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WIP: Manipulate the assembly #29

Draft
Vectornaut wants to merge 8 commits from tangent-space into main
pull from: tangent-space
merge into: glen:main
Conversation 0 Commits 8 Files Changed 7 +282 -25
7 changed files with 282 additions and 25 deletions
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2
app-proto/examples/irisawa-hexlet.rs
View File

@ -2,7 +2,7 @@ use dyna3::engine::{Q, irisawa::realize_irisawa_hexlet};
fn main() {
const SCALED_TOL: f64 = 1.0e-12;
let (config, success, history) = realize_irisawa_hexlet(SCALED_TOL);
let (config, _, success, history) = realize_irisawa_hexlet(SCALED_TOL);
print!("\nCompleted Gram matrix:{}", config.tr_mul(&*Q) * &config);
if success {
println!("Target accuracy achieved!");

2
app-proto/examples/point-on-sphere.rs
View File

@ -18,7 +18,7 @@ fn main() {
]);
let frozen = [(3, 0)];
println!();
let (config, success, history) = realize_gram(
let (config, _, success, history) = realize_gram(
&gram, guess, &frozen,
1.0e-12, 0.5, 0.9, 1.1, 200, 110
);

2
app-proto/examples/three-spheres.rs
View File

@ -21,7 +21,7 @@ fn main() {
])
};
println!();
let (config, success, history) = realize_gram(
let (config, _, success, history) = realize_gram(
&gram, guess, &[],
1.0e-12, 0.5, 0.9, 1.1, 200, 110
);

63
app-proto/src/assembly.rs
View File

@ -1,11 +1,11 @@
use nalgebra::{DMatrix, DVector, Vector3};
use nalgebra::{DMatrix, DVector, DVectorView, Vector3};
use rustc_hash::FxHashMap;
use slab::Slab;
use std::{collections::BTreeSet, sync::atomic::{AtomicU64, Ordering}};
use sycamore::prelude::*;
use web_sys::{console, wasm_bindgen::JsValue}; /* DEBUG */
use crate::engine::{realize_gram, PartialMatrix};
use crate::engine::{realize_gram, ConfigSubspace, PartialMatrix, Q};
// the types of the keys we use to access an assembly's elements and constraints
pub type ElementKey = usize;
@ -110,7 +110,6 @@ impl Element {
}
}
#[derive(Clone)]
pub struct Constraint {
pub subjects: (ElementKey, ElementKey),
@ -127,6 +126,9 @@ pub struct Assembly {
pub elements: Signal<Slab<Element>>,
pub constraints: Signal<Slab<Constraint>>,
// solution variety tangent space
pub tangent: Signal<ConfigSubspace>,
// indexing
pub elements_by_id: Signal<FxHashMap<String, ElementKey>>
}
@ -136,6 +138,7 @@ impl Assembly {
Assembly {
elements: create_signal(Slab::new()),
constraints: create_signal(Slab::new()),
tangent: create_signal(ConfigSubspace::zero()),
elements_by_id: create_signal(FxHashMap::default())
}
}
@ -149,6 +152,13 @@ impl Assembly {
let id = elt.id.clone();
let key = self.elements.update(|elts| elts.insert(elt));
self.elements_by_id.update(|elts_by_id| elts_by_id.insert(id, key));
// realize to update the tangent space
/* KLUDGE */
// since the newly inserted element is unconstrained, we should be able
// to update the tangent space without recomputing the Hessian and its
// eigendecomposition
self.realize();
}
pub fn try_insert_element(&self, elt: Element) -> bool {
@ -247,7 +257,7 @@ impl Assembly {
}
// look for a configuration with the given Gram matrix
let (config, success, history) = realize_gram(
let (config, tangent, success, history) = realize_gram(
&gram, guess, &[],
1.0e-12, 0.5, 0.9, 1.1, 200, 110
);
@ -263,6 +273,7 @@ impl Assembly {
));
console::log_2(&JsValue::from("Steps:"), &JsValue::from(history.scaled_loss.len() - 1));
console::log_2(&JsValue::from("Loss:"), &JsValue::from(*history.scaled_loss.last().unwrap()));
console::log_2(&JsValue::from("Tangent dimension:"), &JsValue::from(tangent.dim()));
if success {
// read out the solution
@ -271,6 +282,50 @@ impl Assembly {
|rep| rep.set_column(0, &config.column(elt.column_index))
);
}
// save the tangent space
self.tangent.set_silent(tangent);
}
}
// --- deformation ---
pub fn deform(&self, element_motions: Vec<(ElementKey, DVectorView<f64>)>) {
/* KLUDGE */
// when the tangent space is zero, we currently need to avoid calling
// its `proj` method, because it will panic rather than returning zero.
// in the future, we'll want a more intentionally designed system for
// handling this case
if self.tangent.with(|tan| tan.dim() <= 0) {
console::log_1(&JsValue::from("The assembly is rigid"));
return;
}
const ELEMENT_DIM: usize = 5;
let assembly_dim = self.elements.with(|elts| elts.len());
let mut motion_proj = DMatrix::zeros(ELEMENT_DIM, assembly_dim);
// project the element motions onto the tangent space of the solution
// variety, and sum them to get a deformation of the whole assembly
for (elt_key, elt_motion) in element_motions {
let column_index = self.elements.with(|elts| elts[elt_key].column_index);
motion_proj += self.tangent.with(|tan| tan.proj(&elt_motion, column_index));
}
// step each element along the mass shell geodesic that matches its
// velocity in the deformation found above
/* KLUDGE */
// since our test assemblies only include spheres, we assume that every
// element is on the 1 mass shell
for (_, elt) in self.elements.get_clone_untracked() {
elt.representation.update_silent(|rep| {
let rep_next = &*rep + motion_proj.column(elt.column_index);
let normalizer = rep_next.dot(&(&*Q * &rep_next));
rep.set_column(0, &(rep_next / normalizer));
});
}
// bring the configuration back onto the solution variety
self.realize();
}
}

