ti.no_activate(self.particle)
ti.block_dim(256)
ti.block_local(*self.grid_v.entries)
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)
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.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:
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 * 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
def fill_vbo(vbo: template(), value: template(), offset: template(),
num_components: template()):
for i in vbo:
for c in ti.static(range(num_components)):
vbo[i][offset + c] = value
def substep():
for i, j in grid_m:
grid_v[i, j] = [0, 0]
grid_m[i, j] = 0
for p in x:
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),
0.5 * ti.sqr(fx - 0.5)
]
F[p] = (ti.Matrix.identity(ti.f32, 2) + dt * C[p]) @ F[p]
h = ti.exp(10 * (1.0 - Jp[p]))
if material[p] == 0:
h = 0.3
mu, la = mu_0 * h, lambda_0 * h
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] == 1:
new_sig = min(max(sig[d, d], 1 - 2.5e-2), 1 + 4.5e-3)
Jp[p] *= sig[d, d] / new_sig
sig[d, d] = new_sig
J *= new_sig
if material[p] == 1:
F[p] = U @ sig @ V.T()
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)):
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:
grid_v[i, j] = (1 / grid_m[i, j]) * grid_v[i, j]
grid_v[i, j][1] -= dt * 50
if i < 3 and grid_v[i, j][0] < 0: grid_v[i, j][0] = 0
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 x:
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)):
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]
def copy_to_vbo(vbo: template(), src: template(), offset: template(),
num_components: template()):
for i in src:
for c in ti.static(range(num_components)):
vbo[i][offset + c] = src[i][c]
def render():
ti.parallelize(6)
for u, v in color_buffer:
pos = camera_pos
d = ti.Vector([(2 * fov * (u + ti.random(ti.f32)) / res[1] -
fov * aspect_ratio - 1e-5),
2 * fov * (v + ti.random(ti.f32)) / res[1] - fov - 1e-5,
-1.0])
d = ti.Matrix.normalized(d)
t = (ti.random() - 0.5) * shutter_time
contrib = ti.Vector([0.0, 0.0, 0.0])
throughput = ti.Vector([1.0, 1.0, 1.0])
depth = 0
hit_sky = 1
ray_depth = 0
while depth < max_ray_depth:
closest, normal, c = next_hit(pos, d, t)
hit_pos = pos + closest * d
depth += 1
ray_depth = depth
if normal.norm() != 0:
d = out_dir(normal)
pos = hit_pos + 1e-4 * d
throughput *= c
if ti.static(use_directional_light):
dir_noise = ti.Vector([
ti.random() - 0.5,
ti.random() - 0.5,
ti.random() - 0.5
]) * light_direction_noise
direct = ti.Matrix.normalized(
ti.Vector(light_direction) + dir_noise)
dot = direct.dot(normal)
if dot > 0:
dist, _, _ = next_hit(pos, direct, t)
if dist > dist_limit:
contrib += throughput * ti.Vector(
light_color) * dot
else: # hit sky
hit_sky = 1
depth = max_ray_depth
max_c = throughput.max()
if ti.random() > max_c:
depth = max_ray_depth
throughput = [0, 0, 0]
else:
throughput /= max_c
if hit_sky:
if ray_depth != 1:
# contrib *= max(d[1], 0.05)
pass
else:
# directly hit sky
pass
else:
throughput *= 0
# contrib += throughput
color_buffer[u, v] += contrib
def dda_particle(eye_pos, d, t):
grid_res = particle_grid_res
bbox_min = bbox[0]
bbox_max = bbox[1]
hit_pos = ti.Vector([0.0, 0.0, 0.0])
normal = ti.Vector([0.0, 0.0, 0.0])
