-
Notifications
You must be signed in to change notification settings - Fork 0
/
pt.py
473 lines (375 loc) · 15.9 KB
/
pt.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
import taichi as ti
import numpy as np
import math
ti.init(arch=ti.gpu)
inf = 1e10
eps = 1e-4
max_luminance = 100
class Image:
def __init__(self, path):
self.img = ti.tools.imread(path)
tex_w, tex_h = self.img.shape[0:2]
self.field = ti.Vector.field(3, dtype=ti.u8, shape=(tex_w, tex_h))
def load(self):
self.field.from_numpy(self.img)
@ti.func
def tex2d(tex_field, uv):
tex_w, tex_h = tex_field.shape[0:2]
p = uv * ti.Vector([tex_w, tex_h])
l = int(ti.floor(p))
t = p - l
# bilinear interp
return (
((tex_field[l] * (1 - t[0])) + tex_field[l + ti.Vector([1, 0])] * t[0]) * (1 - t[1])
+ (tex_field[l + ti.Vector([0, 1])] * (1 - t[0]) + tex_field[l + ti.Vector([1, 1])] * t[0]) * t[1]) / 255.0
def gaussian_kernel(l=5, sig=1.):
"""\
creates gaussian kernel with side length `l` and a sigma of `sig`
"""
ax = np.linspace(-(l - 1) / 2., (l - 1) / 2., l, dtype=np.single)
gauss = np.exp(-0.5 * np.square(ax) / np.square(sig), dtype=np.single)
kernel = np.outer(gauss, gauss)
return kernel / np.sum(kernel)
@ti.data_oriented
class SphereSOA:
def __init__(self, array_length):
self.center_radius = ti.Vector.field(4, dtype=ti.f32, shape=(array_length))
self.albedos = ti.Vector.field(3, dtype=ti.f32, shape=(array_length))
self.emissions = ti.Vector.field(3, dtype=ti.f32, shape=(array_length))
self.roughness = ti.field(dtype=ti.f32, shape=(array_length))
self.metallics = ti.field(dtype=ti.f32, shape=(array_length))
self.iors = ti.field(dtype=ti.f32, shape=(array_length))
self.array_length = array_length
@ ti.func
def intersect(self, o, d):
min_t = inf
min_index = -1
sp_index = 0
for i in ti.ndrange(self.array_length):
c_r = self.center_radius[i]
r = c_r[3]
p = ti.Vector([c_r[0], c_r[1], c_r[2]])
op = p - o
b = op.dot(d)
det = b * b - op.dot(op) + r * r
t = inf
if det > 0:
det = ti.sqrt(det)
t = (b - det) if ((b - det) > eps) else ((b + det)
if (b + det > eps) else inf)
if t < min_t:
min_index = sp_index
min_t = t
sp_index += 1
return ti.Vector([min_t, min_index])
width, height = 1080, 720
linear_pixel = ti.Vector.field(3, dtype=ti.f32, shape=(width, height))
errors = ti.field(dtype=ti.f32, shape=(width, height))
ray_count = ti.field(dtype=ti.i32, shape=(width, height))
bloom_pixel = ti.Vector.field(3, dtype=ti.f32, shape=(width, height))
pixel = ti.Vector.field(3, dtype=ti.f32, shape=(width, height))
gaussian_kernel_size = 9
bloom_strength = 0.02
ambient_weight = 0.2
start_cursor = [0.0, 0.0]
blur_kernel = ti.field(ti.f32, shape=(gaussian_kernel_size, gaussian_kernel_size))
blur_kernel.from_numpy(gaussian_kernel(gaussian_kernel_size, 1.))
