Gravity Sim Overview

This is a more in depth overview of how my gravity simulator works. You should read my previous post if you haven’t.


I’m using Rust and a game engine called ggez. The main method is pretty short.

pub fn main() -> GameResult{
    let (ctx, event_loop) = &mut ggez::ContextBuilder::new("N-body gravity sim", "Fish")
        .window_setup(ggez::conf::WindowSetup::default().title("N-body gravity sim"))
        .window_mode(ggez::conf::WindowMode::default().dimensions(1000.0, 800.0))
        .build().expect("error building context");
    let state = &mut MainState::new().clone();

    event::run(ctx, event_loop, state)

All this does is initialize a ggez window that uses MainState, a struct that controls the whole game.

struct MainState {
        bodies: Vec<Body>,
        start_point: Point2,
        zoom: f32,
        offset: Point2,
        density: f32,
        radius: f32,
        mouse_pos: Point2,
        trail_length: usize,
        mouse_pressed: bool,
        paused: bool,
        predict_body: Body,
        predict_speed: usize,
        integrator: Integrator,
        help_menu: bool,
        fast_forward: usize,
        step_size: f32,

There’s a lot of stuff stored inside of MainState, but most important is bodies. This is where every planet/star is stored. This is the declaration for the Body struct:

pub struct Body {
        pub pos: Point2,
        pub mass: f32,
        pub radius: f32,
        pub velocity: Vector2,
        pub trail: VecDeque<Point2>,
        pub trail_length: usize,
        pub past_accel: Vector2,
        pub current_accel: Vector2,

To run the actual simulation, ggez runs a method, update, every frame. Here’s the most important part of it:

if !self.paused{ //physics sim
            self.bodies = update_velocities_and_collide(&self.bodies, &self.integrator, &self.step_size);

Basically, it calls the actual physics sim method fast_forward times. fast_forward is a simple multiplier on simulation time so that when the step size is decreased to increase precision I can keep things from getting stagnant.

The actual math and physics is in update_velocities_and_collide. For simplicity, I removed everything unrelated to the actual gravity.

pub fn update_velocities_and_collide(bodies: &Vec<Body>, method: &Integrator, step_size: &f32) -> Vec<Body>{
    let mut bodies = bodies.clone();


        for current_body_i in 0..bodies.len(){
            bodies[current_body_i].current_accel = Vector2::new(0.0, 0.0);

            for other_body_i in 0..bodies.len(){
                if other_body_i != current_body_i {
                    let other_body = &bodies[other_body_i].clone();
                    let current_body = &mut bodies[current_body_i];

                    let r = distance(&other_body.pos, &current_body.pos);
                    let a_mag = (G*other_body.mass)/(r.powi(2)); //acceleration = Gm_2/r^2
                    let angle = angle(&other_body.pos, &current_body.pos);

                    //if two bodies collide, add them to remove list and create new body that's a combination of both
                    if r <= other_body.radius + current_body.radius && !collision_blacklist.contains(&current_body_i){
                        collision_bodies.push(collide(&current_body, &other_body));

                    current_body.current_accel += Vector2::new(angle.cos() * a_mag, angle.sin() * a_mag);

            match method {
                &Integrator::Euler => bodies[current_body_i].update_euler(step_size),
                    &Integrator::Verlet => bodies[current_body_i].update_verlet(step_size),

    return bodies;

What this method does is loop through the Vec<Body> and calculate the acceleration of each individual body. It’s O(n^2), but I don’t think there’s a way around that. This is one of the first bits of code I wrote for this, and looking at it now I think I would’ve used fold() to make it a bit neater. Maybe I’ll change it eventually.

At the bottom, you can see a match statement for the integration method. update_velocities_and_collide calculates the accelerations, but it doesn’t apply them. I partially explained the difference between Euler integration and Verlet integration in my previous post.

pub fn update_euler(&mut self, step_size: &f32){
    microprofile::scope!("Update", "Bodies");

    self.pos += Vector2::new(self.velocity.x * step_size, self.velocity.y * step_size);
    self.velocity += self.current_accel * step_size.powi(2);

pub fn update_verlet(&mut self, step_size: &f32){ //verlet velocity
    microprofile::scope!("Update", "Bodies");

    self.velocity += ((self.current_accel + self.past_accel)/2.0) * *step_size;
    self.pos += self.velocity * *step_size + (self.current_accel/2.0) * (*step_size).powi(2);
    self.past_accel = self.current_accel;

Ggez also calls draw() every frame. draw() is the longest method but only because of all the conditionals. The important part is here:

let params = graphics::DrawParam::new()
                .scale(Vector2::new(self.zoom, self.zoom));

            for i in 0..self.bodies.len(){ //draw bodies
                let body = graphics::Mesh::new_circle( //draw body
                    graphics::Color::new(1.0, 1.0, 1.0, 1.0))
                    .expect("error building body mesh");

                graphics::draw(ctx, &body, params).expect("error drawing body");

First, I create the DrawParams that tell ggez how to draw the object. At first I was implementing camera movement by manually editing the position of each body in this method, but then I read the ggez documentation and that made it a lot easier.

I also learned about error management in Rust from this method. Instead of catching and throwing errors, methods that have the potential to error must return an Option that might be an Err. If I want to ignore an error, I can match (Rust switch statements) it to empty braces. If I want to close the program with an error message, I use expect(). If I want to tell Rust that I know that there’s definitely no error, I can use unwrap(). You can see a lot more error management with how I drew trails if you look at the code here.

The rest is just processing input. Ggez gives methods like key_down_event and mouse_motion_event, and the rest is pretty simple. I might change how camera movement works because while key_down_event is automatically debounced, there’s also ggez::input::keyboard::pressed_keys() which returns a set of all the keys pressed during a frame, which I can use to make the movement smoother. I’d also like to add a GUI but there aren’t many good options for Rust GUIs yet, so I think I’ll implement a simple one myself.