2D Physics Simulation with Spatial Partitioning

A C++ implementation of a 2D physics engine using SFML for rendering and spatial grid partitioning for efficient collision detection.

Features

• Real-time 2D physics simulation
• Spatial grid-based collision detection (O(n) complexity)
• Elastic and inelastic collisions
• Gravity and viscosity effects
• Particle-based rigid body dynamics
• Boundary collision handling
• Energy conservation and dissipation

Physics Concepts

• Newton's Laws of Motion
• Conservation of Momentum
• Elastic Collisions
• Impulse-Based Physics
• Spatial Partitioning
• Collision Detection and Resolution
• Energy Dissipation

Dependencies

• SFML 2.5+
• C++17 or higher
• CMake 3.10+ (optional)

Installation

1. Install SFML:

sudo apt-get install libsfml-dev

2. Clone the repository:

git clone https://github.com/yourusername/physics-simulation.git
cd physics-simulation

3. Compile the code:

g++ -o spatial spatial.cpp -lsfml-graphics -lsfml-window -lsfml-system

Usage

Run the simulation:

./spatial

Controls

• Close window: Click the X button
• Physics parameters can be adjusted in the source code:
  • NUM_OF_BODIES: Number of particles
  • GRAVITY: Gravity constant
  • VISCOSITY: Damping factor
  • CELL_SIZE: Size of grid cells for collision detection

Implementation Details

Spatial Grid System

• Divides the window into a grid of cells
• Each cell tracks particles within its bounds
• Reduces collision checks to nearby particles only

Collision Detection

• Circle-circle intersection tests
• Grid-based broad phase
• Precise narrow phase checking

Physics Resolution

• Impulse-based collision response
• Energy conservation with optional damping
• Position correction to prevent sinking

License

This project is licensed under the MIT License - see the LICENSE file for details.

Contributing

1. Fork the repository
2. Create your feature branch
3. Commit your changes
4. Push to the branch
5. Create a new Pull Request