27 files changed, 1194 insertions, 128 deletions
diff --git a/.gitignore b/physics/.gitignore
index c868ffa..c868ffa 100644
--- a/.gitignore
+++ b/physics/.gitignore
diff --git a/Cargo.lock b/physics/Cargo.lock
index a26bd90..98fe5af 100644
--- a/Cargo.lock
+++ b/physics/Cargo.lock
@@ -115,7 +115,7 @@ source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "57c0d7b74b563b49d38dae00a0c37d4d6de9b432382b2892f0574ddcae73fd0a"
 
 [[package]]
-name = "physics-rust"
+name = "physics"
 version = "0.1.0"
 dependencies = [
  "nalgebra",
diff --git a/Cargo.toml b/physics/Cargo.toml
index 11c9611..e5db63e 100644
--- a/Cargo.toml
+++ b/physics/Cargo.toml
@@ -1,5 +1,5 @@
 [package]
-name = "physics-rust"
+name = "physics"
 version = "0.1.0"
 edition = "2021"
 
diff --git a/README.md b/physics/README.md
index 59d5c16..59d5c16 100644
--- a/README.md
+++ b/physics/README.md
diff --git a/physics/src/algebra/mod.rs b/physics/src/algebra/mod.rs
new file mode 100644
index 0000000..47efba8
--- /dev/null
+++ b/physics/src/algebra/mod.rs
@@ -0,0 +1,9 @@
+use nalgebra::{Point as PointBase, SVector};
+
+pub const N: usize = 2;
+pub type Scalar = f64;
+
+pub type Vector = SVector<Scalar, N>;
+pub type Point = PointBase<Scalar, N>;
+
+pub mod subspace;
diff --git a/src/algebra/subspace.rs b/physics/src/algebra/subspace.rs
index 3b32ba7..9fb944e 100644
--- a/src/algebra/subspace.rs
+++ b/physics/src/algebra/subspace.rs
@@ -1,6 +1,7 @@
 use nalgebra::SMatrix;
 
-use crate::{particle_system::Scalar, particle_system::N, Point, Vector};
+use super::{Scalar, N, Point, Vector};
+
 
 type ProjectionMatrix = SMatrix<Scalar, N, N>;
 
@@ -43,7 +44,7 @@ impl<const DIM: usize> Subspace<DIM> {
 
 #[cfg(test)]
 mod tests {
-    use crate::{algebra::subspace::Line, Point, Vector};
+    use crate::algebra::{subspace::Line, Point, Vector};
 
     #[test]
     fn test_projection_onto_line() {
diff --git a/src/constraint/anchor.rs b/physics/src/constraint/anchor.rs
index 3ef94ff..c90cfb2 100644
--- a/src/constraint/anchor.rs
+++ b/physics/src/constraint/anchor.rs
@@ -1,6 +1,7 @@
 use nalgebra::{DVector, RowDVector};
 
-use crate::particle_system::{ParticleSystem, Point, Scalar, N};
+use crate::particle_system::ParticleSystem;
+use crate::algebra::{Point, Scalar, N};
 
 use super::Constraint;
 
diff --git a/src/constraint/beam.rs b/physics/src/constraint/beam.rs
index c953920..14b1c1f 100644
--- a/src/constraint/beam.rs
+++ b/physics/src/constraint/beam.rs
@@ -1,6 +1,7 @@
 use nalgebra::{DVector, RowDVector};
 
-use crate::particle_system::{ParticleSystem, Scalar, N};
+use crate::particle_system::ParticleSystem;
+use crate::algebra::{Scalar, N};
 
 use super::Constraint;
 
diff --git a/src/constraint/mod.rs b/physics/src/constraint/mod.rs
index 6028b42..b2958ec 100644
--- a/src/constraint/mod.rs
+++ b/physics/src/constraint/mod.rs
@@ -1,12 +1,13 @@
 use nalgebra::{DMatrix, DVector, RowDVector};
 
-use crate::particle_system::{ParticleSystem, Scalar, Vector, N};
+use crate::particle_system::ParticleSystem;
+use crate::algebra::{Scalar, Vector, N};
 pub mod anchor;
 pub mod slider;
 pub mod beam;
 
-const SPRING_CONSTANT: Scalar = 0.75;
-const DAMPING_CONSTANT: Scalar = 0.45;
+const SPRING_CONSTANT: Scalar = 0.65;
+const DAMPING_CONSTANT: Scalar = 0.85;
 
