def max_starred() -> ti.i32:
a = ti.Vector([1, 2, 3])
b = ti.Vector([4, 5, 6])
return ti.max(*a, *b)
def max_u16(a: ti.u16, b: ti.u16) -> ti.u16:
return ti.max(a, b)
(lambda x: ti.sqrt(x), lambda x: np.sqrt(x)),
(lambda x: ti.exp(x), lambda x: np.exp(x)),
(lambda x: ti.log(x), lambda x: np.log(x)),
])
@if_has_autograd
@test_utils.test()
def test_unary(tifunc, npfunc):
grad_test(tifunc, npfunc)
@pytest.mark.parametrize('tifunc,npfunc', [
(lambda x: ti.min(x, 0), lambda x: np.minimum(x, 0)),
(lambda x: ti.min(x, 1), lambda x: np.minimum(x, 1)),
(lambda x: ti.min(0, x), lambda x: np.minimum(0, x)),
(lambda x: ti.min(1, x), lambda x: np.minimum(1, x)),
(lambda x: ti.max(x, 0), lambda x: np.maximum(x, 0)),
(lambda x: ti.max(x, 1), lambda x: np.maximum(x, 1)),
(lambda x: ti.max(0, x), lambda x: np.maximum(0, x)),
(lambda x: ti.max(1, x), lambda x: np.maximum(1, x)),
])
@if_has_autograd
@test_utils.test()
def test_minmax(tifunc, npfunc):
grad_test(tifunc, npfunc)
@if_has_autograd
@test_utils.test()
def test_mod():
x = ti.field(ti.i32)
y = ti.field(ti.i32)
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])
d = d_
for i in ti.static(range(3)):
if ti.abs(d[i]) < 1e-6:
d[i] = 1e-6
inter, near, far = ray_aabb_intersection(bbox_min, bbox_max, eye_pos, d)
near = ti.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(ti.i32)
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 // 256**2 / 255.0, color / 256 % 256 / 255.0,
color % 256 / 255.0
]
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 max_i64(a: ti.i64, b: ti.i64) -> ti.i64:
return ti.max(a, b)
def dot_or_zero(n, l):
return ti.max(0.0, n.dot(l))
def max(self):
import taichi as ti
ret = self.entries[0]
for i in range(1, len(self.entries)):
ret = ti.max(ret, self.entries[i])
return ret
def max_i32(a: ti.i32, b: ti.i32) -> ti.i32:
return ti.max(a, b)
def clamp(x):
return ti.max(0, ti.min(1.0, x))
def boxSDF(p, b):
q = ti.abs(p) - b
return length(ti.max(q, 0.0)) + ti.min(q.max(), 0.0)
ti.init(ti.cpu)
scene = t3.Scene()
obj = t3.Geometry.cube()
model = t3.Model(t3.Mesh.from_obj(obj))
model.material = t3.Material(
t3.BlinnPhong(
# https://learnopengl.com/img/textures/container2.png
color=t3.Texture('docs/_media/container2.png'),
specular=t3.Texture('docs/_media/container2_specular.png'),
))
scene.add_model(model)
camera = t3.Camera()
scene.add_camera_d(camera)
original = t3.FrameBuffer(camera)
filted = t3.ImgUnaryOp(original, lambda x: ti.max(0, x - 1))
blurred = t3.GaussianBlur(filted, radius=21)
final = t3.ImgBinaryOp(original, blurred, lambda x, y: x + y)
scene.add_buffer(final)
light = t3.Light(dir=[-0.2, -0.6, -1.0], color=1.6)
scene.add_light(light)
gui_original = ti.GUI('Original', filted.res)
gui_filted = ti.GUI('Filted', filted.res)
gui_blurred = ti.GUI('Blurred', blurred.res)
gui_final = ti.GUI('Final', final.res)
gui_original.fps_limit = None
gui_filted.fps_limit = None
gui_blurred.fps_limit = None
gui_final.fps_limit = None
while gui_final.running and gui_filted.running and gui_blurred.running and gui_original.running:
def saturate(x):
return ti.max(0, ti.min(1.0, x))
def SdfCapsule(X, radius, half_length):
alpha = ti.min(ti.max((X[0] / half_length + 1.0) * 0.5, 0.0), 1.0)
tmp = ti.Vector([X[0], X[1]])
tmp[0] += (1.0 - 2.0 * alpha) * half_length
return tmp.norm() - radius
def max_i16(a: ti.i16, b: ti.i16) -> ti.i16:
return ti.max(a, b)
def plane(pos):
return ts.length(ti.max(ti.abs(pos) - ts.vec(12.0, 0.5, 12.0), 0.0))
def max_u32(a: ti.u32, b: ti.u32) -> ti.u32:
return ti.max(a, b)
def sdfBox(p, length):
p = ti.abs(p) - length
d = ti.max(p, ti.Vector([0., 0., 0.])).norm()
d += ti.min(ti.max(p[0], ti.max(p[1], p[2])), 0.)
