Spaces:
Running on A10G

File size: 5,587 Bytes
f2a2544
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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
# Copyright (c) 2023-2024, Zexin He
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     https://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.


import math
import torch

"""
R: (N, 3, 3)
T: (N, 3)
E: (N, 4, 4)
vector: (N, 3)
"""


def compose_extrinsic_R_T(R: torch.Tensor, T: torch.Tensor):
    """
    Compose the standard form extrinsic matrix from R and T.
    Batched I/O.
    """
    RT = torch.cat((R, T.unsqueeze(-1)), dim=-1)
    return compose_extrinsic_RT(RT)


def compose_extrinsic_RT(RT: torch.Tensor):
    """
    Compose the standard form extrinsic matrix from RT.
    Batched I/O.
    """
    return torch.cat([
        RT,
        torch.tensor([[[0, 0, 0, 1]]], dtype=RT.dtype, device=RT.device).repeat(RT.shape[0], 1, 1)
        ], dim=1)


def decompose_extrinsic_R_T(E: torch.Tensor):
    """
    Decompose the standard extrinsic matrix into R and T.
    Batched I/O.
    """
    RT = decompose_extrinsic_RT(E)
    return RT[:, :, :3], RT[:, :, 3]


def decompose_extrinsic_RT(E: torch.Tensor):
    """
    Decompose the standard extrinsic matrix into RT.
    Batched I/O.
    """
    return E[:, :3, :]


def get_normalized_camera_intrinsics(intrinsics: torch.Tensor):
    """
    intrinsics: (N, 3, 2), [[fx, fy], [cx, cy], [width, height]]
    Return batched fx, fy, cx, cy
    """
    fx, fy = intrinsics[:, 0, 0], intrinsics[:, 0, 1]
    cx, cy = intrinsics[:, 1, 0], intrinsics[:, 1, 1]
    width, height = intrinsics[:, 2, 0], intrinsics[:, 2, 1]
    fx, fy = fx / width, fy / height
    cx, cy = cx / width, cy / height
    return fx, fy, cx, cy


def build_camera_principle(RT: torch.Tensor, intrinsics: torch.Tensor):
    """
    RT: (N, 3, 4)
    intrinsics: (N, 3, 2), [[fx, fy], [cx, cy], [width, height]]
    """
    fx, fy, cx, cy = get_normalized_camera_intrinsics(intrinsics)
    return torch.cat([
        RT.reshape(-1, 12),
        fx.unsqueeze(-1), fy.unsqueeze(-1), cx.unsqueeze(-1), cy.unsqueeze(-1),
    ], dim=-1)


def build_camera_standard(RT: torch.Tensor, intrinsics: torch.Tensor):
    """
    RT: (N, 3, 4)
    intrinsics: (N, 3, 2), [[fx, fy], [cx, cy], [width, height]]
    """
    E = compose_extrinsic_RT(RT)
    fx, fy, cx, cy = get_normalized_camera_intrinsics(intrinsics)
    I = torch.stack([
        torch.stack([fx, torch.zeros_like(fx), cx], dim=-1),
        torch.stack([torch.zeros_like(fy), fy, cy], dim=-1),
        torch.tensor([[0, 0, 1]], dtype=torch.float32, device=RT.device).repeat(RT.shape[0], 1),
    ], dim=1)
    return torch.cat([
        E.reshape(-1, 16),
        I.reshape(-1, 9),
    ], dim=-1)


def center_looking_at_camera_pose(
    camera_position: torch.Tensor, look_at: torch.Tensor = None, up_world: torch.Tensor = None,
    device: torch.device = torch.device('cpu'),
    ):
    """
    camera_position: (M, 3)
    look_at: (3)
    up_world: (3)
    return: (M, 3, 4)
    """
    # by default, looking at the origin and world up is pos-z
    if look_at is None:
        look_at = torch.tensor([0, 0, 0], dtype=torch.float32, device=device)
    if up_world is None:
        up_world = torch.tensor([0, 0, 1], dtype=torch.float32, device=device)
    look_at = look_at.unsqueeze(0).repeat(camera_position.shape[0], 1)
    up_world = up_world.unsqueeze(0).repeat(camera_position.shape[0], 1)

    z_axis = camera_position - look_at
    z_axis = z_axis / z_axis.norm(dim=-1, keepdim=True)
    x_axis = torch.cross(up_world, z_axis)
    x_axis = x_axis / x_axis.norm(dim=-1, keepdim=True)
    y_axis = torch.cross(z_axis, x_axis)
    y_axis = y_axis / y_axis.norm(dim=-1, keepdim=True)
    extrinsics = torch.stack([x_axis, y_axis, z_axis, camera_position], dim=-1)
    return extrinsics


def surrounding_views_linspace(n_views: int, radius: float = 2.0, height: float = 0.8, device: torch.device = torch.device('cpu')):
    """
    n_views: number of surrounding views
    radius: camera dist to center
    height: height of the camera
    return: (M, 3, 4)
    """
    assert n_views > 0
    assert radius > 0

    theta = torch.linspace(-torch.pi / 2, 3 * torch.pi / 2, n_views, device=device)
    projected_radius = math.sqrt(radius ** 2 - height ** 2)
    x = torch.cos(theta) * projected_radius
    y = torch.sin(theta) * projected_radius
    z = torch.full((n_views,), height, device=device)

    camera_positions = torch.stack([x, y, z], dim=1)
    extrinsics = center_looking_at_camera_pose(camera_positions, device=device)

    return extrinsics


def create_intrinsics(
    f: float,
    c: float = None, cx: float = None, cy: float = None,
    w: float = 1., h: float = 1.,
    dtype: torch.dtype = torch.float32,
    device: torch.device = torch.device('cpu'),
    ):
    """
    return: (3, 2)
    """
    fx = fy = f
    if c is not None:
        assert cx is None and cy is None, "c and cx/cy cannot be used together"
        cx = cy = c
    else:
        assert cx is not None and cy is not None, "cx/cy must be provided when c is not provided"
    fx, fy, cx, cy, w, h = fx/w, fy/h, cx/w, cy/h, 1., 1.
    intrinsics = torch.tensor([
        [fx, fy],
        [cx, cy],
        [w, h],
    ], dtype=dtype, device=device)
    return intrinsics