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 | import torch
import torch.nn.functional as F
class ONB(object):
def __init__(self, batch_size : int):
"""
uvw - xyz - tbn
"""
self.batch_size = batch_size
self.axis = torch.zeros(batch_size, 3, 3) # (batch, 3, 3)
self.axis[:, 0, 0] = 1
self.axis[:, 1, 1] = 1
self.axis[:, 2, 2] = 1
def u(self) -> torch.Tensor:
"""
Returns:
u axis of shape (batch, 3)
"""
return self.axis[:, 0, :]
def v(self) -> torch.Tensor:
return self.axis[:, 1, :]
def w(self) -> torch.Tensor:
return self.axis[:, 2, :]
def inverse_transform(self, p : torch.Tensor) -> torch.Tensor:
"""
Convert local coordinate(in onb) back to global
coordinate(onb in).
Args:
p: local coordinates of shape (batch, 3) or (batch, N, 3)
Returns:
global coordinates of shape (batch, 3) or (batch, N, 3)
"""
assert(self.batch_size == p.size(0))
assert(len(p.size()) in [2, 3])
if len(p.size()) == 2:
return p[:, 0:1] * self.u() + p[:, 1:2] * self.v() + p[:, 2:3] * self.w()
elif len(p.size()) == 3:
u = self.u().unsqueeze(1)
v = self.v().unsqueeze(1)
w = self.w().unsqueeze(1)
return p[:, :, [0]] * u + p[:, :, [1]] * v + p[:, :, [2]] * w
def transform(self, p : torch.Tensor) -> torch.Tensor:
"""
Convert global coordinate(onb in) to local
coordinate(in onb).
Args:
p: global coordinates of shape (batch, 3) or (batch, lightnum, 3)
Returns:
local coordinates of shape (batch, 3) or (batch, lightnum, 3)
"""
assert(self.batch_size == p.size(0))
assert(len(p.size()) in [2, 3])
if len(p.size()) == 2:
x = torch.sum(p * self.u(), dim=1, keepdim=True)
y = torch.sum(p * self.v(), dim=1, keepdim=True)
z = torch.sum(p * self.w(), dim=1, keepdim=True)
return torch.cat([x, y, z], dim=1)
elif len(p.size()) == 3:
lightnum = p.size(1)
u = self.u().unsqueeze(1).repeat(1, lightnum, 1)
v = self.v().unsqueeze(1).repeat(1, lightnum, 1)
w = self.w().unsqueeze(1).repeat(1, lightnum, 1)
x = torch.sum(p * u, dim=2, keepdim=True)
y = torch.sum(p * v, dim=2, keepdim=True)
z = torch.sum(p * w, dim=2, keepdim=True)
return torch.cat([x, y, z], dim=2)
def build_from_ntb(
self,
n : torch.Tensor,
t : torch.Tensor,
b : torch.Tensor,
) -> None:
"""
Args:
n, t, b: The local frame, of shape (batch, 3)
"""
batch_size = n.size(0)
self.axis = torch.zeros((batch_size, 3, 3)).to(n.device)
self.axis[:, 2, :] = F.normalize(n, dim=1)
self.axis[:, 1, :] = F.normalize(b, dim=1)
self.axis[:, 0, :] = F.normalize(t, dim=1)
def build_from_w(self, normal : torch.Tensor) -> None:
"""
Build the local frame based on the normal.
Args:
normal: The normal coordinates of shape (batch, 3)
"""
assert(self.batch_size == normal.size(0))
device = normal.device
n = F.normalize(normal, dim=1)
nz = n[:, [2]]
batch_size = n.shape[0]
constant_001 = torch.zeros_like(normal).to(device)
constant_001[:, 2] = 1.0
constant_100 = torch.zeros_like(normal).to(device)
constant_100[:, 0] = 1.0
nz_notequal_1 = torch.gt(torch.abs(nz - 1.0), 1e-6)
nz_notequal_m1 = torch.gt(torch.abs(nz + 1.0), 1e-6)
t = torch.where(nz_notequal_1 & nz_notequal_m1, constant_001, constant_100)
# Optix version
# b = F.normalize(torch.cross(normal, t), dim=1)
# t = torch.cross(b, normal)
# Original pytorch version
t = F.normalize(torch.cross(t, normal), dim=1)
b = torch.cross(n, t)
self.axis = torch.zeros((batch_size, 3, 3)).to(device)
self.axis[:, 2, :] = n
self.axis[:, 1, :] = b
self.axis[:, 0, :] = t
def rotate_frame(self, theta : torch.Tensor) -> None:
"""
Rotate local frame along the normal axis
Args:
theta: the degrees of counterclockwise rotation, of shape (batch, 1)
"""
assert(self.batch_size == theta.size(0))
n = self.w()
t = self.u()
b = self.v()
t = F.normalize(t * torch.cos(theta) + b * torch.sin(theta), dim=1)
b = F.normalize(torch.cross(n, t), dim=1)
self.axis = torch.zeros((self.batch_size, 3, 3)).to(theta.device)
self.axis[:, 0, :] = t
self.axis[:, 1, :] = b
self.axis[:, 2, :] = n
def _back_hemi_octa_map(self, n_2d : torch.Tensor) -> torch.Tensor:
"""
The original normal is (0, 0, 1), we should use this method to
perturb the original normal to get a new normal and then build
a new local frame based on the new normal.
Args:
n_2d: shape (batch, 2)
Returns:
local_n: shape (batch, 3), which is define in geometry local
frame.
"""
p = (n_2d - 0.5) * 2.0
resultx = (p[:, [0]] + p[:, [1]]) * 0.5
resulty = (p[:, [1]] - p[:, [0]]) * 0.5
resultz = 1.0 - torch.abs(resultx) - torch.abs(resulty)
result = torch.cat([resultx, resulty, resultz], dim=1)
return F.normalize(result, dim=1)
def hemi_octa_map(self, dir : torch.Tensor) -> torch.Tensor:
"""
Args:
dir: shape (batch, 3)
Returns:
n2d: shape (batch, 2), which is define in circle coordinate
"""
high_dim = False
batch_size = dir.shape[0]
if len(dir.shape) > 2:
high_dim = True
dir = dir.reshape(-1, 3)
p = dir/torch.sum(torch.abs(dir), dim=1, keepdim=True) # (batch,3)
n_2d = torch.cat([p[:,[0]] - p[:,[1]],p[:,[0]] + p[:, [1]]],dim=1) * 0.5 + 0.5
if high_dim:
n_2d = n_2d.reshape(batch_size, -1, 2)
return n_2d
def build_from_n2d(self, n_2d : torch.Tensor, theta : torch.Tensor) -> None:
"""
Args:
n_2d: tensor of shape (batch, 2). the param defines how
to perturb local normal.
theta: the degrees of rotation of tangent.
"""
assert(self.batch_size == n_2d.size(0))
local_n = self._back_hemi_octa_map(n_2d)
self.build_from_w(local_n)
self.rotate_frame(theta)
|