return d
def max_u64(a: ti.u64, b: ti.u64) -> ti.u64:
return ti.max(a, b)
def apply_grad(self, lr: float, gamma: float, max_grad: float):
for i in self.tf_tex:
self.tf_momentum[i] = gamma * self.tf_momentum[i] + \
lr * tl.clamp(self.tf_tex.grad[i], -max_grad, max_grad)
self.tf_tex[i] -= self.tf_momentum[i]
self.tf_tex[i] = ti.max(self.tf_tex[i], 0)
def fill_color(ipixels: ti.template(), idyef: ti.template()):
for i, j in ipixels:
density = ti.min(1.0, ti.max(0.0, idyef[i, j]))
ipixels[i, j] = density
def computeNormalAndCurvature():
"""
Compute the normal and the curvature at all points voxels.
Based on the PC limplementation:
https://pointclouds.org/documentation/group__features.html
"""
radius = 50
for i,j in pts:
nb_pts = ti.cast(0, ti.f32)
accu_0 = ti.cast(0, ti.f32)
accu_1 = ti.cast(0, ti.f32)
accu_2 = ti.cast(0, ti.f32)
accu_3 = ti.cast(0, ti.f32)
accu_4 = ti.cast(0, ti.f32)
accu_5 = ti.cast(0, ti.f32)
accu_6 = ti.cast(0, ti.f32)
accu_7 = ti.cast(0, ti.f32)
accu_8 = ti.cast(0, ti.f32)
z = 0
for x in range(i-radius, i+radius):
for y in range(j-radius, j+radius):
if ti.is_active(block1, [x,y]):
accu_0 += x * x
accu_1 += x * y
accu_2 += x * z
accu_3 += y * y
accu_4 += y * z
accu_5 += z * z
accu_6 += x
accu_7 += y
accu_8 += z
nb_pts += 1
accu_0 /= nb_pts
accu_1 /= nb_pts
accu_2 /= nb_pts
accu_3 /= nb_pts
accu_4 /= nb_pts
accu_5 /= nb_pts
accu_6 /= nb_pts
accu_7 /= nb_pts
accu_8 /= nb_pts
cov_mat_0 = accu_0 - accu_6 * accu_6
cov_mat_1 = accu_1 - accu_6 * accu_7
cov_mat_2 = accu_2 - accu_6 * accu_8
cov_mat_4 = accu_3 - accu_7 * accu_7
cov_mat_5 = accu_4 - accu_7 * accu_8
cov_mat_8 = accu_5 - accu_8 * accu_8
cov_mat_3 = cov_mat_1
cov_mat_6 = cov_mat_2
cov_mat_7 = cov_mat_5
# Compute eigen value and eigen vector
# Make sure in [-1, 1]
scale = ti.max(1.0, ti.abs(cov_mat_0))
scale = ti.max(scale, ti.abs(cov_mat_1))
scale = ti.max(scale, ti.abs(cov_mat_2))
scale = ti.max(scale, ti.abs(cov_mat_3))
scale = ti.max(scale, ti.abs(cov_mat_4))
scale = ti.max(scale, ti.abs(cov_mat_5))
scale = ti.max(scale, ti.abs(cov_mat_6))
scale = ti.max(scale, ti.abs(cov_mat_7))
scale = ti.max(scale, ti.abs(cov_mat_8))
if scale > 1.0:
cov_mat_0 /= scale
cov_mat_1 /= scale
cov_mat_2 /= scale
cov_mat_3 /= scale
cov_mat_4 /= scale
cov_mat_5 /= scale
cov_mat_6 /= scale
cov_mat_7 /= scale
cov_mat_8 /= scale
# Compute roots
eigen_val_0 = ti.cast(0, ti.f32)
eigen_val_1 = ti.cast(0, ti.f32)
eigen_val_2 = ti.cast(0, ti.f32)
c0 = cov_mat_0 * cov_mat_4 * cov_mat_8 \
+ 2 * cov_mat_3 * cov_mat_6 * cov_mat_7 \
- cov_mat_0 * cov_mat_7 * cov_mat_7 \
- cov_mat_4 * cov_mat_6 * cov_mat_6 \
- cov_mat_8 * cov_mat_3 * cov_mat_3
c1 = cov_mat_0 * cov_mat_4 \
- cov_mat_3 * cov_mat_3 \
+ cov_mat_0 * cov_mat_8 \
- cov_mat_6 * cov_mat_6 \
+ cov_mat_4 * cov_mat_8 \
- cov_mat_7 * cov_mat_7
c2 = cov_mat_0 + cov_mat_4 + cov_mat_8
if ti.abs(c0) < 0.00001:
eigen_val_0 = 0
d = c2 * c2 - 4.0 * c1
if d < 0.0: # no real roots ! THIS SHOULD NOT HAPPEN!
