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math_utils.py
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math_utils.py
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import torch
import math
import numpy as np
from uhc.utils.transformation import (
quaternion_matrix,
quaternion_about_axis,
quaternion_inverse,
quaternion_multiply,
rotation_from_quaternion,
rotation_from_matrix,
)
def gmof(res, sigma):
"""
Geman-McClure error function
- residual
- sigma scaling factor
"""
x_squared = res**2
sigma_squared = sigma**2
return (sigma_squared * x_squared) / (sigma_squared + x_squared)
def ewma(x, alpha=0.05):
avg = x[0]
for i in x[1:]:
avg = alpha * i + (1 - alpha) * avg
return avg
def normal_entropy(std):
var = std.pow(2)
entropy = 0.5 + 0.5 * torch.log(2 * var * math.pi)
return entropy.sum(1, keepdim=True)
def normal_log_density(x, mean, log_std, std):
var = std.pow(2)
log_density = -(x - mean).pow(2) / (2 * var) - 0.5 * math.log(
2 * math.pi) - log_std
return log_density.sum(1, keepdim=True)
def get_qvel_fd_new(cur_qpos, next_qpos, dt, transform=None):
v = (next_qpos[:3] - cur_qpos[:3]) / dt
qrel = quaternion_multiply(next_qpos[3:7],
quaternion_inverse(cur_qpos[3:7]))
axis, angle = rotation_from_quaternion(qrel, True)
while angle > np.pi:
angle -= 2 * np.pi
while angle < -np.pi:
angle += 2 * np.pi
rv = (axis * angle) / dt
rv = transform_vec(rv, cur_qpos[3:7],
"root") # angular velocity is in root coord
diff = next_qpos[7:] - cur_qpos[7:]
while np.any(diff > np.pi):
diff[diff > np.pi] -= 2 * np.pi
while np.any(diff < -np.pi):
diff[diff < -np.pi] += 2 * np.pi
qvel = diff / dt
qvel = np.concatenate((v, rv, qvel))
if transform is not None:
v = transform_vec(v, cur_qpos[3:7], transform)
qvel[:3] = v
return qvel
def get_qvel_fd(cur_qpos, next_qpos, dt, transform=None):
v = (next_qpos[:3] - cur_qpos[:3]) / dt
qrel = quaternion_multiply(next_qpos[3:7],
quaternion_inverse(cur_qpos[3:7]))
# qrel /= np.linalg.norm(qrel)
axis, angle = rotation_from_quaternion(qrel, True)
if angle > np.pi: # -180 < angle < 180
angle -= 2 * np.pi #
elif angle < -np.pi:
angle += 2 * np.pi
rv = (axis * angle) / dt
rv = transform_vec(rv, cur_qpos[3:7], "root")
qvel = (next_qpos[7:] - cur_qpos[7:]) / dt
qvel = np.concatenate((v, rv, qvel))
if transform is not None:
v = transform_vec(v, cur_qpos[3:7], transform)
qvel[:3] = v
return qvel
def get_angvel_fd(prev_bquat, cur_bquat, dt):
q_diff = multi_quat_diff(cur_bquat, prev_bquat)
n_joint = q_diff.shape[0] // 4
body_angvel = np.zeros(n_joint * 3)
for i in range(n_joint):
body_angvel[3 * i:3 * i +
3] = (rotation_from_quaternion(q_diff[4 * i:4 * i + 4]) /
dt)
return body_angvel
def transform_vec(v, q, trans="root"):
if trans == "root":
rot = quaternion_matrix(q)[:3, :3]
elif trans == "heading":
hq = q.copy()
hq[1] = 0.0
hq[2] = 0.0
hq /= np.linalg.norm(hq)
rot = quaternion_matrix(hq)[:3, :3]
else:
assert False
v = rot.T.dot(v[:, None]).ravel()
return v
def transform_vec_batch(v_b, q, trans="root"):
if trans == "root":
rot = quaternion_matrix(q)[:3, :3]
elif trans == "heading":
hq = q.copy()
hq[1] = 0
hq[2] = 0
hq /= np.linalg.norm(hq)
rot = quaternion_matrix(hq)[:3, :3]
else:
assert False
v_b = rot.T.dot(v_b[:, :, None]).squeeze()
return v_b
def get_heading_q(q):
hq = q.copy()
hq[1] = 0.0
hq[2] = 0.0
hq /= np.linalg.norm(hq)
return hq
def transform_vec_new(v, q, trans="root"):
old_shape = v.shape
v = v.reshape(-1, 3)
if trans == "root":
rot_q = q
elif trans == "heading":
rot_q = get_heading_q_new(q)
else:
raise ValueError("undefined trans!")
