81 lines
2.8 KiB
Rust
81 lines
2.8 KiB
Rust
use nalgebra::DMatrix;
|
|
use std::{array, f64::consts::PI};
|
|
|
|
use dyna3::engine::{Q, point, realize_gram, PartialMatrix};
|
|
|
|
fn main() {
|
|
// set up a kaleidocycle, made of points with fixed distances between them,
|
|
// and find its tangent space
|
|
const N_POINTS: usize = 12;
|
|
let gram = {
|
|
let mut gram_to_be = PartialMatrix::new();
|
|
for block in (0..N_POINTS).step_by(2) {
|
|
let block_next = (block + 2) % N_POINTS;
|
|
for j in 0..2 {
|
|
// diagonal and hinge edges
|
|
for k in j..2 {
|
|
gram_to_be.push_sym(block + j, block + k, if j == k { 0.0 } else { -0.5 });
|
|
}
|
|
|
|
// non-hinge edges
|
|
for k in 0..2 {
|
|
gram_to_be.push_sym(block + j, block_next + k, -0.625);
|
|
}
|
|
}
|
|
}
|
|
gram_to_be
|
|
};
|
|
let guess = {
|
|
const N_HINGES: usize = 6;
|
|
let guess_elts = (0..N_HINGES).step_by(2).flat_map(
|
|
|n| {
|
|
let ang_hor = (n as f64) * PI/3.0;
|
|
let ang_vert = ((n + 1) as f64) * PI/3.0;
|
|
let x_vert = ang_vert.cos();
|
|
let y_vert = ang_vert.sin();
|
|
[
|
|
point(0.0, 0.0, 0.0),
|
|
point(ang_hor.cos(), ang_hor.sin(), 0.0),
|
|
point(x_vert, y_vert, -0.5),
|
|
point(x_vert, y_vert, 0.5)
|
|
]
|
|
}
|
|
).collect::<Vec<_>>();
|
|
DMatrix::from_columns(&guess_elts)
|
|
};
|
|
let frozen: [_; N_POINTS] = array::from_fn(|k| (3, k));
|
|
let (config, tangent, success, history) = realize_gram(
|
|
&gram, guess, &frozen,
|
|
1.0e-12, 0.5, 0.9, 1.1, 200, 110
|
|
);
|
|
print!("Completed Gram matrix:{}", config.tr_mul(&*Q) * &config);
|
|
print!("Configuration:{}", config);
|
|
if success {
|
|
println!("Target accuracy achieved!");
|
|
} else {
|
|
println!("Failed to reach target accuracy");
|
|
}
|
|
println!("Steps: {}", history.scaled_loss.len() - 1);
|
|
println!("Loss: {}\n", history.scaled_loss.last().unwrap());
|
|
|
|
// find the kaleidocycle's twist motion
|
|
let twist_motion: DMatrix<_> = (0..N_POINTS).step_by(4).flat_map(
|
|
|n| {
|
|
let up_field = {
|
|
DMatrix::from_column_slice(5, 5, &[
|
|
0.0, 0.0, 0.0, 0.0, 0.0,
|
|
0.0, 0.0, 0.0, 0.0, 0.0,
|
|
0.0, 0.0, 0.0, 0.0, 1.0,
|
|
0.0, 0.0, 2.0, 0.0, 0.0,
|
|
0.0, 0.0, 0.0, 0.0, 0.0
|
|
])
|
|
};
|
|
[
|
|
tangent.proj(&(&up_field * config.column(n)).as_view(), n),
|
|
tangent.proj(&(-&up_field * config.column(n+1)).as_view(), n+1)
|
|
]
|
|
}
|
|
).sum();
|
|
let normalization = 5.0 / twist_motion[(2, 0)];
|
|
print!("Twist motion:{}", normalization * twist_motion);
|
|
} |