Move the components into their own module

This makes the module tree more reflective of module use patterns. In particular, it restores the condition that every top-level module is used in top-level code, which was broken by the addition of the `test_assembly_chooser` module in commit 91e4e1f.
Make the test assembly chooser its own component
2025-07-22 13:28:48 -07:00 · 2025-07-21 12:16:16 -07:00 · 2025-07-20 23:27:10 -07:00 · 2025-07-20 23:27:10 -07:00 · 2025-07-20 23:27:10 -07:00 · 2025-07-20 23:27:10 -07:00
30 changed files with 839 additions and 1098 deletions
--- a/.forgejo/setup-trunk/action.yaml
+++ b/.forgejo/setup-trunk/action.yaml
@ -10,7 +10,7 @@ runs:
  using: "composite"
  steps:
    - run: rustup target add wasm32-unknown-unknown
-
+    
    # install the Trunk binary to `ci-bin` within the workspace directory, which
    # is determined by the `github.workspace` label and reflected in the
    # `GITHUB_WORKSPACE` environment variable. then, make the `trunk` command
--- a/.forgejo/workflows/continuous-integration.yaml
+++ b/.forgejo/workflows/continuous-integration.yaml
@ -24,6 +24,6 @@ jobs:
      # workspace directory (action variable `github.workspace`, environment
      # variable `$GITHUB_WORKSPACE`):
      - uses: https://code.forgejo.org/actions/checkout@v4
-
+      
      - uses: ./.forgejo/setup-trunk
-      - run: RUSTFLAGS='-D warnings' cargo test
+      - run: RUSTFLAGS='-D warnings' cargo test
--- a/README.md
+++ b/README.md
@ -12,11 +12,11 @@ Note that currently this is just the barest beginnings of the project, more of a
 ### Implementation goals
-* Provide a comfortable, intuitive UI
+* Comfortable, intuitive UI
-* Allow execution in browser (so implemented in WASM-compatible language)
+* Able to run in browser (so implemented in WASM-compatible language)
-* Produce scalable graphics of 3D diagrams, and maybe STL files (or other fabricatable file format) as well
+* Produce scalable graphics of 3D diagrams, and maybe STL files (or other fabricatable file format) as well.
 ## Prototype
@ -24,66 +24,44 @@ The latest prototype is in the folder `app-proto`. It includes both a user inter
 ### Install the prerequisites
-1. Install [`rustup`](https://rust-lang.github.io/rustup/): the officially recommended Rust toolchain manager.
+1. Install [`rustup`](https://rust-lang.github.io/rustup/): the officially recommended Rust toolchain manager
-   - It's available on Ubuntu as a [Snap](https://snapcraft.io/rustup).
+   * It's available on Ubuntu as a [Snap](https://snapcraft.io/rustup)
-2. Call `rustup default stable` to "download the latest stable release of Rust and set it as your default toolchain".
+2. Call `rustup default stable` to "download the latest stable release of Rust and set it as your default toolchain"
-   - If you forget, the `rustup` [help system](https://github.com/rust-lang/rustup/blob/d9b3601c3feb2e88cf3f8ca4f7ab4fdad71441fd/src/errors.rs#L109-L112) will remind you.
+   * If you forget, the `rustup` [help system](https://github.com/rust-lang/rustup/blob/d9b3601c3feb2e88cf3f8ca4f7ab4fdad71441fd/src/errors.rs#L109-L112) will remind you
-3. Call `rustup target add wasm32-unknown-unknown` to add the [most generic 32-bit WebAssembly target](https://doc.rust-lang.org/nightly/rustc/platform-support/wasm32-unknown-unknown.html).
+3. Call `rustup target add wasm32-unknown-unknown` to add the [most generic 32-bit WebAssembly target](https://doc.rust-lang.org/nightly/rustc/platform-support/wasm32-unknown-unknown.html)
-4. Call `cargo install wasm-pack` to install the [WebAssembly toolchain](https://rustwasm.github.io/docs/wasm-pack/).
+4. Call `cargo install wasm-pack` to install the [WebAssembly toolchain](https://rustwasm.github.io/docs/wasm-pack/)
-5. Call `cargo install trunk` to install the [Trunk](https://trunkrs.dev/) web-build tool.
+5. Call `cargo install trunk` to install the [Trunk](https://trunkrs.dev/) web-build tool
   - In the future, `trunk` can be updated with the same command. (You may need the `--locked` flag if your ambient version of `rustc` does not match that required by `trunk`.)
 6. Add the `.cargo/bin` folder in your home directory to your executable search path
-   - This lets you call Trunk, and other tools installed by Cargo, without specifying their paths.
+   * This lets you call Trunk, and other tools installed by Cargo, without specifying their paths
-   - On POSIX systems, the search path is stored in the `PATH` environment variable.
+   * On POSIX systems, the search path is stored in the `PATH` environment variable
   - Alternatively, if you don't want to adjust your `PATH`, you can install `trunk` in another directory `DIR` via `cargo install --root DIR trunk`.
 ### Play with the prototype
-1. From the `app-proto` folder, call `trunk serve --release` to build and serve the prototype.
+1. From the `app-proto` folder, call `trunk serve --release` to build and serve the prototype
-   - The crates the prototype depends on will be downloaded and served automatically.
+   * *The crates the prototype depends on will be downloaded and served automatically*
-   - For a faster build, at the expense of a much slower prototype, you can call `trunk serve` without the `--release` flag.
+   * *For a faster build, at the expense of a much slower prototype, you can call `trunk serve` without the `--release` flag*
-   - If you want to stay in the top-level folder, you can call `trunk serve --config app-proto [--release]` from there instead.
+   * *If you want to stay in the top-level folder, you can call `trunk serve --config app-proto [--release]`* from there instead.
-3. In a web browser, visit one of the URLs listed under the message `INFO 📡 server listening at:`.
+3. In a web browser, visit one of the URLs listed under the message `INFO 📡 server listening at:`
-   - Touching any file in the `app-proto` folder will make Trunk rebuild and live-reload the prototype.
+   * *Touching any file in the `app-proto` folder will make Trunk rebuild and live-reload the prototype*
-4. Press *ctrl+C* in the shell where Trunk is running to stop serving the prototype.
+4. Press *ctrl+C* in the shell where Trunk is running to stop serving the prototype
 ### Run the engine on some example problems
-1. Use `sh` to run the script `tools/run-examples.sh`.
+1. Go into the `app-proto` folder
-   - The script is location-independent, so you can do this from anywhere in the dyna3 repository.
+2. Call `./run-examples`
-   - The call from the top level of the repository is:
+   * *For each example problem, the engine will print the value of the loss function at each optimization step*
-
+   * *The first example that prints is the same as the Irisawa hexlet example from the Julia version of the engine prototype. If you go into `engine-proto/gram-test`, launch Julia, and then*
-     ```bash
+     
     sh tools/run-examples.sh
     ```
   - For each example problem, the engine will print the value of the loss function at each optimization step.
   - The first example that prints is the same as the Irisawa hexlet example from the Julia version of the engine prototype. If you go into `engine-proto/gram-test`, launch Julia, and then execute
     ```julia
     include("irisawa-hexlet.jl")
     for (step, scaled_loss) in enumerate(history_alt.scaled_loss)
       println(rpad(step-1, 4), " | ", scaled_loss)
     end
     ```
-
+     
-     you should see that it prints basically the same loss history until the last few steps, when the lower default precision of the Rust engine really starts to show.
+     *you should see that it prints basically the same loss history until the last few steps, when the lower default precision of the Rust engine really starts to show*
 ### Run the automated tests
-1. Go into the `app-proto` folder.
+1. Go into the `app-proto` folder
-2. Call `cargo test`.
+2. Call `cargo test`
 ### Deploy the prototype
 1. From the `app-proto` folder, call `trunk build --release`.
   - Building in [release mode](https://doc.rust-lang.org/cargo/reference/profiles.html#release) produces an executable which is smaller and often much faster, but harder to debug and more time-consuming to build.
   - If you want to stay in the top-level folder, you can call `trunk build --config app-proto --release` from there instead.
 2. Use `sh` to run the packaging script `tools/package-for-deployment.sh`.
   - The script is location-independent, so you can do this from anywhere in the dyna3 repository.
   - The call from the top level of the repository is:
     ```bash
     sh tools/package-for-deployment.sh
     ```
   - This will overwrite or replace the files in `deploy/dyna3`.
 3. Put the contents of `deploy/dyna3` in the folder on your server that the prototype will be served from.
   - To simplify uploading, you might want to combine these files into an archive called `deploy/dyna3.zip`. Git has been set to ignore this path.