89
app-proto/src/display.rs
View File

@ -1,5 +1,5 @@
use core::array;
use nalgebra::{DMatrix, Rotation3, Vector3};
use nalgebra::{DMatrix, DVector, Rotation3, Vector3};
use sycamore::{prelude::*, motion::create_raf};
use web_sys::{
console,
@ -123,6 +123,14 @@ pub fn Display() -> View {
let zoom_out = create_signal(0.0);
let turntable = create_signal(false); /* BENCHMARKING */
// manipulation
let translate_neg_x = create_signal(0.0);
let translate_pos_x = create_signal(0.0);
let translate_neg_y = create_signal(0.0);
let translate_pos_y = create_signal(0.0);
let translate_neg_z = create_signal(0.0);
let translate_pos_z = create_signal(0.0);
// change listener
let scene_changed = create_signal(true);
create_effect(move || {
@ -141,6 +149,7 @@ pub fn Display() -> View {
let mut frames_since_last_sample = 0;
let mean_frame_interval = create_signal(0.0);
let assembly_for_raf = state.assembly.clone();
on_mount(move || {
// timing
let mut last_time = 0.0;
@ -153,6 +162,9 @@ pub fn Display() -> View {
let mut rotation = DMatrix::<f64>::identity(5, 5);
let mut location_z: f64 = 5.0;
// manipulation
const TRANSLATION_SPEED: f64 = 0.15; // in length units per second
// display parameters
const OPACITY: f32 = 0.5; /* SCAFFOLDING */
const HIGHLIGHT: f32 = 0.2; /* SCAFFOLDING */
@ -273,6 +285,14 @@ pub fn Display() -> View {
let zoom_out_val = zoom_out.get();
let turntable_val = turntable.get(); /* BENCHMARKING */
// get the manipulation state
let translate_neg_x_val = translate_neg_x.get();
let translate_pos_x_val = translate_pos_x.get();
let translate_neg_y_val = translate_neg_y.get();
let translate_pos_y_val = translate_pos_y.get();
let translate_neg_z_val = translate_neg_z.get();
let translate_pos_z_val = translate_pos_z.get();
// update the assembly's orientation
let ang_vel = {
let pitch = pitch_up_val - pitch_down_val;
@ -298,6 +318,34 @@ pub fn Display() -> View {
let zoom = zoom_out_val - zoom_in_val;
location_z *= (time_step * ZOOM_SPEED * zoom).exp();
// manipulate the assembly
if state.selection.with(|sel| sel.len() == 1) {
let sel = state.selection.with(
|sel| *sel.into_iter().next().unwrap()
);
let rep = state.assembly.elements.with_untracked(
|elts| elts[sel].representation.get_clone_untracked()
);
let translate_x = translate_pos_x_val - translate_neg_x_val;
let translate_y = translate_pos_y_val - translate_neg_y_val;
let translate_z = translate_pos_z_val - translate_neg_z_val;
if translate_x != 0.0 || translate_y != 0.0 || translate_z != 0.0 {
let vel_field = {
let u = Vector3::new(translate_x, translate_y, translate_z).normalize();
DMatrix::from_column_slice(5, 5, &[
