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use crate::particle_system::{ParticleSystem, Point, Scalar, Vector, N};
use nalgebra::{Const, DVector, Dyn, Matrix, ViewStorage};
mod midpoint;
/// A vector of concatenated position and velocity components of each particle
#[derive(Debug, Clone)]
pub struct PhaseSpace(DVector<Scalar>);
type ParticleView<'a> = Matrix<
Scalar,
Const<{ PhaseSpace::PARTICLE_DIM }>,
Const<1>,
ViewStorage<'a, Scalar, 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];
}
}
}
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 trait Solver {
fn step(&mut self, dt: Scalar);
}
#[cfg(test)]
mod tests {
use super::{ParticleSystem, PhaseSpace, Point, Scalar, Solver, Vector};
use crate::particle_system::Particle;
#[test]
fn test_collect_phase_space() {
let system = ParticleSystem {
particles: vec![Particle::new(Point::new(2.0, 3.0), 1.0)],
constraints: vec![],
forces: vec![],
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),
],
constraints: vec![],
forces: vec![],
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,
mass: Scalar,
) -> (Vector, Vector, ParticleSystem) {
let gravity = -9.8 * Vector::y();
let mut system = ParticleSystem {
particles: vec![Particle::new(Point::origin(), mass)],
constraints: vec![],
forces: vec![],
t: 0.0,
};
let iterations = (fall_time / dt) as usize;
for _ in 0..iterations {
for particle in &mut system.particles {
particle.reset_force();
particle.apply_force(gravity * particle.mass);
}
system.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,
system,
)
}
#[test]
fn ball_should_fall() {
let (position_error, velocity_error, _) = simulate_falling_ball(10.0, 0.01, 3.0);
assert!(
position_error.norm() < 0.01,
"Position error is too high: {}",
position_error,
);
assert!(
velocity_error.norm() < 0.01,
"Velocity error is too high: {}",
velocity_error,
);
}
#[test]
fn freefall_different_masses() {
let (_, _, system1) = simulate_falling_ball(10.0, 0.01, 2.0);
let (_, _, system2) = simulate_falling_ball(10.0, 0.01, 10.0);
let diff = system1.particles[0].position - system2.particles[0].position;
assert!(
diff.norm() < 0.01,
"Points with different masses should fall with the same speed, diff: {}",
diff
);
}
}
|
