utils/utils_poses/lie_group_helper.py

import numpy as np
import torch
from scipy.spatial.transform import Rotation as RotLib


def SO3_to_quat(R):
 """
 :param R: (N, 3, 3) or (3, 3) np
 :return: (N, 4, ) or (4, ) np
 """
 x = RotLib.from_matrix(R)
 quat = x.as_quat()
 return quat


def quat_to_SO3(quat):
 """
 :param quat: (N, 4, ) or (4, ) np
 :return: (N, 3, 3) or (3, 3) np
 """
 x = RotLib.from_quat(quat)
 R = x.as_matrix()
 return R


def convert3x4_4x4(input):
 """
 :param input: (N, 3, 4) or (3, 4) torch or np
 :return: (N, 4, 4) or (4, 4) torch or np
 """
 if torch.is_tensor(input):
 if len(input.shape) == 3:
 output = torch.cat([input, torch.zeros_like(input[:, 0:1])], dim=1) # (N, 4, 4)
 output[:, 3, 3] = 1.0
 else:
 output = torch.cat([input, torch.tensor([[0,0,0,1]], dtype=input.dtype, device=input.device)], dim=0) # (4, 4)
 else:
 if len(input.shape) == 3:
 output = np.concatenate([input, np.zeros_like(input[:, 0:1])], axis=1) # (N, 4, 4)
 output[:, 3, 3] = 1.0
 else:
 output = np.concatenate([input, np.array([[0,0,0,1]], dtype=input.dtype)], axis=0) # (4, 4)
 output[3, 3] = 1.0
 return output


def vec2skew(v):
 """
 :param v: (3, ) torch tensor
 :return: (3, 3)
 """
 zero = torch.zeros(1, dtype=torch.float32, device=v.device)
 skew_v0 = torch.cat([ zero, -v[2:3], v[1:2]]) # (3, 1)
 skew_v1 = torch.cat([ v[2:3], zero, -v[0:1]])
 skew_v2 = torch.cat([-v[1:2], v[0:1], zero])
 skew_v = torch.stack([skew_v0, skew_v1, skew_v2], dim=0) # (3, 3)
 return skew_v # (3, 3)


def Exp(r):
 """so(3) vector to SO(3) matrix
 :param r: (3, ) axis-angle, torch tensor
 :return: (3, 3)
 """
 skew_r = vec2skew(r) # (3, 3)
 norm_r = r.norm() + 1e-15
 eye = torch.eye(3, dtype=torch.float32, device=r.device)
 R = eye + (torch.sin(norm_r) / norm_r) * skew_r + ((1 - torch.cos(norm_r)) / norm_r**2) * (skew_r @ skew_r)
 return R


def make_c2w(r, t):
 """
 :param r: (3, ) axis-angle torch tensor
 :param t: (3, ) translation vector torch tensor
 :return: (4, 4)
 """
 R = Exp(r) # (3, 3)
 c2w = torch.cat([R, t.unsqueeze(1)], dim=1) # (3, 4)
 c2w = convert3x4_4x4(c2w) # (4, 4)
 return c2w