dyna3/app-proto/src/assembly.rs
Vectornaut a4565281d5 Refactor: rename loaders and adopt 'Self' type convention (#111)
Resolves #109.
Resolves #110.

Co-authored-by: Aaron Fenyes <aaron.fenyes@fareycircles.ooo>
Reviewed-on: StudioInfinity/dyna3#111
Co-authored-by: Vectornaut <vectornaut@nobody@nowhere.net>
Co-committed-by: Vectornaut <vectornaut@nobody@nowhere.net>
2025-08-07 23:24:07 +00:00

899 lines
No EOL
29 KiB
Rust

use nalgebra::{DMatrix, DVector, DVectorView};
use std::{
cell::Cell,
cmp::Ordering,
collections::{BTreeMap, BTreeSet},
fmt,
fmt::{Debug, Formatter},
hash::{Hash, Hasher},
rc::Rc,
sync::{atomic, atomic::AtomicU64},
};
use sycamore::prelude::*;
use web_sys::{console, wasm_bindgen::JsValue}; /* DEBUG */
use crate::{
components::{display::DisplayItem, outline::OutlineItem},
engine::{
Q,
local_unif_to_std,
point,
project_point_to_normalized,
project_sphere_to_normalized,
realize_gram,
sphere,
ConfigNeighborhood,
ConfigSubspace,
ConstraintProblem,
DescentHistory,
Realization,
},
specified::SpecifiedValue,
};
pub type ElementColor = [f32; 3];
/* KLUDGE */
// we should reconsider this design when we build a system for switching between
// assemblies. at that point, we might want to switch to hierarchical keys,
// where each each item has a key that identifies it within its assembly and
// each assembly has a key that identifies it within the sesssion
static NEXT_SERIAL: AtomicU64 = AtomicU64::new(0);
pub trait Serial {
// a serial number that uniquely identifies this element
fn serial(&self) -> u64;
// take the next serial number, panicking if that was the last one left
fn next_serial() -> u64 where Self: Sized {
// the technique we use to panic on overflow is taken from _Rust Atomics
// and Locks_, by Mara Bos
//
// https://marabos.nl/atomics/atomics.html#example-handle-overflow
//
NEXT_SERIAL.fetch_update(
atomic::Ordering::SeqCst, atomic::Ordering::SeqCst,
|serial| serial.checked_add(1)
).expect("Out of serial numbers for elements")
}
}
impl Hash for dyn Serial {
fn hash<H: Hasher>(&self, state: &mut H) {
self.serial().hash(state)
}
}
impl PartialEq for dyn Serial {
fn eq(&self, other: &Self) -> bool {
self.serial() == other.serial()
}
}
impl Eq for dyn Serial {}
impl PartialOrd for dyn Serial {
fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
Some(self.cmp(other))
}
}
impl Ord for dyn Serial {
fn cmp(&self, other: &Self) -> Ordering {
self.serial().cmp(&other.serial())
}
}
pub trait ProblemPoser {
fn pose(&self, problem: &mut ConstraintProblem);
}
pub trait Element: Serial + ProblemPoser + DisplayItem {
// the default identifier for an element of this type
fn default_id() -> String where Self: Sized;
// the default example of an element of this type
fn default(id: String, id_num: u64) -> Self where Self: Sized;
// the default regulators that come with this element
fn default_regulators(self: Rc<Self>) -> Vec<Rc<dyn Regulator>> {
Vec::new()
}
fn id(&self) -> &String;
fn label(&self) -> &String;
fn representation(&self) -> Signal<DVector<f64>>;
fn ghost(&self) -> Signal<bool>;
// the regulators the element is subject to. the assembly that owns the
// element is responsible for keeping this set up to date
fn regulators(&self) -> Signal<BTreeSet<Rc<dyn Regulator>>>;
// project a representation vector for this kind of element onto its
// normalization variety
fn project_to_normalized(&self, rep: &mut DVector<f64>);
// the configuration matrix column index that was assigned to the element
// last time the assembly was realized, or `None` if the element has never
// been through a realization
fn column_index(&self) -> Option<usize>;
// assign the element a configuration matrix column index. this method must
// be used carefully to preserve invariant (1), described in the comment on
