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'''
LastEditTime: 2022-05-21 01:13:08
Description: More utilities
Date: 2021-10-28 05:01:01
Author: Aiden Li
LastEditors: Aiden Li ([email protected])
'''
import numpy as np
# import open3d as o3d
import torch
import torch.nn.functional as F
def cross_product(u, v):
batch = u.shape[0]
i = u[:, 1] * v[:, 2] - u[:, 2] * v[:, 1]
j = u[:, 2] * v[:, 0] - u[:, 0] * v[:, 2]
k = u[:, 0] * v[:, 1] - u[:, 1] * v[:, 0]
out = torch.cat((i.view(batch, 1), j.view(batch, 1), k.view(batch, 1)), 1)
return out
def rot_to_orthod6d(rot):
return rot.transpose(1, 2)[:, :2].reshape([-1, 6])
def orthod6d_to_rot(o6d):
x_raw = o6d[:, 0:3] # batch*3
y_raw = o6d[:, 3:6] # batch*3
x = x_raw / torch.norm(x_raw, dim=-1, keepdim=True) # batch*3
z = cross_product(x, y_raw) # batch*3
z = z / torch.norm(z, dim=-1, keepdim=True) # batch*3
y = cross_product(z, x) # batch*3
matrix = torch.cat([
x.view(-1, 3, 1),
y.view(-1, 3, 1),
z.view(-1, 3, 1)
], 2) # batch*3*3
return matrix
def do_rotation(points, rots, rot_cents=None):
"""
Args:
`points`: `[batch_shape]` x `num_points` x 3
`rots`: `[batch_shape]` x 3 x 3
`rot_cents`: `[batch_shape]` x 3
"""
shape = points.shape
if rot_cents is not None:
# Send to rotation-center coordinate
points = undo_translation(points, rot_cents)
# Calculate rotation
points_local = torch.bmm(
rots.unsqueeze(-3).expand(list(points.shape) + [3]).reshape([-1, 3, 3]),
points.reshape([-1, 3]).unsqueeze(-1)
).reshape(shape)
if rot_cents is not None:
# Send to world coordinate
points = do_translation(points, rot_cents)
return points_local
def do_translation(points, trans):
"""
Args:
`points`: `[batch_shape]` x `num_points` x 3
`trans`: `[batch_shape]` x 3
"""
trans = trans.unsqueeze(-2).expand(points.shape)
return points + trans
def undo_rotation(points, rots, cents=None):
return do_rotation(points, torch.transpose(rots, -1, -2), cents)
def undo_translation(points, trans):
return do_translation(points, -trans)
def random_rot(device='cuda'):
rot_angles = np.random.random(3) * np.pi * 2
theta_x, theta_y, theta_z = rot_angles[0], rot_angles[1], rot_angles[2]
Rx = torch.tensor([[1, 0, 0], [0, np.cos(theta_x), -np.sin(theta_x)], [0, np.sin(theta_x), np.cos(theta_x)]]).to(device)
Ry = torch.tensor([[np.cos(theta_y), 0, np.sin(theta_y)], [0, 1, 0], [-np.sin(theta_y), 0, np.cos(theta_y)]]).to(device)
Rz = torch.tensor([[np.cos(theta_z), -np.sin(theta_z), 0], [np.sin(theta_z), np.cos(theta_z), 0], [0, 0, 1]]).to(device)
return torch.tensor(Rx @ Ry @ Rz, device=device).float() # [3, 3]
def hand_param_comp(hand_param, mode='mano_right'):
if mode == 'mano_right':
return torch.concat([ torch.tensor([[0., 0., 0., 1., 0., 0., 0., 1., 0.]]).to(hand_param.device).tile((hand_param.shape[0], 1)), hand_param ])
else:
raise NotImplementedError()
def btrace(matrix):
return torch.diagonal(matrix, offset=0, dim1=-1, dim2=-2).sum(dim=-1)
def rot_to_quaternion(rotations):
"""
Args:
rotations: B x 3 x 3
"""
w = torch.sqrt(btrace(rotations) + 1 / 2).unsqueeze(-1)
return torch.concat([
w,
(rotations[:, 1, 2] - rotations[:, 2, 1]).unsqueeze(-1) / w / 4,
(rotations[:, 2, 0] - rotations[:, 0, 2]).unsqueeze(-1) / w / 4,
(rotations[:, 0, 1] - rotations[:, 1, 0]).unsqueeze(-1) / w / 4
], dim=-1)
def quaternion_to_rot(quaternions):
"""
Args:
`quaternions`: B x 4
Returns:
B x 3 x 3
"""
w, a, b, c = quaternions.chunk(quaternions.shape[-1], dim=1)
return torch.concat([
torch.concat([
1 - 2 * (b**2 + c**2),
2 * (a * b - w * c),
2 * (a * c + w * b)
], dim=-1).unsqueeze(-2),
torch.concat([
2 * (a * b + w * c),
1 - 2 * (a**2 + c**2),
2 * (b * c - w * a)
], dim=-1).unsqueeze(-2),
torch.concat([
2 * (a * c - w * b),
2 * (b * c - w * a),
1 - 2 * (a**2 + b**2)
], dim=-1).unsqueeze(-2)
], dim=-2)
def do_rotation(points, rots, rot_cents=None):
"""
Args:
