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#!/usr/bin/env python
# Copyright 2025 The HuggingFace Inc. team. All rights reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
"""Custom rotation utilities to replace scipy.spatial.transform.Rotation."""
import numpy as np
class Rotation:
"""
Custom rotation class that provides a subset of scipy.spatial.transform.Rotation functionality.
Supports conversions between rotation vectors, rotation matrices, and quaternions.
"""
def __init__(self, quat: np.ndarray) -> None:
"""Initialize rotation from quaternion [x, y, z, w]."""
self._quat = np.asarray(quat, dtype=float)
# Normalize quaternion
norm = np.linalg.norm(self._quat)
if norm > 0:
self._quat = self._quat / norm
@classmethod
def from_rotvec(cls, rotvec: np.ndarray) -> "Rotation":
"""
Create rotation from rotation vector using Rodrigues' formula.
Args:
rotvec: Rotation vector [x, y, z] where magnitude is angle in radians
Returns:
Rotation instance
"""
rotvec = np.asarray(rotvec, dtype=float)
angle = np.linalg.norm(rotvec)
if angle < 1e-8:
# For very small angles, use identity quaternion
quat = np.array([0.0, 0.0, 0.0, 1.0])
else:
axis = rotvec / angle
half_angle = angle / 2.0
sin_half = np.sin(half_angle)
cos_half = np.cos(half_angle)
# Quaternion [x, y, z, w]
quat = np.array([axis[0] * sin_half, axis[1] * sin_half, axis[2] * sin_half, cos_half])
return cls(quat)
@classmethod
def from_matrix(cls, matrix: np.ndarray) -> "Rotation":
"""
Create rotation from 3x3 rotation matrix.
Args:
matrix: 3x3 rotation matrix
Returns:
Rotation instance
"""
matrix = np.asarray(matrix, dtype=float)
# Shepherd's method for converting rotation matrix to quaternion
trace = np.trace(matrix)
if trace > 0:
s = np.sqrt(trace + 1.0) * 2 # s = 4 * qw
qw = 0.25 * s
qx = (matrix[2, 1] - matrix[1, 2]) / s
qy = (matrix[0, 2] - matrix[2, 0]) / s
qz = (matrix[1, 0] - matrix[0, 1]) / s
elif matrix[0, 0] > matrix[1, 1] and matrix[0, 0] > matrix[2, 2]:
s = np.sqrt(1.0 + matrix[0, 0] - matrix[1, 1] - matrix[2, 2]) * 2 # s = 4 * qx
qw = (matrix[2, 1] - matrix[1, 2]) / s
qx = 0.25 * s
qy = (matrix[0, 1] + matrix[1, 0]) / s
qz = (matrix[0, 2] + matrix[2, 0]) / s
elif matrix[1, 1] > matrix[2, 2]:
s = np.sqrt(1.0 + matrix[1, 1] - matrix[0, 0] - matrix[2, 2]) * 2 # s = 4 * qy
qw = (matrix[0, 2] - matrix[2, 0]) / s
qx = (matrix[0, 1] + matrix[1, 0]) / s
qy = 0.25 * s
qz = (matrix[1, 2] + matrix[2, 1]) / s
else:
s = np.sqrt(1.0 + matrix[2, 2] - matrix[0, 0] - matrix[1, 1]) * 2 # s = 4 * qz
qw = (matrix[1, 0] - matrix[0, 1]) / s
qx = (matrix[0, 2] + matrix[2, 0]) / s
qy = (matrix[1, 2] + matrix[2, 1]) / s
qz = 0.25 * s
quat = np.array([qx, qy, qz, qw])
return cls(quat)
@classmethod
def from_quat(cls, quat: np.ndarray) -> "Rotation":
"""
Create rotation from quaternion.
Args:
quat: Quaternion [x, y, z, w] or [w, x, y, z] (specify convention in docstring)
This implementation expects [x, y, z, w] format
Returns:
Rotation instance
"""
return cls(quat)
def as_matrix(self) -> np.ndarray:
"""
Convert rotation to 3x3 rotation matrix.
