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use nalgebra::{DMatrix, DVector, RowDVector};
use crate::algebra::{Scalar, N};
use crate::particle_system::ParticleSystem;
pub mod beam;
pub mod slider;
pub const SPRING_CONSTANT: Scalar = 16.0;
pub const DAMPING_CONSTANT: Scalar = 4.0;
pub trait Constraint {
fn get_particles(&self) -> Vec<usize>;
/// Constraint function: C = 0 <=> constrained satisfied
fn c(&self, q: &DVector<Scalar>) -> Scalar;
/// J = dC / dq
/// This implementation computes partial derivative via
/// finite differences method: stepping +-dQ along each axis
///
/// NOTE: this is rather computationally intensive so
/// providing constraint-specific analytical implementation is preferred
fn jacobian(&self, q: &DVector<Scalar>) -> RowDVector<Scalar> {
let dq = 1e-10;
let mut result = RowDVector::zeros(q.len());
// The only non-zero components of derivative vector are
// the particles that this constraint affects
for particle_id in self.get_particles() {
for i in 0..N {
let index = particle_id * N + i;
let mut q = q.clone();
q[index] += dq;
let c_a = self.c(&q);
q[index] -= 2.0 * dq;
let c_b = self.c(&q);
result[index] = (c_a - c_b) / (2.0 * dq)
}
}
result
}
/// C' = J * q'
fn c_dot(&self, jacobian: &RowDVector<Scalar>, q_dot: &DVector<Scalar>) -> Scalar {
(jacobian * q_dot)[0]
}
/// J' = dC' / dq
fn jacobian_dot(&self, q: &DVector<Scalar>, q_dot: &DVector<Scalar>) -> RowDVector<Scalar> {
let dq = 1e-4;
let mut result = RowDVector::zeros(q.len());
// The only non-zero components of derivative vector are
// the particles that this constraint affects
for particle_id in self.get_particles() {
for i in 0..N {
let index = particle_id * N + i;
let mut q = q.clone();
q[index] += dq;
let j_a = self.jacobian(&q);
q[index] -= 2.0 * dq;
let j_b = self.jacobian(&q);
result[index] = (self.c_dot(&j_a, q_dot) - self.c_dot(&j_b, q_dot)) / (2.0 * dq)
}
}
result
}
}
impl ParticleSystem {
/// q is a state vector - concatenated positions of particles
/// q' - its derivative - concatenated velocities
pub fn collect_q(&self) -> (DVector<Scalar>, DVector<Scalar>) {
let size = self.q_dim();
let mut q = DVector::zeros(size);
let mut q_dot = DVector::zeros(size);
for (p, particle) in self.particles.iter().enumerate() {
for i in 0..N {
q[p * N + i] = particle.position[i];
q_dot[p * N + i] = particle.velocity[i];
}
}
(q, q_dot)
}
/// dim(q) = #particles * N
fn q_dim(&self) -> usize {
self.particles.len() * N
}
/// Diagonal matrix of particle masses (each repeated N times to match dim(q))
fn mass_matrix(&self) -> DMatrix<Scalar> {
DMatrix::from_diagonal(&DVector::from_iterator(
self.q_dim(),
self.particles
.iter()
.flat_map(|particle| (0..N).map(|_i| 1.0 / particle.mass)),
))
}
pub fn enforce_constraints(&mut self) {
if self.constraints.len() == 0 {
return;
}
let (q, q_dot) = self.collect_q();
let dim_q = self.q_dim();
let dim_c = self.constraints.len();
let c = DVector::from_iterator(
dim_c,
self.constraints.iter().map(|constraint| constraint.c(&q)),
);
let jacobian = DMatrix::from_rows(
&self
.constraints
.iter()
.map(|constraint| constraint.jacobian(&q))
.collect::<Vec<_>>(),
);
let jacobian_dot = DMatrix::from_rows(
&self
.constraints
.iter()
.map(|constraint| constraint.jacobian_dot(&q, &q_dot))
.collect::<Vec<_>>(),
);
let c_dot = &jacobian * &q_dot;
let forces = DVector::from_iterator(
dim_q,
self.particles
.iter()
.flat_map(|particle| particle.force.iter().map(|&v| v)),
);
let jacobian_times_w = &jacobian * self.mass_matrix();
let jacobian_transpose = &jacobian.transpose();
let lhs = &jacobian_times_w * jacobian_transpose;
let rhs = -(&jacobian_dot * &q_dot
+ jacobian_times_w * &forces
+ SPRING_CONSTANT * &c
+ DAMPING_CONSTANT * &c_dot);
match lhs.lu().solve(&rhs) {
Some(lambda) => {
let constraint_force = jacobian_transpose * lambda;
for i in 0..self.particles.len() {
let force = constraint_force.fixed_rows::<N>(i * N);
self.particles[i].apply_force(force.into());
}
}
None => println!("Lambda not found"),
}
}
}
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