# Send Pywayne Vio So3 to your agent
Hand the extracted package to your coding agent with a concrete install brief instead of figuring it out manually.
## Fast path
- Download the package from Yavira.
- Extract it into a folder your agent can access.
- Paste one of the prompts below and point your agent at the extracted folder.
## Suggested prompts
### New install

```text
I downloaded a skill package from Yavira. Read SKILL.md from the extracted folder and install it by following the included instructions. Tell me what you changed and call out any manual steps you could not complete.
```
### Upgrade existing

```text
I downloaded an updated skill package from Yavira. Read SKILL.md from the extracted folder, compare it with my current installation, and upgrade it while preserving any custom configuration unless the package docs explicitly say otherwise. Summarize what changed and any follow-up checks I should run.
```
## Machine-readable fields
```json
{
  "schemaVersion": "1.0",
  "item": {
    "slug": "so3",
    "name": "Pywayne Vio So3",
    "source": "tencent",
    "type": "skill",
    "category": "AI 智能",
    "sourceUrl": "https://clawhub.ai/wangyendt/so3",
    "canonicalUrl": "https://clawhub.ai/wangyendt/so3",
    "targetPlatform": "OpenClaw"
  },
  "install": {
    "downloadUrl": "/downloads/so3",
    "sourceDownloadUrl": "https://wry-manatee-359.convex.site/api/v1/download?slug=so3",
    "sourcePlatform": "tencent",
    "targetPlatform": "OpenClaw",
    "packageFormat": "ZIP package",
    "primaryDoc": "SKILL.md",
    "includedAssets": [
      "SKILL.md"
    ],
    "downloadMode": "redirect",
    "sourceHealth": {
      "source": "tencent",
      "slug": "so3",
      "status": "healthy",
      "reason": "direct_download_ok",
      "recommendedAction": "download",
      "checkedAt": "2026-05-03T07:42:25.074Z",
      "expiresAt": "2026-05-10T07:42:25.074Z",
      "httpStatus": 200,
      "finalUrl": "https://wry-manatee-359.convex.site/api/v1/download?slug=so3",
      "contentType": "application/zip",
      "probeMethod": "head",
      "details": {
        "probeUrl": "https://wry-manatee-359.convex.site/api/v1/download?slug=so3",
        "contentDisposition": "attachment; filename=\"so3-0.1.0.zip\"",
        "redirectLocation": null,
        "bodySnippet": null,
        "slug": "so3"
      },
      "scope": "item",
      "summary": "Item download looks usable.",
      "detail": "Yavira can redirect you to the upstream package for this item.",
      "primaryActionLabel": "Download for OpenClaw",
      "primaryActionHref": "/downloads/so3"
    },
    "validation": {
      "installChecklist": [
        "Use the Yavira download entry.",
        "Review SKILL.md after the package is downloaded.",
        "Confirm the extracted package contains the expected setup assets."
      ],
      "postInstallChecks": [
        "Confirm the extracted package includes the expected docs or setup files.",
        "Validate the skill or prompts are available in your target agent workspace.",
        "Capture any manual follow-up steps the agent could not complete."
      ]
    }
  },
  "links": {
    "detailUrl": "https://openagent3.xyz/skills/so3",
    "downloadUrl": "https://openagent3.xyz/downloads/so3",
    "agentUrl": "https://openagent3.xyz/skills/so3/agent",
    "manifestUrl": "https://openagent3.xyz/skills/so3/agent.json",
    "briefUrl": "https://openagent3.xyz/skills/so3/agent.md"
  }
}
```
## 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)
## Trust
- Source: tencent
- Verification: Indexed source record
- Publisher: wangyendt
- Version: 0.1.0
## Source health
- Status: healthy
- Item download looks usable.
- Yavira can redirect you to the upstream package for this item.
- Health scope: item
- Reason: direct_download_ok
- Checked at: 2026-05-03T07:42:25.074Z
- Expires at: 2026-05-10T07:42:25.074Z
- Recommended action: Download for OpenClaw
## Links
- [Detail page](https://openagent3.xyz/skills/so3)
- [Send to Agent page](https://openagent3.xyz/skills/so3/agent)
- [JSON manifest](https://openagent3.xyz/skills/so3/agent.json)
- [Markdown brief](https://openagent3.xyz/skills/so3/agent.md)
- [Download page](https://openagent3.xyz/downloads/so3)