Returns:
3x3 rotation matrix
"""
qx, qy, qz, qw = self._quat
# Compute rotation matrix from quaternion
return np.array(
[
[1 - 2 * (qy * qy + qz * qz), 2 * (qx * qy - qz * qw), 2 * (qx * qz + qy * qw)],
[2 * (qx * qy + qz * qw), 1 - 2 * (qx * qx + qz * qz), 2 * (qy * qz - qx * qw)],
[2 * (qx * qz - qy * qw), 2 * (qy * qz + qx * qw), 1 - 2 * (qx * qx + qy * qy)],
],
dtype=float,
)
def as_rotvec(self) -> np.ndarray:
"""
Convert rotation to rotation vector.
Returns:
Rotation vector [x, y, z] where magnitude is angle in radians
"""
qx, qy, qz, qw = self._quat
# Ensure qw is positive for unique representation
if qw < 0:
qx, qy, qz, qw = -qx, -qy, -qz, -qw
# Compute angle and axis
angle = 2.0 * np.arccos(np.clip(abs(qw), 0.0, 1.0))
sin_half_angle = np.sqrt(1.0 - qw * qw)
if sin_half_angle < 1e-8:
# For very small angles, use linearization: rotvec ≈ 2 * [qx, qy, qz]
return 2.0 * np.array([qx, qy, qz])
# Extract axis and scale by angle
axis = np.array([qx, qy, qz]) / sin_half_angle
return angle * axis
def as_quat(self) -> np.ndarray:
"""
Get quaternion representation.
Returns:
Quaternion [x, y, z, w]
"""
return self._quat.copy()
def apply(self, vectors: np.ndarray, inverse: bool = False) -> np.ndarray:
"""
Apply this rotation to a set of vectors.
This is equivalent to applying the rotation matrix to the vectors:
self.as_matrix() @ vectors (or self.as_matrix().T @ vectors if inverse=True).
Args:
vectors: Array of shape (3,) or (N, 3) representing vectors in 3D space
inverse: If True, apply the inverse of the rotation. Default is False.
Returns:
Rotated vectors with shape:
- (3,) if input was single vector with shape (3,)
- (N, 3) in all other cases
"""
vectors = np.asarray(vectors, dtype=float)
original_shape = vectors.shape
# Handle single vector case - ensure it's 2D for matrix multiplication
if vectors.ndim == 1:
if len(vectors) != 3:
raise ValueError("Single vector must have length 3")
vectors = vectors.reshape(1, 3)
single_vector = True
elif vectors.ndim == 2:
if vectors.shape[1] != 3:
raise ValueError("Vectors must have shape (N, 3)")
single_vector = False
else:
raise ValueError("Vectors must be 1D or 2D array")
# Get rotation matrix
rotation_matrix = self.as_matrix()
# Apply inverse if requested (transpose for orthogonal rotation matrices)
if inverse:
rotation_matrix = rotation_matrix.T
# Apply rotation: (N, 3) @ (3, 3).T -> (N, 3)
rotated_vectors = vectors @ rotation_matrix.T
# Return original shape for single vector case
if single_vector and original_shape == (3,):
return rotated_vectors.flatten()
return rotated_vectors
def inv(self) -> "Rotation":
"""
Invert this rotation.
Composition of a rotation with its inverse results in an identity transformation.
Returns:
Rotation instance containing the inverse of this rotation
"""
qx, qy, qz, qw = self._quat
# For a unit quaternion, the inverse is the conjugate: [-x, -y, -z, w]
inverse_quat = np.array([-qx, -qy, -qz, qw])
return Rotation(inverse_quat)
def __mul__(self, other: "Rotation") -> "Rotation":
"""
Compose this rotation with another rotation using the * operator.
The composition `r2 * r1` means "apply r1 first, then r2".
This is equivalent to applying rotation matrices: r2.as_matrix() @ r1.as_matrix()
Args:
other: Another Rotation instance to compose with
Returns:
Rotation instance representing the composition of rotations
"""
if not isinstance(other, Rotation):
return NotImplemented
# Get quaternions [x, y, z, w]
x1, y1, z1, w1 = other._quat # Apply first
x2, y2, z2, w2 = self._quat # Apply second
# Quaternion multiplication: q2 * q1 (apply q1 first, then q2)
composed_quat = np.array(
[
w2 * x1 + x2 * w1 + y2 * z1 - z2 * y1, # x component
w2 * y1 - x2 * z1 + y2 * w1 + z2 * x1, # y component
w2 * z1 + x2 * y1 - y2 * x1 + z2 * w1, # z component
w2 * w1 - x2 * x1 - y2 * y1 - z2 * z1, # w component
]
)
return Rotation(composed_quat)
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