skybox = Image('skybox.jpg') # z > 0
last_camera_pos = ti.field(ti.f32, 3)
camera_pos = ti.field(ti.f32, 3)
focal_length = ti.field(ti.f32, shape=())
class SphereAOS:
def __init__(self, center_radius, albedo, emission, roughness, metallic, ior):
self.center_radius = center_radius
self.albedo = albedo
self.emission = emission
self.roughness = roughness
self.metallic = metallic
self.ior = ior
spheres_aos = [
SphereAOS(
center_radius=ti.Vector([-2.,0.0, -3.0, 2.5]), albedo=ti.Vector([1.0, 1.0, 0.0]), emission=ti.Vector([0, 0, 0]), roughness=0.2, metallic=1.0, ior=2.495),
SphereAOS(
center_radius=ti.Vector([1.0, -1.5, 1.0, 1.0]), albedo=ti.Vector([1.0, 1.0, 1.0]), emission=ti.Vector([0, 0, 0]), roughness=0.0, metallic=0.0, ior=1.4),
SphereAOS(
center_radius=ti.Vector([0.0, -500., 0., 497.5]), albedo=ti.Vector([1.0, 0.8, 0.6]), emission=ti.Vector([0, 0, 0]), roughness=0.5, metallic=0.95, ior=2.90),
SphereAOS(
center_radius=ti.Vector([-1, -2.0, 0.5, 0.5]), albedo=ti.Vector([1.0, 1.0, 1.0]), emission=ti.Vector([0, 0, 0]), roughness=0.0, metallic=1.0, ior=2.5),
SphereAOS(
center_radius=ti.Vector([2.0, 0, -2.0, 0.7]), albedo=ti.Vector([0, 0, 0]), emission=ti.Vector([15, 1, 1]), roughness=0.0, metallic=0.8, ior=2.0),
SphereAOS(
center_radius=ti.Vector([-2.0, 1.0, 1.0, 0.7]), albedo=ti.Vector([0, 0, 0]), emission=ti.Vector([0.2, 15, 15]), roughness=0.0, metallic=0.8, ior=2.0),
SphereAOS(
center_radius=ti.Vector([-8.0, -1.5, -5, 1.01]), albedo=ti.Vector([1.0, 1.0, 1.0]), emission=ti.Vector([4, 4, 0.5]), roughness=0.5, metallic=0.2, ior=2.0),
]
spheres_soa = SphereSOA(len(spheres_aos))
for i, sphere in enumerate(spheres_aos):
spheres_soa.center_radius[i] = sphere.center_radius
spheres_soa.albedos[i] = sphere.albedo
spheres_soa.emissions[i] = sphere.emission
spheres_soa.roughness[i] = sphere.roughness
spheres_soa.metallics[i] = sphere.metallic
spheres_soa.iors[i] = sphere.ior
skybox.load()
@ ti.func
def reflect(I, N):
return I - 2 * N.dot(I) * N
@ ti.func
def lerp(vl, vr, frac):
return vl + frac * (vr - vl)
@ ti.func
def cubemap_coord(dir):
eps = 1e-7
coor = ti.Vector([0., 0.])
if dir.z >= 0 and dir.z >= abs(dir.y) - eps and dir.z >= abs(dir.x) - eps:
coor = ti.Vector([3 / 8, 1 / 2]) + \
ti.Vector([dir.x / 8, dir.y / 6]) / dir.z
if dir.z <= 0 and -dir.z >= abs(dir.y) - eps and -dir.z >= abs(dir.x) - eps:
coor = ti.Vector([7 / 8, 1 / 2]) + \
ti.Vector([-dir.x / 8, dir.y / 6]) / -dir.z
if dir.x <= 0 and -dir.x >= abs(dir.y) - eps and -dir.x >= abs(dir.z) - eps:
coor = ti.Vector([1 / 8, 1 / 2]) + \
ti.Vector([dir.z / 8, dir.y / 6]) / -dir.x
if dir.x >= 0 and dir.x >= abs(dir.y) - eps and dir.x >= abs(dir.z) - eps:
coor = ti.Vector([5 / 8, 1 / 2]) + \
ti.Vector([-dir.z / 8, dir.y / 6]) / dir.x
if dir.y >= 0 and dir.y >= abs(dir.x) - eps and dir.y >= abs(dir.z) - eps:
coor = ti.Vector([3 / 8, 5 / 6]) + \
ti.Vector([dir.x / 8, -dir.z / 6]) / dir.y
if dir.y <= 0 and -dir.y >= abs(dir.x) - eps and -dir.y >= abs(dir.z) - eps:
coor = ti.Vector([3 / 8, 1 / 6]) + \
