elastic-collision

In physics, an elastic collision is an encounter (collision) between two bodies in which the total kinetic energy of the two bodies remains the same. In an ideal, perfectly elastic collision, there is no net conversion of kinetic energy into other forms such as heat, noise, or potential energy.

This C++ project implements an elastic collision physics simulation using the SFML (Simple and Fast Multimedia Library). The simulation includes balls bouncing within a confined space, and users can manipulate gravity, restitution, and restart the simulation. This project was coded and tested with Ubuntu 22.04 LTS.

How it works

Collision in Two Dimensions

A collision in two dimensions obeys the same rules as a collision in one dimension. Total momentum in each direction is always the same before and after the collision. Total kinetic energy is the same before and after an elastic collision. Note that the kinetic energy is not calculated for each direction separately but depends on the magnitude of the total velocity of each object.

Momentun is conserved in each dimension always (restitution = 1):

Kinetic energy is conserved in elastic collision (restitution = 1):

Collision

After Collision:

Note that, for a collision:

Restitution = 1 indicates an elastic collision.
0 < Restitution < 1 indicates a partially elastic collision.
Restitution = 0 indicates a perfectly inelastic collision.
-1 < Restitution < 0 indicates a collision with some degree of "stickiness."
Restitution = -1 indicates a perfectly sticky collision.

Getting Started

Prerequisites

C++ Compiler
SFML library (Simple and Fast Multimedia Library)
optional Makefile (for much easier compilation)

Installation (with Makefile)

Clone the repository:

git clone https://github.com/raphsenn/elastic-collision

Install SFML by following the instructions on the official SFML website.

https://www.sfml-dev.org/tutorials/2.6/start-linux.php (linux)
https://www.sfml-dev.org/tutorials/2.6/start-osx.php (macOS)
https://www.sfml-dev.org/tutorials/2.6/start-vc.php (windows)

Compile the project:

make

Run the executable:

./main

Installation (without Makefile)

Clone the repository:

git clone https://github.com/raphsenn/elastic-collision

Install SFML by following the instructions on the official SFML website. Just download SFML folder and put it into this folder.

https://www.sfml-dev.org/tutorials/2.6/start-linux.php (linux)
https://www.sfml-dev.org/tutorials/2.6/start-osx.php (macOS)
https://www.sfml-dev.org/tutorials/2.6/start-vc.php (windows)

Create the build directory:

mkdir -p build

Compile the project:

g++ -std=c++11 -Wall -Wextra -pedantic -c src/ball.cpp -o build/ball.o -Iinclude
g++ -std=c++11 -Wall -Wextra -pedantic -c src/button.cpp -o build/button.o -Iinclude
g++ -std=c++11 -Wall -Wextra -pedantic -c src/main.cpp -o build/main.o -Iinclude
g++ -std=c++11 -Wall -Wextra -pedantic -c src/random.cpp -o build/random.o -Iinclude
g++ -std=c++11 -Wall -Wextra -pedantic -c src/sandbox.cpp -o build/sandbox.o -Iinclude
g++ -std=c++11 -Wall -Wextra -pedantic -c src/slider.cpp -o build/slider.o -Iinclude
g++ -std=c++11 -Wall -Wextra -pedantic -c src/vector2.cpp -o build/vector2.o -Iinclude

Linking (dont forget the sfml flags!)

g++ -std=c++11 -Wall -Wextra -pedantic -o main build/ball.o build/button.o build/main.o build/random.o build/sandbox.o build/slider.o build/vector2.o -lsfml-graphics -lsfml-window -lsfml-system

Run the executable

./main

Code structure

vector2.h and vector2.cpp: Define and implement the Vector2 class, providing vector operations.
sandbox.h and sandbox.cpp: Manage the physics simulation using the SandBox class.
ball.h and ball.cpp: Define and implement the Ball class, representing bouncing balls in the simulation.
random.h and random.cpp: Implement utility functions for generating random values used in the simulation.
slider.h and slider.cpp: Handle slider UI elements with the Slider class.
button.h and button.cpp: Handle UI elements with the Button class.
main.cpp: Serve as the entry point for the program.