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aceb411 | 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 | import numpy as np
import scipy.spatial.transform as st
from scipy.spatial.transform import Rotation as R
def pos_rot_to_mat(pos, rot):
shape = pos.shape[:-1]
mat = np.zeros(shape + (4,4), dtype=pos.dtype)
mat[...,:3,3] = pos
mat[...,:3,:3] = rot.as_matrix()
mat[...,3,3] = 1
return mat
def mat_to_pos_rot(mat):
pos = (mat[...,:3,3].T / mat[...,3,3].T).T
rot = st.Rotation.from_matrix(mat[...,:3,:3])
return pos, rot
def pos_rot_to_pose(pos, rot):
shape = pos.shape[:-1]
pose = np.zeros(shape+(6,), dtype=pos.dtype)
pose[...,:3] = pos
pose[...,3:] = rot.as_rotvec()
return pose
def pose_to_pos_rot(pose):
pos = pose[...,:3]
rot = st.Rotation.from_rotvec(pose[...,3:])
return pos, rot
def pose_to_mat(pose):
return pos_rot_to_mat(*pose_to_pos_rot(pose))
def pose7d_to_mat(pose):
return pos_rot_to_mat(pose[..., :3], R.from_quat(pose[..., 3:]))
def mat_to_pose(mat):
return pos_rot_to_pose(*mat_to_pos_rot(mat))
def transform_pose(tx, pose):
"""
tx: tx_new_old
pose: tx_old_obj
result: tx_new_obj
"""
pose_mat = pose_to_mat(pose)
tf_pose_mat = tx @ pose_mat
tf_pose = mat_to_pose(tf_pose_mat)
return tf_pose
def transform_point(tx, point):
return point @ tx[:3,:3].T + tx[:3,3]
def project_point(k, point):
x = point @ k.T
uv = x[...,:2] / x[...,[2]]
return uv
def apply_delta_pose(pose, delta_pose):
new_pose = np.zeros_like(pose)
# simple add for position
new_pose[:3] = pose[:3] + delta_pose[:3]
# matrix multiplication for rotation
rot = st.Rotation.from_rotvec(pose[3:])
drot = st.Rotation.from_rotvec(delta_pose[3:])
new_pose[3:] = (drot * rot).as_rotvec()
return new_pose
def normalize(vec, tol=1e-7):
return vec / np.maximum(np.linalg.norm(vec), tol)
def rot_from_directions(from_vec, to_vec):
from_vec = normalize(from_vec)
to_vec = normalize(to_vec)
axis = np.cross(from_vec, to_vec)
axis = normalize(axis)
angle = np.arccos(np.dot(from_vec, to_vec))
rotvec = axis * angle
rot = st.Rotation.from_rotvec(rotvec)
return rot
def normalize(vec, eps=1e-12):
norm = np.linalg.norm(vec, axis=-1)
norm = np.maximum(norm, eps)
out = (vec.T / norm).T
return out
def rot6d_to_mat(d6):
a1, a2 = d6[..., :3], d6[..., 3:]
b1 = normalize(a1)
b2 = a2 - np.sum(b1 * a2, axis=-1, keepdims=True) * b1
b2 = normalize(b2)
b3 = np.cross(b1, b2, axis=-1)
out = np.stack((b1, b2, b3), axis=-2)
return out
def mat_to_rot6d(mat):
batch_dim = mat.shape[:-2]
out = mat[..., :2, :].copy().reshape(batch_dim + (6,))
return out
def mat_to_pose10d(mat):
pos = mat[...,:3,3]
rotmat = mat[...,:3,:3]
d6 = mat_to_rot6d(rotmat)
d10 = np.concatenate([pos, d6], axis=-1)
return d10
def pose10d_to_mat(d10):
pos = d10[...,:3]
d6 = d10[...,3:]
rotmat = rot6d_to_mat(d6)
out = np.zeros(d10.shape[:-1]+(4,4), dtype=d10.dtype)
out[...,:3,:3] = rotmat
out[...,:3,3] = pos
out[...,3,3] = 1
return out |