// the `tangent` field of the `Assembly` structure
fn set_column_index(&self, index: usize);
}
impl Debug for dyn Element {
fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), fmt::Error> {
self.id().fmt(f)
}
}
impl Hash for dyn Element {
fn hash<H: Hasher>(&self, state: &mut H) {
<dyn Serial>::hash(self, state)
}
}
impl PartialEq for dyn Element {
fn eq(&self, other: &Self) -> bool {
<dyn Serial>::eq(self, other)
}
}
impl Eq for dyn Element {}
impl PartialOrd for dyn Element {
fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
<dyn Serial>::partial_cmp(self, other)
}
}
impl Ord for dyn Element {
fn cmp(&self, other: &Self) -> Ordering {
<dyn Serial>::cmp(self, other)
}
}
pub struct Sphere {
pub id: String,
pub label: String,
pub color: ElementColor,
pub representation: Signal<DVector<f64>>,
pub ghost: Signal<bool>,
pub regulators: Signal<BTreeSet<Rc<dyn Regulator>>>,
serial: u64,
column_index: Cell<Option<usize>>,
}
impl Sphere {
const CURVATURE_COMPONENT: usize = 3;
pub fn new(
id: String,
label: String,
color: ElementColor,
representation: DVector<f64>,
) -> Self {
Self {
id,
label,
color,
representation: create_signal(representation),
ghost: create_signal(false),
regulators: create_signal(BTreeSet::new()),
serial: Self::next_serial(),
column_index: None.into(),
}
}
}
impl Element for Sphere {
fn default_id() -> String {
"sphere".to_string()
}
fn default(id: String, id_num: u64) -> Self {
Self::new(
id,
format!("Sphere {id_num}"),
[0.75_f32, 0.75_f32, 0.75_f32],
sphere(0.0, 0.0, 0.0, 1.0),
)
}
fn default_regulators(self: Rc<Self>) -> Vec<Rc<dyn Regulator>> {
vec![Rc::new(HalfCurvatureRegulator::new(self))]
}
fn id(&self) -> &String {
&self.id
}
fn label(&self) -> &String {
&self.label
}
fn representation(&self) -> Signal<DVector<f64>> {
self.representation
}
fn ghost(&self) -> Signal<bool> {
self.ghost
}
fn regulators(&self) -> Signal<BTreeSet<Rc<dyn Regulator>>> {
self.regulators
}
fn project_to_normalized(&self, rep: &mut DVector<f64>) {
project_sphere_to_normalized(rep);
}
fn column_index(&self) -> Option<usize> {
self.column_index.get()
}
fn set_column_index(&self, index: usize) {
self.column_index.set(Some(index));
}
}
impl Serial for Sphere {
fn serial(&self) -> u64 {
self.serial
}
}
impl ProblemPoser for Sphere {
fn pose(&self, problem: &mut ConstraintProblem) {
let index = self.column_index().expect(
format!("Sphere \"{}\" should be indexed before writing problem data", self.id).as_str()
);
problem.gram.push_sym(index, index, 1.0);
problem.guess.set_column(index, &self.representation.get_clone_untracked());
}
}
pub struct Point {
pub id: String,
pub label: String,
pub color: ElementColor,
pub representation: Signal<DVector<f64>>,
pub ghost: Signal<bool>,
pub regulators: Signal<BTreeSet<Rc<dyn Regulator>>>,
serial: u64,
column_index: Cell<Option<usize>>,
}
impl Point {
const WEIGHT_COMPONENT: usize = 3;
pub fn new(
id: String,
label: String,
color: ElementColor,
representation: DVector<f64>,
) -> Self {
Self {
id,
label,
color,
representation: create_signal(representation),
ghost: create_signal(false),
regulators: create_signal(BTreeSet::new()),
serial: Self::next_serial(),
column_index: None.into(),
}
}
}
impl Element for Point {
fn default_id() -> String {
"point".to_string()
}
fn default(id: String, id_num: u64) -> Self {
Self::new(
id,
format!("Point {id_num}"),
[0.75_f32, 0.75_f32, 0.75_f32],
point(0.0, 0.0, 0.0),
)
}
fn id(&self) -> &String {
&self.id
}
fn label(&self) -> &String {
&self.label
}
fn representation(&self) -> Signal<DVector<f64>> {
self.representation
}
fn ghost(&self) -> Signal<bool> {
self.ghost
}
fn regulators(&self) -> Signal<BTreeSet<Rc<dyn Regulator>>> {
self.regulators
}
