def render_func(self, pos, normal, dir, light_dir):
color = ts.vec3(0.0)
shineness = self.shineness
half_lambert = ts.dot(normal, light_dir) * 0.5 + 0.5
lambert = max(0, ts.dot(normal, light_dir))
blinn_phong = ts.dot(normal, ts.mix(light_dir, -dir, 0.5))
blinn_phong = pow(max(blinn_phong, 0), shineness)
refl_dir = ts.reflect(light_dir, normal)
phong = -ts.dot(normal, refl_dir)
phong = pow(max(phong, 0), shineness)
strength = 0.0
if ti.static(self.lambert != 0.0):
strength += lambert * self.lambert
if ti.static(self.half_lambert != 0.0):
strength += half_lambert * self.half_lambert
if ti.static(self.blinn_phong != 0.0):
strength += blinn_phong * self.blinn_phong
if ti.static(self.phong != 0.0):
strength += phong * self.phong
color = ts.vec3(strength)
if ti.static(self.is_normal_map):
color = normal * 0.5 + 0.5
return color
def render_floor(self, camera):
scene = camera.scene
c_floor = ts.vec3(*self.floor_color)
c_sky = ts.vec3(*self.sky_color)
for X in ti.grouped(camera.img):
W = ti.cast(ti.Vector([X.x, X.y, 1]), ti.f32)
x = cook_coord(camera, W)
world_dir = camera.trans_dir(ts.normalize(x))
if world_dir[1] > 0 or camera.pos[None][1] < floor_y:
camera.img[X] = c_sky
else:
f = min(1, -world_dir[1] * 50)
n = camera.untrans_dir(ts.vec3(0, 1, 0))
pos = camera.pos[None] + world_dir * (
camera.pos[None][1] - floor_y) / abs(world_dir[1])
#print(pos)
pos = camera.untrans_pos(pos)
#print(pos)
color = ambient * c_sky * c_floor
for light in ti.static(scene.lights):
light_color = scene.opt.render_func(pos, n, \
ts.normalize(pos), light, c_floor)
color += light_color
camera.img[X] = c_sky * (1 - f) + color * f
camera.nbuf[X] = n
camera.zbuf[X] = 1 / pos.z
def render_particle(model, camera, index):
scene = model.scene
a = (model.L2C[None] @ ts.vec4(model.pos[index], 1)).xyz
r = model.radius[index]
A = camera.uncook(a)
rad = camera.uncook(ts.vec3(r, r, a.z), False)
M = int(ti.floor(A - rad))
N = int(ti.ceil(A + rad))
M = ts.clamp(M, 0, ti.Vector(camera.res))
N = ts.clamp(N, 0, ti.Vector(camera.res))
for X in ti.grouped(ti.ndrange((M.x, N.x), (M.y, N.y))):
pos = camera.cook(float(ts.vec3(X, a.z)))
dp = pos - a
dp2 = dp.norm_sqr()
if dp2 > r**2:
continue
dz = ti.sqrt(r**2 - dp2)
if camera.fb.atomic_depth(X, a.z - dz):
continue
n = ts.vec3(dp.xy, -dz)
normal = ts.normalize(n)
view = ts.normalize(a + n)
color = model.colorize(pos, normal)
camera.fb['img'][X] = color
camera.fb['normal'][X] = normal
def pixel_shader(self, pos, texcoor, normal, tangent, bitangent):
ndir = self.sample('normal', texcoor, ts.vec3(0.0, 0.0, 1.0))
normal = ti.Matrix.cols([tangent, bitangent, normal]) @ ndir
normal = normal.normalized()
color = self.sample('color', texcoor, ts.vec3(1.0))
color = self.colorize(pos, texcoor, normal, color)
return dict(img=color, normal=normal,
tangent=tangent, bitangent=bitangent)
def trace(self, orig, dir):
pos = orig
color = ts.vec3(0.0)
normal = ts.vec3(0.0)
for s in range(100):
t = self.calc_sdf(pos)
if t <= 0:
normal = ts.normalize(self.calc_grad(pos) - t)
break
pos += dir * t
return pos, normal
def normal(pos):
eps = 0.005
v1 = ts.vec3(1.0, -1.0, -1.0)
v2 = ts.vec3(-1.0, -1.0, 1.0)
v3 = ts.vec3(-1.0, 1.0, -1.0)
v4 = ts.vec3(1.0, 1.0, 1.0)
return ts.normalize(v1 * scene(pos + v1 * eps) +
v2 * scene(pos + v2 * eps) +
v3 * scene(pos + v3 * eps) +
v4 * scene(pos + v4 * eps))
def get_volume_normal(self, pos):
delta = 1e-3
x_delta = tl.vec3(delta, 0.0, 0.0)
y_delta = tl.vec3(0.0, delta, 0.0)
z_delta = tl.vec3(0.0, 0.0, delta)
dx = self.sample_volume_trilinear(pos + x_delta) \
