Geometry

GeoGebra is a widely used, free software application that combines geometry, algebra, calculus, and other branches of mathematics into a single, interactive platform. It is particularly popular in educational settings for teaching and learning mathematics, as well as for exploring mathematical concepts visually and dynamically.

The Geometry project is a Python-based graphical application mainly built using Pygame and Numpy. Its goal is to create a 3D interactive geometric exploration tool inspired by GeoGebra. The tool features an original mathematics engine to handle advanced geometric transformations, projections, and object manipulations.

Main Features

1. Interactive Visualization:
   • A user-friendly Pygame interface with a resizable canvas for geometric visualization.
   • An interactive coordinate axis that can respond to user actions like mouse clicks and drags.
2. Mathematical Engine:
   • Core mathematical functions include:
     • Change of Basis: Converts vectors between arbitrary bases for advanced linear algebra operations.
     • Translation: Moves points in space using specified directional vectors.
     • Homothety: Scales objects relative to a center point with a specific ratio.
     • Rotation: Supports 3D rotations using roll, pitch, and yaw angles.
     • Projection: Projects 3D points into 2D space for visualization.
3. Modular Object-Oriented Design:
   • The code separates concerns through modules for rendering (objects.py), mathematical transformations (transformations.py), and the main application logic (main.py).
   • Scalability is inherent, allowing for the integration of new shapes or geometric tools.
4. Real-Time Updates:
   • The application employs a delta-time loop to ensure smooth and consistent animation and interaction across different hardware.
5. Customizable Geometry:
   • Users can define, manipulate, and observe geometric entities like axes and vectors, allowing hands-on exploration of mathematical concepts.

Functionalities Available

• Axis Manipulation:
  • The 3D coordinate axis is rendered dynamically. Users can click and drag to reposition it within the viewport.
• Projection to 2D:
  • Points in 3D space are projected onto a 2D plane, offering insights into 3D-to-2D transformations.
• Advanced Transformations:
  • Perform translations, rotations, and scalings on geometric entities with intuitive results.
• Event Handling:
  • Responds to mouse clicks and movement for interactive geometry exploration.

Planned Enhancements

1. Enhanced Shape Library:
   • Add common geometric objects like circles, polygons, and curves for visualization.
2. Dynamic Inputs:
   • Implement input dialogs for users to provide equations, coordinates, or parameters dynamically.
3. Educational Tools:
   • Include step-by-step explanations and visualizations for transformations.
4. Export Features:
   • Save visualizations as image files or export data for further analysis.
5. 3D Object Rendering:
   • Extend the engine to render 3D objects with depth, lighting, and perspective.

Technological Highlights

• Python + Pygame:
  • Delivers a simple yet powerful interactive graphics framework.
• Numpy Integration:
  • Efficient mathematical computation and matrix manipulation.
• Object-Oriented Programming:
  • Ensures modularity and extensibility.

Project Repository

• GitHub Repository provides access to the source code, detailed documentation, and examples.