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use nalgebra::{Const, DVector, Dyn, Matrix, Point as PointBase, SVector, ViewStorage};
const N: usize = 2;
pub type Scalar = f32;
pub type Vector = SVector<Scalar, N>;
pub type Point = PointBase<Scalar, N>;
#[derive(Debug)]
pub struct Particle {
pub mass: Scalar,
pub position: Point,
pub velocity: Vector,
/// Force accumulator
pub force: Vector,
}
impl Particle {
pub fn new(position: Point, mass: Scalar) -> Self {
Self {
mass,
position,
velocity: Vector::zeros(),
force: Vector::zeros(),
}
}
pub fn apply_force(&mut self, force: Vector) {
self.force += force;
}
pub fn reset_force(&mut self) {
self.force = Vector::zeros()
}
}
/// A vector of concatenated position and velocity components of each particle
#[derive(Debug)]
pub struct PhaseSpace(DVector<Scalar>);
type ParticleView<'a> = Matrix<
f32,
Const<{ PhaseSpace::PARTICLE_DIM }>,
Const<1>,
ViewStorage<'a, f32, Const<{ PhaseSpace::PARTICLE_DIM }>, Const<1>, Const<1>, Dyn>,
>;
impl PhaseSpace {
/// Each particle spans 2N elements in a vector
/// first N for position, then N more for velocity
const PARTICLE_DIM: usize = N * 2;
pub fn new(particle_count: usize) -> Self {
let dimension = particle_count * PhaseSpace::PARTICLE_DIM;
Self(DVector::<Scalar>::zeros(dimension))
}
pub fn particle_view(&self, i: usize) -> ParticleView {
self.0
.fixed_rows::<{ PhaseSpace::PARTICLE_DIM }>(i * PhaseSpace::PARTICLE_DIM)
}
pub fn set_particle(&mut self, i: usize, position: Point, velocity: Vector) {
let mut view = self
.0
.fixed_rows_mut::<{ PhaseSpace::PARTICLE_DIM }>(i * PhaseSpace::PARTICLE_DIM);
for i in 0..N {
view[i] = position[i];
view[i + N] = velocity[i];
}
}
}
#[derive(Debug)]
pub struct ParticleSystem {
pub particles: Vec<Particle>,
/// Simulation clock
pub t: Scalar,
}
impl ParticleSystem {
fn collect_phase_space(&self) -> PhaseSpace {
let mut phase_space = PhaseSpace::new(self.particles.len());
for (particle_index, particle) in self.particles.iter().enumerate() {
phase_space.set_particle(particle_index, particle.position, particle.velocity);
}
phase_space
}
fn compute_derivative(&self) -> PhaseSpace {
let mut phase_space = PhaseSpace::new(self.particles.len());
for (particle_index, particle) in self.particles.iter().enumerate() {
phase_space.set_particle(
particle_index,
particle.velocity.into(),
particle.force / particle.mass,
);
}
phase_space
}
fn scatter_phase_space(&mut self, phase_space: &PhaseSpace) {
for (particle_index, particle) in &mut self.particles.iter_mut().enumerate() {
let view = phase_space.particle_view(particle_index);
for i in 0..N {
particle.position[i] = view[i];
particle.velocity[i] = view[i + N];
}
}
}
pub fn euler_step(&mut self, dt: Scalar) {
let derivative = self.compute_derivative();
let mut state = self.collect_phase_space();
state.0 += derivative.0 * dt;
self.scatter_phase_space(&state);
self.t += dt;
}
}
#[cfg(test)]
mod tests {
use super::{Particle, ParticleSystem, PhaseSpace, Point, Scalar, Vector};
#[test]
fn test_collect_phase_space() {
let system = ParticleSystem {
particles: vec![Particle::new(Point::new(2.0, 3.0), 1.0)],
t: 0.0,
};
let phase_space = system.collect_phase_space();
assert!(
!phase_space.0.is_empty(),
"Phase space has to contain non-zero values"
);
}
#[test]
fn test_scatter_phase_space() {
let mut phase_space = PhaseSpace::new(2);
phase_space.set_particle(1, Point::new(5.0, 7.0), Vector::x());
let mut system = ParticleSystem {
particles: vec![
Particle::new(Point::new(0.0, 0.0), 1.0),
Particle::new(Point::new(0.0, 0.0), 1.0),
],
t: 0.0,
};
system.scatter_phase_space(&phase_space);
assert!(
!system.particles[1].velocity.is_empty(),
"Velocity has to be set"
);
assert!(
!system.particles[1].position.is_empty(),
"Position has to be set"
);
}
fn simulate_falling_ball(fall_time: Scalar, dt: Scalar) -> (Vector, Vector) {
let gravity = -9.8 * Vector::y();
let mut system = ParticleSystem {
particles: vec![Particle::new(Point::origin(), 1.0)],
t: 0.0,
};
let iterations = (fall_time / dt) as usize;
for _ in 0..iterations {
for particle in &mut system.particles {
particle.reset_force();
}
for particle in &mut system.particles {
particle.apply_force(gravity);
}
system.euler_step(dt);
}
let expected_velocity = gravity * fall_time; // vt
let expected_position = gravity * fall_time * fall_time / 2.0; // at^2 / 2
(
system.particles[0].position.coords - expected_position,
system.particles[0].velocity - expected_velocity,
)
}
#[test]
fn ball_should_fall() {
let (position_error, velocity_error) = simulate_falling_ball(10.0, 0.01);
assert!(position_error.norm() < 0.5, "Position error has is too high");
assert!(velocity_error.norm() < 0.5, "Velocity error has is too high");
}
}
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