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# modified from https://github.com/Profactor/continuous-remeshing
import torch
import numpy as np
import trimesh
from typing import Tuple
from pytorch3d.renderer.cameras import camera_position_from_spherical_angles, look_at_rotation
from pytorch3d.renderer import (
FoVOrthographicCameras,
look_at_view_transform,
)
def to_numpy(*args):
def convert(a):
if isinstance(a,torch.Tensor):
return a.detach().cpu().numpy()
assert a is None or isinstance(a,np.ndarray)
return a
return convert(args[0]) if len(args)==1 else tuple(convert(a) for a in args)
def laplacian(
num_verts:int,
edges: torch.Tensor #E,2
) -> torch.Tensor: #sparse V,V
"""create sparse Laplacian matrix"""
V = num_verts
E = edges.shape[0]
#adjacency matrix,
idx = torch.cat([edges, edges.fliplr()], dim=0).type(torch.long).T # (2, 2*E)
ones = torch.ones(2*E, dtype=torch.float32, device=edges.device)
A = torch.sparse.FloatTensor(idx, ones, (V, V))
#degree matrix
deg = torch.sparse.sum(A, dim=1).to_dense()
idx = torch.arange(V, device=edges.device)
idx = torch.stack([idx, idx], dim=0)
D = torch.sparse.FloatTensor(idx, deg, (V, V))
return D - A
def _translation(x, y, z, device):
return torch.tensor([[1., 0, 0, x],
[0, 1, 0, y],
[0, 0, 1, z],
[0, 0, 0, 1]],device=device) #4,4
def _perspective(fovy, aspect=1.0, n=0.1, f=1000.0, device=None):
fovy = fovy * torch.pi / 180
y = np.tan(fovy / 2)
return torch.tensor([[1/(y*aspect), 0, 0, 0],
[ 0, 1/-y, 0, 0],
[ 0, 0, -(f+n)/(f-n), -(2*f*n)/(f-n)],
[ 0, 0, -1, 0]], dtype=torch.float32, device=device)
def _projection(r, device, l=None, t=None, b=None, n=1.0, f=50.0, flip_y=True):
"""
see https://blog.csdn.net/wodownload2/article/details/85069240/
"""
if l is None:
l = -r
if t is None:
t = r
if b is None:
b = -t
p = torch.zeros([4,4],device=device)
p[0,0] = 2*n/(r-l)
p[0,2] = (r+l)/(r-l)
p[1,1] = 2*n/(t-b) * (-1 if flip_y else 1)
p[1,2] = (t+b)/(t-b)
p[2,2] = -(f+n)/(f-n)
p[2,3] = -(2*f*n)/(f-n)
p[3,2] = -1
return p #4,4
def _orthographic(r, device, l=None, t=None, b=None, n=1.0, f=50.0, flip_y=True):
if l is None:
l = -r
if t is None:
t = r
if b is None:
b = -t
o = torch.zeros([4,4],device=device)
o[0,0] = 2/(r-l)
o[0,3] = -(r+l)/(r-l)
o[1,1] = 2/(t-b) * (-1 if flip_y else 1)
o[1,3] = -(t+b)/(t-b)
o[2,2] = -2/(f-n)
o[2,3] = -(f+n)/(f-n)
o[3,3] = 1
return o #4,4
def make_star_cameras_orig(phis,pol_count,distance:float=10.,r=None,image_size=[512,512],device='cuda'):
if r is None:
r = 1/distance
A = len(phis)
P = pol_count
C = A * P # total number of cameras
phi = phis * torch.pi / 180
phi_rot = torch.eye(3,device=device)[None,None].expand(A,1,3,3).clone()
phi_rot[:,0,2,2] = phi.cos()
phi_rot[:,0,2,0] = -phi.sin()
phi_rot[:,0,0,2] = phi.sin()
phi_rot[:,0,0,0] = phi.cos()
theta = torch.arange(1,P+1) * (torch.pi/(P+1)) - torch.pi/2
theta_rot = torch.eye(3,device=device)[None,None].expand(1,P,3,3).clone()
theta_rot[0,:,1,1] = theta.cos()
theta_rot[0,:,1,2] = -theta.sin()
theta_rot[0,:,2,1] = theta.sin()
theta_rot[0,:,2,2] = theta.cos()
mv = torch.empty((C,4,4), device=device)
mv[:] = torch.eye(4, device=device)
mv[:,:3,:3] = (theta_rot @ phi_rot).reshape(C,3,3)
mv_ = _translation(0, 0, -distance, device) @ mv
return mv_, _projection(r,device)
def make_star_cameras_mv_new(phis,eles,distance:float=10.,r=None,fov=None,image_size=[512,512],device='cuda',translation=True):
import glm
def sample_spherical(phi, theta, cam_radius):
theta = torch.deg2rad(theta)
