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

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.
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.
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.
Real-Time Updates:
- The application employs a delta-time loop to ensure smooth and consistent animation and interaction across different hardware.
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

Enhanced Shape Library:
- Add common geometric objects like circles, polygons, and curves for visualization.
Dynamic Inputs:
- Implement input dialogs for users to provide equations, coordinates, or parameters dynamically.
Educational Tools:
- Include step-by-step explanations and visualizations for transformations.
Export Features:
- Save visualizations as image files or export data for further analysis.
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.

How to Download the Project from GitHub

GitHub Repository provides access to the source code.

To download the full project, follow one of these two steps:

1. Clone Using Git (Recommended)

To clone the repository using Git, follow these steps:

Open a terminal or command prompt.
Ensure you have Git installed. If not, download and install it from git-scm.com.

Run the following command:

git clone https://github.com/Tutusaus/Geometry.git