d = 0.0
sd = ti.sqrt(d)
eigen_val_2 = 0.5 * (c2 + sd)
eigen_val_1 = 0.5 * (c2 - sd)
else:
s_inv3 = ti.cast(1.0 / 3.0, ti.f32)
s_sqrt3 = ti.sqrt(3.0)
c2_over_3 = c2 * s_inv3
a_over_3 = (c1 - c2 * c2_over_3) * s_inv3
if a_over_3 > 0:
a_over_3 = 0
half_b = 0.5 * (c0 + c2_over_3 * (2 * c2_over_3 * c2_over_3 - c1))
q = half_b * half_b + a_over_3 * a_over_3 * a_over_3
if q > 0:
q = 0
rho = ti.sqrt(-a_over_3)
theta = ti.atan2(ti.sqrt(-q), half_b) * s_inv3
cos_theta = ti.cos(theta)
sin_theta = ti.sin(theta)
eigen_val_0 = c2_over_3 + 2 * rho * cos_theta
eigen_val_1 = c2_over_3 - rho * (cos_theta + s_sqrt3 * sin_theta)
eigen_val_2 = c2_over_3 - rho * (cos_theta - s_sqrt3 * sin_theta)
temp_swap = ti.cast(0, ti.f32)
# Sort in increasing order.
if eigen_val_0 >= eigen_val_1:
temp_swap = eigen_val_1
eigen_val_1 = eigen_val_0
eigen_val_0 = temp_swap
if eigen_val_1 >= eigen_val_2:
temp_swap = eigen_val_2
eigen_val_2 = eigen_val_1
eigen_val_1 = temp_swap
if eigen_val_0 >= eigen_val_1:
temp_swap = eigen_val_1
eigen_val_1 = eigen_val_0
eigen_val_0 = temp_swap
if eigen_val_0 <= 0:
eigen_val_0 = 0
d = c2 * c2 - 4.0 * c1
if d < 0.0: # no real roots ! THIS SHOULD NOT HAPPEN!
d = 0.0
sd = ti.sqrt(d)
eigen_val_2 = 0.5 * (c2 + sd)
eigen_val_1 = 0.5 * (c2 - sd)
# end of compute roots
eigen_value = eigen_val_1 * scale # eigen value for 2D SDF
# eigen value for 3D SDF
#eigen_value = eigen_val_0 * scale
#print("eigen_val_0 ", eigen_val_0)
#print("eigen_val_1 ", eigen_val_1)
#print("eigen_val_2 ", eigen_val_2)
# TODO
#scaledMat.diagonal ().array () -= eigenvalues (0)
#eigenvector = detail::getLargest3x3Eigenvector<Vector> (scaledMat).vector;
# Compute normal vector (TODO)
#visual_norm[i,j][0] = eigen_val_0 #eigen_vector[0]
#visual_norm[i,j][1] = eigen_val_1 #eigen_vector[1]
#visual_norm[i,j][2] = eigen_val_2 #eigen_vector[2]
# Compute the curvature surface change
eig_sum = cov_mat_0 + cov_mat_1 + cov_mat_2
visual_curv[i,j][0] = 0
if eig_sum != 0:
visual_curv[i,j][0] = eigen_val_1 # true curvature is: ti.abs(eigen_value / eig_sum)
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 (p - o).norm_sqr()
def util_color_map_value(self, c0, c1, v) -> ti.i32:
vl = ti.max(0.0, ti.min(1.0, v))
r = c1 - c0
d = ti.cast(c0 + r * vl, ti.i32)
return d
def apply_grad():
# gradient descent
for i, j, k in density:
density[i, j, k] -= learning_rate * density.grad[i, j, k]
density[i, j, k] = ti.max(density[i, j, k], 0)
def substep():
for i, j in grid_m:
grid_v[i, j] = [0, 0]
grid_m[i, j] = 0
grid_v_int[i, j] = [0, 0]
grid_m_int[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 * (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 = 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 = ti.min(ti.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(float, 2) * ti.sqrt(J)
elif material[p] == 2:
F[p] = U @ sig @ V.transpose(
) # Reconstruct elastic deformation gradient after plasticity
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 node neighborhood
offset = ti.Vector([i, j])
dpos = (offset.cast(float) - fx) * dx
weight = w[i][0] * w[j][1]
grid_v_int[base + offset] += int(
ti.floor(0.5 + weight * (p_mass * v[p] + affine @ dpos) *
(2.0**v_exp)))