- self.sample_volume_trilinear(pos - x_delta)
dy = self.sample_volume_trilinear(pos + y_delta) \
- self.sample_volume_trilinear(pos - y_delta)
dz = self.sample_volume_trilinear(pos + z_delta) \
- self.sample_volume_trilinear(pos - z_delta)
return tl.vec3(dx, dy, dz).normalized()
def get_ambient(camera, normal, view):
c_floor = ts.vec3(0.75)
c_sky = ts.vec3(0.8, 0.9, 0.95)
refl_dir = -ts.reflect(-view, normal)
refl_dir = ts.normalize(camera.trans_dir(refl_dir))
color = ts.vec3(ambient)
if refl_dir[1] > 0:
color *= c_sky
else:
f = min(1.0, -refl_dir[1] * 25.0)
color *= c_sky * (1 - f) + c_floor * f
return color
def pixel_shader(self, mid: ti.template(), pos, tex, nrm, tan, bitan):
if ti.static(isinstance(mid, int)):
return ti.static(self.materials[mid]).pixel_shader(
pos, tex, nrm, tan, bitan)
color = ts.vec3(0.0)
if mid != 0:
color = ts.vec3(1.0, 0.0,
1.0) # magenta, for debugging missing materials
for i, material in ti.static(self.materials.items()):
if mid == i:
color = material.pixel_shader(pos, tex, nrm, tan, bitan)
return color
def compute_tangent(dp1, dp2, duv1, duv2):
if ti.static(0):
return ts.vec3(0.0), ts.vec3(0.0)
IDUV = ti.Matrix([[duv1.x, duv1.y], [duv2.x, duv2.y]]).inverse()
DPx = ti.Vector([dp1.x, dp2.x])
DPy = ti.Vector([dp1.y, dp2.y])
DPz = ti.Vector([dp1.z, dp2.z])
T = ti.Vector([0.0, 0.0, 0.0])
B = ti.Vector([0.0, 0.0, 0.0])
T.x, B.x = IDUV @ DPx
T.y, B.y = IDUV @ DPy
T.z, B.z = IDUV @ DPz
return T, B
def calc_gi(self, camera):
scene = camera.scene
for X in ti.grouped(camera.img):
if self.enable_gi[None] == 0:
continue
# use an additional normal buffer at this time
if camera.zbuf[X] > 0:
z = 1 / camera.zbuf[X]
pos = cook_coord(camera,
ti.cast(ti.Vector([X.x, X.y, z]), ti.f32))
pos_world = camera.trans_pos(pos)
norm_world = camera.trans_dir(camera.nbuf[X])
dy = pos_world[1] - floor_y
ftot = 0.0
if dy > 0:
ftot = form_factor_floor(norm_world, dy, self.radius)
gtot = ts.vec3(0.0)
if ti.static(self.grid is not None):
base = self.grid.grid_index(pos_world)
for dI in ti.grouped(ti.ndrange((-4, 5), (-4, 5),
(-4, 5))):
I = max(0, min(base + dI, self.grid.gridsize - 1))
for p in range(self.grid_n[I + dI]):
i = self.grid_list[I + dI, p]
if (self.particles[i] - pos_world).norm_sqr() \
> (self.gi_cutoff * self.boxlength) ** 2:
continue
f, gi = get_gi_factors(camera, scene,
self.particles[i],
pos_world, norm_world,
self.radius,
self.colors[self.type[i]])
ftot += f
gtot += gi
else:
for i in range(self.particles.shape[0]):
# don't compute for particles behind the normal
if ti.dot(self.particles[i] - pos_world,
norm_world) < 0:
continue
f, gi = get_gi_factors(camera, scene,
self.particles[i], pos_world,
norm_world, self.radius,
self.colors[self.type[i]])
ftot += f
gtot += gi
camera.img[X] = camera.img[X] * ts.vec3(max(1 - ftot,
0)) + gtot * 0.3
def render_line(model, camera, face, w0=0, w1=1):
posa, posb = face.pos # Position
texa, texb = face.tex # TexCoord
nrma, nrmb = face.nrm # Normal
clra = [posa, texa, nrma]
clrb = [posb, texb, nrmb]
A = camera.uncook(posa)
B = camera.uncook(posb)
M = int(ti.floor(min(A, B) - 1))
N = int(ti.ceil(max(A, B) + 1))
M = ts.clamp(M, 0, ti.Vector(camera.fb.res))
N = ts.clamp(N, 0, ti.Vector(camera.fb.res))
B_A = (B - A).normalized()
for X in ti.grouped(ti.ndrange((M.x, N.x), (M.y, N.y))):
udf = abs((X - A).cross(B_A))
if udf >= w1:
continue
strength = ts.smoothstep(udf, w1, w0)
color = ts.vec3(strength)
camera.img[X] += color
def sample_volume_trilinear(self, pos):
''' Samples volume data at `pos` and trilinearly interpolates the value