fn project_to_normalized(&self, rep: &mut DVector<f64>) {
project_point_to_normalized(rep);
}
fn column_index(&self) -> Option<usize> {
self.column_index.get()
}
fn set_column_index(&self, index: usize) {
self.column_index.set(Some(index));
}
}
impl Serial for Point {
fn serial(&self) -> u64 {
self.serial
}
}
impl ProblemPoser for Point {
fn pose(&self, problem: &mut ConstraintProblem) {
let index = self.column_index().expect(
format!("Point \"{}\" should be indexed before writing problem data", self.id).as_str()
);
problem.gram.push_sym(index, index, 0.0);
problem.frozen.push(Self::WEIGHT_COMPONENT, index, 0.5);
problem.guess.set_column(index, &self.representation.get_clone_untracked());
}
}
pub trait Regulator: Serial + ProblemPoser + OutlineItem {
fn subjects(&self) -> Vec<Rc<dyn Element>>;
fn measurement(&self) -> ReadSignal<f64>;
fn set_point(&self) -> Signal<SpecifiedValue>;
}
impl Hash for dyn Regulator {
fn hash<H: Hasher>(&self, state: &mut H) {
<dyn Serial>::hash(self, state)
}
}
impl PartialEq for dyn Regulator {
fn eq(&self, other: &Self) -> bool {
<dyn Serial>::eq(self, other)
}
}
impl Eq for dyn Regulator {}
impl PartialOrd for dyn Regulator {
fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
<dyn Serial>::partial_cmp(self, other)
}
}
impl Ord for dyn Regulator {
fn cmp(&self, other: &Self) -> Ordering {
<dyn Serial>::cmp(self, other)
}
}
pub struct InversiveDistanceRegulator {
pub subjects: [Rc<dyn Element>; 2],
pub measurement: ReadSignal<f64>,
pub set_point: Signal<SpecifiedValue>,
serial: u64,
}
impl InversiveDistanceRegulator {
pub fn new(subjects: [Rc<dyn Element>; 2]) -> Self {
let representations = subjects.each_ref().map(|subj| subj.representation());
let measurement = create_memo(move || {
representations[0].with(|rep_0|
representations[1].with(|rep_1|
rep_0.dot(&(&*Q * rep_1))
)
)
});
let set_point = create_signal(SpecifiedValue::from_empty_spec());
let serial = Self::next_serial();
Self { subjects, measurement, set_point, serial }
}
}
impl Regulator for InversiveDistanceRegulator {
fn subjects(&self) -> Vec<Rc<dyn Element>> {
self.subjects.clone().into()
}
fn measurement(&self) -> ReadSignal<f64> {
self.measurement
}
fn set_point(&self) -> Signal<SpecifiedValue> {
self.set_point
}
}
impl Serial for InversiveDistanceRegulator {
fn serial(&self) -> u64 {
self.serial
}
}
impl ProblemPoser for InversiveDistanceRegulator {
fn pose(&self, problem: &mut ConstraintProblem) {
self.set_point.with_untracked(|set_pt| {
if let Some(val) = set_pt.value {
let [row, col] = self.subjects.each_ref().map(
|subj| subj.column_index().expect(
"Subjects should be indexed before inversive distance regulator writes problem data"
)
);
problem.gram.push_sym(row, col, val);
}
});
}
}
pub struct HalfCurvatureRegulator {
pub subject: Rc<dyn Element>,
pub measurement: ReadSignal<f64>,
pub set_point: Signal<SpecifiedValue>,
serial: u64,
}
impl HalfCurvatureRegulator {
pub fn new(subject: Rc<dyn Element>) -> Self {
let measurement = subject.representation().map(
|rep| rep[Sphere::CURVATURE_COMPONENT]
);
let set_point = create_signal(SpecifiedValue::from_empty_spec());
let serial = Self::next_serial();
Self { subject, measurement, set_point, serial }
}
}
impl Regulator for HalfCurvatureRegulator {
fn subjects(&self) -> Vec<Rc<dyn Element>> {
vec![self.subject.clone()]
}
fn measurement(&self) -> ReadSignal<f64> {
self.measurement
}
fn set_point(&self) -> Signal<SpecifiedValue> {
self.set_point
}
}
impl Serial for HalfCurvatureRegulator {
fn serial(&self) -> u64 {
self.serial
}
}
impl ProblemPoser for HalfCurvatureRegulator {
fn pose(&self, problem: &mut ConstraintProblem) {
self.set_point.with_untracked(|set_pt| {
if let Some(val) = set_pt.value {