 /// SIZE is always 3xN, but this operation can't be done at compile time yet:
 /// "generic parameters may not be used in const operations"
diff --git a/src/constraint/slider.rs b/physics/src/constraint/slider.rs
index 9f7973b..fa7e840 100644
--- a/src/constraint/slider.rs
+++ b/physics/src/constraint/slider.rs
@@ -1,11 +1,8 @@
-use std::usize;
-
 use nalgebra::{DVector, RowDVector};
 
 use crate::{
-    algebra::subspace::Line,
-    particle_system::{Scalar, N},
-    ParticleSystem, Point, Vector,
+    algebra::{subspace::Line, Point, Scalar, Vector, N},
+    particle_system::ParticleSystem,
 };
 
 use super::Constraint;
diff --git a/src/force/drag.rs b/physics/src/force/drag.rs
index ef859a0..c54dc40 100644
--- a/src/force/drag.rs
+++ b/physics/src/force/drag.rs
@@ -1,4 +1,4 @@
-use crate::particle_system::Scalar;
+use crate::algebra::Scalar;
 
 use super::Force;
 
diff --git a/src/force/gravity.rs b/physics/src/force/gravity.rs
index b023e63..dd600a4 100644
--- a/src/force/gravity.rs
+++ b/physics/src/force/gravity.rs
@@ -1,4 +1,4 @@
-use crate::particle_system::Vector;
+use crate::algebra::Vector;
 
 use super::Force;
 
diff --git a/src/force/mod.rs b/physics/src/force/mod.rs
index ce10f9f..ce10f9f 100644
--- a/src/force/mod.rs
+++ b/physics/src/force/mod.rs
diff --git a/physics/src/force/spring.rs b/physics/src/force/spring.rs
new file mode 100644
index 0000000..6c2cf67
--- /dev/null
+++ b/physics/src/force/spring.rs
@@ -0,0 +1,28 @@
+use crate::algebra::Scalar;
+
+use super::Force;
+
+pub struct Spring {
+    pub particle_ids: [usize; 2],
+    pub rest_length: Scalar,
+    pub spring_constant: Scalar,
+    pub damping_constant: Scalar,
+}
+
+impl Force for Spring {
+    fn apply(&self, particles: &mut Vec<crate::particle_system::Particle>) {
+        let a = &particles[self.particle_ids[0]];
+        let b = &particles[self.particle_ids[1]];
+        let i = a.position - b.position;
+        let i_dot = a.velocity - b.velocity;
+        let i_norm = i.norm();
+
+        let force = -(self.spring_constant * (i_norm - self.rest_length)
+        + (self.damping_constant * i.dot(&i_dot) / i_norm))
+        * i
+        / i_norm;
+
+        particles[self.particle_ids[0]].apply_force(force);
+        particles[self.particle_ids[1]].apply_force(-force);
+    }
+}
diff --git a/physics/src/lib.rs b/physics/src/lib.rs
new file mode 100644
index 0000000..8c24a10
--- /dev/null
+++ b/physics/src/lib.rs
@@ -0,0 +1,9 @@
+pub use nalgebra;
+
+pub mod algebra;
+pub mod constraint;
+pub mod force;
+pub mod particle_system;
+mod ppm;
+pub mod renderer;
+pub mod solver;
diff --git a/src/particle_system.rs b/physics/src/particle_system.rs
index a3d7a4b..30255ec 100644
--- a/src/particle_system.rs
+++ b/physics/src/particle_system.rs
@@ -1,12 +1,8 @@
-use nalgebra::{Point as PointBase, SVector};
-
-use crate::{constraint::Constraint, force::Force};
-
-pub const N: usize = 2;
-pub type Scalar = f64;
-
-pub type Vector = SVector<Scalar, N>;
-pub type Point = PointBase<Scalar, N>;
+use crate::{
+    algebra::{Point, Scalar, Vector},
+    constraint::Constraint,
+    force::Force,
+};
 
