src/utils/torch_utils.py

# Copyright (c) 2018-2022, NVIDIA Corporation
# All rights reserved.
#
# Redistribution and use in source and binary forms, with or without
# modification, are permitted provided that the following conditions are met:
#
# 1. Redistributions of source code must retain the above copyright notice, this
#    list of conditions and the following disclaimer.
#
# 2. Redistributions in binary form must reproduce the above copyright notice,
#    this list of conditions and the following disclaimer in the documentation
#    and/or other materials provided with the distribution.
#
# 3. Neither the name of the copyright holder nor the names of its
#    contributors may be used to endorse or promote products derived from
#    this software without specific prior written permission.
#
# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
# AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
# IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
# DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
# FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
# DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
# SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
# CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
# OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
# OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

from typing import Tuple

import torch
from torch import Tensor

def euler_from_quaternion(quat_angle):
        """
        Convert a quaternion into euler angles (roll, pitch, yaw)
        roll is rotation around x in radians (counterclockwise)
        pitch is rotation around y in radians (counterclockwise)
        yaw is rotation around z in radians (counterclockwise)
        """
        x = quat_angle[:,0]; y = quat_angle[:,1]; z = quat_angle[:,2]; w = quat_angle[:,3]
        t0 = +2.0 * (w * x + y * z)
        t1 = +1.0 - 2.0 * (x * x + y * y)
        roll_x = torch.atan2(t0, t1)
     
        t2 = +2.0 * (w * y - z * x)
        t2 = torch.clip(t2, -1, 1)
        pitch_y = torch.asin(t2)
     
        t3 = +2.0 * (w * z + x * y)
        t4 = +1.0 - 2.0 * (y * y + z * z)
        yaw_z = torch.atan2(t3, t4)
     
        return roll_x, pitch_y, yaw_z # in radians


@torch.jit.script
def normalize(x, eps: float = 1e-9):
    return x / x.norm(p=2, dim=-1).clamp(min=eps, max=None).unsqueeze(-1)

@torch.jit.script
def normalize_angle(x):
    return torch.atan2(torch.sin(x), torch.cos(x))

@torch.jit.script
def quat_rotate(q, v):
    shape = q.shape
    q_w = q[:, -1]
    q_vec = q[:, :3]
    a = v * (2.0 * q_w ** 2 - 1.0).unsqueeze(-1)
    b = torch.cross(q_vec, v, dim=-1) * q_w.unsqueeze(-1) * 2.0
    c = q_vec * \
        torch.bmm(q_vec.view(shape[0], 1, 3), v.view(
            shape[0], 3, 1)).squeeze(-1) * 2.0
    return a + b + c

@torch.jit.script
def quat_rotate_inverse(q, v):
    shape = q.shape
    q_w = q[:, -1]
    q_vec = q[:, :3]
    a = v * (2.0 * q_w ** 2 - 1.0).unsqueeze(-1)
    b = torch.cross(q_vec, v, dim=-1) * q_w.unsqueeze(-1) * 2.0
    c = q_vec * \
        torch.bmm(q_vec.view(shape[0], 1, 3), v.view(
            shape[0], 3, 1)).squeeze(-1) * 2.0
    return a - b + c

@torch.jit.script
def quat_from_euler_xyz(roll, pitch, yaw):
    cy = torch.cos(yaw * 0.5)
    sy = torch.sin(yaw * 0.5)
    cr = torch.cos(roll * 0.5)
    sr = torch.sin(roll * 0.5)
    cp = torch.cos(pitch * 0.5)
    sp = torch.sin(pitch * 0.5)

    qw = cy * cr * cp + sy * sr * sp
    qx = cy * sr * cp - sy * cr * sp
    qy = cy * cr * sp + sy * sr * cp
    qz = sy * cr * cp - cy * sr * sp

    return torch.stack([qx, qy, qz, qw], dim=-1)

@torch.jit.script
def quat_unit(a):
    return normalize(a)


@torch.jit.script
def quat_from_angle_axis(angle, axis):
    theta = (angle / 2).unsqueeze(-1)
    xyz = normalize(axis) * theta.sin()
    w = theta.cos()
    return quat_unit(torch.cat([xyz, w], dim=-1))