let col = self.subject.column_index().expect(
"Subject should be indexed before half-curvature regulator writes problem data"
);
problem.frozen.push(Sphere::CURVATURE_COMPONENT, col, val);
}
});
}
}
// the velocity is expressed in uniform coordinates
pub struct ElementMotion<'a> {
pub element: Rc<dyn Element>,
pub velocity: DVectorView<'a, f64>,
}
type AssemblyMotion<'a> = Vec<ElementMotion<'a>>;
// a complete, view-independent description of an assembly
#[derive(Clone)]
pub struct Assembly {
// elements and regulators
pub elements: Signal<BTreeSet<Rc<dyn Element>>>,
pub regulators: Signal<BTreeSet<Rc<dyn Regulator>>>,
// solution variety tangent space. the basis vectors are stored in
// configuration matrix format, ordered according to the elements' column
// indices. when you realize the assembly, every element that's present
// during realization gets a column index and is reflected in the tangent
// space. since the methods in this module never assign column indices
// without later realizing the assembly, we get the following invariant:
//
// (1) if an element has a column index, its tangent motions can be found
// in that column of the tangent space basis matrices
//
pub tangent: Signal<ConfigSubspace>,
// indexing
pub elements_by_id: Signal<BTreeMap<String, Rc<dyn Element>>>,
// realization control
pub realization_trigger: Signal<()>,
// realization diagnostics
pub realization_status: Signal<Result<(), String>>,
pub descent_history: Signal<DescentHistory>,
}
impl Assembly {
pub fn new() -> Assembly {
// create an assembly
let assembly = Assembly {
elements: create_signal(BTreeSet::new()),
regulators: create_signal(BTreeSet::new()),
tangent: create_signal(ConfigSubspace::zero(0)),
elements_by_id: create_signal(BTreeMap::default()),
realization_trigger: create_signal(()),
realization_status: create_signal(Ok(())),
descent_history: create_signal(DescentHistory::new()),
};
// realize the assembly whenever the element list, the regulator list,
// a regulator's set point, or the realization trigger is updated
let assembly_for_effect = assembly.clone();
create_effect(move || {
assembly_for_effect.elements.track();
assembly_for_effect.regulators.with(
|regs| for reg in regs {
reg.set_point().track();
}
);
assembly_for_effect.realization_trigger.track();
assembly_for_effect.realize();
});
assembly
}
// --- inserting elements and regulators ---
// insert an element into the assembly without checking whether we already
// have an element with the same identifier. any element that does have the
// same identifier will get kicked out of the `elements_by_id` index
fn insert_element_unchecked(&self, elt: impl Element + 'static) {
// insert the element
let id = elt.id().clone();
let elt_rc = Rc::new(elt);
self.elements.update(|elts| elts.insert(elt_rc.clone()));
self.elements_by_id.update(|elts_by_id| elts_by_id.insert(id, elt_rc.clone()));
// create and insert the element's default regulators
for reg in elt_rc.default_regulators() {
self.insert_regulator(reg);
}
}
pub fn try_insert_element(&self, elt: impl Element + 'static) -> bool {
let can_insert = self.elements_by_id.with_untracked(
|elts_by_id| !elts_by_id.contains_key(elt.id())
);
if can_insert {
self.insert_element_unchecked(elt);
}
can_insert
}
pub fn insert_element_default<T: Element + 'static>(&self) {
// find the next unused identifier in the default sequence
let default_id = T::default_id();
let mut id_num = 1;
let mut id = format!("{default_id}{id_num}");
while self.elements_by_id.with_untracked(
|elts_by_id| elts_by_id.contains_key(&id)
) {
id_num += 1;
id = format!("{default_id}{id_num}");
}
// create and insert the default example of `T`
let _ = self.insert_element_unchecked(T::default(id, id_num));
}
