Building a Rust Physics Engine with SAT Collision Detection

In this article we explore how to create a physics engine in Rust, focusing on implementing collision detection using the Separating Axis Theorem (SAT).

pub fn get_all_points(&self) -> [[f64; 2]; 4] {
  [
    [((*self).rect.x as f64) + (*self).rect.w as f64, (*self).rect.y as f64],
    [((*self).rect.x as f64) + (*self).rect.w as f64, ((*self).rect.y as f64) + (*self).rect.h as f64],
    [((*self).rect.x as f64), ((*self).rect.y as f64) + (*self).rect.h as f64],
    [(*self).rect.x as f64, (*self).rect.y as f64],
  ]
}

This function returns the four corner points of a rectangle in the order: top‑right, bottom‑right, bottom‑left, top‑left.

Collision detection functions

Vector operations needed for SAT:

fn subtract(p1: [f64; 2], p2: [f64; 2]) -> [f64; 2] {
  [p1[0] - p2[0], p1[1] - p2[1]]
}

fn perpendicular(edge: [f64; 2]) -> [f64; 2] {
  [-edge[1], edge[0]]
}

fn normalize(v: [f64; 2]) -> [f64; 2] {
  let length = (v[0].powi(2) + v[1].powi(2)).sqrt();
  if length > 0.0 {
    [v[0] / length, v[1] / length]
  } else {
    [0.0, 0.0] // handle zero‑length vector
  }
}

Dot product calculation

The dot product multiplies corresponding components of two vectors.

fn dot(v1: [f64; 2], v2: [f64; 2]) -> f64 {
  v1[0] * v2[0] + v1[1] * v2[1]
}

Projection and overlap detection

Project a shape onto an axis and obtain the minimum and maximum scalar values.

fn project(shape: &[[f64; 2]; 4], axis: [f64; 2]) -> (f64, f64) {
  let mut min = dot(shape[0], axis);
  let mut max = min;
  for &point in shape.iter().skip(1) {
    let projection = dot(point, axis);
    if projection < min { min = projection; }
    if projection > max { max = projection; }
  }
  (min, max)
}

fn overlap(proj1: (f64, f64), proj2: (f64, f64)) -> bool {
  const EPSILON: f64 = 1e-9;
  proj1.1 + EPSILON >= proj2.0 && proj2.1 + EPSILON >= proj1.0
}

Putting it all together

Gather points for both rectangles, compute edge vectors, generate axes from the perpendicular normalized edges, and test each axis for a separating axis.

let points1: [[f64; 2]; 4] = self.get_all_points();
let points2: [[f64; 2]; 4] = rect.get_all_points();

let edges1: Vec<[f64; 2]> = points1
  .iter()
  .zip(points1.iter().cycle().skip(1))
  .map(|(p1, p2)| subtract(*p2, *p1))
  .collect();
let edges2: Vec<[f64; 2]> = points2
  .iter()
  .zip(points2.iter().cycle().skip(1))
  .map(|(p1, p2)| subtract(*p2, *p1))
  .collect();

let axes: Vec<[f64; 2]> = edges1
  .iter()
  .chain(edges2.iter())
  .map(|edge| normalize(perpendicular(*edge)))
  .collect();

for axis in axes {
  let proj1 = project(&points1, axis);
  let proj2 = project(&points2, axis);
  if !overlap(proj1, proj2) {
    // Found a separating axis – no collision
    return false;
  }
}
// All projections overlap – collision detected
true

Circle‑square collision detection

Approximate a circle with its bounding box and test overlap with a rectangle.

pub fn detect_collision(&self, rect: &Rect) -> bool {
  // Use diameter to build the circle's bounding rectangle
  let circle_diameter = (self.r * 2) as u32;
  let circle_rect = sdl2::rect::Rect::new(
    self.x as i32,
    self.y as i32,
    circle_diameter,
    circle_diameter,
  );
  // Check overlap between the two axis‑aligned rectangles
  let r = rect.get_rect();
  let overlap_x = circle_rect.x < r.x + r.w && circle_rect.x + circle_rect.w > r.x;
  let overlap_y = circle_rect.y < r.y + r.h && circle_rect.y + circle_rect.h > r.y;
  overlap_x && overlap_y
}

This completes a basic SAT‑based collision system for rectangles and an approximate method for circle‑square collisions in Rust.