This Python script provides an interactive visualization tool for exploring 3D transformations including rotations and translations. It is designed to be used within a Jupyter Notebook environment, which supports interactive widgets and inline plotting. The script uses matplotlib for 3D plotting, numpy for matrix operations, and ipywidgets for interactive sliders.
- Visualize 3D Transformations: Users can visually explore how rotations and translations affect objects in 3D space.
- Interactive Controls: The script includes sliders to adjust the degrees of rotation around the X, Y, and Z axes, and sliders to translate along these axes.
- Dual Representation: It displays both the original and transformed states of a 3D sphere and coordinate axes, helping users understand the transformation effects.
To run this script, you must have the following packages installed:
numpymatplotlibipywidgetsThese can be installed via pip:
pip install numpy matplotlib ipywidgetsTo use this tool, paste the code into a Jupyter Notebook cell and run it. The interface will present two sets of three sliders each. The first set controls the rotation around the X, Y, and Z axes, and the second set controls translation along these axes.
- draw_sphere function: Draws a sphere in 3D space at a specified center.
- draw_axes function: Draws the XYZ axes in 3D space, indicating direction and magnitude.
- update_matrix function: Computes the transformation matrix based on rotation and translation values.
- plot_3d function: Plots the original and transformed spheres and axes.
- interactive_transformations function: Updates and displays the transformations based on slider inputs.
- This script is intended for educational purposes to assist in visualizing and understanding 3D transformations.
- Ensure that the Jupyter Notebook interface is compatible with interactive widgets for this script to function correctly.