0.0, 0.0, 0.0, 0.0, u[0],
0.0, 0.0, 0.0, 0.0, u[1],
0.0, 0.0, 0.0, 0.0, u[2],
2.0*u[0], 2.0*u[1], 2.0*u[2], 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0
])
};
let elt_motion: DVector<f64> = time_step * TRANSLATION_SPEED * vel_field * rep;
assembly_for_raf.deform(vec![(sel, elt_motion.as_view())]);
scene_changed.set(true);
}
}
if scene_changed.get() {
/* INSTRUMENTS */
// measure mean frame interval
@ -416,7 +464,7 @@ pub fn Display() -> View {
start_animation_loop();
});
let set_nav_signal = move |event: KeyboardEvent, value: f64| {
let set_nav_signal = move |event: &KeyboardEvent, value: f64| {
let mut navigating = true;
let shift = event.shift_key();
match event.key().as_str() {
@ -436,6 +484,23 @@ pub fn Display() -> View {
}
};
let set_manip_signal = move |event: &KeyboardEvent, value: f64| {
let mut manipulating = true;
let shift = event.shift_key();
match event.key().as_str() {
"d" | "D" => translate_pos_x.set(value),
"a" | "A" => translate_neg_x.set(value),
"w" | "W" if shift => translate_neg_z.set(value),
"s" | "S" if shift => translate_pos_z.set(value),
"w" | "W" => translate_pos_y.set(value),
"s" | "S" => translate_neg_y.set(value),
_ => manipulating = false
};
if manipulating {
event.prevent_default();
}
};
view! {
/* TO DO */
// switch back to integer-valued parameters when that becomes possible
@ -447,6 +512,7 @@ pub fn Display() -> View {
tabindex="0",
on:keydown=move |event: KeyboardEvent| {
if event.key() == "Shift" {
// swap navigation inputs
roll_cw.set(yaw_right.get());
roll_ccw.set(yaw_left.get());
zoom_in.set(pitch_up.get());
@ -455,16 +521,24 @@ pub fn Display() -> View {
yaw_left.set(0.0);
pitch_up.set(0.0);
pitch_down.set(0.0);
// swap manipulation inputs
translate_pos_z.set(translate_neg_y.get());
translate_neg_z.set(translate_pos_y.get());
translate_pos_y.set(0.0);
translate_neg_y.set(0.0);
} else {
if event.key() == "Enter" { /* BENCHMARKING */
turntable.set_fn(|turn| !turn);
scene_changed.set(true);
}
set_nav_signal(event, 1.0);
set_nav_signal(&event, 1.0);
set_manip_signal(&event, 1.0);
}
},
on:keyup=move |event: KeyboardEvent| {
if event.key() == "Shift" {
// swap navigation inputs
yaw_right.set(roll_cw.get());
yaw_left.set(roll_ccw.get());
pitch_up.set(zoom_in.get());
@ -473,8 +547,15 @@ pub fn Display() -> View {
roll_ccw.set(0.0);
zoom_in.set(0.0);
zoom_out.set(0.0);
// swap manipulation inputs
translate_pos_y.set(translate_neg_z.get());
translate_neg_y.set(translate_pos_z.get());
translate_pos_z.set(0.0);
translate_neg_z.set(0.0);
} else {
set_nav_signal(event, 0.0);
set_nav_signal(&event, 0.0);
set_manip_signal(&event, 0.0);
}
},
on:blur=move |_| {