--- a/app-proto/Cargo.lock
+++ b/app-proto/Cargo.lock
@ -255,7 +255,6 @@ dependencies = [
 "charming",
 "console_error_panic_hook",
 "dyna3",
 "enum-iterator",
 "itertools",
 "js-sys",
 "lazy_static",
@ -272,26 +271,6 @@ version = "1.13.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "60b1af1c220855b6ceac025d3f6ecdd2b7c4894bfe9cd9bda4fbb4bc7c0d4cf0"
 [[package]]
 name = "enum-iterator"
 version = "2.3.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "a4549325971814bda7a44061bf3fe7e487d447cba01e4220a4b454d630d7a016"
 dependencies = [
 "enum-iterator-derive",
 ]
 [[package]]
 name = "enum-iterator-derive"
 version = "1.5.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "685adfa4d6f3d765a26bc5dbc936577de9abf756c1feeb3089b01dd395034842"
 dependencies = [
 "proc-macro2",
 "quote",
 "syn",
 ]
 [[package]]
 name = "equivalent"
 version = "1.0.1"
--- a/app-proto/Cargo.toml
+++ b/app-proto/Cargo.toml
@ -10,7 +10,6 @@ default = ["console_error_panic_hook"]
 dev = []
 [dependencies]
 enum-iterator = "2.3.0"
 itertools = "0.13.0"
 js-sys = "0.3.70"
 lazy_static = "1.5.0"
--- a/app-proto/Trunk.toml
+++ b/app-proto/Trunk.toml
@ -1,2 +0,0 @@
 [build]
 public_url = "./"
--- a/app-proto/examples/irisawa-hexlet.rs
+++ b/app-proto/examples/irisawa-hexlet.rs
@ -15,9 +15,9 @@ fn main() {
        for k in 4..9 {
            println!("  {} sun", 1.0 / config[(3, k)]);
        }
-
+        
        // print the completed Gram matrix
        print::gram_matrix(&config);
    }
    print::loss_history(&realization.history);
-}
+}
--- a/app-proto/examples/kaleidocycle.rs
+++ b/app-proto/examples/kaleidocycle.rs
@ -14,7 +14,7 @@ fn main() {
        // print the completed Gram matrix and the realized configuration
        print::gram_matrix(&config);
        print::config(&config);
-
+        
        // find the kaleidocycle's twist motion by projecting onto the tangent
        // space
        const N_POINTS: usize = 12;
@ -23,10 +23,10 @@ fn main() {
        let twist_motion: DMatrix<_> = (0..N_POINTS).step_by(4).flat_map(
            |n| [
                tangent.proj(&up.as_view(), n),
-                tangent.proj(&down.as_view(), n+1),
+                tangent.proj(&down.as_view(), n+1)
            ]
        ).sum();
        let normalization = 5.0 / twist_motion[(2, 0)];
        println!("\nTwist motion:{}", (normalization * twist_motion).to_string().trim_end());
    }
-}
+}
--- a/app-proto/examples/point-on-sphere.rs
+++ b/app-proto/examples/point-on-sphere.rs
@ -6,7 +6,7 @@ use dyna3::engine::{
    realize_gram,
    sphere,
    ConfigNeighborhood,
-    ConstraintProblem,
+    ConstraintProblem
 };
 fn main() {
@ -25,7 +25,7 @@ fn main() {
    );
    print::title("Point on a sphere");
    print::realization_diagnostics(&realization);
-    if let Ok(ConfigNeighborhood { config, .. }) = realization.result {
+    if let Ok(ConfigNeighborhood{ config, .. }) = realization.result {
        print::gram_matrix(&config);
        print::config(&config);
    }
--- a/app-proto/examples/three-spheres.rs
+++ b/app-proto/examples/three-spheres.rs
@ -5,7 +5,7 @@ use dyna3::engine::{
    realize_gram,
    sphere,
    ConfigNeighborhood,
-    ConstraintProblem,
+    ConstraintProblem
 };
 fn main() {
@ -14,7 +14,7 @@ fn main() {
        &[
            sphere(1.0, 0.0, 0.0, 1.0),
            sphere(-0.5, a, 0.0, 1.0),
-            sphere(-0.5, -a, 0.0, 1.0),
+            sphere(-0.5, -a, 0.0, 1.0)
        ]
    });
    for j in 0..3 {
@ -27,7 +27,7 @@ fn main() {
    );
    print::title("Three spheres");
    print::realization_diagnostics(&realization);
-    if let Ok(ConfigNeighborhood { config, .. }) = realization.result {
+    if let Ok(ConfigNeighborhood{ config, .. }) = realization.result {
        print::gram_matrix(&config);
    }
    print::loss_history(&realization.history);
--- a/app-proto/index.html
+++ b/app-proto/index.html
@ -6,7 +6,7 @@
    <link data-trunk rel="css" href="main.css"/>
    <link href="https://fonts.bunny.net/css?family=fira-sans:ital,wght@0,400;1,400&display=swap" rel="stylesheet">
    <link href="https://fonts.bunny.net/css?family=noto-emoji:wght@400&text=%f0%9f%94%97%e2%9a%a0&display=swap" rel="stylesheet">
-
+    
    <!--
      the Charming visualization crate, which we use to show engine diagnostics,
      depends the ECharts JavaScript package
--- a/app-proto/main.css
+++ b/app-proto/main.css
@ -184,7 +184,6 @@ details[open]:has(li) .element-switch::after {
 #diagnostics-bar {
  display: flex;
  gap: 8px;
 }
 #realization-status {
@ -208,14 +207,6 @@ details[open]:has(li) .element-switch::after {
  content: '⚠';
 }
 #step-input > label {
  padding-right: 4px;
 }
 #step-input > input {
  width: 45px;
 }
 .diagnostics-panel {
  margin-top: 10px;
  min-height: 180px;
--- a/app-proto/run-examples.sh
+++ b/app-proto/run-examples.sh
@ -8,7 +8,7 @@
 # the application prototype
 # find the manifest file for the application prototype
-MANIFEST="$(dirname -- $0)/../app-proto/Cargo.toml"
+MANIFEST="$(dirname -- $0)/Cargo.toml"
 # set up the command that runs each example
 RUN_EXAMPLE="cargo run --manifest-path $MANIFEST --example"
--- a/app-proto/src/assembly.rs
+++ b/app-proto/src/assembly.rs
@ -1,14 +1,13 @@
 use enum_iterator::{all, Sequence};
 use nalgebra::{DMatrix, DVector, DVectorView};
 use std::{
    cell::Cell,
    cmp::Ordering,
    collections::{BTreeMap, BTreeSet},
    cmp::Ordering,
    fmt,
-    fmt::{Debug, Display, Formatter},
+    fmt::{Debug, Formatter},
    hash::{Hash, Hasher},
    rc::Rc,
-    sync::{atomic, atomic::AtomicU64},
+    sync::{atomic, atomic::AtomicU64}
 };
 use sycamore::prelude::*;
 use web_sys::{console, wasm_bindgen::JsValue}; /* DEBUG */
@ -17,6 +16,7 @@ use crate::{
    components::{display::DisplayItem, outline::OutlineItem},
    engine::{
        Q,
        change_half_curvature,
        local_unif_to_std,
        point,
        project_point_to_normalized,
@ -27,10 +27,9 @@ use crate::{
        ConfigSubspace,
        ConstraintProblem,
        DescentHistory,
-        MatrixEntry,
+        Realization
        Realization,
    },
-    specified::SpecifiedValue,
+    specified::SpecifiedValue
 };
 pub type ElementColor = [f32; 3];
@ -45,7 +44,7 @@ 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
@ -86,14 +85,6 @@ impl Ord for dyn Serial {
    }
 }
 // Small helper function to generate consistent errors when there
 // are indexing issues in a ProblemPoser
 fn indexing_error(item: &str, name: &str, actor: &str) -> String {
    format!(
        "{item} \"{name}\" must be indexed before {actor} writes problem data"
    )
 }
 pub trait ProblemPoser {
    fn pose(&self, problem: &mut ConstraintProblem);
 }
@ -101,33 +92,33 @@ pub trait ProblemPoser {
 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
@ -135,8 +126,8 @@ pub trait Element: Serial + ProblemPoser + DisplayItem {
 }
 impl Debug for dyn Element {
-    fn fmt(&self, f: &mut Formatter<'_>) -> fmt::Result {
+    fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), fmt::Error> {
-        Debug::fmt(&self.id(), f)
+        self.id().fmt(f)
    }
 }
@ -174,27 +165,27 @@ pub struct Sphere {
    pub ghost: Signal<bool>,
    pub regulators: Signal<BTreeSet<Rc<dyn Regulator>>>,
    serial: u64,
-    column_index: Cell<Option<usize>>,
+    column_index: Cell<Option<usize>>
 }
 impl Sphere {
    const CURVATURE_COMPONENT: usize = 3;
-
+    
    pub fn new(
        id: String,
        label: String,
        color: ElementColor,
-        representation: DVector<f64>,
+        representation: DVector<f64>
-    ) -> Self {
+    ) -> Sphere {
-        Self {
+        Sphere {
-            id,
+            id: id,
-            label,
+            label: label,
-            color,
+            color: color,
            representation: create_signal(representation),
            ghost: create_signal(false),
            regulators: create_signal(BTreeSet::new()),
            serial: Self::next_serial(),
-            column_index: None.into(),
+            column_index: None.into()
        }
    }
 }
@ -203,48 +194,48 @@ impl Element for Sphere {
    fn default_id() -> String {
        "sphere".to_string()
    }
-
+    
-    fn default(id: String, id_num: u64) -> Self {
+    fn default(id: String, id_num: u64) -> Sphere {
-        Self::new(
+        Sphere::new(
            id,
            format!("Sphere {id_num}"),
            [0.75_f32, 0.75_f32, 0.75_f32],
-            sphere(0.0, 0.0, 0.0, 1.0),
+            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));
    }
@ -259,7 +250,8 @@ impl Serial for Sphere {
 impl ProblemPoser for Sphere {
    fn pose(&self, problem: &mut ConstraintProblem) {
        let index = self.column_index().expect(
-            indexing_error("Sphere", &self.id, "it").as_str());
+            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());
    }
@ -273,20 +265,19 @@ pub struct Point {
    pub ghost: Signal<bool>,
    pub regulators: Signal<BTreeSet<Rc<dyn Regulator>>>,
    serial: u64,
-    column_index: Cell<Option<usize>>,
+    column_index: Cell<Option<usize>>
 }
 impl Point {
    const WEIGHT_COMPONENT: usize = 3;
-    const NORM_COMPONENT: usize = 4;
+    
    pub fn new(
        id: String,
        label: String,
        color: ElementColor,
-        representation: DVector<f64>,
+        representation: DVector<f64>
-    ) -> Self {
+    ) -> Point {
-        Self {
+        Point {
            id,
            label,
            color,
@ -294,7 +285,7 @@ impl Point {
            ghost: create_signal(false),
            regulators: create_signal(BTreeSet::new()),
            serial: Self::next_serial(),
-            column_index: None.into(),
+            column_index: None.into()
        }
    }
 }
@ -303,53 +294,44 @@ impl Element for Point {
    fn default_id() -> String {
        "point".to_string()
    }
-
+    
-    fn default(id: String, id_num: u64) -> Self {
+    fn default(id: String, id_num: u64) -> Point {
-        Self::new(
+        Point::new(
            id,
            format!("Point {id_num}"),
            [0.75_f32, 0.75_f32, 0.75_f32],
-            point(0.0, 0.0, 0.0),
+            point(0.0, 0.0, 0.0)
        )
    }
-
+    
    fn default_regulators(self: Rc<Self>) -> Vec<Rc<dyn Regulator>> {
        all::<Axis>()
            .map(|axis| {
                Rc::new(PointCoordinateRegulator::new(self.clone(), axis))
                    as Rc::<dyn Regulator>
            })
            .collect()
    }
    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));
    }
@ -364,9 +346,10 @@ impl Serial for Point {
 impl ProblemPoser for Point {
    fn pose(&self, problem: &mut ConstraintProblem) {
        let index = self.column_index().expect(
-            indexing_error("Point", &self.id, "it").as_str());
+            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.frozen.push(Point::WEIGHT_COMPONENT, index, 0.5);
        problem.guess.set_column(index, &self.representation.get_clone_untracked());
    }
 }
@ -375,6 +358,16 @@ pub trait Regulator: Serial + ProblemPoser + OutlineItem {
    fn subjects(&self) -> Vec<Rc<dyn Element>>;
    fn measurement(&self) -> ReadSignal<f64>;
    fn set_point(&self) -> Signal<SpecifiedValue>;
    // this method is used to responsively precondition the assembly for
    // realization when the regulator becomes a constraint, or is edited while
    // acting as a constraint. it should track the set point, do any desired
    // preconditioning when the set point is present, and use its return value
    // to report whether the set is present. the default implementation does no
    // preconditioning
    fn try_activate(&self) -> bool {
        self.set_point().with(|set_pt| set_pt.is_present())
    }
 }
 impl Hash for dyn Regulator {
@ -407,11 +400,11 @@ pub struct InversiveDistanceRegulator {
    pub subjects: [Rc<dyn Element>; 2],
    pub measurement: ReadSignal<f64>,
    pub set_point: Signal<SpecifiedValue>,
-    serial: u64,
+    serial: u64
 }
 impl InversiveDistanceRegulator {
-    pub fn new(subjects: [Rc<dyn Element>; 2]) -> Self {
+    pub fn new(subjects: [Rc<dyn Element>; 2]) -> InversiveDistanceRegulator {
        let representations = subjects.each_ref().map(|subj| subj.representation());
        let measurement = create_memo(move || {
            representations[0].with(|rep_0|
