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base: glen:kaleidocycle-example
Branches Tags
glen:main
glen:uniform-projection
glen:kaleidocycle-example
glen:tangent-space
glen:select-in-display
glen:cargo-examples_on_main
glen:element-serial
glen:outline-update-fix
glen:outline-cleanup_on_main
glen:engine-integration
glen:cargo-examples
glen:outline-cleanup
glen:app-proto
glen:engine-proto
glen:lang-trials
glen:gram
glen:macaulay2
glen:seed-problem
glen:v0.1.1
glen:v0.1.0
..
compare: glen:main
Branches Tags
glen:uniform-projection
glen:kaleidocycle-example
glen:main
glen:tangent-space
glen:select-in-display
glen:cargo-examples_on_main
glen:element-serial
glen:outline-update-fix
glen:outline-cleanup_on_main
glen:engine-integration
glen:cargo-examples
glen:outline-cleanup
glen:app-proto
glen:engine-proto
glen:lang-trials
glen:gram
glen:macaulay2
glen:seed-problem
glen:v0.1.1
glen:v0.1.0

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kaleidocyc ... main

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81
app-proto/examples/kaleidocycle.rs
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@ -1,81 +0,0 @@
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);
}

1
app-proto/run-examples
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@ -9,4 +9,3 @@
cargo run --example irisawa-hexlet
cargo run --example three-spheres
cargo run --example point-on-sphere
cargo run --example kaleidocycle