 #[derive(Debug)]
 pub struct Particle {
@@ -45,3 +41,13 @@ pub struct ParticleSystem {
     /// Simulation clock
     pub t: Scalar,
 }
+
+impl ParticleSystem {
+    pub fn get_kinetic_energy(&self) -> Scalar {
+        self.particles.iter().fold(0.0, |acc, p| {
+            let velocity = p.velocity.norm();
+            let energy = p.mass * velocity * velocity / 2.0;
+            acc + energy
+        })
+    }
+}
diff --git a/physics/src/ppm.rs b/physics/src/ppm.rs
new file mode 100644
index 0000000..be26127
--- /dev/null
+++ b/physics/src/ppm.rs
@@ -0,0 +1,67 @@
+use std::{fs::File, io::Write, path::PathBuf};
+
+use nalgebra::Point2;
+use crate::algebra::{Scalar, N};
+use crate::renderer::Camera;
+use crate::particle_system::Particle;
+
+pub struct PPM<const WIDTH: usize, const HEIGHT: usize> {
+    pub prefix: PathBuf,
+
+    buffer: [[bool; WIDTH]; HEIGHT],
+    // pixels_per_unit: usize,
+}
+
+impl<const WIDTH: usize, const HEIGHT: usize> PPM<WIDTH, HEIGHT> {
+    pub fn new(prefix: PathBuf) -> Self {
+        Self {
+            prefix,
+            buffer: [[false; WIDTH]; HEIGHT],
+        }
+    }
+
+    pub fn clear_buffer(&mut self) {
+        self.buffer = [[false; WIDTH]; HEIGHT]
+    }
+
+    pub fn draw_circle(&mut self, center: Point2<Scalar>, radius: Scalar) {
+        let screen_center = Point2::new((WIDTH / 2) as Scalar, (HEIGHT / 2) as Scalar);
+
+        for pixel_row in 0..HEIGHT {
+            for pixel_col in 0..WIDTH {
+                let point = Point2::new(pixel_col as Scalar, pixel_row as Scalar);
+
+                if (point - center - screen_center.coords).norm() <= radius {
+                    self.buffer[HEIGHT - pixel_row - 1][pixel_col] = true
+                }
+            }
+        }
+    }
+
+    pub fn render_particles(&mut self, particles: &Vec<Particle>, camera: &Camera) {
+        for p in particles {
+            let point = camera.world_to_screen_space(p.position);
+            self.draw_circle(point, p.mass.powf(1.0 / N as Scalar));
+        }
+    }
+
+    pub fn save_frame(&self, time: Scalar) {
+        let file_name = format!("frame-{:08.3}", time);
+        let path = self.prefix.join(file_name);
+        let mut file = File::create(path).unwrap();
+
+        let mut s = format!("P3\n{} {}\n255\n", WIDTH, HEIGHT);
+        let white = "255 255 255 ";
+        let black = "0 0 0 ";
+
+        for row in self.buffer {
+            for pixel in row {
+                let color = if pixel { black } else { white };
+                s += color
+            }
+            s += "\n";
+        }
+
+        file.write(s.as_bytes()).unwrap();
+    }
+}
diff --git a/physics/src/renderer/mod.rs b/physics/src/renderer/mod.rs
new file mode 100644
index 0000000..63894b3
--- /dev/null
+++ b/physics/src/renderer/mod.rs
@@ -0,0 +1,68 @@
+use nalgebra::{Point2, SMatrix};
+
+use crate::{
+    algebra::subspace::Plane,
+    algebra::{Point, Scalar, Vector, N},
+};
+
+pub struct Camera {
+    plane: Plane,
+    up: Vector,
+    origin: Point,
+    world_to_screen_space: SMatrix<Scalar, 2, N>,
+    screen_space_to_world: SMatrix<Scalar, N, 2>,
+}
+
+impl Camera {
+    pub fn new(origin: Point, up: Vector, right: Vector) -> Self {
+        assert!(
+            up.dot(&right) == 0.0,
+            "Up and right vectors must be orthogonal"
+        );
+        let plane = Plane::new(origin, [up, right]);
+
+        let screen_space_to_world = SMatrix::<Scalar, N, 2>::from_columns(&[right, up]);
+        let world_to_screen_space = screen_space_to_world.pseudo_inverse(0.001).unwrap();
+
+        Self {
+            plane,
+            up,
+            origin,
+            world_to_screen_space,
+            screen_space_to_world,
+        }
+    }
+
+    pub fn world_to_screen_space(&self, point: Point) -> Point2<Scalar> {
+        let projected = self.plane.project_point(point);
+        let in_screen_space = self.world_to_screen_space * (projected - self.origin);
+        in_screen_space.into()
+    }
+    pub fn screen_space_to_world(&self, point: Point2<Scalar>) -> Point {
+        (self.screen_space_to_world * point) + self.origin.coords
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use crate::algebra::{Point, Vector};
+
+    use super::Camera;
+
+    #[test]
+    fn test_projection() {
+        let camera = Camera::new(
+            Point::new(1.0, 0.0),
+            Vector::new(1.0, 2.0),
+            Vector::new(2.0, -1.0),
+        );
+
+        let point = Point::new(3.0, 1.0);
+
+        let diff = camera.world_to_screen_space * point - Point::new(1.0, 1.0);
+        assert!(
+            diff.norm() < 0.001,
+            "Camera translated point into screen_space incorrectly"
+        );
+    }
+}
diff --git a/src/solver/midpoint.rs b/physics/src/solver/midpoint.rs
index 08a3e3c..2d71758 100644
--- a/src/solver/midpoint.rs
+++ b/physics/src/solver/midpoint.rs
@@ -1,4 +1,4 @@
-use crate::particle_system::{ParticleSystem, Scalar};
+use crate::{algebra::Scalar, particle_system::ParticleSystem};
 use super::{PhaseSpace, Solver};
 