`points`: `[batch_shape]` x `num_points` x 3
`rots`: `[batch_shape]` x 3 x 3
`rot_cents`: `[batch_shape]` x 3
"""
shape = points.shape
if rot_cents is not None:
# Send to rotation-center coordinate
points = undo_translation(points, rot_cents)
# Calculate rotation
points_local = torch.bmm(rots.unsqueeze(-3).expand(list(points.shape) + [3]).reshape([-1, 3, 3]), points.reshape([-1, 3]).unsqueeze(-1)
).reshape(shape)
if rot_cents is not None:
# Send to world coordinate
points = do_translation(points, rot_cents)
return points_local
def do_translation(points, trans):
"""
Args:
`points`: `[batch_shape]` x `num_points` x 3
`trans`: `[batch_shape]` x 3
"""
trans = trans.unsqueeze(-2).expand(points.shape)
return points + trans
def undo_rotation(points, rots, cents=None):
return do_rotation(points, torch.transpose(rots, -1, -2), cents)
def undo_translation(points, trans):
return do_translation(points, -trans)
def trans_rot_to_homo_matrix(translation, rotation):
"""
Args:
`translation`: `batch_size` x 3 x 3
`rotation`: `batch_size` x 3
"""
batch_size = translation.shape[0]
# `batch_size` x 4 x 3
rotation = torch.concat([rotation, torch.zeros([batch_size, 1, 3], device=rotation.device)], dim=-2)
# `batch_size` x 4 x 1
translation = torch.concat([translation.unsqueeze(-1), torch.ones([batch_size, 1, 1], device=translation.device)], dim=-2)
# `batch_size` x 4 x 4
return torch.concat([rotation, translation], dim=-1)
def meshgrid_points(range, ticks, device='cuda', requires_grad=True):
[[x_lo, x_hi], [y_lo, y_hi], [z_lo, z_hi]] = range
x_ticks, y_ticks, z_ticks = ticks
xx = torch.linspace(x_lo, x_hi, x_ticks, device=device, requires_grad=requires_grad)
yy = torch.linspace(y_lo, y_hi, y_ticks, device=device, requires_grad=requires_grad)
zz = torch.linspace(z_lo, z_hi, z_ticks, device=device, requires_grad=requires_grad)
ii, jj, kk = torch.meshgrid([xx, yy, zz])
return torch.concat([ii.unsqueeze(-1), jj.unsqueeze(-1), kk.unsqueeze(-1)], dim=-1).reshape([-1, 3])
# def mesh_from_points(points, radii=[0.005, 0.01, 0.02, 0.04]):
# pcd = o3d.geometry.PointCloud()
# pcd.points = o3d.utility.Vector3dVector(points[0])
# pcd = pcd.voxel_down_sample(voxel_size=0.5)
# pcd.estimate_normals()
def mesh_to_pts(mesh, padding=False):
if padding:
padding_len = np.max([ m.vertices.shape[0] for m in mesh ])
pts = [
F.pad(F.pad(torch.Tensor(m.vertices), [0, 1], mode='constant', value=1.), [0, 0, 0, padding_len - m.vertices.shape[0]], mode='constant', value=0.)
for m in mesh
]
return torch.stack(pts, dim=0)
else:
pts = [ torch.Tensor(m.verties) for m in mesh ]
return torch.stack(pts, dim=0)
def shuffle_tensor(tensor, dim=-1):
return tensor[:, torch.randperm(tensor.shape[dim])].view(tensor.size())
def accept_and_tile(tensor, accept_indices, trim=False):
"""Accept parts of a tensor and retile them to recover (may outnumbers by a bit) the batch size.
"""
old_batch_size = tensor.shape[0]
tile_factor = [int(tensor.shape[0] / accept_indices.shape[0])] + [1] * (tensor.dim() - 1)
if trim:
return tensor[accept_indices].tile(tile_factor)[:old_batch_size]
else:
return tensor[accept_indices].tile(tile_factor)
def tensor_in_arr(ten, dic):
for elem in dic:
if ten.equal(elem):
return True
return False
def neighbors_on_mesh(ind, tri=None, neighbor_array=None):
if tri is None:
return neighbor_array[ind]
elif neighbor_array is None:
neighbors = []
for t in tri:
if ind == t[0]:
if t[1] not in neighbors:
neighbors.append(t[1])
if t[2] not in neighbors:
neighbors.append(t[2])
if ind == t[1]:
if t[0] not in neighbors:
neighbors.append(t[0])
if t[2] not in neighbors:
neighbors.append(t[2])
if ind == t[2]:
if t[0] not in neighbors:
neighbors.append(t[0])
if t[1] not in neighbors:
neighbors.append(t[1])
else:
raise NotImplementedError()
return neighbors
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