@ -420,11 +413,11 @@ impl InversiveDistanceRegulator {
                )
            )
        });
-
+        
        let set_point = create_signal(SpecifiedValue::from_empty_spec());
        let serial = Self::next_serial();
-
+        
-        Self { subjects, measurement, set_point, serial }
+        InversiveDistanceRegulator { subjects, measurement, set_point, serial }
    }
 }
@ -432,11 +425,11 @@ 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
    }
@ -454,8 +447,8 @@ impl ProblemPoser for InversiveDistanceRegulator {
            if let Some(val) = set_pt.value {
                let [row, col] = self.subjects.each_ref().map(
                    |subj| subj.column_index().expect(
-                        indexing_error("Subject", subj.id(),
+                        "Subjects should be indexed before inversive distance regulator writes problem data"
-                            "inversive distance regulator").as_str())
+                    )
                );
                problem.gram.push_sym(row, col, val);
            }
@ -464,22 +457,22 @@ impl ProblemPoser for InversiveDistanceRegulator {
 }
 pub struct HalfCurvatureRegulator {
-    pub subject: Rc<Sphere>,
+    pub subject: Rc<dyn Element>,
    pub measurement: ReadSignal<f64>,
    pub set_point: Signal<SpecifiedValue>,
-    serial: u64,
+    serial: u64
 }
 impl HalfCurvatureRegulator {
-    pub fn new(subject: Rc<Sphere>) -> Self {
+    pub fn new(subject: Rc<dyn Element>) -> HalfCurvatureRegulator {
        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 }
+        HalfCurvatureRegulator { subject, measurement, set_point, serial }
    }
 }
@ -487,14 +480,26 @@ 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
    }
    fn try_activate(&self) -> bool {
        match self.set_point.with(|set_pt| set_pt.value) {
            Some(half_curv) => {
                self.subject.representation().update(
                    |rep| change_half_curvature(rep, half_curv)
                );
                true
            }
            None => false
        }
    }
 }
 impl Serial for HalfCurvatureRegulator {
@ -508,88 +513,18 @@ impl ProblemPoser for HalfCurvatureRegulator {
        self.set_point.with_untracked(|set_pt| {
            if let Some(val) = set_pt.value {
                let col = self.subject.column_index().expect(
-                    indexing_error("Subject", &self.subject.id,
+                    "Subject should be indexed before half-curvature regulator writes problem data"
-                        "half-curvature regulator").as_str());
+                );
                problem.frozen.push(Sphere::CURVATURE_COMPONENT, col, val);
            }
        });
    }
 }
 #[derive(Clone, Copy, Sequence)]
 pub enum Axis { X = 0, Y = 1, Z = 2 }
 impl Axis {
    fn name(&self) -> &'static str {
        match self { Axis::X => "X", Axis::Y => "Y", Axis::Z => "Z" }
    }
 }
 impl Display for Axis {
    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
        f.write_str(self.name())
    }
 }
 pub struct PointCoordinateRegulator {
    pub subject: Rc<Point>,
    pub axis: Axis,
    pub measurement: ReadSignal<f64>,
    pub set_point: Signal<SpecifiedValue>,
    serial: u64
 }
 impl PointCoordinateRegulator {
    pub fn new(subject: Rc<Point>, axis: Axis) -> Self {
        let measurement = subject.representation().map(
            move |rep| rep[axis as usize]
        );
        let set_point = create_signal(SpecifiedValue::from_empty_spec());
        Self { subject, axis, measurement, set_point, serial: Self::next_serial() }
    }
 }
 impl Serial for PointCoordinateRegulator {
    fn serial(&self) -> u64 { self.serial }
 }
 impl Regulator for PointCoordinateRegulator {
    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 ProblemPoser for PointCoordinateRegulator {
    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(
                    indexing_error("Subject", &self.subject.id,
                        "point-coordinate regulator").as_str());
                problem.frozen.push(self.axis as usize, col, val);
                // If all three of the subject's spatial coordinates have been
                // frozen, then freeze its norm component:
                let mut coords = [0.0; Axis::CARDINALITY];
                let mut nset: usize = 0;
                for &MatrixEntry {index, value} in &(problem.frozen) {
                    if index.1 == col && index.0 < Axis::CARDINALITY {
                        nset += 1;
                        coords[index.0] = value
                    }
                }
                if nset == Axis::CARDINALITY {
                    let [x, y, z] = coords;
                    problem.frozen.push(
                        Point::NORM_COMPONENT, col, point(x,y,z)[Point::NORM_COMPONENT]);
                }
            }
        });
    }
 }
 // the velocity is expressed in uniform coordinates
 pub struct ElementMotion<'a> {
    pub element: Rc<dyn Element>,
-    pub velocity: DVectorView<'a, f64>,
+    pub velocity: DVectorView<'a, f64>
 }
 type AssemblyMotion<'a> = Vec<ElementMotion<'a>>;
@ -600,7 +535,7 @@ 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
@ -612,17 +547,17 @@ pub struct Assembly {
    //      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<()>,
+    pub keep_realized: Signal<bool>,
-
+    pub needs_realization: Signal<bool>,
    // realization diagnostics
    pub realization_status: Signal<Result<(), String>>,
-    pub descent_history: Signal<DescentHistory>,
+    pub descent_history: Signal<DescentHistory>
    pub step: Signal<SpecifiedValue>,
 }
 impl Assembly {
@ -633,43 +568,28 @@ impl Assembly {
            regulators: create_signal(BTreeSet::new()),
            tangent: create_signal(ConfigSubspace::zero(0)),
            elements_by_id: create_signal(BTreeMap::default()),
-            realization_trigger: create_signal(()),
+            keep_realized: create_signal(true),
            needs_realization: create_signal(false),
            realization_status: create_signal(Ok(())),
-            descent_history: create_signal(DescentHistory::new()),
+            descent_history: create_signal(DescentHistory::new())
            step: create_signal(SpecifiedValue::from_empty_spec()),
        };
-
+        
-        // realize the assembly whenever the element list, the regulator list,
+        // realize the assembly whenever it becomes simultaneously true that
-        // a regulator's set point, or the realization trigger is updated
+        // we're trying to keep it realized and it needs realization
-        let assembly_for_realization = assembly.clone();
+        let assembly_for_effect = assembly.clone();
        create_effect(move || {
-            assembly_for_realization.elements.track();
+            let should_realize = assembly_for_effect.keep_realized.get()
-            assembly_for_realization.regulators.with(
+                && assembly_for_effect.needs_realization.get();
-                |regs| for reg in regs {
+            if should_realize {
-                    reg.set_point().track();
+                assembly_for_effect.realize();
                }
            );
            assembly_for_realization.realization_trigger.track();
            assembly_for_realization.realize();
        });
        // load a configuration from the descent history whenever the active
        // step is updated
        let assembly_for_step_selection = assembly.clone();
        create_effect(move || {
            if let Some(step) = assembly.step.with(|n| n.value) {
                let config = assembly.descent_history.with_untracked(
                    |history| history.config[step as usize].clone()
                );
                assembly_for_step_selection.load_config(&config)
            }
        });
-
+        
        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
@ -679,13 +599,13 @@ impl Assembly {
        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())
@ -695,7 +615,7 @@ impl Assembly {
        }
        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();
@ -707,17 +627,17 @@ impl Assembly {
            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()
@ -725,7 +645,20 @@ impl Assembly {
        for regulators in subject_regulators {
            regulators.update(|regs| regs.insert(regulator.clone()));
        }
-
+        
        // request a realization when the regulator becomes a constraint, or is
        // edited while acting as a constraint
        let self_for_effect = self.clone();
        create_effect(move || {
            /* DEBUG */
            // log the regulator update
            console_log!("Updated regulator with subjects {:?}", regulator.subjects());
            if regulator.try_activate() {
                self_for_effect.needs_realization.set(true);
            }
        });
        /* DEBUG */
        // print an updated list of regulators
        console_log!("Regulators:");
@ -748,19 +681,9 @@ impl Assembly {
            }
        });
    }
-
+    
    // --- updating the configuration ---
    pub fn load_config(&self, config: &DMatrix<f64>) {
        for elt in self.elements.get_clone_untracked() {
            elt.representation().update(
                |rep| rep.set_column(0, &config.column(elt.column_index().unwrap()))
            );
        }
    }
    // --- realization ---
-
+    
    pub fn realize(&self) {
        // index the elements
        self.elements.update_silent(|elts| {
@ -768,7 +691,7 @@ impl Assembly {
                elt.set_column_index(index);
            }
        });
-
+        
        // set up the constraint problem
        let problem = self.elements.with_untracked(|elts| {
            let mut problem = ConstraintProblem::new(elts.len());
@ -782,21 +705,20 @@ impl Assembly {
            });
            problem
        });
-
+        
        /* DEBUG */
        // log the Gram matrix
        console_log!("Gram matrix:\n{}", problem.gram);
-        console_log!("Frozen entries:\n{}", problem.frozen);
+        
        /* 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 {
@ -804,52 +726,46 @@ impl Assembly {
        } else {
            console_log!("✅️ Target accuracy achieved!");
        }
-        if history.scaled_loss.len() > 0 {
+        console_log!("Steps: {}", history.scaled_loss.len() - 1);
-            console_log!("Steps: {}", history.scaled_loss.len() - 1);
+        console_log!("Loss: {}", history.scaled_loss.last().unwrap());
-            console_log!("Loss: {}", history.scaled_loss.last().unwrap());
+        
-        }
+        // report the loss history
        // report the descent history
        let step_cnt = history.config.len();
        self.descent_history.set(history);
-
+        
        match result {
-            Ok(ConfigNeighborhood { nbhd: tangent, .. }) => {
+            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(()));
-
+                
-                // display the last realization step
+                // read out the solution
-                self.step.set(
+                for elt in self.elements.get_clone_untracked() {
-                    if step_cnt > 0 {
+                    elt.representation().update(
-                        let last_step = step_cnt - 1;
+                        |rep| rep.set_column(0, &config.column(elt.column_index().unwrap()))
-                        SpecifiedValue::try_from(last_step.to_string()).unwrap()
+                    );
-                    } else {
+                }
-                        SpecifiedValue::from_empty_spec()
+                
                    }
                );
                // save the tangent space
                self.tangent.set_silent(tangent);
                // clear the realization request flag
                self.needs_realization.set(false);
            },
            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));
+                self.realization_status.set(Err(message))
-
+            }
                // display the initial guess
                self.step.set(SpecifiedValue::from(Some(0.0)));
            },
        }
    }
-
+    
    // --- 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:
@ -866,7 +782,7 @@ impl Assembly {
        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.