 impl Solver for ParticleSystem {
diff --git a/src/solver/mod.rs b/physics/src/solver/mod.rs
index 1544378..726dcae 100644
--- a/src/solver/mod.rs
+++ b/physics/src/solver/mod.rs
@@ -1,4 +1,5 @@
-use crate::particle_system::{ParticleSystem, Point, Scalar, Vector, N};
+use crate::particle_system::ParticleSystem;
+use crate::algebra::{Point, Scalar, Vector, N};
 use nalgebra::{Const, DVector, Dyn, Matrix, ViewStorage};
 
 mod midpoint;
diff --git a/playground/.gitignore b/playground/.gitignore
new file mode 100644
index 0000000..c868ffa
--- /dev/null
+++ b/playground/.gitignore
@@ -0,0 +1,2 @@
+/target
+out
diff --git a/playground/Cargo.lock b/playground/Cargo.lock
new file mode 100644
index 0000000..51c385d
--- /dev/null
+++ b/playground/Cargo.lock
@@ -0,0 +1,783 @@
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diff --git a/playground/Cargo.toml b/playground/Cargo.toml
new file mode 100644
index 0000000..163ad90
--- /dev/null
+++ b/playground/Cargo.toml
@@ -0,0 +1,8 @@
+[package]
+name = "playground"
+version = "0.1.0"
+edition = "2021"
+
+[dependencies]
+physics = { path = "../physics" }
+raylib = "5.0.2"
diff --git a/playground/src/main.rs b/playground/src/main.rs
new file mode 100644
index 0000000..1cb8198
--- /dev/null
+++ b/playground/src/main.rs
@@ -0,0 +1,185 @@
+use raylib::prelude::*;
+
+use physics::force::{drag::Drag, gravity::Gravity, spring::Spring};
+use physics::nalgebra::Point as PointBase;
+use physics::particle_system::{Particle, ParticleSystem};
+use physics::algebra::{Point, Scalar, Vector, N};
+use physics::renderer::Camera;
+use physics::solver::Solver;
+
+const SCALE: i32 = 5;
+fn screen_space_to_raylib(p: PointBase<Scalar, 2>, d: &RaylibDrawHandle) -> PointBase<i32, 2> {
+    PointBase::<i32, 2>::new(
+        d.get_screen_width() / 2 + p.x as i32 * SCALE,
+        d.get_screen_height() / 2 - p.y as i32 * SCALE,
+    )
+}
+fn raylib_to_screen_space(p: PointBase<i32, 2>, d: &RaylibDrawHandle) -> PointBase<Scalar, 2> {
+    PointBase::<Scalar, 2>::new(
+        ((p.x - d.get_screen_width() / 2) / SCALE) as Scalar,
+        ((p.y - d.get_screen_height() / 2) / -SCALE) as Scalar,
+    )
+}
+
+fn main() {
+    let dt = 0.0001;
+    let mut system = ParticleSystem {
+        particles: vec![
+            Particle::new(Point::origin(), 4.0),
+            Particle::new(Point::new(-30.0, 0.0), 15.0),
+            Particle::new(Point::new(20.0, 0.0), 30.0),
+            Particle::new(Point::new(5.0, 20.0), 50.0),
+            Particle::new(Point::origin(), 25.0),
+            Particle::new(Point::new(50.0, 0.0), 10.0),
+            Particle::new(Point::new(-100.0, -100.0), 100.0),
+        ],
+        constraints: vec![],
+        forces: vec![
+            Box::new(Gravity {
+                vector: Vector::y() * -9.8,
+            }),
+            Box::new(Drag { coefficient: 0.2 }),
+            Box::new(Spring {
+                particle_ids: [4, 2],
+                spring_constant: 0.75,
+                damping_constant: 0.1,
+                rest_length: 20.0,
+            }),
+        ],
+        t: 0.0,
+    };
+
+    system.add_anchor_constraint(0);
+    system.add_beam_constraint([0, 2]);
+    system.add_beam_constraint([1, 2]);
+    system.add_beam_constraint([1, 3]);
+    system.add_beam_constraint([2, 3]);
+    system.add_slider_constraint(5, Vector::x());
+    system.add_beam_constraint([5, 4]);
+
+    let mut selected_particle_id = None;
+
+    let (mut rl, thread) = raylib::init()
+        .size(640, 480)
+        .title("Physics simulation")
+        .resizable()
+        .build();
+
+    while !rl.window_should_close() {
+        let mut d = rl.begin_drawing(&thread);
+
+        d.clear_background(Color::WHITE);
+        d.draw_text(
+            format!(