Args:
pos (tl.vec3): Position to sample the volume in [-1, 1]^3
Returns:
float: Sampled interpolated intensity
'''
pos = tl.clamp(((0.5 * pos) + 0.5), 0.0, 1.0) \
* ti.static(tl.vec3(*self.volume.shape) - 1.0 - 1e-4)
x_low, x_high, x_frac = low_high_frac(pos.x)
y_low, y_high, y_frac = low_high_frac(pos.y)
z_low, z_high, z_frac = low_high_frac(pos.z)
x_high = min(x_high, ti.static(self.volume.shape[0] - 1))
y_high = min(y_high, ti.static(self.volume.shape[1] - 1))
z_high = min(z_high, ti.static(self.volume.shape[2] - 1))
# on z_low
v000 = self.volume[x_low, y_low, z_low]
v100 = self.volume[x_high, y_low, z_low]
x_val_y_low = tl.mix(v000, v100, x_frac)
v010 = self.volume[x_low, y_high, z_low]
v110 = self.volume[x_high, y_high, z_low]
x_val_y_high = tl.mix(v010, v110, x_frac)
xy_val_z_low = tl.mix(x_val_y_low, x_val_y_high, y_frac)
# on z_high
v001 = self.volume[x_low, y_low, z_high]
v101 = self.volume[x_high, y_low, z_high]
x_val_y_low = tl.mix(v001, v101, x_frac)
v011 = self.volume[x_low, y_high, z_high]
v111 = self.volume[x_high, y_high, z_high]
x_val_y_high = tl.mix(v011, v111, x_frac)
xy_val_z_high = tl.mix(x_val_y_low, x_val_y_high, y_frac)
return tl.mix(xy_val_z_low, xy_val_z_high, z_frac)
def intersect(self, orig, dir):
ret, normal = INF, ts.vec3(0.0)
for b in ti.static(self.balls):
t, n = b.intersect(orig, dir)
if t < ret:
ret, normal = t, n
return ret, normal
def intersect(self, orig, dir):
ret, normal = INF, ts.vec3(0.0)
for I in ti.grouped(ti.ndrange(*self.pos.shape())):
t, n = self.make_one(I).do_intersect(orig, dir)
if t < ret:
ret, normal = t, n
return ret, normal
def cal_look_at_mat(ro, ta, roll):
ww = (ta - ro).normalized()
uu = ts.cross(ww, ts.vec3(ts.sin(roll), ts.cos(roll), 0.0)).normalized()
vv = ts.cross(uu, ww).normalized()
return ts.mat([uu[0], vv[0], ww[0]], [uu[1], vv[1], ww[1]],
[uu[2], vv[2], ww[2]])
def intersect_triangle(model, orig, dir, face):
posa, posb, posc = face.pos
texa, texb, texc = face.tex
nrma, nrmb, nrmc = face.nrm
L2C = model.L2W[None]
posa = (L2C @ ts.vec4(posa, 1)).xyz
posb = (L2C @ ts.vec4(posb, 1)).xyz
posc = (L2C @ ts.vec4(posc, 1)).xyz
nrma = (L2C @ ts.vec4(nrma, 0)).xyz
nrmb = (L2C @ ts.vec4(nrmb, 0)).xyz
nrmc = (L2C @ ts.vec4(nrmc, 0)).xyz
tan, bitan = compute_tangent(posb - posa, posc - posa, texb - texa, texc - texa)
hit = 1e6
clr = ts.vec3(0.0)
sa, sb, sc = plucker_bcoor(orig, orig + dir, posa, posb, posc)
if (sa >= 0 and sb >= 0 and sc >= 0) or (sa <= 0 and sb <= 0 and sc <= 0):
snorm = sa + sb + sc
sa /= snorm
sb /= snorm
sc /= snorm
pos = posa * sa + posb * sb + posc * sc
tex = texa * sa + texb * sb + texc * sc
nrm = nrma * sa + nrmb * sb + nrmc * sc
if dir.dot(pos - orig) > 1e-4:
hit = (pos - orig).norm()
orig, dir, clr = model.material.radiance(model, pos, dir, tex, nrm, tan, bitan)
return hit, orig, dir, clr
def _render(self):
for I in ti.grouped(self.img):
self.img[I] = ts.vec3(0.0)
self.zbuf[I] = 0.0
if ti.static(len(self.models)):
for model in ti.static(self.models):
model.render()
def __init__(self,
volume_resolution,
render_resolution,
max_samples=512,
tf_resolution=128,
fov=30.0,
nearfar=(0.1, 100.0)):
''' Initializes Volume Raycaster. Make sure to .set_volume() and .set_tf_tex() after initialization
Args:
volume_resolution (3-tuple of int): Resolution of the volume data (w,h,d)
render_resolution (2-tuple of int): Resolution of the rendering (w,h)
tf_resolution (int): Resolution of the transfer function texture
fov (float, optional): Field of view of the camera in degrees. Defaults to 60.0.