rot = quaternion_matrix(rot_q)[:3, :3]
v = v.dot(rot).ravel()
return v.reshape(old_shape)
def transform_vec_batch_new(v_b, q, trans="root"):
if trans == "root":
rot = quaternion_matrix(q)[:3, :3]
elif trans == "heading":
rot_q = get_heading_q_new(q)
rot = quaternion_matrix(rot_q)[:3, :3]
else:
assert False
v_b = rot.T.dot(v_b[:, :, None]).squeeze()
return v_b
def get_heading_q_new(q):
yaw = get_heading_new(q)
hq = quaternion_about_axis(yaw, [0, 0, 1])
return hq
def get_heading(q):
hq = q.copy()
hq[1] = 0
hq[2] = 0
if hq[3] < 0:
hq *= -1
hq /= np.linalg.norm(hq)
return 2 * math.acos(hq[0])
def get_heading_new(q):
yaw = math.atan2(2 * (q[0] * q[3] + q[1] * q[2]),
1 - 2 * (q[2] * q[2] + q[3] * q[3]))
# pitch = math.asin(2*(q[0]*q[2] - q[1]*q[3]))
# roll = math.atan2(2*(q[0]*q[1] + q[2]*q[3]), 1 - 2*(q[1]*q[1] + q[2]*q[2]))
return yaw
def get_pyr(q):
yaw = math.atan2(2 * (q[0] * q[3] + q[1] * q[2]),
1 - 2 * (q[2] * q[2] + q[3] * q[3]))
pitch = math.asin(2 * (q[0] * q[2] - q[1] * q[3]))
roll = math.atan2(2 * (q[0] * q[1] + q[2] * q[3]),
1 - 2 * (q[1] * q[1] + q[2] * q[2]))
return pitch, yaw, roll
def de_heading(q):
return quaternion_multiply(quaternion_inverse(get_heading_q(q)), q)
def de_heading_new(q):
return quaternion_multiply(quaternion_inverse(get_heading_q_new(q)), q)
def multi_quat_diff(nq1, nq0):
"""return the relative quaternions q1-q0 of N joints"""
nq_diff = np.zeros_like(nq0)
for i in range(nq1.shape[0] // 4):
ind = slice(4 * i, 4 * i + 4)
q1 = nq1[ind]
q0 = nq0[ind]
nq_diff[ind] = quaternion_multiply(q1, quaternion_inverse(q0))
return nq_diff
def multi_quat_norm(nq):
"""return the scalar rotation of a N joints"""
nq_norm = np.arccos(np.clip(nq[::4], -1.0, 1.0))
return nq_norm
def multi_quat_norm_v2(nq):
_diff = []
for i in range(nq.shape[0] // 4):
q = nq[4 * i:4 * (i + 1)]
d = np.array([abs(q[0]) - 1.0, q[1], q[2], q[3]])
_diff.append(np.linalg.norm(d))
return np.array(_diff)
def quat_mul_vec(q, v):
return quaternion_matrix(q)[:3, :3].dot(v[:, None]).ravel()
def quat_to_bullet(q):
return np.array([q[1], q[2], q[3], q[0]])
def quat_from_bullet(q):
return np.array([q[3], q[0], q[1], q[2]])
def quat_from_expmap(e):
angle = np.linalg.norm(e)
if angle < 1e-8:
axis = np.array([1.0, 0.0, 0.0], dtype=np.float64)
angle = 0.0
else:
axis = e / angle
return quaternion_about_axis(angle, axis)
def quat_correct(quat):
""" Converts quaternion to minimize Euclidean distance from previous quaternion (wxyz order) """
for q in range(1, quat.shape[0]):
if np.linalg.norm(quat[q - 1] - quat[q], axis=0) > np.linalg.norm(
quat[q - 1] + quat[q], axis=0):
quat[q] = -quat[q]
return quat
def normalize_screen_coordinates(X, w=1920, h=1080):
assert X.shape[-1] == 2
# Normalize so that [0, w] is mapped to
# [-1, 1], while preserving the aspect ratio
return X / w * 2 - np.array([1, h / w])
def op_to_root_orient(op_3d_pos):
body_triangle = op_3d_pos[:, [7, 8, 11]]
body_triangle_a = body_triangle[:, 0, :]
body_triangle_b = body_triangle[:, 1, :]
body_triangle_c = body_triangle[:, 2, :]
num_s = body_triangle_c.shape[0]
y_axis = np.cross((body_triangle_c - body_triangle_a),
(body_triangle_b - body_triangle_a))
y_axis = y_axis / np.linalg.norm(y_axis, axis=1)[:, None]
x_axis = (body_triangle_c - body_triangle_b)
x_axis = x_axis / np.linalg.norm(x_axis, axis=1)[:, None]
z_axis = np.cross(
x_axis,
y_axis,
)
np_rotmat = np.stack([x_axis, y_axis, z_axis], axis=1).transpose(0, 2, 1)
root_mat = np.array([[[1., 0., 0.], [0., 0., -1.], [0., 1., 0.]]])
root_mat = np.matmul(np_rotmat, root_mat)
return root_mat
def smpl_op_to_op(pred_joints2d):
new_2d = np.concatenate([pred_joints2d[..., [1, 4], :].mean(axis = -2, keepdims = True), \
pred_joints2d[..., 1:8, :], \
pred_joints2d[..., 9:11, :], \
pred_joints2d[..., 12:, :]], \
axis = -2)
return new_2d