@ -884,7 +800,7 @@ impl Assembly {
            }
            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
@ -895,7 +811,7 @@ impl Assembly {
            // 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
@ -913,7 +829,7 @@ impl Assembly {
                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() {
@ -927,37 +843,35 @@ impl Assembly {
                    },
                    None => {
                        console_log!("No velocity to unpack for fresh element \"{}\"", elt.id())
-                    },
+                    }
                };
            });
        }
-
+        
-        // trigger a realization to bring the configuration back onto the
+        // request 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(());
+        self.needs_realization.set(true);
    }
 }
 #[cfg(test)]
 mod tests {
    use super::*;
-
+    
    use crate::engine;
-
+    
    #[test]
-    #[should_panic(expected =
+    #[should_panic(expected = "Sphere \"sphere\" should be indexed before writing problem data")]
        "Sphere \"sphere\" must be indexed before it writes 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 = "Subject \"sphere1\" must be indexed before \
+    #[should_panic(expected = "Subjects should be indexed before inversive distance regulator writes problem data")]
        inversive distance regulator writes problem data")]
    fn unindexed_subject_test_inversive_distance() {
        let _ = create_root(|| {
            let subjects = [0, 1].map(
@ -972,7 +886,7 @@ mod tests {
            }.pose(&mut ConstraintProblem::new(2));
        });
    }
-
+    
    #[test]
    fn curvature_drift_test() {
        const INITIAL_RADIUS: f64 = 0.25;
@ -989,10 +903,10 @@ mod tests {
                    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),
+                    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;
@ -1003,12 +917,12 @@ mod tests {
                    vec![
                        ElementMotion {
                            element: sphere.clone(),
-                            velocity: velocity.as_view(),
+                            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;
@ -1018,4 +932,4 @@ mod tests {
            assert!((final_half_curv / INITIAL_HALF_CURV - 1.0).abs() < DRIFT_TOL);
        });
    }
-}
+}
--- a/app-proto/src/components/add_remove.rs
+++ b/app-proto/src/components/add_remove.rs
@ -4,47 +4,32 @@ use sycamore::prelude::*;
 use super::test_assembly_chooser::TestAssemblyChooser;
 use crate::{
    AppState,
-    assembly::{InversiveDistanceRegulator, Point, Sphere},
+    assembly::{InversiveDistanceRegulator, Point, Sphere}
 };
 #[component]
 pub fn AddRemove() -> View {
    view! {
-        div(id = "add-remove") {
+        div(id="add-remove") {
            button(
-                on:click = |_| {
+                on:click=|_| {
                    let state = use_context::<AppState>();
-                    batch(|| {
+                    state.assembly.insert_element_default::<Sphere>();
                        // this call is batched to avoid redundant realizations.
                        // it updates the element list and the regulator list,
                        // which are both tracked by the realization effect
                        /* TO DO */
                        // it would make more to do the batching inside
                        // `insert_element_default`, but that will have to wait
                        // until Sycamore handles nested batches correctly.
                        //
                        //   https://github.com/sycamore-rs/sycamore/issues/802
                        //
                        // the nested batch issue is relevant here because the
                        // assembly loaders in the test assembly chooser use
                        // `insert_element_default` within larger batches
                        state.assembly.insert_element_default::<Sphere>();
                    });
                }
            ) { "Add sphere" }
            button(
-                on:click = |_| {
+                on:click=|_| {
                    let state = use_context::<AppState>();
                    state.assembly.insert_element_default::<Point>();
                }
            ) { "Add point" }
            button(
-                class = "emoji", /* KLUDGE */ // for convenience, we're using an emoji as a temporary icon for this button
+                class="emoji", /* KLUDGE */ // for convenience, we're using an emoji as a temporary icon for this button
-                disabled = {
+                disabled={
                    let state = use_context::<AppState>();
                    state.selection.with(|sel| sel.len() != 2)
                },
-                on:click = |_| {
+                on:click=|_| {
                    let state = use_context::<AppState>();
                    let subjects: [_; 2] = state.selection.with(
                        // the button is only enabled when two elements are
--- a/app-proto/src/components/diagnostics.rs
+++ b/app-proto/src/components/diagnostics.rs
@ -7,16 +7,18 @@ use charming::{
 };
 use sycamore::prelude::*;
-use crate::{AppState, specified::SpecifiedValue};
+use crate::AppState;
 #[derive(Clone)]
 struct DiagnosticsState {
-    active_tab: Signal<String>,
+    active_tab: Signal<String>
 }
 impl DiagnosticsState {
-    fn new(initial_tab: String) -> Self {
+    fn new(initial_tab: String) -> DiagnosticsState {
-        Self { active_tab: create_signal(initial_tab) }
+        DiagnosticsState {
            active_tab: create_signal(initial_tab)
        }
    }
 }
@ -27,20 +29,20 @@ fn RealizationStatus() -> View {
    let realization_status = state.assembly.realization_status;
    view! {
        div(
-            id = "realization-status",
+            id="realization-status",
-            class = realization_status.with(
+            class=realization_status.with(
                |status| match status {
                    Ok(_) => "",
-                    Err(_) => "invalid",
+                    Err(_) => "invalid"
                }
            )
        ) {
-            div(class = "status")
+            div(class="status")
            div {
                (realization_status.with(
                    |status| match status {
                        Ok(_) => "Target accuracy achieved".to_string(),
-                        Err(message) => message.clone(),
+                        Err(message) => message.clone()
                    }
                ))
            }
@ -48,73 +50,10 @@ fn RealizationStatus() -> View {
    }
 }
 // history step input
 #[component]
 fn StepInput() -> View {
    // get the assembly
    let state = use_context::<AppState>();
    let assembly = state.assembly;
    // the `last_step` signal holds the index of the last step
    let last_step = assembly.descent_history.map(
        |history| match history.config.len() {
            0 => None,
            n => Some(n - 1),
        }
    );
    let input_max = last_step.map(|last| last.unwrap_or(0));
    // these signals hold the entered step number
    let value = create_signal(String::new());
    let value_as_number = create_signal(0.0);
    create_effect(move || {
        value.set(assembly.step.with(|n| n.spec.clone()));
    });
    view! {
        div(id = "step-input") {
            label { "Step" }
            input(
                r#type = "number",
                min = "0",
                max = input_max.with(|max| max.to_string()),
                bind:value = value,
                bind:valueAsNumber = value_as_number,
                on:change = move |_| {
                    if last_step.with(|last| last.is_some()) {
                        // clamp the step within its allowed range. the lower
                        // bound is redundant on browsers that make it
                        // impossible to type negative values into a number
                        // input with a non-negative `min`, but there's no harm
                        // in being careful
                        let step_raw = value.with(
                            |val| SpecifiedValue::try_from(val.clone())
                                .unwrap_or(SpecifiedValue::from_empty_spec()
                            )
                        );
                        let step = SpecifiedValue::from(
                            step_raw.value.map(
                                |val| val.clamp(0.0, input_max.get() as f64)
                            )
                        );
                        // set the input string and the assembly's active step
                        value.set(step.spec.clone());
                        assembly.step.set(step);
                    } else {
                        value.set(String::new());
                    }
                },
            )
        }
    }
 }
 fn into_log10_time_point((step, value): (usize, f64)) -> Vec<Option<f64>> {
    vec![
        Some(step as f64),
-        if value == 0.0 { None } else { Some(value.abs().log10()) },
+        if value == 0.0 { None } else { Some(value.abs().log10()) }
    ]
 }
@ -124,7 +63,7 @@ fn LossHistory() -> View {
    const CONTAINER_ID: &str = "loss-history";
    let state = use_context::<AppState>();
    let renderer = WasmRenderer::new_opt(None, Some(178));
-
+    
    on_mount(move || {
        create_effect(move || {
            // get the loss history
@ -136,13 +75,13 @@ fn LossHistory() -> View {
                    .map(into_log10_time_point)
                    .collect()
            );
-
+            
            // initialize the chart axes
            let step_axis = Axis::new()
                .type_(AxisType::Category)
                .boundary_gap(false);
            let scaled_loss_axis = Axis::new();
-
+            
            // load the chart data. when there's no history, we load the data
            // point (0, None) to clear the chart. it would feel more natural to
            // load empty data vectors, but that turns out not to clear the
@ -164,9 +103,9 @@ fn LossHistory() -> View {
            renderer.render(CONTAINER_ID, &chart).unwrap();
        });
    });
-
+    
    view! {
-        div(id = CONTAINER_ID, class = "diagnostics-chart")
+        div(id=CONTAINER_ID, class="diagnostics-chart")
    }
 }
@ -176,14 +115,14 @@ fn SpectrumHistory() -> View {
    const CONTAINER_ID: &str = "spectrum-history";
    let state = use_context::<AppState>();
    let renderer = WasmRenderer::new(478, 178);
-
+    
    on_mount(move || {
        create_effect(move || {
            // get the spectrum of the Hessian at each step, split into its
            // positive, negative, and strictly-zero parts
            let (
                hess_eigvals_zero,
-                hess_eigvals_nonzero,
+                hess_eigvals_nonzero
            ): (Vec<_>, Vec<_>) = state.assembly.descent_history.with(
                |history| history.hess_eigvals
                    .iter()
@ -204,17 +143,17 @@ fn SpectrumHistory() -> View {
                .unwrap_or(1.0);
            let (
                hess_eigvals_pos,
-                hess_eigvals_neg,
+                hess_eigvals_neg
            ): (Vec<_>, Vec<_>) = hess_eigvals_nonzero
                .into_iter()
                .partition(|&(_, val)| val > 0.0);
-
+            
            // initialize the chart axes
            let step_axis = Axis::new()
                .type_(AxisType::Category)
                .boundary_gap(false);
            let eigval_axis = Axis::new();