nearfar (2-tuple of float, optional): Near and far plane distance used for perspective projection. Defaults to (0.1, 100.0).
'''
self.resolution = render_resolution
self.aspect = render_resolution[0] / render_resolution[1]
self.fov_deg = fov
self.fov_rad = np.radians(fov)
self.near, self.far = nearfar
# Taichi Fields
self.volume = ti.field(ti.f32, needs_grad=True)
self.tf_tex = ti.Vector.field(4, dtype=ti.f32, needs_grad=True)
self.render_tape = ti.Vector.field(4, dtype=ti.f32, needs_grad=True)
self.output_rgba = ti.Vector.field(4, dtype=ti.f32, needs_grad=True)
self.valid_sample_step_count = ti.field(ti.i32)
self.sample_step_nums = ti.field(ti.i32)
self.entry = ti.field(ti.f32)
self.exit = ti.field(ti.f32)
self.rays = ti.Vector.field(3, dtype=ti.f32)
self.max_valid_sample_step_count = ti.field(ti.i32, ())
self.max_samples = max_samples
self.ambient = 0.4
self.diffuse = 0.8
self.specular = 0.3
self.shininess = 32.0
self.light_color = tl.vec3(1.0)
self.cam_pos = ti.Vector.field(3, dtype=ti.f32)
volume_resolution = tuple(map(lambda d: d // 4, volume_resolution))
render_resolution = tuple(map(lambda d: d // 8, render_resolution))
ti.root.dense(ti.ijk,
volume_resolution).dense(ti.ijk,
(4, 4, 4)).place(self.volume)
ti.root.dense(ti.ijk, (*render_resolution, max_samples)).dense(
ti.ijk, (8, 8, 1)).place(self.render_tape)
ti.root.dense(ti.ij, render_resolution).dense(ti.ij, (8, 8)).place(
self.valid_sample_step_count, self.sample_step_nums)
ti.root.dense(ti.ij, render_resolution).dense(ti.ij, (8, 8)).place(
self.output_rgba)
ti.root.dense(ti.ij, render_resolution).dense(ti.ij, (8, 8)).place(
self.entry, self.exit)
ti.root.dense(ti.ij,
render_resolution).dense(ti.ij,
(8, 8)).place(self.rays)
ti.root.dense(ti.i, tf_resolution).place(self.tf_tex)
ti.root.dense(ti.i, tf_resolution).place(self.tf_tex.grad)
ti.root.place(self.cam_pos)
ti.root.lazy_grad()
def radiance(self):
outdir = ts.vec3(0.0)
clr = ts.vec3(0.0)
if ti.random() < self.emission:
clr = ts.vec3(self.emission_color)
elif ti.random() < self.specular:
clr = ts.vec3(self.specular_color)
outdir = ts.reflect(self.indir, self.normal)
elif ti.random() < self.diffuse:
clr = ts.vec3(self.diffuse_color)
outdir = ts.randUnit3D()
if outdir.dot(self.normal) < 0:
outdir = -outdir
#s = ti.random()
#outdir = ts.vec3(ti.sqrt(1 - s**2) * ts.randUnit2D(), s)
#outdir = ti.Matrix.cols([self.tangent, self.bitangent, self.normal]) @ outdir
return self.pos, outdir, clr
def clear_framebuffer(self):
self.max_valid_sample_step_count[None] = 0
for i, j, k in self.render_tape:
self.render_tape[i, j, k] = tl.vec4(0.0)
for i, j in self.valid_sample_step_count:
self.valid_sample_step_count[i, j] = 1
self.output_rgba[i, j] = tl.vec4(0.0)
self.output_rgb[i, j] = tl.vec3(0.0)
def render_func(self, pos, normal, viewdir, light, color):
lightdir = light.get_dir(pos)
costheta = max(0, ti.dot(normal, lightdir))
l_out = ts.vec3(0.0)
if costheta > 0:
l_out = self.brdf(normal, -viewdir, lightdir, color)\
