Requirements
- Target platform
- OpenClaw
- Install method
- Manual import
- Extraction
- Extract archive
- Prerequisites
- OpenClaw
- Primary doc
- SKILL.md
Tencent SkillHub Β· AI
Pywayne Vio So3
SO(3) rotation matrix utilities including Lie group/ Lie algebra operations, rotation representation conversions, skew-symmetric matrix operations, and rotat...
skill openclawclawhub Free
SO(3) rotation matrix utilities including Lie group/ Lie algebra operations, rotation representation conversions, skew-symmetric matrix operations, and rotat...
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- Tencent SkillHub
- What's included
- SKILL.md
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Trust & source
Release facts
- Source
- Tencent SkillHub
- Verification
- Indexed source record
- Version
- 0.1.0
Provenance
- Publisher
- wangyendt
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Documentation
Overview
Complete SO(3) rotation matrix toolkit for 3D rotations with Lie group/ Lie algebra operations, rotation representation conversions, skew-symmetric matrix operations, and rotation averaging.
Quick Start
from pywayne.vio.SO3 import SO3_skew, SO3_Exp, SO3_Log, SO3_to_quat import numpy as np # Skew-symmetric matrix vec = np.array([1, 2, 3]) skew = SO3_skew(vec) # Returns 3x3 skew-symmetric matrix # Log/Exp mapping R = np.eye(3) rotvec = SO3_Log(R) # Rotation vector (Lie algebra) R_recon = SO3_Exp(rotvec) # Back to rotation matrix # Quaternion conversion quat = SO3_to_quat(R) # Returns [w, x, y, z]
Basic Operations
check_SO3(R) Check if matrix is a valid SO(3) rotation matrix. Validates shape (3, 3) Checks R.T @ R = I (orthogonality) SO3_mul(R1, R2) Multiply two rotation matrices: R1 @ R2. SO3_diff(R1, R2, from_1_to_2=True) Compute relative rotation between two matrices. from_1_to_2=True: Returns R1.T @ R2 from_1_to_2=False: Returns R2.T @ R1 SO3_inv(R) Compute inverse of rotation matrix (transpose). Supports single (3, 3) or batch (N, 3, 3) inputs
Skew-Symmetric Matrices
SO3_skew(vec) Convert 3D vector to skew-symmetric matrix. vec = [x, y, z] -> [[ 0, -z, y], [ z, 0, -x], [-y, x, 0]] Supports single vector (3,) or batch (N, 3) SO3_unskew(skew) Extract vector from skew-symmetric matrix. Single matrix (3, 3) -> vector (3,) Batch (N, 3, 3) -> vectors (N, 3)
Rotation Representation Conversions
Quaternion SO3_from_quat(q) - Quaternion [w, x, y, z] to rotation matrix SO3_to_quat(R) - Rotation matrix to quaternion [w, x, y, z] Uses Hamilton convention (wxyz) Axis-Angle SO3_from_axis_angle(axis, angle) - Axis-angle to rotation matrix SO3_to_axis_angle(R) - Returns (axis, angle) tuple Euler Angles SO3_from_euler(euler_angles, axes='zyx', intrinsic=True) - Euler to matrix SO3_to_euler(R, axes='zyx', intrinsic=True) - Matrix to Euler Supports all rotation sequences
Lie Group/ Lie Algebra Mapping
SO3_Log(R) SO(3) to so(3) log map, returns rotation vector (3D). Input: (3, 3) or (N, 3, 3) Output: (3,) or (N, 3) SO3_log(R) SO(3) to so(3) log map, returns skew-symmetric matrix (3x3). Equivalent to SO3_skew(SO3_Log(R)) SO3_Exp(rotvec) so(3) to SO(3) exp map from rotation vector. Handles zero vectors gracefully Input: (3,) or (N, 3) Output: (3, 3) or (N, 3, 3) SO3_exp(omega_hat) so(3) to SO(3) exp map from skew-symmetric matrix. Equivalent to SO3_Exp(SO3_unskew(omega_hat))
Averaging
SO3_mean(R) Compute mean rotation matrix from multiple rotations. Uses scipy Rotation.mean() Input: (N, 3, 3) Output: (3, 3)
Single vs Batch
Single matrix: shape (3, 3) Batch: shape (N, 3, 3) Most functions handle both automatically.
SO(3) Matrix Properties
R @ R.T = I (orthogonal) det(R) = 1 (special)
Lie Algebra Vector
Rotation vector where direction is axis, magnitude is angle.
Dependencies
Required packages: numpy - Array operations qmt - Quaternion utilities scipy - Rotation averaging Install with: pip install numpy qmt scipy
Example Usage
# Create rotation from axis-angle axis = np.array([0, 0, 1]) # Z-axis angle = np.pi / 4 # 45 degrees R = SO3_from_axis_angle(axis, angle) # Verify it's valid print(check_SO3(R)) # True # Get Lie algebra representation rotvec = SO3_Log(R) print(f"Rotation vector: {rotvec}") # Convert back R_recon = SO3_Exp(rotvec) print(f"Reconstruction error: {np.linalg.norm(R - R_recon):.2e}") # Batch averaging R_batch = np.array([R, SO3_inv(R), SO3_mul(R, R)]) R_mean = SO3_mean(R_batch)
Category context
Agent frameworks, memory systems, reasoning layers, and model-native orchestration.
Source: Tencent SkillHub
Largest current source with strong distribution and engagement signals.
Package contents
Included in package
1 Docs
- SKILL.md