145
app-proto/src/engine.rs
View File

@ -1,5 +1,5 @@
use lazy_static::lazy_static;
use nalgebra::{Const, DMatrix, DVector, Dyn};
use nalgebra::{Const, DMatrix, DVector, DVectorView, Dyn, SymmetricEigen};
use web_sys::{console, wasm_bindgen::JsValue}; /* DEBUG */
// --- elements ---
@ -85,6 +85,61 @@ impl PartialMatrix {
}
}
// --- configuration subspaces ---
#[derive(Clone)]
pub struct ConfigSubspace(Vec<DMatrix<f64>>);
impl ConfigSubspace {
pub fn zero() -> ConfigSubspace {
ConfigSubspace(Vec::new())
}
// approximate the kernel of a symmetric endomorphism of the configuration
// space for `assembly_dim` elements. we consider an eigenvector to be part
// of the kernel if its eigenvalue is smaller than the constant `THRESHOLD`
fn symmetric_kernel(a: DMatrix<f64>, assembly_dim: usize) -> ConfigSubspace {
const ELEMENT_DIM: usize = 5;
const THRESHOLD: f64 = 1.0e-4;
let eig = SymmetricEigen::new(a);
let eig_vecs = eig.eigenvectors.column_iter();
let eig_pairs = eig.eigenvalues.iter().zip(eig_vecs);
let basis = eig_pairs.filter_map(
|(λ, v)| (λ.abs() < THRESHOLD).then_some(
Into::<DMatrix<f64>>::into(
v.reshape_generic(Dyn(ELEMENT_DIM), Dyn(assembly_dim))
)
)
);
/* DEBUG */
// print the eigenvalues
#[cfg(all(target_family = "wasm", target_os = "unknown"))]
console::log_1(&JsValue::from(
format!("Eigenvalues used to find kernel: {}", eig.eigenvalues)
));
ConfigSubspace(basis.collect())
}
pub fn dim(&self) -> usize {
let ConfigSubspace(basis) = self;
basis.len()
}
// find the projection onto this subspace of the motion where the element
// with the given column index has velocity `v`
/* TO DO */
// for the zero subspace, this method's behavior doesn't match its name: it
// panics rather than returning zero
pub fn proj(&self, v: &DVectorView<f64>, column_index: usize) -> DMatrix<f64> {
let ConfigSubspace(basis) = self;
basis.into_iter().map(
|b| b.column(column_index).dot(&v) * b
).sum()
}
}
// --- descent history ---
pub struct DescentHistory {
@ -181,7 +236,7 @@ pub fn realize_gram(
reg_scale: f64,
max_descent_steps: i32,
max_backoff_steps: i32
) -> (DMatrix<f64>, bool, DescentHistory) {
) -> (DMatrix<f64>, ConfigSubspace, bool, DescentHistory) {
// start the descent history
let mut history = DescentHistory::new();
@ -201,12 +256,8 @@ pub fn realize_gram(
// use Newton's method with backtracking and gradient descent backup
let mut state = SearchState::from_config(gram, guess);
let mut hess = DMatrix::zeros(element_dim, assembly_dim);
for _ in 0..max_descent_steps {
// stop if the loss is tolerably low
history.config.push(state.config.clone());
history.scaled_loss.push(state.loss / scale_adjustment);
if state.loss < tol { break; }
// find the negative gradient of the loss function
let neg_grad = 4.0 * &*Q * &state.config * &state.err_proj;
let mut neg_grad_stacked = neg_grad.clone().reshape_generic(Dyn(total_dim), Const::<1>);
@ -229,7 +280,7 @@ pub fn realize_gram(
hess_cols.push(deriv_grad.reshape_generic(Dyn(total_dim), Const::<1>));
}
}
let mut hess = DMatrix::from_columns(hess_cols.as_slice());
hess = DMatrix::from_columns(hess_cols.as_slice());
// regularize the Hessian
let min_eigval = hess.symmetric_eigenvalues().min();
@ -249,6 +300,11 @@ pub fn realize_gram(
hess[(k, k)] = 1.0;
}
// stop if the loss is tolerably low
history.config.push(state.config.clone());
history.scaled_loss.push(state.loss / scale_adjustment);
if state.loss < tol { break; }
// compute the Newton step
/*
we need to either handle or eliminate the case where the minimum
@ -256,7 +312,7 @@ pub fn realize_gram(
singular. right now, this causes the Cholesky decomposition to return
`None`, leading to a panic when we unrap
*/
let base_step_stacked = hess.cholesky().unwrap().solve(&neg_grad_stacked);