* costheta * light.get_color(pos)
return l_out
def generate(self, coor):
orig = ts.vec3(0.0)
dir = ts.vec3(0.0, 0.0, 1.0)
if ti.static(self.type == self.ORTHO):
orig = ts.vec3(coor, 0.0)
elif ti.static(self.type == self.TAN_FOV):
uv = coor * self.fov
dir = ts.normalize(ts.vec3(uv, 1))
elif ti.static(self.type == self.COS_FOV):
uv = coor * self.fov
dir = ts.vec3(ti.sin(uv), ti.cos(uv.norm()))
orig = (self.L2W[None] @ ts.vec4(orig, 1)).xyz
dir = (self.L2W[None] @ ts.vec4(dir, 0)).xyz
return orig, dir
def flush_taa(self):
if ti.static(self.n_taa):
self.ntaa[None] = 0
self.itaa[None] = 0
for I in ti.grouped(ti.ndrange(*self.res)):
r = ts.vec3(0.0)
for i in ti.static(range(self.n_taa)):
self.taa[i, I] *= 0
def render(self, camera):
for I in ti.grouped(ti.ndrange(*camera.res)):
if camera.fb.idepth[I] != 0:
continue
id = I / ts.vec(*camera.res) * 2 - 1
dir = ts.vec3(id * ti.tan(camera.fov), 1.0)
dir = v4trans(self.L2C[None].inverse(), dir, 0).normalized()
color = self.sample(dir)
camera.fb.update(I, dict(img=color))
def my_render_func(pos, normal, dir, light_dir):
n = cartoon_level[None]
refl_dir = ts.reflect(light_dir, normal)
#refl_dir = ts.mix(light_dir, -dir, 0.5)
NoL = pow(ts.dot(normal, refl_dir), 12)
NoL = ts.mix(NoL, ts.dot(normal, light_dir) * 0.5 + 0.5, 0.5)
strength = 0.2
if any(normal):
strength = ti.floor(max(0, NoL * n + 0.5)) / n
return ts.vec3(strength)
def do_render(self, scene):
W = 1
A = scene.uncook_coor(scene.camera.untrans_pos(self.a))
B = scene.uncook_coor(scene.camera.untrans_pos(self.b))
M, N = int(ti.floor(min(A, B) - W)), int(ti.ceil(max(A, B) + W))
for X in ti.grouped(ti.ndrange((M.x, N.x), (M.y, N.y))):
P = B - A
udf = (ts.cross(X, P) + ts.cross(B, A))**2 / P.norm_sqr()
XoP = ts.dot(X, P)
AoB = ts.dot(A, B)
if XoP > B.norm_sqr() - AoB:
udf = (B - X).norm_sqr()
elif XoP < AoB - A.norm_sqr():
udf = (A - X).norm_sqr()
if udf < 0:
scene.img[X] = ts.vec3(1.0)
elif udf < W**2:
t = ts.smoothstep(udf, 0, W**2)
ti.atomic_min(scene.img[X], ts.vec3(t))
def render_func(self, pos, normal, viewdir, light): # TODO: move render_func to Light.render_func?
if ti.static(isinstance(light, AmbientLight)):
return light.get_color(pos) * self.get_ambient()
lightdir = light.get_dir(pos)
NoL = ts.dot(normal, lightdir)
l_out = ts.vec3(0.0)
if NoL > EPS:
l_out = light.get_color(pos)
l_out *= NoL * self.brdf(normal, lightdir, -viewdir)
return l_out
def render(self):
self.src.render()
for I in ti.grouped(self.img):
mid = self.src['mid'][I]
pos = self.src['position'][I]
texcoor = self.src['texcoord'][I]
normal = self.src['normal'][I]
tangent = self.src['tangent'][I]
bitangent = normal.cross(tangent)
color = ts.vec3(0.0)
if mid != 0:
color = ts.vec3(1.0, 0.0,
1.0) # magenta for debugging missing material
if ti.static(len(self.mtllib)):
for i, material in ti.static(enumerate(self.mtllib)):
if ti.static(material is not None):
if i == mid:
color = material.pixel_shader(
self, pos, texcoor, normal, tangent, bitangent)
self.img[I] = color