-
+            
            // load the chart data. when there's no history, we load the data
            // point (0, None) to clear the chart. it would feel more natural to
            // load empty data vectors, but that turns out not to clear the
@ -270,9 +209,9 @@ fn SpectrumHistory() -> View {
            renderer.render(CONTAINER_ID, &chart).unwrap();
        });
    });
-
+    
    view! {
-        div(id = CONTAINER_ID, class = "diagnostics-chart")
+        div(id=CONTAINER_ID, class="diagnostics-chart")
    }
 }
@ -281,8 +220,8 @@ fn DiagnosticsPanel(name: &'static str, children: Children) -> View {
    let diagnostics_state = use_context::<DiagnosticsState>();
    view! {
        div(
-            class = "diagnostics-panel",
+            class="diagnostics-panel",
-            "hidden" = diagnostics_state.active_tab.with(
+            "hidden"=diagnostics_state.active_tab.with(
                |active_tab| {
                    if active_tab == name {
                        None
@ -302,19 +241,18 @@ pub fn Diagnostics() -> View {
    let diagnostics_state = DiagnosticsState::new("loss".to_string());
    let active_tab = diagnostics_state.active_tab.clone();
    provide_context(diagnostics_state);
-
+    
    view! {
-        div(id = "diagnostics") {
+        div(id="diagnostics") {
-            div(id = "diagnostics-bar") {
+            div(id="diagnostics-bar") {
                RealizationStatus {}
-                select(bind:value = active_tab) {
+                select(bind:value=active_tab) {
-                    option(value = "loss") { "Loss" }
+                    option(value="loss") { "Loss" }
-                    option(value = "spectrum") { "Spectrum" }
+                    option(value="spectrum") { "Spectrum" }
                }
                StepInput {}
            }
-            DiagnosticsPanel(name = "loss") { LossHistory {} }
+            DiagnosticsPanel(name="loss") { LossHistory {} }
-            DiagnosticsPanel(name = "spectrum") { SpectrumHistory {} }
+            DiagnosticsPanel(name="spectrum") { SpectrumHistory {} }
        }
    }
-}
+}
--- a/app-proto/src/components/display.rs
+++ b/app-proto/src/components/display.rs
@ -12,12 +12,12 @@ use web_sys::{
    WebGlProgram,
    WebGlShader,
    WebGlUniformLocation,
-    wasm_bindgen::{JsCast, JsValue},
+    wasm_bindgen::{JsCast, JsValue}
 };
 use crate::{
    AppState,
-    assembly::{Element, ElementColor, ElementMotion, Point, Sphere},
+    assembly::{Element, ElementColor, ElementMotion, Point, Sphere}
 };
 // --- color ---
@ -37,26 +37,23 @@ fn combine_channels(color: ElementColor, opacity: f32) -> ColorWithOpacity {
 struct SceneSpheres {
    representations: Vec<DVector<f64>>,
    colors_with_opacity: Vec<ColorWithOpacity>,
-    highlights: Vec<f32>,
+    highlights: Vec<f32>
 }
 impl SceneSpheres {
-    fn new() -> Self {
+    fn new() -> SceneSpheres{
-        Self {
+        SceneSpheres {
            representations: Vec::new(),
            colors_with_opacity: Vec::new(),
-            highlights: Vec::new(),
+            highlights: Vec::new()
        }
    }
-
+    
    fn len_i32(&self) -> i32 {
        self.representations.len().try_into().expect("Number of spheres must fit in a 32-bit integer")
    }
-
+    
-    fn push(
+    fn push(&mut self, representation: DVector<f64>, color: ElementColor, opacity: f32, highlight: f32) {
        &mut self, representation: DVector<f64>,
        color: ElementColor, opacity: f32, highlight: f32,
    ) {
        self.representations.push(representation);
        self.colors_with_opacity.push(combine_channels(color, opacity));
        self.highlights.push(highlight);
@ -67,23 +64,20 @@ struct ScenePoints {
    representations: Vec<DVector<f64>>,
    colors_with_opacity: Vec<ColorWithOpacity>,
    highlights: Vec<f32>,
-    selections: Vec<f32>,
+    selections: Vec<f32>
 }
 impl ScenePoints {
-    fn new() -> Self {
+    fn new() -> ScenePoints {
-        Self {
+        ScenePoints {
            representations: Vec::new(),
            colors_with_opacity: Vec::new(),
            highlights: Vec::new(),
-            selections: Vec::new(),
+            selections: Vec::new()
        }
    }
-
+    
-    fn push(
+    fn push(&mut self, representation: DVector<f64>, color: ElementColor, opacity: f32, highlight: f32, selected: bool) {
        &mut self, representation: DVector<f64>,
        color: ElementColor, opacity: f32, highlight: f32, selected: bool,
    ) {
        self.representations.push(representation);
        self.colors_with_opacity.push(combine_channels(color, opacity));
        self.highlights.push(highlight);
@ -93,30 +87,25 @@ impl ScenePoints {
 pub struct Scene {
    spheres: SceneSpheres,
-    points: ScenePoints,
+    points: ScenePoints
 }
 impl Scene {
-    fn new() -> Self {
+    fn new() -> Scene {
-        Self {
+        Scene {
            spheres: SceneSpheres::new(),
-            points: ScenePoints::new(),
+            points: ScenePoints::new()
        }
    }
 }
 pub trait DisplayItem {
    fn show(&self, scene: &mut Scene, selected: bool);
-
+    
    // the smallest positive depth, represented as a multiple of `dir`, where
    // the line generated by `dir` hits the element. returns `None` if the line
    // misses the element
-    fn cast(
+    fn cast(&self, dir: Vector3<f64>, assembly_to_world: &DMatrix<f64>, pixel_size: f64) -> Option<f64>;
        &self,
        dir: Vector3<f64>,
        assembly_to_world: &DMatrix<f64>,
        pixel_size: f64,
    ) -> Option<f64>;
 }
 impl DisplayItem for Sphere {
@ -125,31 +114,26 @@ impl DisplayItem for Sphere {
        const DEFAULT_OPACITY: f32 = 0.5;
        const GHOST_OPACITY: f32 = 0.2;
        const HIGHLIGHT: f32 = 0.2;
-
+        
        let representation = self.representation.get_clone_untracked();
        let color = if selected { self.color.map(|channel| 0.2 + 0.8*channel) } else { self.color };
        let opacity = if self.ghost.get() { GHOST_OPACITY } else { DEFAULT_OPACITY };
        let highlight = if selected { 1.0 } else { HIGHLIGHT };
        scene.spheres.push(representation, color, opacity, highlight);
    }
-
+    
    // this method should be kept synchronized with `sphere_cast` in
    // `spheres.frag`, which does essentially the same thing on the GPU side
-    fn cast(
+    fn cast(&self, dir: Vector3<f64>, assembly_to_world: &DMatrix<f64>, _pixel_size: f64) -> Option<f64> {
        &self,
        dir: Vector3<f64>,
        assembly_to_world: &DMatrix<f64>,
        _pixel_size: f64,
    ) -> Option<f64> {
        // if `a/b` is less than this threshold, we approximate
        // `a*u^2 + b*u + c` by the linear function `b*u + c`
        const DEG_THRESHOLD: f64 = 1e-9;
-
+        
        let rep = self.representation.with_untracked(|rep| assembly_to_world * rep);
        let a = -rep[3] * dir.norm_squared();
        let b = rep.rows_range(..3).dot(&dir);
        let c = -rep[4];
-
+        
        let adjust = 4.0*a*c/(b*b);
        if adjust < 1.0 {
            // as long as `b` is non-zero, the linear approximation of
@ -184,35 +168,30 @@ impl DisplayItem for Point {
        /* SCAFFOLDING */
        const GHOST_OPACITY: f32 = 0.4;
        const HIGHLIGHT: f32 = 0.5;
-
+        
        let representation = self.representation.get_clone_untracked();
        let color = if selected { self.color.map(|channel| 0.2 + 0.8*channel) } else { self.color };
        let opacity = if self.ghost.get() { GHOST_OPACITY } else { 1.0 };
        let highlight = if selected { 1.0 } else { HIGHLIGHT };
        scene.points.push(representation, color, opacity, highlight, selected);
    }
-
+    
    /* SCAFFOLDING */
-    fn cast(
+    fn cast(&self, dir: Vector3<f64>, assembly_to_world: &DMatrix<f64>, pixel_size: f64) -> Option<f64> {
        &self,
        dir: Vector3<f64>,
        assembly_to_world: &DMatrix<f64>,
        pixel_size: f64,
    ) -> Option<f64> {
        let rep = self.representation.with_untracked(|rep| assembly_to_world * rep);
        if rep[2] < 0.0 {
            // this constant should be kept synchronized with `point.frag`
            const POINT_RADIUS_PX: f64 = 4.0;
-
+            
            // find the radius of the point in screen projection units
            let point_radius_proj = POINT_RADIUS_PX * pixel_size;
-
+            
            // find the squared distance between the screen projections of the
            // ray and the point
            let dir_proj = -dir.fixed_rows::<2>(0) / dir[2];
            let rep_proj = -rep.fixed_rows::<2>(0) / rep[2];
            let dist_sq = (dir_proj - rep_proj).norm_squared();
-
+            
            // if the ray hits the point, return its depth
            if dist_sq < point_radius_proj * point_radius_proj {
                Some(rep[2] / dir[2])
@ -241,7 +220,7 @@ fn compile_shader(
 fn set_up_program(
    context: &WebGl2RenderingContext,
    vertex_shader_source: &str,
-    fragment_shader_source: &str,
+    fragment_shader_source: &str
 ) -> WebGlProgram {
    // compile the shaders
    let vertex_shader = compile_shader(
@ -254,13 +233,13 @@ fn set_up_program(
        WebGl2RenderingContext::FRAGMENT_SHADER,
        fragment_shader_source,
    );
-
+    
    // create the program and attach the shaders
    let program = context.create_program().unwrap();
    context.attach_shader(&program, &vertex_shader);
    context.attach_shader(&program, &fragment_shader);
    context.link_program(&program);
-
+    
    /* DEBUG */
    // report whether linking succeeded
    let link_status = context
@ -273,7 +252,7 @@ fn set_up_program(
        "Linking failed"
    };
    console::log_1(&JsValue::from(link_msg));
-
+    
    program
 }
@ -281,12 +260,12 @@ fn get_uniform_array_locations<const N: usize>(
    context: &WebGl2RenderingContext,
    program: &WebGlProgram,
    var_name: &str,
-    member_name_opt: Option<&str>,
+    member_name_opt: Option<&str>
 ) -> [Option<WebGlUniformLocation>; N] {
    array::from_fn(|n| {
        let name = match member_name_opt {
            Some(member_name) => format!("{var_name}[{n}].{member_name}"),
-            None => format!("{var_name}[{n}]"),
+            None => format!("{var_name}[{n}]")
        };
        context.get_uniform_location(&program, name.as_str())
    })
@ -297,7 +276,7 @@ fn bind_to_attribute(
    context: &WebGl2RenderingContext,
    attr_index: u32,
    attr_size: i32,
-    buffer: &Option<WebGlBuffer>,
+    buffer: &Option<WebGlBuffer>
 ) {
    context.bind_buffer(WebGl2RenderingContext::ARRAY_BUFFER, buffer.as_ref());
    context.vertex_attrib_pointer_with_i32(
@ -313,12 +292,12 @@ fn bind_to_attribute(
 // load the given data into a new vertex buffer object
 fn load_new_buffer(
    context: &WebGl2RenderingContext,
-    data: &[f32],
+    data: &[f32]
 ) -> Option<WebGlBuffer> {
    // create a buffer and bind it to ARRAY_BUFFER
    let buffer = context.create_buffer();
    context.bind_buffer(WebGl2RenderingContext::ARRAY_BUFFER, buffer.as_ref());
-
+    
    // load the given data into the buffer. this block is unsafe because
    // `Float32Array::view` creates a raw view into our module's
    // `WebAssembly.Memory` buffer. allocating more memory will change the
@ -332,7 +311,7 @@ fn load_new_buffer(
            WebGl2RenderingContext::STATIC_DRAW,
        );
    }
-
+    
    buffer
 }
@ -340,7 +319,7 @@ fn bind_new_buffer_to_attribute(
    context: &WebGl2RenderingContext,
    attr_index: u32,
    attr_size: i32,
-    data: &[f32],
+    data: &[f32]
 ) {
    let buffer = load_new_buffer(context, data);
