LatticeVisualizer

LatticeVisualizer is a React-based application for visualizing lattice points in 2D and 3D space. I created this project to visualize lattices while studying lattice-based cryptography independently.

Features

• 2D and 3D Visualization: Visualize lattice points in 2D and 3D space.
• Dynamic Basis Vectors: Modify the basis vectors to see how the lattice changes.
• Dimension Support: Supports up to 3D visualization.
• Shading Parallelepiped: Shade a random parallelepiped within the lattice.
• Unshading Parallelepiped: Unshade the previously shaded parallelepiped.

Getting Started

Prerequisites

• Node.js and npm installed on your machine.

Installation

1. Clone the repository:

   git clone https://github.com/yourusername/LatticeVisualizer.git
   cd LatticeVisualizer

2. Install the dependencies:

   npm install

Running the Application

1. Start the development server:

   npm start

2. Open your web browser and navigate to http://localhost:3000 to see the application in action.

Usage

Controls

• Dimension: Use the input field to set the lattice dimension (2D or 3D).
• Sum Limit: Set the range for the coefficients used in generating lattice points.
• Basis Vectors: Modify the basis vectors to see how the lattice changes.
• Shade Parallelepiped: Click the "Shade Parallelepiped" button to shade a random parallelepiped within the lattice.
• Unshade Parallelepiped: Click the "Unshade Parallelepiped" button to remove the shading.

Example

To visualize a 2D lattice:

1. Set the dimension to 2.
2. Set the basis vectors to [[1, 0], [0, 1]].
3. Click "Shade Parallelepiped" to shade a random area within the lattice.

To visualize a 3D lattice:

1. Set the dimension to 3.
2. Set the basis vectors to [[1, 0, 0], [0, 1, 0], [0, 0, 1]].
3. Click "Shade Parallelepiped" to shade a random area within the lattice.

See It in Action

You can see it in action on my blog: CryptiCosmos

Code Overview

Main Component

LatticeVisualizer.js:

• Handles the state and logic for dimension, basis vectors, sum limit, and shading.
• Generates lattice points based on user inputs.
• Renders 2D and 3D lattice visualizations using D3.js and Three.js.
• Provides buttons to shade and unshade parallelepipeds within the lattice.

Dependencies

• React: UI library for building the application.
• Three.js: Library for 3D visualization.
• D3.js: Library for 2D visualization.
• OrbitControls: Three.js add-on for interactive controls.

Contributing

Contributions are welcome! Please fork the repository and submit a pull request for any feature requests, bug fixes, or improvements.

License

This project is licensed under the MIT License.

Acknowledgements

• React
• Three.js
• D3.js