+                "Time: {:03.3}\n\nFPS: {}\n\nKinetic energy: {:03.0}",
+                system.t,
+                d.get_fps(),
+                system.get_kinetic_energy()
+            )
+            .as_str(),
+            12,
+            12,
+            20,
+            Color::BLACK,
+        );
+
+        let camera = Camera::new(Point::origin(), Vector::y(), Vector::x());
+
+        match selected_particle_id {
+            Some(particle_id) => {
+                // let p: &Particle = &system.particles[particle_id];
+
+                let mouse_point = PointBase::<i32, 2>::new(d.get_mouse_x(), d.get_mouse_y());
+                let screen_space = raylib_to_screen_space(mouse_point, &d);
+                let world_mouse = camera.screen_space_to_world(screen_space);
+
+                let mouse_particle_id = system.particles.len() - 1;
+                system.particles[mouse_particle_id].position = world_mouse;
+
+                system.forces.push(Box::new(Spring {
+                    particle_ids: [mouse_particle_id, particle_id],
+                    spring_constant: 0.99,
+                    damping_constant: 0.99,
+                    rest_length: 1.0,
+                }));
+            }
+            None => (),
+        }
+
+        for _ in 0..10 {
+            system.apply_forces();
+            system.enforce_constraints(dt);
+            system.step(dt);
+        }
+
+        match selected_particle_id {
+            Some(_) => {
+                system.forces.pop();
+            }
+            None => (),
+        }
+
+        if d.is_mouse_button_released(MouseButton::MOUSE_BUTTON_LEFT) {
+            selected_particle_id = None
+        }
+
+        for (particle_id, particle) in system.particles.iter().enumerate() {
+            let position =
+                screen_space_to_raylib(camera.world_to_screen_space(particle.position), &d);
+            let radius = particle.mass.powf(1.0 / (N as f64)) as f32 * SCALE as f32;
+
+            if d.is_mouse_button_down(MouseButton::MOUSE_BUTTON_LEFT)
+                && selected_particle_id.is_none()
+            {
+                let mouse_point =
+                    PointBase::<f32, 2>::new(d.get_mouse_x() as f32, d.get_mouse_y() as f32);
+                let position = PointBase::<f32, 2>::new(position.x as f32, position.y as f32);
+                if (position - mouse_point).norm() < radius {
+                    selected_particle_id = Some(particle_id)
+                }
+            }
+
+            d.draw_circle(
+                position.x,
+                position.y,
+                radius,
+                if selected_particle_id.is_some_and(|v| v == particle_id) {
+                    Color::RED
+                } else {
+                    Color::BLACK
+                },
+            );
+        }
+        for c in &system.constraints {
+            let particle_ids = c.get_particles();
+            if particle_ids.len() == 2 {
+                let a = screen_space_to_raylib(system.particles[particle_ids[0]].position, &d);
+                let b = screen_space_to_raylib(system.particles[particle_ids[1]].position, &d);
+
+                d.draw_line(a.x, a.y, b.x, b.y, Color::GRAY);
+            }
+        }
+
+        {
+            // Hard-coded spring
+            let particle_ids = [4, 2];
+            let a = screen_space_to_raylib(system.particles[particle_ids[0]].position, &d);
+            let b = screen_space_to_raylib(system.particles[particle_ids[1]].position, &d);
+            d.draw_line(a.x, a.y, b.x, b.y, Color::GREEN);
+        }
+        {
+            // Hard-coded spring
+            match selected_particle_id {
+                Some(id) => {