grid_m_int[base + offset] += int(
ti.floor(0.5 + weight * p_mass * (2.0**m_exp)))
for i, j in grid_m:
if grid_m_int[i, j] > 0: # No need for epsilon here
# grid_v[i, j] = (1.0 / grid_m[i, j]) * grid_v[i, j] # Momentum to velocity
grid_v[i, j] = (2**(m_exp - v_exp) / grid_m_int[i, j]
) * grid_v_int[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 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 * (1.5 - fx)**2, 0.75 - (fx - 1.0)**2, 0.5 * (fx - 0.5)**2
]
new_v = ti.Vector.zero(float, 2)
new_C = ti.Matrix.zero(float, 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 * g_v.outer_product(dpos)
v[p], C[p] = new_v, new_C
x[p] += dt * v[p] # advection
def color_f32_to_i8(x):
return ti.cast(ti.min(ti.max(x, 0.0), 1.0) * 255, ti.i32)
def trace(sample: ti.u32):
for i, j in linear_pixel:
o = ti.Vector([camera_pos[0], camera_pos[1], camera_pos[2]])
aperture_size = 0.2
forward = -o.normalized()
u = ti.Vector([0.0, 1.0, 0.0]).cross(forward).normalized()
v = forward.cross(u).normalized()
u = -u
# anti aliasing
d = ((i + ti.random() - width / 2.0) / width * u * 1.5
+ (j + ti.random() - height / 2.0) / width * v * 1.5
+ width / width * forward).normalized()
focal_point = d * focal_length / d.dot(forward) + o
o += d * 0.01
# assuming a circle-like aperture
phi = 2.0 * math.pi * ti.random()
aperture_radius = ti.random() * aperture_size
o += u * aperture_radius * ti.cos(phi) + \
v * aperture_radius * ti.sin(phi)
d = (focal_point - o).normalized()
uv = cubemap_coord(d)
albedo_factor = ti.Vector([1.0, 1.0, 1.0])
radiance = ti.Vector([0.0, 0.0, 0.0])
for step in ti.ndrange(32):
sp = spheres.intersect(o, d)
uv = cubemap_coord(d)
if sp[1] > -1:
sp_index = int(sp[1])
p = sp[0] * d + o
c_ = spheres.center_radius[sp_index]
c = ti.Vector([c_[0], c_[1], c_[2]])
n = (p - c).normalized()
wo = -d
albedo = spheres.albedos[sp_index]
metallic = spheres.metallics[sp_index]
ior = spheres.iors[sp_index]
roughness = ti.max(0.04, spheres.roughness[sp_index])
f0 = (1.0 - ior) / (1.0 + ior)
f0 = f0 * f0
f0 = lerp(f0, luma(albedo), metallic)
wi = reflect(-wo, n)
radiance += spheres.emissions[sp_index] * albedo_factor
view_fresnel = schlick2(wo, n, f0)
sample_weights = ti.Vector([1.0 - view_fresnel, view_fresnel])
weight = 0.0
h = (wi + wo).normalized()
shaded = ti.Vector([0.0, 0.0, 0.0])
if ti.random() < sample_weights[0]:
wi = cosine_sample(n).normalized()
h = (wi + wo).normalized()
shaded = ti.max(0.00, wi.dot(n) * albedo / math.pi)
else:
wi = ggx_sample(n, wo, roughness).normalized()
h = (wi + wo).normalized()
F = schlick2(wi, n, f0)
shaded = ti.max(0.0, wi.dot(n) * albedo * ggx_smith_uncorrelated(
roughness, h.dot(n), wo.dot(n), wi.dot(n), F))
pdf_lambert = wi.dot(n) / math.pi
pdf_ggx = ggx_pdf(roughness, h.dot(n), wo.dot(h))
weight = ti.max(0.0, 1.0 / (sample_weights[0] *
pdf_lambert + sample_weights[1] * pdf_ggx))
# russian roule
albedo_factor *= shaded * weight
if step > 5:
if luma(albedo) < ti.random():
break
else:
albedo_factor /= luma(albedo)
d = wi
o = p + eps * d
else:
radiance += albedo_factor * tex2d(skybox.field, uv) / 255
break
linear_pixel[i, j] = (linear_pixel[i, j] *
(sample - 1) + radiance) / sample
pixel[i, j] = ti.sqrt(linear_pixel[i, j])