ti.Vector([dir.x / 8, dir.z / 6]) / -dir.y
return coor
@ ti.func
def cosine_sample(n):
u = ti.Vector([1.0, 0.0, 0.0])
if abs(n[1]) < 1 - eps:
u = n.cross(ti.Vector([0.0, 1.0, 0.0])).normalized()
v = n.cross(u)
phi = 2.0 * math.pi * ti.random()
ay = ti.sqrt(ti.random())
ax = ti.sqrt(1.0 - ay**2.0)
return ax * (ti.cos(phi) * u + ti.sin(phi) * v) + ay * n
@ ti.func
def ggx_sample(n, wo, roughness):
u = ti.Vector([1.0, 0.0, 0.0])
if abs(n[1]) < 1.0 - eps:
u = n.cross(ti.Vector([0.0, 1.0, 0.0])).normalized()
v = n.cross(u)
r0 = ti.random()
r1 = ti.random()
a = roughness ** 2.0
a2 = a * a
theta = ti.acos(ti.sqrt((1.0 - r0) / ((a2-1.0)*r0 + 1.0)))
phi = 2.0 * math.pi * r1
wm = ti.cos(theta) * n + ti.sin(theta) * ti.cos(phi) * \
u + ti.sin(theta) * ti.sin(phi) * v
wi = reflect(-wo, wm)
return wi
@ ti.func
def ggx_ndf(wi, wo, n, roughness):
m = (wi + wo).normalized()
a = roughness * roughness
nm2 = n.dot(m) ** 2.0
return (a * a) / (math.pi * nm2*(a*a-1.0)+1.0**2.0)
@ ti.func
def ggx_ndf_wi(wi, wo, n, roughness):
m = (wi + wo).normalized()
wm_pdf = ggx_ndf(wi, wo, n, roughness)
wi_pf = n.dot(m) / (4 * m.dot(wi))
return wi_pf
@ ti.func
def ggx_pdf(roughness, hdotn, vdoth):
t = hdotn*hdotn*roughness*roughness - (hdotn*hdotn - 1.0)
D = (roughness*roughness) * math.pi / (t*t)
return D*hdotn / (4.0 * abs(vdoth))
@ ti.func
def schlick2(wi, n, f0):
return f0 + (1.0-f0) * (1-n.dot(wi))**5.0
@ ti.func
def smith_g(NoV, NoL, roughness):
a2 = roughness * roughness
ggx_v = NoL * ti.sqrt(NoV * NoV * (1.0 - a2) + a2)
ggx_l = NoV * ti.sqrt(NoL * NoL * (1.0 - a2) + a2)
return 0.5 / (ggx_v + ggx_l)
@ti.func
def ggx_smith_uncorrelated(roughness, hdotn, vdotn, ldotn, fresnel):
t = hdotn*hdotn*roughness*roughness - (hdotn*hdotn - 1.0)
D = (roughness*roughness) * math.pi / (t*t)
F = fresnel
Gv = vdotn * ti.sqrt(roughness*roughness +
(1.0 - roughness * roughness)*ldotn*ldotn)
Gl = ldotn * ti.sqrt(roughness*roughness +
(1.0 - roughness * roughness)*vdotn*vdotn)
G = 1.0 / (Gv + Gl)
return F*G*D / 2.0
@ ti.func
def luma(albedo):
return albedo.dot(ti.Vector([0.2126, 0.7152, 0.0722]))
@ti.func
def tone(x):
A = 2.51
B = 0.03
C = 2.43
D = 0.59
E = 0.14
return (x * (A * x + B)) / (x * (C * x + D) + E)
gui = ti.GUI("Path Tracer", res=(width, height))
@ ti.kernel
def trace():
for i, j in linear_pixel:
adaptive_sampler_count = int(16 * tone(errors[i, j] / ray_count[i, j]))
# pixel[i, j].fill(adaptive_sampler_count / 16)
for addition_sampler in ti.ndrange(16):
if addition_sampler > adaptive_sampler_count:
continue
ray_count[i, j] += 1
sample = ray_count[i, j]
o = ti.Vector([camera_pos[0], camera_pos[1], camera_pos[2]])
aperture_size = 0.1
forward = -o.normalized()
u = ti.Vector([0.0, 1.0, 0.0]).cross(forward).normalized()
v = forward.cross(u).normalized()
u = -u
d = ((i + ti.random() - width / 2.0) / width * u
+ (j + ti.random() - height / 2.0) / width * v
+ width / width * forward).normalized()
focal_point = d * focal_length[None] / d.dot(forward) + o