+                    let mouse_particle_id = system.particles.len() - 1;
+                    let a = screen_space_to_raylib(system.particles[id].position, &d);
+                    let b =
+                        screen_space_to_raylib(system.particles[mouse_particle_id].position, &d);
+
+                    d.draw_line(a.x, a.y, b.x, b.y, Color::GREEN);
+                }
+                None => (),
+            }
+        }
+    }
+}
diff --git a/src/algebra/mod.rs b/src/algebra/mod.rs
deleted file mode 100644
index 13dcd6a..0000000
--- a/src/algebra/mod.rs
+++ /dev/null
@@ -1 +0,0 @@
-pub mod subspace;
diff --git a/src/main.rs b/src/main.rs
deleted file mode 100644
index 0b5704b..0000000
--- a/src/main.rs
+++ /dev/null
@@ -1,59 +0,0 @@
-use std::path::PathBuf;
-
-use force::{drag::Drag, gravity::Gravity};
-use particle_system::{Particle, ParticleSystem, Point, Vector};
-use ppm::PPM;
-use solver::Solver;
-
-mod constraint;
-mod particle_system;
-mod ppm;
-mod solver;
-mod force;
-mod algebra;
-
-fn main() {
-    let ppm = PPM {
-        width: 100,
-        height: 200,
-        prefix: PathBuf::from("./out"),
-    };
-
-    let dt = 0.01;
-    let mut system = ParticleSystem {
-        particles: vec![
-            Particle::new(Point::origin(), 4.0),
-            Particle::new(Point::new(-30.0, 0.0), 15.0),
-            Particle::new(Point::new(20.0, 0.0), 30.0),
-            Particle::new(Point::new(5.0, 20.0), 50.0),
-        ],
-        constraints: vec![],
-        forces: vec![
-            Box::new(Gravity {
-                vector: Vector::y() * -9.8,
-            }),
-            Box::new(Drag { coefficient: 0.0 }),
-        ],
-        t: 0.0,
-    };
-
-    system.add_anchor_constraint(0);
-    system.add_beam_constraint([0, 2]);
-    system.add_beam_constraint([1, 2]);
-    system.add_beam_constraint([1, 3]);
-    system.add_beam_constraint([2, 3]);
-
-    for i in 0..150_00 {
-        system.apply_forces();
-
-        if i % 10 == 0 {
-            println!("Iteration #{i}");
-            println!("{:#?}", system.particles);
-            ppm.save_frame(&system.particles, system.t);
-        }
-
-        system.enforce_constraints(dt);
-
-        system.step(dt);
-    }
-}
diff --git a/src/ppm.rs b/src/ppm.rs
deleted file mode 100644
index 01cdebb..0000000
--- a/src/ppm.rs
+++ /dev/null
@@ -1,41 +0,0 @@
-use std::{fs::File, io::Write, path::PathBuf};
-
-use crate::particle_system::{Particle, Vector, N, Scalar};
-
-pub struct PPM {
-    pub prefix: PathBuf,
-    pub width: usize,
-    pub height: usize,
-    // pixels_per_unit: usize,
-}
-
-impl PPM {
-    fn render_particles(&self, particles: &Vec<Particle>) -> String {
-        let mut s = format!("P3\n{} {}\n255\n", self.width, self.height);
-        let white = "255 255 255 ";
-        let black = "0 0 0 ";
-
-        for pixel_row in 0..self.height {
-            for pixel_col in 0..self.width {
-                let point = Vector::new(pixel_col as Scalar, (pixel_row as Scalar) * -1.0)
-                    + Vector::new(self.width as Scalar / -2.0, self.height as Scalar / 2.0);
-                let color = match particles.iter().any(|p| {
-                    (p.position - point).coords.norm() <= (p.mass).powf(1.0 / (N as f64))
-                }) {
-                    true => black,
-                    false => white,
-                };
-                s += color;
-            }
-        }
-        s
-    }
-
-    pub fn save_frame(&self, particles: &Vec<Particle>, time: Scalar) {
-        let file_name = format!("frame-{:08.3}", time);
-        let path = self.prefix.join(file_name);
-        let mut file = File::create(path).unwrap();
-        let data = self.render_particles(particles);
-        file.write(data.as_bytes()).unwrap();
-    }
-}