phi = torch.deg2rad(phi)
z = cam_radius * torch.cos(phi) * torch.sin(theta)
x = cam_radius * torch.sin(phi) * torch.sin(theta)
y = cam_radius * torch.cos(theta)
return x, y, z
all_mvs = []
for i in range(len(phis)):
azimuth = - phis[i] + 1e-10
ele = - eles[i] + 1e-10 + 90
x, y, z = sample_spherical(azimuth, ele, distance)
eye = glm.vec3(x, y, z)
at = glm.vec3(0.0, 0.0, 0.0)
up = glm.vec3(0.0, 1.0, 0.0)
view_matrix = glm.lookAt(eye, at, up)
all_mvs.append(torch.from_numpy(np.array(view_matrix)).cuda())
mv = torch.stack(all_mvs)
return mv
def make_star_cameras_mv(phis,eles,distance:float=10.,r=None,fov=None,image_size=[512,512],device='cuda',translation=True):
if r is None:
r = 0.15
A = len(phis)
assert len(eles) == A, f'len(phis): {len(phis)}, len(eles): {len(eles)}'
phi = phis * torch.pi / 180
phi_rot = torch.eye(3,device=device)[None].expand(A,3,3).clone()
phi_rot[:,2,2] = phi.cos()
phi_rot[:,2,0] = -phi.sin()
phi_rot[:,0,2] = phi.sin()
phi_rot[:,0,0] = phi.cos()
theta = eles * torch.pi / 180
theta_rot = torch.eye(3,device=device)[None].expand(A,3,3).clone()
theta_rot[:,1,1] = theta.cos()
theta_rot[:,1,2] = -theta.sin()
theta_rot[:,2,1] = theta.sin()
theta_rot[:,2,2] = theta.cos()
mv = torch.empty((A,4,4), device=device)
mv[:] = torch.eye(4, device=device)
mv[:,:3,:3] = (theta_rot @ phi_rot).reshape(A,3,3)
if translation:
mv_ = _translation(0, 0, -distance, device) @ mv
else:
mv_ = mv
return mv_
def make_star_cameras(phis,eles,distance:float=10.,r=None,fov=None,image_size=[512,512],device='cuda',translation=True):
mv_ = make_star_cameras_mv_new(phis, eles, distance, r, device=device, translation=translation)
return mv_, _perspective(fov,device=device)
def make_star_cameras_perspective(phis, eles, distance:float=10., r=None, fov=None, device='cuda'):
return make_star_cameras(phis, eles, distance, r, fov=fov, device=device, translation=True)
def make_star_cameras_orthographic(phis, eles, distance:float=10., r=None, device='cuda'):
mv = make_star_cameras_mv_new(phis, eles, distance, r, device=device)
if r is None:
r = 1
return mv, _orthographic(r,device)
def make_sphere(level:int=2,radius=1.,device='cuda') -> Tuple[torch.Tensor,torch.Tensor]:
sphere = trimesh.creation.icosphere(subdivisions=level, radius=1.0, color=None)
vertices = torch.tensor(sphere.vertices, device=device, dtype=torch.float32) * radius
faces = torch.tensor(sphere.faces, device=device, dtype=torch.long)
return vertices,faces
def get_camera(R, T, focal_length=1 / (2**0.5)):
focal_length = 1 / focal_length
camera = FoVOrthographicCameras(device=R.device, R=R, T=T, min_x=-focal_length, max_x=focal_length, min_y=-focal_length, max_y=focal_length)
return camera
def make_star_cameras_orthographic_py3d(azim_list, device, focal=2/1.35, dist=1.1):
R, T = look_at_view_transform(dist, 0, azim_list)
focal_length = 1 / focal
return FoVOrthographicCameras(device=R.device, R=R, T=T, min_x=-focal_length, max_x=focal_length, min_y=-focal_length, max_y=focal_length).to(device)
def rotation_matrix_to_euler_angles(R, return_degrees=True):
sy = torch.sqrt(R[0, 0] * R[0, 0] + R[1, 0] * R[1, 0])
singular = sy < 1e-6
if not singular:
x = torch.atan2(R[2, 1], R[2, 2])
y = torch.atan2(-R[2, 0], sy)
z = torch.atan2(R[1, 0], R[0, 0])
else:
x = torch.atan2(-R[1, 2], R[1, 1])
y = torch.atan2(-R[2, 0], sy)
z = 0
if return_degrees:
return torch.tensor([x, y, z]) * 180 / np.pi
else:
return torch.tensor([x, y, z])
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