@torch.jit.script
def quat_mul(a, b):
    assert a.shape == b.shape
    shape = a.shape
    a = a.reshape(-1, 4)
    b = b.reshape(-1, 4)

    x1, y1, z1, w1 = a[:, 0], a[:, 1], a[:, 2], a[:, 3]
    x2, y2, z2, w2 = b[:, 0], b[:, 1], b[:, 2], b[:, 3]
    ww = (z1 + x1) * (x2 + y2)
    yy = (w1 - y1) * (w2 + z2)
    zz = (w1 + y1) * (w2 - z2)
    xx = ww + yy + zz
    qq = 0.5 * (xx + (z1 - x1) * (x2 - y2))
    w = qq - ww + (z1 - y1) * (y2 - z2)
    x = qq - xx + (x1 + w1) * (x2 + w2)
    y = qq - yy + (w1 - x1) * (y2 + z2)
    z = qq - zz + (z1 + y1) * (w2 - x2)

    quat = torch.stack([x, y, z, w], dim=-1).view(shape)

    return quat

@torch.jit.script
def quat_conjugate(a):
    shape = a.shape
    a = a.reshape(-1, 4)
    return torch.cat((-a[:, :3], a[:, -1:]), dim=-1).view(shape)


@torch.jit.script
def quat_to_angle_axis(q):
    # computes axis-angle representation from quaternion q
    # q must be normalized
    min_theta = 1e-5
    qx, qy, qz, qw = 0, 1, 2, 3

    sin_theta = torch.sqrt(1 - q[..., qw] * q[..., qw])
    angle = 2 * torch.acos(q[..., qw])
    angle = normalize_angle(angle)
    sin_theta_expand = sin_theta.unsqueeze(-1)
    axis = q[..., qx:qw] / sin_theta_expand

    mask = torch.abs(sin_theta) > min_theta
    default_axis = torch.zeros_like(axis)
    default_axis[..., -1] = 1

    angle = torch.where(mask, angle, torch.zeros_like(angle))
    mask_expand = mask.unsqueeze(-1)
    axis = torch.where(mask_expand, axis, default_axis)
    return angle, axis

@torch.jit.script
def angle_axis_to_exp_map(angle, axis):
    # compute exponential map from axis-angle
    angle_expand = angle.unsqueeze(-1)
    exp_map = angle_expand * axis
    return exp_map

@torch.jit.script
def quat_to_exp_map(q):
    # compute exponential map from quaternion
    # q must be normalized
    angle, axis = quat_to_angle_axis(q)
    exp_map = angle_axis_to_exp_map(angle, axis)
    return exp_map

@torch.jit.script
def quat_to_tan_norm(q):
    # represents a rotation using the tangent and normal vectors
    ref_tan = torch.zeros_like(q[..., 0:3])
    ref_tan[..., 0] = 1
    tan = quat_rotate(q, ref_tan)
    
    ref_norm = torch.zeros_like(q[..., 0:3])
    ref_norm[..., -1] = 1
    norm = quat_rotate(q, ref_norm)
    
    norm_tan = torch.cat([tan, norm], dim=len(tan.shape) - 1)
    return norm_tan

@torch.jit.script
def euler_xyz_to_exp_map(roll, pitch, yaw):
    q = quat_from_euler_xyz(roll, pitch, yaw)
    exp_map = quat_to_exp_map(q)
    return exp_map

@torch.jit.script
def exp_map_to_angle_axis(exp_map):
    min_theta = 1e-5

    angle = torch.norm(exp_map, dim=-1)
    angle_exp = torch.unsqueeze(angle, dim=-1)
    axis = exp_map / angle_exp
    angle = normalize_angle(angle)

    default_axis = torch.zeros_like(exp_map)
    default_axis[..., -1] = 1

    mask = torch.abs(angle) > min_theta
    angle = torch.where(mask, angle, torch.zeros_like(angle))
    mask_expand = mask.unsqueeze(-1)
    axis = torch.where(mask_expand, axis, default_axis)

    return angle, axis

@torch.jit.script
def exp_map_to_quat(exp_map):
    angle, axis = exp_map_to_angle_axis(exp_map)
    q = quat_from_angle_axis(angle, axis)
    return q