    bind_to_attribute(context, attr_index, attr_size, &buffer);
@ -353,18 +332,18 @@ fn event_dir(event: &MouseEvent) -> (Vector3<f64>, f64) {
    let width = rect.width();
    let height = rect.height();
    let shortdim = width.min(height);
-
+    
    // this constant should be kept synchronized with `spheres.frag` and
    // `point.vert`
    const FOCAL_SLOPE: f64 = 0.3;
-
+    
    (
        Vector3::new(
            FOCAL_SLOPE * (2.0*(f64::from(event.client_x()) - rect.left()) - width) / shortdim,
            FOCAL_SLOPE * (2.0*(rect.bottom() - f64::from(event.client_y())) - height) / shortdim,
-            -1.0,
+            -1.0
        ),
-        FOCAL_SLOPE * 2.0 / shortdim,
+        FOCAL_SLOPE * 2.0 / shortdim
    )
 }
@ -373,13 +352,13 @@ fn event_dir(event: &MouseEvent) -> (Vector3<f64>, f64) {
 #[component]
 pub fn Display() -> View {
    let state = use_context::<AppState>();
-
+    
    // canvas
    let display = create_node_ref();
-
+    
    // viewpoint
    let assembly_to_world = create_signal(DMatrix::<f64>::identity(5, 5));
-
+    
    // navigation
    let pitch_up = create_signal(0.0);
    let pitch_down = create_signal(0.0);
@ -390,7 +369,7 @@ pub fn Display() -> View {
    let zoom_in = create_signal(0.0);
    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);
@ -400,7 +379,7 @@ pub fn Display() -> View {
    let translate_pos_z = create_signal(0.0);
    let shrink_neg = create_signal(0.0);
    let shrink_pos = create_signal(0.0);
-
+    
    // change listener
    let scene_changed = create_signal(true);
    create_effect(move || {
@ -413,18 +392,18 @@ pub fn Display() -> View {
        state.selection.track();
        scene_changed.set(true);
    });
-
+    
    /* INSTRUMENTS */
    const SAMPLE_PERIOD: i32 = 60;
    let mut last_sample_time = 0.0;
    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;
-
+        
        // viewpoint
        const ROT_SPEED: f64 = 0.4; // in radians per second
        const ZOOM_SPEED: f64 = 0.15; // multiplicative rate per second
@ -432,18 +411,18 @@ pub fn Display() -> View {
        let mut orientation = DMatrix::<f64>::identity(5, 5);
        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
        const SHRINKING_SPEED: f64 = 0.15; // in length units per second
-
+        
        // display parameters
        const LAYER_THRESHOLD: i32 = 0; /* DEBUG */
        const DEBUG_MODE: i32 = 0; /* DEBUG */
-
+        
        /* INSTRUMENTS */
        let performance = window().unwrap().performance().unwrap();
-
+        
        // get the display canvas
        let canvas = display.get().unchecked_into::<web_sys::HtmlCanvasElement>();
        let ctx = canvas
@ -452,28 +431,28 @@ pub fn Display() -> View {
            .unwrap()
            .dyn_into::<WebGl2RenderingContext>()
            .unwrap();
-
+        
        // disable depth testing
        ctx.disable(WebGl2RenderingContext::DEPTH_TEST);
-
+        
        // set blend mode
        ctx.enable(WebGl2RenderingContext::BLEND);
        ctx.blend_func(WebGl2RenderingContext::SRC_ALPHA, WebGl2RenderingContext::ONE_MINUS_SRC_ALPHA);
-
+        
        // set up the sphere rendering program
        let sphere_program = set_up_program(
            &ctx,
            include_str!("identity.vert"),
-            include_str!("spheres.frag"),
+            include_str!("spheres.frag")
        );
-
+        
        // set up the point rendering program
        let point_program = set_up_program(
            &ctx,
            include_str!("point.vert"),
-            include_str!("point.frag"),
+            include_str!("point.frag")
        );
-
+        
        /* DEBUG */
        // print the maximum number of vectors that can be passed as
        // uniforms to a fragment shader. the OpenGL ES 3.0 standard
@ -488,12 +467,12 @@ pub fn Display() -> View {
        // capped at 1024 elements
        console::log_2(
            &ctx.get_parameter(WebGl2RenderingContext::MAX_FRAGMENT_UNIFORM_VECTORS).unwrap(),
-            &JsValue::from("uniform vectors available"),
+            &JsValue::from("uniform vectors available")
        );
-
+        
        // find the sphere program's vertex attribute
        let viewport_position_attr = ctx.get_attrib_location(&sphere_program, "position") as u32;
-
+        
        // find the sphere program's uniforms
        const SPHERE_MAX: usize = 200;
        let sphere_cnt_loc = ctx.get_uniform_location(&sphere_program, "sphere_cnt");
@ -513,7 +492,7 @@ pub fn Display() -> View {
        let shortdim_loc = ctx.get_uniform_location(&sphere_program, "shortdim");
        let layer_threshold_loc = ctx.get_uniform_location(&sphere_program, "layer_threshold");
        let debug_mode_loc = ctx.get_uniform_location(&sphere_program, "debug_mode");
-
+        
        // load the viewport vertex positions into a new vertex buffer object
        const VERTEX_CNT: usize = 6;
        let viewport_positions: [f32; 3*VERTEX_CNT] = [
@ -524,23 +503,23 @@ pub fn Display() -> View {
            // southeast triangle
            -1.0, -1.0, 0.0,
             1.0,  1.0, 0.0,
-             1.0, -1.0, 0.0,
+             1.0, -1.0, 0.0
        ];
        let viewport_position_buffer = load_new_buffer(&ctx, &viewport_positions);
-
+        
        // find the point program's vertex attributes
        let point_position_attr = ctx.get_attrib_location(&point_program, "position") as u32;
        let point_color_attr = ctx.get_attrib_location(&point_program, "color") as u32;
        let point_highlight_attr = ctx.get_attrib_location(&point_program, "highlight") as u32;
        let point_selection_attr = ctx.get_attrib_location(&point_program, "selected") as u32;
-
+        
        // set up a repainting routine
        let (_, start_animation_loop, _) = create_raf(move || {
            // get the time step
            let time = performance.now();
            let time_step = 0.001*(time - last_time);
            last_time = time;
-
+            
            // get the navigation state
            let pitch_up_val = pitch_up.get();
            let pitch_down_val = pitch_down.get();
@ -551,7 +530,7 @@ pub fn Display() -> View {
            let zoom_in_val = zoom_in.get();
            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();
@ -561,7 +540,7 @@ pub fn Display() -> View {
            let translate_pos_z_val = translate_pos_z.get();
            let shrink_neg_val = shrink_neg.get();
            let shrink_pos_val = shrink_pos.get();
-
+            
            // update the assembly's orientation
            let ang_vel = {
                let pitch = pitch_up_val - pitch_down_val;
@ -582,31 +561,13 @@ pub fn Display() -> View {
                Rotation3::from_scaled_axis(time_step * ang_vel).matrix()
            );
            orientation = &rotation * &orientation;
-
+            
            // update the assembly's location
            let zoom = zoom_out_val - zoom_in_val;
            location_z *= (time_step * ZOOM_SPEED * zoom).exp();
-
+            
            // manipulate the assembly
-            /* KLUDGE */
+            if state.selection.with(|sel| sel.len() == 1) {
            // to avoid the complexity of making tangent space projection
            // conditional and dealing with unnormalized representation vectors,
            // we only allow manipulation when we're looking at the last step of
            // a successful realization
            let realization_successful = state.assembly.realization_status.with(
                |status| status.is_ok()
            );
            let step_val = state.assembly.step.with_untracked(|step| step.value);
            let on_init_step = step_val.is_some_and(|n| n == 0.0);
            let on_last_step = step_val.is_some_and(
                |n| state.assembly.descent_history.with_untracked(
                    |history| n as usize + 1 == history.config.len().max(1)
                )
            );
            let on_manipulable_step =
                !realization_successful && on_init_step
                || realization_successful && on_last_step;
            if on_manipulable_step && state.selection.with(|sel| sel.len() == 1) {
                let sel = state.selection.with(
                    |sel| sel.into_iter().next().unwrap().clone()
                );
@ -635,18 +596,18 @@ pub fn Display() -> View {
                        vec![
                            ElementMotion {
                                element: sel,
-                                velocity: elt_motion.as_view(),
+                                velocity: elt_motion.as_view()
                            }
                        ]
                    );
                    scene_changed.set(true);
                }
            }
-
+            
            if scene_changed.get() {
                const SPACE_DIM: usize = 3;
                const COLOR_SIZE: usize = 3;
-
+                
                /* INSTRUMENTS */
                // measure mean frame interval
                frames_since_last_sample += 1;
@ -655,11 +616,11 @@ pub fn Display() -> View {
                    last_sample_time = time;
                    frames_since_last_sample = 0;
                }
-
+                
                // --- get the assembly ---
-
+                
                let mut scene = Scene::new();
-
+                
                // find the map from assembly space to world space
                let location = {
                    let u = -location_z;
@ -668,11 +629,11 @@ pub fn Display() -> View {
                        0.0, 1.0,   0.0, 0.0, 0.0,
                        0.0, 0.0,   1.0, 0.0,   u,
                        0.0, 0.0, 2.0*u, 1.0, u*u,
-                        0.0, 0.0,   0.0, 0.0, 1.0,
+                        0.0, 0.0,   0.0, 0.0, 1.0
                    ])
                };
                let asm_to_world = &location * &orientation;
-
+                
                // set up the scene
                state.assembly.elements.with_untracked(
                    |elts| for elt in elts {
@ -681,74 +642,74 @@ pub fn Display() -> View {
                    }
                );
                let sphere_cnt = scene.spheres.len_i32();
-
+                
                // --- draw the spheres ---
-
+                
                // use the sphere rendering program
                ctx.use_program(Some(&sphere_program));
-
+                
                // enable the sphere program's vertex attribute
                ctx.enable_vertex_attrib_array(viewport_position_attr);
-
+                
                // write the spheres in world coordinates
                let sphere_reps_world: Vec<_> = scene.spheres.representations.into_iter().map(
                    |rep| (&asm_to_world * rep).cast::<f32>()
                ).collect();
-
+                
                // set the resolution
                let width = canvas.width() as f32;
                let height = canvas.height() as f32;
                ctx.uniform2f(resolution_loc.as_ref(), width, height);
                ctx.uniform1f(shortdim_loc.as_ref(), width.min(height));
-
+                
                // pass the scene data
                ctx.uniform1i(sphere_cnt_loc.as_ref(), sphere_cnt);
                for n in 0..sphere_reps_world.len() {
                    let v = &sphere_reps_world[n];
                    ctx.uniform3fv_with_f32_array(
                        sphere_sp_locs[n].as_ref(),
-                        v.rows(0, 3).as_slice(),
+                        v.rows(0, 3).as_slice()
                    );
