Verlet Physics

A simple Verlet physics engine written in C++ using SFML.

Dependencies

• C++
• SFML 3
• CMake

Build and Compile

cmake -S . -B build
cmake --build build

Features

• Objects and obstacles
  • Rainbow bouncy balls
  • Ropes made of white balls
  • 3 different sized square obstacles
  • 2 different rectangles obstacles (vertical and horizontal)
• Performance
  • Grid based partioning for balls and ropes
  • Parallelization for obstacle collisions
• Other
  • FPS, objects count, and obstacles count
  • Collision detection for window boundaries
  • Substepping for updating and collisions, to prevent overlap
  • 3 different ways to launch balls: sin, random, and manual direction

Usage

Run the code and use settings.hpp to change constants. Pressing keys 1 through 5 spawns the obstacle where your mouse is.

Control	Action
Hold left click	Spawn balls
Right click in two different places	Spawn rope
1	Small square
2	Medium square
3	Big square
4	Horizontal rectangle
5	Vertical rectangle
Backspace	Delete balls and rops
Enter	Delete obstacles
ESC	Close window

Notes

• If the speed of the balls while initially spawning in is not great enough, the balls will collide and go in multiple different directions, instead of one steady stream.
• Certain combinations of SLACK and SLACK_GAP_EXTRA_PX creates tension which can make the rope have waves. However this can happen with real ropes too, such as a bungee coords, so I kept this in. Also, with higher values of SLACK balls will clump together, but it can be fixed when shooting at it.

• To many balls in the window will cause them to "explode" but the window constraints will keep them in so they just bounce around super quickly.

Inspiration

This project was inspired from these two videos on youtube:

I thought this project was an important one to do because it combines performance and physics. I wanted to add more shapes, and implement the ropes, collision detection, and other aspects from the video by Pezzza's Network.

Newton's Kinematic Equations ⇒ Solver::Update():

Newton's second equation of motion:

$$\vec{x} = \vec{x}_0 + \vec{v}_{x0} t + \frac{1}{2} \vec{a}_x t^2$$

Our code uses deltaTime, or $\Delta t$:

$$x = x_0 + v_0 \Delta t + \frac{1}{2} a \Delta t^2$$

velocity takes into account $\Delta t$:

$$v_0 \approx \frac{x_n - x_{n-1}}{\Delta t}$$

Substituting this in, $\Delta t$ cancels out:

$$x = x_n + (x_n - x_{n-1}) + \frac{1}{2} a \Delta t^2$$

Drop the $\frac{1}{2}$ since we already scale gravity by SCALE in settings.hpp:

$$x = x_n + (x_n - x_{n-1}) + a \Delta t^2$$

Simplify to get your standard Verlet integration formula:

$$x_{n+1} = 2x_n - x_{n-1} + a \Delta t^2$$

In the code:

Vec2 velocity = ball.position - ball.previousPosition;
Vec2 newPosition = ball.position + velocity + acceleration * (deltaTime * deltaTime);

ball.previousPosition = ball.position;
ball.position = newPosition;

Media