@torch.jit.script
def slerp(q0, q1, t):
    assert(len(t.shape) == len(q0.shape) - 1)
    cos_half_theta = torch.sum(q0 * q1, dim=-1)

    neg_mask = cos_half_theta < 0
    q1 = torch.where(neg_mask.unsqueeze(-1), -q1, q1)
    
    cos_half_theta = torch.abs(cos_half_theta)
    cos_half_theta = torch.unsqueeze(cos_half_theta, dim=-1)

    half_theta = torch.acos(cos_half_theta)
    sin_half_theta = torch.sqrt(1.0 - cos_half_theta * cos_half_theta)

    t = t.unsqueeze(-1)
    ratioA = torch.sin((1 - t) * half_theta) / sin_half_theta
    ratioB = torch.sin(t * half_theta) / sin_half_theta
    
    new_q = ratioA * q0 + ratioB * q1

    new_q = torch.where(torch.abs(sin_half_theta) < 0.001, 0.5 * q0 + 0.5 * q1, new_q)
    new_q = torch.where(torch.abs(cos_half_theta) >= 1, q0, new_q)

    return new_q

@torch.jit.script
def slerp2(q0, q1, t):
    cos_half_theta = torch.sum(q0 * q1, dim=-1)

    neg_mask = cos_half_theta < 0
    q1 = q1.clone()
    q1[neg_mask] = -q1[neg_mask]
    cos_half_theta = torch.abs(cos_half_theta)
    cos_half_theta = torch.unsqueeze(cos_half_theta, dim=-1)

    half_theta = torch.acos(cos_half_theta);
    sin_half_theta = torch.sqrt(1.0 - cos_half_theta * cos_half_theta);

    ratioA = torch.sin((1 - t) * half_theta) / sin_half_theta;
    ratioB = torch.sin(t * half_theta) / sin_half_theta; 
    
    new_q = ratioA * q0 + ratioB * q1

    new_q = torch.where(torch.abs(sin_half_theta) < 0.001, 0.5 * q0 + 0.5 * q1, new_q)
    new_q = torch.where(torch.abs(cos_half_theta) >= 1, q0, new_q)

    return new_q

@torch.jit.script
def calc_heading(q):
    # calculate heading direction from quaternion
    # the heading is the direction on the xy plane
    # q must be normalized
    ref_dir = torch.zeros_like(q[..., 0:3])
    ref_dir[..., 0] = 1
    rot_dir = quat_rotate(q, ref_dir)

    heading = torch.atan2(rot_dir[..., 1], rot_dir[..., 0])
    return heading

@torch.jit.script
def calc_heading_quat(q):
    # calculate heading rotation from quaternion
    # the heading is the direction on the xy plane
    # q must be normalized
    heading = calc_heading(q)
    axis = torch.zeros_like(q[..., 0:3])
    axis[..., 2] = 1

    heading_q = quat_from_angle_axis(heading, axis)
    return heading_q

@torch.jit.script
def calc_heading_quat_inv(q):
    # calculate heading rotation from quaternion
    # the heading is the direction on the xy plane
    # q must be normalized
    heading = calc_heading(q)
    axis = torch.zeros_like(q[..., 0:3])
    axis[..., 2] = 1

    heading_q = quat_from_angle_axis(-heading, axis)
    return heading_q

@torch.jit.script
def quat_pos(x):
    q = x
    z = (q[..., 3:] < 0).float()
    q = (1 - 2 * z) * q
    return q

@torch.jit.script
def quat_to_axis_angle(q):
    eps = 1e-5
    qx, qy, qz, qw = 0, 1, 2, 3
    
    # need to make sure w is not negative to calculate geodesic distance
    q = quat_pos(q)
    length = torch.norm(q[..., 0:3], dim=-1, p=2)
    
    angle = 2.0 * torch.atan2(length, q[..., qw])
    axis = q[..., qx:qw] / length.unsqueeze(-1)

    default_axis = torch.zeros_like(axis)
    default_axis[..., -1] = 1
    mask = length > eps

    angle = torch.where(mask, angle, torch.zeros_like(angle))
    mask_expand = mask.unsqueeze(-1)
    axis = torch.where(mask_expand, axis, default_axis)

    return axis, angle

@torch.jit.script
def quat_diff(q0, q1):
    dq = quat_mul(q1, quat_conjugate(q0))
    return dq

@torch.jit.script
def quat_diff_angle(q0, q1):
    dq = quat_diff(q0, q1)
    _, angle = quat_to_axis_angle(dq)
    return angle

@torch.jit.script
def axis_angle_to_quat(axis, angle):
    # type: (Tensor, Tensor) -> Tensor
    theta = (angle / 2).unsqueeze(-1)
    xyz = normalize(axis) * theta.sin()
    w = theta.cos()
    return quat_unit(torch.cat([xyz, w], dim=-1))