c = ti.Vector([0.0, 0.0, 0.0])
for i in ti.static(range(3)):
if abs(d[i]) < 1e-6:
d[i] = 1e-6
inter, near, far = ray_aabb_intersection(bbox_min, bbox_max, eye_pos, d)
near = max(0, near)
closest_intersection = inf
if inter:
pos = eye_pos + d * (near + eps)
rinv = 1.0 / d
rsign = ti.Vector([0, 0, 0])
for i in ti.static(range(3)):
if d[i] > 0:
rsign[i] = 1
else:
rsign[i] = -1
o = grid_res * pos
ipos = ti.Matrix.floor(o).cast(int)
dis = (ipos - o + 0.5 + rsign * 0.5) * rinv
running = 1
while running:
inside = inside_particle_grid(ipos)
if inside:
num_particles = voxel_has_particle[ipos]
if num_particles != 0:
num_particles = ti.length(pid.parent(), ipos)
for k in range(num_particles):
p = pid[ipos[0], ipos[1], ipos[2], k]
v = particle_v[p]
x = particle_x[p] + t * v
color = particle_color[p]
dist, poss = intersect_sphere(eye_pos, d, x, sphere_radius)
hit_pos = poss
if dist < closest_intersection and dist > 0:
hit_pos = eye_pos + dist * d
closest_intersection = dist
normal = ti.Matrix.normalized(hit_pos - x)
c = color
else:
running = 0
normal = [0, 0, 0]
if closest_intersection < inf:
running = 0
else:
# hits nothing. Continue ray marching
mm = ti.Vector([0, 0, 0])
if dis[0] <= dis[1] and dis[0] <= dis[2]:
mm[0] = 1
elif dis[1] <= dis[0] and dis[1] <= dis[2]:
mm[1] = 1
else:
mm[2] = 1
dis += mm * rsign * rinv
ipos += mm * rsign
return closest_intersection, normal, c
def run(self):
for I in ti.static(self.src):
self.buf[I] = self.src[I]
def copy_dynamic_nd(self, np_x: ti.ext_arr(), input_x: ti.template()):
for i in self.x:
for j in ti.static(range(self.dim)):
np_x[i, j] = input_x[i][j]
def _run(self, nxt: ti.template(), src: ti.template()):
for I in ti.static(src):
nxt[I] = src[I]
def util_vector_to_plain_array(self, v: ti.template()) -> ti.template():
### used .mat of Proxy object, PROBLEM?
return list([v[i] for i in ti.static(range(v.mat.n))])
def update():
for i in ti.static(range(number_coeffs)):
coeffs[i] -= learning_rate * coeffs.grad[i]
def util_matrix_to_plain_array(self, v: ti.template()) -> ti.template():
### used .mat of Proxy object, PROBLEM?
return list([[v[n, m] for m in ti.static(range(v.mat.m))]
for n in ti.static(range(v.mat.n))])
def test():
for i in ti.static(range(8)):
pass
print(i)
def cook_coor(self, I, camera):
scale = ti.static(2 / min(*camera.img.shape()))
coor = (I - ts.vec2(*camera.img.shape()) / 2) * scale
return coor
def static():
if ti.static(val > 0.5):
x[0] = 1
else:
x[0] = 0
def uncook_coor(self, coor, camera):
scale = ti.static(min(*camera.img.shape()) / 2)
I = coor.xy * scale + ts.vec2(*camera.img.shape()) / 2
return I
def neighbor_sum(self, x, I):
ret = 0.0
for i in ti.static(range(self.dim)):
offset = ti.Vector.unit(self.dim, i)
ret += x[I + offset] + x[I - offset]
return ret
def func():
for i in ti.static(ti.static(range(1))):
pass
def func():
for i in range(ti.static(N // 2 + 3), N):
x[i] = ti.abs(y[i])
def test():
for I in ti.static(ti.grouped(val)):
pass
def clamp(p):
for d in ti.static(range(p.n)):
p[d] = min(1 - 1e-4 - dx + stagger[d] * dx, max(p[d], stagger[d] * dx))
return p
def clamp( val , low , high):
if ti.static(is_scalar(val)):
return clamp
else:
return clamp_vector(val , low , high)