                    ctx.uniform2fv_with_f32_array(
                        sphere_lt_locs[n].as_ref(),
-                        v.rows(3, 2).as_slice(),
+                        v.rows(3, 2).as_slice()
                    );
                    ctx.uniform4fv_with_f32_array(
                        sphere_color_locs[n].as_ref(),
-                        &scene.spheres.colors_with_opacity[n],
+                        &scene.spheres.colors_with_opacity[n]
                    );
                    ctx.uniform1f(
                        sphere_highlight_locs[n].as_ref(),
-                        scene.spheres.highlights[n],
+                        scene.spheres.highlights[n]
                    );
                }
-
+                
                // pass the display parameters
                ctx.uniform1i(layer_threshold_loc.as_ref(), LAYER_THRESHOLD);
                ctx.uniform1i(debug_mode_loc.as_ref(), DEBUG_MODE);
-
+                
                // bind the viewport vertex position buffer to the position
                // attribute in the vertex shader
                bind_to_attribute(&ctx, viewport_position_attr, SPACE_DIM as i32, &viewport_position_buffer);
-
+                
                // draw the scene
                ctx.draw_arrays(WebGl2RenderingContext::TRIANGLES, 0, VERTEX_CNT as i32);
-
+                
                // disable the sphere program's vertex attribute
                ctx.disable_vertex_attrib_array(viewport_position_attr);
-
+                
                // --- draw the points ---
-
+                
                if !scene.points.representations.is_empty() {
                    // use the point rendering program
                    ctx.use_program(Some(&point_program));
-
+                    
                    // enable the point program's vertex attributes
                    ctx.enable_vertex_attrib_array(point_position_attr);
                    ctx.enable_vertex_attrib_array(point_color_attr);
                    ctx.enable_vertex_attrib_array(point_highlight_attr);
                    ctx.enable_vertex_attrib_array(point_selection_attr);
-
+                    
                    // write the points in world coordinates
                    let asm_to_world_sp = asm_to_world.rows(0, SPACE_DIM);
                    let point_positions = DMatrix::from_columns(
@ -756,7 +717,7 @@ pub fn Display() -> View {
                            |rep| &asm_to_world_sp * rep
                        ).collect::<Vec<_>>().as_slice()
                    ).cast::<f32>();
-
+                    
                    // load the point positions and colors into new buffers and
                    // bind them to the corresponding attributes in the vertex
                    // shader
@ -764,22 +725,22 @@ pub fn Display() -> View {
                    bind_new_buffer_to_attribute(&ctx, point_color_attr, (COLOR_SIZE + 1) as i32, scene.points.colors_with_opacity.concat().as_slice());
                    bind_new_buffer_to_attribute(&ctx, point_highlight_attr, 1 as i32, scene.points.highlights.as_slice());
                    bind_new_buffer_to_attribute(&ctx, point_selection_attr, 1 as i32, scene.points.selections.as_slice());
-
+                    
                    // draw the scene
                    ctx.draw_arrays(WebGl2RenderingContext::POINTS, 0, point_positions.ncols() as i32);
-
+                    
                    // disable the point program's vertex attributes
                    ctx.disable_vertex_attrib_array(point_position_attr);
                    ctx.disable_vertex_attrib_array(point_color_attr);
                    ctx.disable_vertex_attrib_array(point_highlight_attr);
                    ctx.disable_vertex_attrib_array(point_selection_attr);
                }
-
+                
                // --- update the display state ---
-
+                
                // update the viewpoint
                assembly_to_world.set(asm_to_world);
-
+                
                // clear the scene change flag
                scene_changed.set(
                    pitch_up_val != 0.0
@ -799,7 +760,7 @@ pub fn Display() -> View {
        });
        start_animation_loop();
    });
-
+    
    let set_nav_signal = move |event: &KeyboardEvent, value: f64| {
        let mut navigating = true;
        let shift = event.shift_key();
@ -812,14 +773,14 @@ pub fn Display() -> View {
            "ArrowLeft" if shift => roll_ccw.set(value),
            "ArrowRight" => yaw_right.set(value),
            "ArrowLeft" => yaw_left.set(value),
-            _ => navigating = false,
+            _ => navigating = false
        };
        if navigating {
            scene_changed.set(true);
            event.prevent_default();
        }
    };
-
+    
    let set_manip_signal = move |event: &KeyboardEvent, value: f64| {
        let mut manipulating = true;
        let shift = event.shift_key();
@ -832,24 +793,24 @@ pub fn Display() -> View {
            "s" | "S" => translate_neg_y.set(value),
            "]" | "}" => shrink_neg.set(value),
            "[" | "{" => shrink_pos.set(value),
-            _ => manipulating = false,
+            _ => manipulating = false
        };
        if manipulating {
            event.prevent_default();
        }
    };
-
+    
    view! {
        /* TO DO */
        // switch back to integer-valued parameters when that becomes possible
        // again
        canvas(
-            ref = display,
+            ref=display,
-            id = "display",
+            id="display",
-            width = "600",
+            width="600",
-            height = "600",
+            height="600",
-            tabindex = "0",
+            tabindex="0",
-            on:keydown = move |event: KeyboardEvent| {
+            on:keydown=move |event: KeyboardEvent| {
                if event.key() == "Shift" {
                    // swap navigation inputs
                    roll_cw.set(yaw_right.get());
@ -860,7 +821,7 @@ 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());
@ -875,7 +836,7 @@ pub fn Display() -> View {
                    set_manip_signal(&event, 1.0);
                }
            },
-            on:keyup = move |event: KeyboardEvent| {
+            on:keyup=move |event: KeyboardEvent| {
                if event.key() == "Shift" {
                    // swap navigation inputs
                    yaw_right.set(roll_cw.get());
@ -886,7 +847,7 @@ 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());
@ -897,7 +858,7 @@ pub fn Display() -> View {
                    set_manip_signal(&event, 0.0);
                }
            },
-            on:blur = move |_| {
+            on:blur=move |_| {
                pitch_up.set(0.0);
                pitch_down.set(0.0);
                yaw_right.set(0.0);
@ -905,7 +866,7 @@ pub fn Display() -> View {
                roll_ccw.set(0.0);
                roll_cw.set(0.0);
            },
-            on:click = move |event: MouseEvent| {
+            on:click=move |event: MouseEvent| {
                // find the nearest element along the pointer direction
                let (dir, pixel_size) = event_dir(&event);
                console::log_1(&JsValue::from(dir.to_string()));
@ -922,18 +883,18 @@ pub fn Display() -> View {
                                    clicked = Some((elt, depth))
                                }
                            },
-                            None => clicked = Some((elt, depth)),
+                            None => clicked = Some((elt, depth))
-                        },
+                        }
-                        None => (),
+                        None => ()
                    };
                }
-
+                
                // if we clicked something, select it
                match clicked {
                    Some((elt, _)) => state.select(&elt, event.shift_key()),
-                    None => state.selection.update(|sel| sel.clear()),
+                    None => state.selection.update(|sel| sel.clear())
                };
-            },
+            }
        )
    }
-}
+}
--- a/app-proto/src/components/outline.rs
+++ b/app-proto/src/components/outline.rs
@ -1,7 +1,11 @@
 use itertools::Itertools;
 use std::rc::Rc;
 use sycamore::prelude::*;
-use web_sys::{KeyboardEvent, MouseEvent, wasm_bindgen::JsCast};
+use web_sys::{
    KeyboardEvent,
    MouseEvent,
    wasm_bindgen::JsCast
 };
 use crate::{
    AppState,
@ -9,8 +13,7 @@ use crate::{
        Element,
        HalfCurvatureRegulator,
        InversiveDistanceRegulator,
-        PointCoordinateRegulator,
+        Regulator
        Regulator,
    },
    specified::SpecifiedValue
 };
@ -21,16 +24,16 @@ fn RegulatorInput(regulator: Rc<dyn Regulator>) -> View {
    // get the regulator's measurement and set point signals
    let measurement = regulator.measurement();
    let set_point = regulator.set_point();
-
+    
    // the `valid` signal tracks whether the last entered value is a valid set
    // point specification
    let valid = create_signal(true);
-
+    
    // the `value` signal holds the current set point specification
    let value = create_signal(
        set_point.with_untracked(|set_pt| set_pt.spec.clone())
    );
-
+    
    // this `reset_value` closure resets the input value to the regulator's set
    // point specification
    let reset_value = move || {
@ -39,15 +42,15 @@ fn RegulatorInput(regulator: Rc<dyn Regulator>) -> View {
            value.set(set_point.with(|set_pt| set_pt.spec.clone()));
        })
    };
-
+    
    // reset the input value whenever the regulator's set point specification
    // is updated
    create_effect(reset_value);
-
+    
    view! {
        input(
-            r#type = "text",
+            r#type="text",
-            class = move || {
+            class=move || {
                if valid.get() {
                    set_point.with(|set_pt| {
                        if set_pt.is_present() {
@ -60,27 +63,27 @@ fn RegulatorInput(regulator: Rc<dyn Regulator>) -> View {
                    "regulator-input invalid"
                }
            },
-            placeholder = measurement.with(|result| result.to_string()),
+            placeholder=measurement.with(|result| result.to_string()),
-            bind:value = value,
+            bind:value=value,
-            on:change = move |_| {
+            on:change=move |_| {
                valid.set(
                    match SpecifiedValue::try_from(value.get_clone_untracked()) {
                        Ok(set_pt) => {
                            set_point.set(set_pt);
                            true
-                        },
+                        }
-                        Err(_) => false,
+                        Err(_) => false
                    }
                )
            },
-            on:keydown = {
+            on:keydown={
                move |event: KeyboardEvent| {
                    match event.key().as_str() {
                        "Escape" => reset_value(),
-                        _ => (),
+                        _ => ()
                    }
                }
-            },
+            }
        )
    }
 }
@ -97,11 +100,11 @@ impl OutlineItem for InversiveDistanceRegulator {
            self.subjects[0].label()
        }.clone();
        view! {
-            li(class = "regulator") {
+            li(class="regulator") {
-                div(class = "regulator-label") { (other_subject_label) }
+                div(class="regulator-label") { (other_subject_label) }
-                div(class = "regulator-type") { "Inversive distance" }