pub fn insert_regulator(&self, regulator: Rc<dyn Regulator>) {
// add the regulator to the assembly's regulator list
self.regulators.update(
|regs| regs.insert(regulator.clone())
);
// add the regulator to each subject's regulator list
let subject_regulators: Vec<_> = regulator.subjects().into_iter().map(
|subj| subj.regulators()
).collect();
for regulators in subject_regulators {
regulators.update(|regs| regs.insert(regulator.clone()));
}
/* DEBUG */
// print an updated list of regulators
console_log!("Regulators:");
self.regulators.with_untracked(|regs| {
for reg in regs.into_iter() {
console_log!(
" {:?}: {}",
reg.subjects(),
reg.set_point().with_untracked(
|set_pt| {
let spec = &set_pt.spec;
if spec.is_empty() {
"__".to_string()
} else {
spec.clone()
}
}
)
);
}
});
}
// --- realization ---
pub fn realize(&self) {
// index the elements
self.elements.update_silent(|elts| {
for (index, elt) in elts.iter().enumerate() {
elt.set_column_index(index);
}
});
// set up the constraint problem
let problem = self.elements.with_untracked(|elts| {
let mut problem = ConstraintProblem::new(elts.len());
for elt in elts {
elt.pose(&mut problem);
}
self.regulators.with_untracked(|regs| {
for reg in regs {
reg.pose(&mut problem);
}
});
problem
});
/* DEBUG */
// log the Gram matrix
console_log!("Gram matrix:\n{}", problem.gram);
/* DEBUG */
// log the initial configuration matrix
console_log!("Old configuration:{:>8.3}", problem.guess);
// look for a configuration with the given Gram matrix
let Realization { result, history } = realize_gram(
&problem, 1.0e-12, 0.5, 0.9, 1.1, 200, 110
);
/* DEBUG */
// report the outcome of the search in the browser console
if let Err(ref message) = result {
console_log!("❌️ {message}");
} else {
console_log!("✅️ Target accuracy achieved!");
}
if history.scaled_loss.len() > 0 {
console_log!("Steps: {}", history.scaled_loss.len() - 1);
console_log!("Loss: {}", history.scaled_loss.last().unwrap());
}
// report the loss history
self.descent_history.set(history);
match result {
Ok(ConfigNeighborhood { config, nbhd: tangent }) => {
/* DEBUG */
// report the tangent dimension
console_log!("Tangent dimension: {}", tangent.dim());
// report the realization status
self.realization_status.set(Ok(()));
// read out the solution
for elt in self.elements.get_clone_untracked() {
elt.representation().update(
|rep| rep.set_column(0, &config.column(elt.column_index().unwrap()))
);
}
// save the tangent space
self.tangent.set_silent(tangent);
},
Err(message) => {
// report the realization status. the `Err(message)` we're
// setting the status to has a different type than the
// `Err(message)` we received from the match: we're changing the
// `Ok` type from `Realization` to `()`
self.realization_status.set(Err(message))
},
}
}
// --- deformation ---
// project the given motion to the tangent space of the solution variety and
// move the assembly along it. the implementation is based on invariant (1)
// from above and the following additional invariant:
//
// (2) if an element is affected by a constraint, it has a column index
//
// we have this invariant because the assembly gets realized each time you
// add a constraint
pub fn deform(&self, motion: AssemblyMotion) {
/* KLUDGE */
// when the tangent space is zero, deformation won't do anything, but
// the attempt to deform should be registered in the UI. this console
// message will do for now
if self.tangent.with(|tan| tan.dim() <= 0 && tan.assembly_dim() > 0) {
console::log_1(&JsValue::from("The assembly is rigid"));
}
// give a column index to each moving element that doesn't have one yet.
// this temporarily breaks invariant (1), but the invariant will be
// restored when we realize the assembly at the end of the deformation.
