Homogeneous Transform

A simple Python library for creating homogeneous transformation matrices for 3D transformations, including rotation, translation, and scaling. This library is built using NumPy and SciPy for efficient numerical computations.

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Features

• Generate homogeneous rotation matrices from scipy.spatial.transform.Rotationinstance.
• Create homogeneous translation matrices from 3D translation vectors.
• Construct homogeneous scaling matrices from 3D scale vectors.
• Easy-to-use functions for common transformation operations.

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Installation

Install the package:

pip install homogeneous-transform

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Usage

Importing the Library

import numpy as np
from homogeneous_transform import rh, th, sh
from scipy.spatial.transform import Rotation as R

Examples

1. Create a Homogeneous Rotation Matrix

Convert a rotation instance (e.g., 45 degrees around the Z-axis) into a 4x4 homogeneous matrix:

rotation = R.from_euler('z', 45, degrees=True)  # Rotation around Z-axis
rotation_matrix = rh(rotation)
print("Homogeneous Rotation Matrix:")
print(rotation_matrix)

Output:

Homogeneous Rotation Matrix:
[[ 0.70710678 -0.70710678  0.          0.        ]
 [ 0.70710678  0.70710678  0.          0.        ]
 [ 0.          0.          1.          0.        ]
 [ 0.          0.          0.          1.        ]]

2. Create a Homogeneous Translation Matrix

Convert a translation vector (e.g., ([1, 2, 3])) into a 4x4 homogeneous matrix:

translation_vector = [1, 2, 3]
translation_matrix = th(translation_vector)
print("Homogeneous Translation Matrix:")
print(translation_matrix)

Output:

Homogeneous Translation Matrix:
[[1. 0. 0. 1.]
 [0. 1. 0. 2.]
 [0. 0. 1. 3.]
 [0. 0. 0. 1.]]

3. Create a Homogeneous Scaling Matrix

Convert a scale vector (e.g., ([2, 3, 4])) into a 4x4 homogeneous matrix:

scale_vector = [2, 3, 4]
scaling_matrix = sh(scale_vector)
print("Homogeneous Scaling Matrix:")
print(scaling_matrix)

Output:

Homogeneous Scaling Matrix:
[[2. 0. 0. 0.]
 [0. 3. 0. 0.]
 [0. 0. 4. 0.]
 [0. 0. 0. 1.]]

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API Reference

rh(rotation_instance)

• Description: Converts a scipy.spatial.transform.Rotation instance into a 4x4 homogeneous rotation matrix.
• Parameters:
  • rotation_instance: A scipy.spatial.transform.Rotation object.
• Returns: A numpy.ndarray representing the 4x4 rotation matrix.

th(translation_vector)

• Description: Converts a 3D translation vector into a 4x4 homogeneous translation matrix.
• Parameters:
  • translation_vector: A 3-element list, tuple, or NumPy array representing x, y, z.
• Returns: A numpy.ndarray representing the 4x4 translation matrix.

sh(scale_vector)

• Description: Converts a 3D scale vector into a 4x4 homogeneous scaling matrix.
• Parameters:
  • scale_vector: A 3-element list, tuple, or NumPy array representing sx, sy, sz.
• Returns: A numpy.ndarray representing the 4x4 scaling matrix.

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License

This project is licensed under the GNU GENERAL PUBLIC License. See the LICENSE file for details.

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Contributing

Contributions are welcome! To contribute:

1. Fork the repository.
2. Create a new branch for your feature or bugfix.
3. Submit a pull request with a clear description of the changes.