# 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_soa.intersect(o, d)
uv = cubemap_coord(d)
if sp[1] > -1:
sp_index = int(sp[1])
p = sp[0] * d + o
c_ = spheres_soa.center_radius[sp_index]
c = ti.Vector([c_[0], c_[1], c_[2]])
radius = c_[3]
n = (p - c).normalized()
wo = -d
albedo = spheres_soa.albedos[sp_index]
metallic = spheres_soa.metallics[sp_index]
ior = spheres_soa.iors[sp_index]
roughness = ti.max(0.04, spheres_soa.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_soa.emissions[sp_index] / (radius * radius) * 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)) * ambient_weight
break
linear_color = radiance
linear_pixel[i, j] = (linear_pixel[i, j] * (sample - 1) + linear_color) / sample
errorVec = linear_color - linear_pixel[i, j]
error = errorVec.dot(errorVec)
errors[i, j] += error
luminance = radiance.dot(ti.Vector([0.2126, 0.7152, 0.0722]))
if(luminance < max_luminance):
if (luminance > 1.0):
bloom_pixel[i, j] = (bloom_pixel[i, j] * (sample - 1) + linear_color) / sample
else:
bloom_pixel[i, j] = (bloom_pixel[i, j] * (sample - 1)) / sample
for i, j in bloom_pixel:
hdr_blur = ti.Vector([0.0, 0.0, 0.0])
for kx in ti.ndrange(gaussian_kernel_size):
for ky in ti.ndrange(gaussian_kernel_size):
hdr_blur += bloom_pixel[i + kx - gaussian_kernel_size // 2, j + ky - gaussian_kernel_size // 2] * blur_kernel[kx, ky]
bloom_pixel[i, j] = hdr_blur
for i, j in pixel:
pixel[i, j] = pow(tone(linear_pixel[i, j] + bloom_pixel[i, j] * bloom_strength), 1.0 / 2.2)
def try_reset(t):
for e in gui.get_events(gui.PRESS, gui.MOTION):
if e.key == gui.LMB:
last_camera_pos[0] = camera_pos[0]
last_camera_pos[1] = camera_pos[1]
last_camera_pos[2] = camera_pos[2]
start_cursor_x, start_cursor_y = gui.get_cursor_pos()
start_cursor[0] = start_cursor_x
start_cursor[1] = start_cursor_y
if e.key == gui.MOVE and gui.is_pressed(gui.LMB, gui.RMB):
(current_cursor_x, current_cursor_y) = gui.get_cursor_pos()
rotateX = (current_cursor_x - start_cursor[0])
rotateY = (current_cursor_y - start_cursor[1])
x = math.cos(
rotateX) * last_camera_pos[0] - math.sin(rotateX) * last_camera_pos[2]
z = math.sin(
rotateX) * last_camera_pos[0] + math.cos(rotateX) * last_camera_pos[2]
y = last_camera_pos[1]
camera_pos[1] = math.cos(
rotateY) * y - math.sin(rotateY) * z
camera_pos[2] = math.sin(
rotateY) * y + math.cos(rotateY) * z
camera_pos[0] = x
return True
if e.key == gui.WHEEL:
dt = e.delta[1] / 1000.0
if gui.is_pressed(gui.SHIFT):
focal_length[None] *= (1.0 + dt)
else:
for i in range(3):
camera_pos[i] *= (1.0 + dt)
return True
return False
# Initialize the camera
sample = 0
t = 1
focal_length[None] = 15.0
last_camera_pos[2] = focal_length[None]
camera_pos[2] = focal_length[None]
print("Start tracing...")
print("0 spp")
while True:
if try_reset(t):
if sample > 1:
print ("\033[A \033[A")
print("Camera moved, restart tracing...")
print("0 spp")
sample = 0
linear_pixel.fill(0)
bloom_pixel.fill(0)
ray_count.fill(0)
errors.fill(0)
print ("\033[A \033[A")
print(f"[{sample} spp]" )
sample += 1
trace()
t += 1
gui.set_image(pixel)
gui.show()