// in the process, we find out how many matrix columns we'll need to
// hold the deformation
let realized_dim = self.tangent.with(|tan| tan.assembly_dim());
let motion_dim = {
let mut next_column_index = realized_dim;
for elt_motion in motion.iter() {
let moving_elt = &elt_motion.element;
if moving_elt.column_index().is_none() {
moving_elt.set_column_index(next_column_index);
next_column_index += 1;
}
}
next_column_index
};
// project the element motions onto the tangent space of the solution
// variety and sum them to get a deformation of the whole assembly. the
// matrix `motion_proj` that holds the deformation has extra columns for
// any moving elements that aren't reflected in the saved tangent space
const ELEMENT_DIM: usize = 5;
let mut motion_proj = DMatrix::zeros(ELEMENT_DIM, motion_dim);
for elt_motion in motion {
// we can unwrap the column index because we know that every moving
// element has one at this point
let column_index = elt_motion.element.column_index().unwrap();
if column_index < realized_dim {
// this element had a column index when we started, so by
// invariant (1), it's reflected in the tangent space
let mut target_columns = motion_proj.columns_mut(0, realized_dim);
target_columns += self.tangent.with(
|tan| tan.proj(&elt_motion.velocity, column_index)
);
} else {
// this element didn't have a column index when we started, so
// by invariant (2), it's unconstrained
let mut target_column = motion_proj.column_mut(column_index);
let unif_to_std = elt_motion.element.representation().with_untracked(
|rep| local_unif_to_std(rep.as_view())
);
target_column += unif_to_std * elt_motion.velocity;
}
}
// step the assembly along the deformation. this changes the elements'
// normalizations, so we restore those afterward
for elt in self.elements.get_clone_untracked() {
elt.representation().update_silent(|rep| {
match elt.column_index() {
Some(column_index) => {
// step the element along the deformation and then
// restore its normalization
*rep += motion_proj.column(column_index);
elt.project_to_normalized(rep);
},
None => {
console_log!("No velocity to unpack for fresh element \"{}\"", elt.id())
},
};
});
}
// trigger a realization to bring the configuration back onto the
// solution variety. this also gets the elements' column indices and the
// saved tangent space back in sync
self.realization_trigger.set(());
}
}
#[cfg(test)]
mod tests {
use super::*;
use crate::engine;
#[test]
#[should_panic(expected = "Sphere \"sphere\" should be indexed before writing problem data")]
fn unindexed_element_test() {
let _ = create_root(|| {
let elt = Sphere::default("sphere".to_string(), 0);
elt.pose(&mut ConstraintProblem::new(1));
});
}
#[test]
#[should_panic(expected = "Subjects should be indexed before inversive distance regulator writes problem data")]
fn unindexed_subject_test_inversive_distance() {
let _ = create_root(|| {
let subjects = [0, 1].map(
|k| Rc::new(Sphere::default(format!("sphere{k}"), k)) as Rc<dyn Element>
);
subjects[0].set_column_index(0);
InversiveDistanceRegulator {
subjects: subjects,
measurement: create_memo(|| 0.0),
set_point: create_signal(SpecifiedValue::try_from("0.0".to_string()).unwrap()),
serial: InversiveDistanceRegulator::next_serial()
}.pose(&mut ConstraintProblem::new(2));
});
}
#[test]
fn curvature_drift_test() {
const INITIAL_RADIUS: f64 = 0.25;
let _ = create_root(|| {
// set up an assembly containing a single sphere centered at the
// origin
let assembly = Assembly::new();
let sphere_id = "sphere0";
let _ = assembly.try_insert_element(
// we create the sphere by hand for two reasons: to choose the
// curvature (which can affect drift rate) and to make the test
// independent of `Sphere::default`
Sphere::new(
String::from(sphere_id),
String::from("Sphere 0"),
[0.75_f32, 0.75_f32, 0.75_f32],
engine::sphere(0.0, 0.0, 0.0, INITIAL_RADIUS),
)
);
// nudge the sphere repeatedly along the `z` axis
const STEP_SIZE: f64 = 0.0025;
const STEP_CNT: usize = 400;
let sphere = assembly.elements_by_id.with(|elts_by_id| elts_by_id[sphere_id].clone());
let velocity = DVector::from_column_slice(&[0.0, 0.0, STEP_SIZE, 0.0]);
for _ in 0..STEP_CNT {
assembly.deform(
vec![
ElementMotion {
element: sphere.clone(),
velocity: velocity.as_view(),
}
]
);
}
// check how much the sphere's curvature has drifted
const INITIAL_HALF_CURV: f64 = 0.5 / INITIAL_RADIUS;
const DRIFT_TOL: f64 = 0.015;
let final_half_curv = sphere.representation().with_untracked(
|rep| rep[Sphere::CURVATURE_COMPONENT]
);
assert!((final_half_curv / INITIAL_HALF_CURV - 1.0).abs() < DRIFT_TOL);
});
}
}