let base_step_stacked = hess.clone().cholesky().unwrap().solve(&neg_grad_stacked);
let base_step = base_step_stacked.reshape_generic(Dyn(element_dim), Dyn(assembly_dim));
history.base_step.push(base_step.clone());
@ -269,10 +325,16 @@ pub fn realize_gram(
state = better_state;
history.backoff_steps.push(backoff_steps);
},
None => return (state.config, false, history)
None => return (state.config, ConfigSubspace::zero(), false, history)
};
}
(state.config, state.loss < tol, history)
let success = state.loss < tol;
let tangent = if success {
ConfigSubspace::symmetric_kernel(hess, assembly_dim)
} else {
ConfigSubspace::zero()
};
(state.config, tangent, success, history)
}
// --- tests ---
@ -291,7 +353,7 @@ pub mod irisawa {
use super::*;
pub fn realize_irisawa_hexlet(scaled_tol: f64) -> (DMatrix<f64>, bool, DescentHistory) {
pub fn realize_irisawa_hexlet(scaled_tol: f64) -> (DMatrix<f64>, ConfigSubspace, bool, DescentHistory) {
let gram = {
let mut gram_to_be = PartialMatrix::new();
for s in 0..9 {
@ -399,7 +461,7 @@ mod tests {
fn irisawa_hexlet_test() {
// solve Irisawa's problem
const SCALED_TOL: f64 = 1.0e-12;
let (config, _, _) = realize_irisawa_hexlet(SCALED_TOL);
let (config, _, _, _) = realize_irisawa_hexlet(SCALED_TOL);
// check against Irisawa's solution
let entry_tol = SCALED_TOL.sqrt();
@ -409,6 +471,61 @@ mod tests {
}
}
#[test]
fn tangent_test() {
const SCALED_TOL: f64 = 1.0e-12;
const ELEMENT_DIM: usize = 5;
const ASSEMBLY_DIM: usize = 3;
let gram = {
let mut gram_to_be = PartialMatrix::new();
for j in 0..3 {
for k in j..3 {
gram_to_be.push_sym(j, k, if j == k { 1.0 } else { -1.0 });
}
}
gram_to_be
};
let guess = DMatrix::from_columns(&[
sphere(0.0, 0.0, 0.0, -2.0),
sphere(0.0, 0.0, 1.0, 1.0),
sphere(0.0, 0.0, -1.0, 1.0)
]);
let frozen: [_; 5] = std::array::from_fn(|k| (k, 0));
let (config, tangent, success, history) = realize_gram(
&gram, guess.clone(), &frozen,
SCALED_TOL, 0.5, 0.9, 1.1, 200, 110
);
assert_eq!(config, guess);
assert_eq!(success, true);
assert_eq!(history.scaled_loss.len(), 1);
// confirm that the tangent space has dimension five or less
let ConfigSubspace(ref tangent_basis) = tangent;
assert_eq!(tangent_basis.len(), 5);
// confirm that the tangent space contains all the motions we expect it
// to. since we've already bounded the dimension of the tangent space,
// this confirms that the tangent space is what we expect it to be
let tangent_motions = vec![
basis_matrix((0, 1), ELEMENT_DIM, ASSEMBLY_DIM),
basis_matrix((1, 1), ELEMENT_DIM, ASSEMBLY_DIM),
basis_matrix((0, 2), ELEMENT_DIM, ASSEMBLY_DIM),
basis_matrix((1, 2), ELEMENT_DIM, ASSEMBLY_DIM),
DMatrix::<f64>::from_column_slice(ELEMENT_DIM, 3, &[
0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, -1.0, -0.25, -1.0,
0.0, 0.0, -1.0, 0.25, 1.0
])
];
let tol_sq = ((ELEMENT_DIM * ASSEMBLY_DIM) as f64) * SCALED_TOL * SCALED_TOL;
for motion in tangent_motions {
let motion_proj: DMatrix<_> = motion.column_iter().enumerate().map(
|(k, v)| tangent.proj(&v, k)
).sum();
assert!((motion - motion_proj).norm_squared() < tol_sq);
}
}
// at the frozen indices, the optimization steps should have exact zeros,
// and the realized configuration should match the initial guess
#[test]
@ -428,7 +545,7 @@ mod tests {
]);
let frozen = [(3, 0), (3, 1)];
println!();
let (config, success, history) = realize_gram(
let (config, _, success, history) = realize_gram(
&gram, guess.clone(), &frozen,
1.0e-12, 0.5, 0.9, 1.1, 200, 110
);

4
app-proto/src/main.rs
View File

@ -46,6 +46,10 @@ impl AppState {
}
fn main() {
// set the console error panic hook
#[cfg(feature = "console_error_panic_hook")]
console_error_panic_hook::set_once();
sycamore::render(|| {
provide_context(AppState::new());