+                div(class="regulator-type") { "Inversive distance" }
-                RegulatorInput(regulator = self)
+                RegulatorInput(regulator=self)
-                div(class = "status")
+                div(class="status")
            }
        }
    }
@ -110,25 +113,11 @@ impl OutlineItem for InversiveDistanceRegulator {
 impl OutlineItem for HalfCurvatureRegulator {
    fn outline_item(self: Rc<Self>, _element: &Rc<dyn Element>) -> View {
        view! {
-            li(class = "regulator") {
+            li(class="regulator") {
-                div(class = "regulator-label") // for spacing
+                div(class="regulator-label") // for spacing
-                div(class = "regulator-type") { "Half-curvature" }
+                div(class="regulator-type") { "Half-curvature" }
-                RegulatorInput(regulator = self)
+                RegulatorInput(regulator=self)
-                div(class = "status")
+                div(class="status")
            }
        }
    }
 }
 impl OutlineItem for PointCoordinateRegulator {
    fn outline_item(self: Rc<Self>, _element: &Rc<dyn Element>) -> View {
        let name = format!("{} coordinate", self.axis);
        view! {
            li(class = "regulator") {
                div(class = "regulator-label") // for spacing
                div(class = "regulator-type") { (name) }
                RegulatorInput(regulator = self)
                div(class = "status")
            }
        }
    }
@ -167,10 +156,10 @@ fn ElementOutlineItem(element: Rc<dyn Element>) -> View {
    let details_node = create_node_ref();
    view! {
        li {
-            details(ref = details_node) {
+            details(ref=details_node) {
                summary(
-                    class = class.get(),
+                    class=class.get(),
-                    on:keydown = {
+                    on:keydown={
                        let element_for_handler = element.clone();
                        move |event: KeyboardEvent| {
                            match event.key().as_str() {
@ -190,18 +179,18 @@ fn ElementOutlineItem(element: Rc<dyn Element>) -> View {
                                        .unchecked_into::<web_sys::Element>()
                                        .remove_attribute("open");
                                },
-                                _ => (),
+                                _ => ()
                            }
                        }
                    }
                ) {
                    div(
-                        class = "element-switch",
+                        class="element-switch",
-                        on:click = |event: MouseEvent| event.stop_propagation()
+                        on:click=|event: MouseEvent| event.stop_propagation()
                    )
                    div(
-                        class = "element",
+                        class="element",
-                        on:click = {
+                        on:click={
                            let state_for_handler = state.clone();
                            let element_for_handler = element.clone();
                            move |event: MouseEvent| {
@ -211,20 +200,20 @@ fn ElementOutlineItem(element: Rc<dyn Element>) -> View {
                            }
                        }
                    ) {
-                        div(class = "element-label") { (label) }
+                        div(class="element-label") { (label) }
-                        div(class = "element-representation") { (rep_components) }
+                        div(class="element-representation") { (rep_components) }
                        input(
-                            r#type = "checkbox",
+                            r#type="checkbox",
-                            bind:checked = element.ghost(),
+                            bind:checked=element.ghost(),
-                            on:click = |event: MouseEvent| event.stop_propagation()
+                            on:click=|event: MouseEvent| event.stop_propagation()
                        )
                    }
                }
-                ul(class = "regulators") {
+                ul(class="regulators") {
                    Keyed(
-                        list = regulator_list,
+                        list=regulator_list,
-                        view = move |reg| reg.outline_item(&element),
+                        view=move |reg| reg.outline_item(&element),
-                        key = |reg| reg.serial()
+                        key=|reg| reg.serial()
                    )
                }
            }
@ -241,7 +230,7 @@ fn ElementOutlineItem(element: Rc<dyn Element>) -> View {
 #[component]
 pub fn Outline() -> View {
    let state = use_context::<AppState>();
-
+    
    // list the elements alphabetically by ID
    /* TO DO */
    // this code is designed to generalize easily to other sort keys. if we only
@ -254,22 +243,22 @@ pub fn Outline() -> View {
            .sorted_by_key(|elt| elt.id().clone())
            .collect::<Vec<_>>()
    );
-
+    
    view! {
        ul(
-            id = "outline",
+            id="outline",
-            on:click = {
+            on:click={
                let state = use_context::<AppState>();
                move |_| state.selection.update(|sel| sel.clear())
            }
        ) {
            Keyed(
-                list = element_list,
+                list=element_list,
-                view = |elt| view! {
+                view=|elt| view! {
-                    ElementOutlineItem(element = elt)
+                    ElementOutlineItem(element=elt)
                },
-                key = |elt| elt.serial()
+                key=|elt| elt.serial()
            )
        }
    }
-}
+}
--- a/app-proto/src/components/point.frag
+++ b/app-proto/src/components/point.frag
@ -10,10 +10,10 @@ out vec4 outColor;
 void main() {
    float r = total_radius * length(2.*gl_PointCoord - vec2(1.));
-
+    
    const float POINT_RADIUS = 4.;
    float border = smoothstep(POINT_RADIUS - 1., POINT_RADIUS, r);
    float disk = 1. - smoothstep(total_radius - 1., total_radius, r);
    vec4 color = mix(point_color, vec4(1.), border * point_highlight);
    outColor = vec4(vec3(1.), disk) * color;
-}
+}
--- a/app-proto/src/components/point.vert
+++ b/app-proto/src/components/point.vert
@ -14,11 +14,11 @@ const float focal_slope = 0.3;
 void main() {
    total_radius = 5. + 0.5*selected;
-
+    
    float depth = -focal_slope * position.z;
    gl_Position = vec4(position.xy / depth, 0., 1.);
    gl_PointSize = 2.*total_radius;
-
+    
    point_color = color;
    point_highlight = highlight;
-}
+}
--- a/app-proto/src/components/spheres.frag
+++ b/app-proto/src/components/spheres.frag
@ -75,7 +75,7 @@ Fragment sphere_shading(vecInv v, vec3 pt, vec4 base_color) {
    // point. i calculated it in my head and decided that the result looked good
    // enough for now
    vec3 normal = normalize(-v.sp + 2.*v.lt.s*pt);
-
+    
    float incidence = dot(normal, light_dir);
    float illum = mix(0.4, 1.0, max(incidence, 0.0));
    return Fragment(pt, normal, vec4(illum * base_color.rgb, base_color.a));
@ -110,7 +110,7 @@ vec2 sphere_cast(vecInv v, vec3 dir) {
    float a = -v.lt.s * dot(dir, dir);
    float b = dot(v.sp, dir);
    float c = -v.lt.t;
-
+    
    float adjust = 4.*a*c/(b*b);
    if (adjust < 1.) {
        // as long as `b` is non-zero, the linear approximation of
@ -136,7 +136,7 @@ vec2 sphere_cast(vecInv v, vec3 dir) {
 void main() {
    vec2 scr = (2.*gl_FragCoord.xy - resolution) / shortdim;
    vec3 dir = vec3(focal_slope * scr, -1.);
-
+    
    // cast rays through the spheres
    const int LAYER_MAX = 12;
    TaggedDepth top_hits [LAYER_MAX];
@ -144,7 +144,7 @@ void main() {
    for (int id = 0; id < sphere_cnt; ++id) {
        // find out where the ray hits the sphere
        vec2 hit_depths = sphere_cast(sphere_list[id], dir);
-
+        
        // insertion-sort the points we hit into the hit list
        float dimming = 1.;
        for (int side = 0; side < 2; ++side) {
@ -169,14 +169,14 @@ void main() {
            }
        }
    }
-
+    
    /* DEBUG */
    // in debug mode, show the layer count instead of the shaded image
    if (debug_mode) {
        // at the bottom of the screen, show the color scale instead of the
        // layer count
        if (gl_FragCoord.y < 10.) layer_cnt = int(16. * gl_FragCoord.x / resolution.x);
-
+        
        // convert number to color
        ivec3 bits = layer_cnt / ivec3(1, 2, 4);
        vec3 color = mod(vec3(bits), 2.);
@ -186,7 +186,7 @@ void main() {
        outColor = vec4(color, 1.);
        return;
    }
-
+    
    // composite the sphere fragments
    vec3 color = vec3(0.);
    int layer = layer_cnt - 1;
@ -203,7 +203,7 @@ void main() {
        // load the current fragment
        Fragment frag = frag_next;
        float highlight = highlight_next;
-
+        
        // shade the next fragment
        hit = top_hits[layer];
        sphere_color = color_list[hit.id];
@ -213,23 +213,23 @@ void main() {
            vec4(hit.dimming * sphere_color.rgb, sphere_color.a)
        );
        highlight_next = highlight_list[hit.id];
-
+        
        // highlight intersections
        float ixn_dist = intersection_dist(frag, frag_next);
        float max_highlight = max(highlight, highlight_next);
        float ixn_highlight = 0.5 * max_highlight * (1. - smoothstep(2./3.*ixn_threshold, 1.5*ixn_threshold, ixn_dist));
        frag.color = mix(frag.color, vec4(1.), ixn_highlight);
        frag_next.color = mix(frag_next.color, vec4(1.), ixn_highlight);
-
+        
        // highlight cusps
        float cusp_cos = abs(dot(dir, frag.normal));
        float cusp_threshold = 2.*sqrt(ixn_threshold * sphere_list[hit.id].lt.s);
        float cusp_highlight = highlight * (1. - smoothstep(2./3.*cusp_threshold, 1.5*cusp_threshold, cusp_cos));
        frag.color = mix(frag.color, vec4(1.), cusp_highlight);
-
+        
        // composite the current fragment
        color = mix(color, frag.color.rgb, frag.color.a);
    }
    color = mix(color, frag_next.color.rgb, frag_next.color.a);
    outColor = vec4(sRGB(color), 1.);
-}
+}
--- a/app-proto/src/components/test_assembly_chooser.rs
+++ b/app-proto/src/components/test_assembly_chooser.rs
@ -6,17 +6,17 @@ use web_sys::{console, wasm_bindgen::JsValue};
 use crate::{
    AppState,
    engine,
    engine::DescentHistory,
    assembly::{
        Assembly,
        Element,
        ElementColor,
        InversiveDistanceRegulator,
        Point,
-        Sphere,
+        Sphere
    },
-    engine,
+    specified::SpecifiedValue
    engine::DescentHistory,
    specified::SpecifiedValue,
 };
 // --- loaders ---
@ -26,13 +26,13 @@ use crate::{
 // done more work on saving and loading assemblies, we should come back to this
 // code to see if it can be simplified
-fn load_general(assembly: &Assembly) {
+fn load_gen_assemb(assembly: &Assembly) {
    let _ = assembly.try_insert_element(
        Sphere::new(
            String::from("gemini_a"),
            String::from("Castor"),
            [1.00_f32, 0.25_f32, 0.00_f32],
-            engine::sphere(0.5, 0.5, 0.0, 1.0),
+            engine::sphere(0.5, 0.5, 0.0, 1.0)
        )
    );
    let _ = assembly.try_insert_element(
@ -40,7 +40,7 @@ fn load_general(assembly: &Assembly) {
            String::from("gemini_b"),
            String::from("Pollux"),
            [0.00_f32, 0.25_f32, 1.00_f32],
-            engine::sphere(-0.5, -0.5, 0.0, 1.0),
+            engine::sphere(-0.5, -0.5, 0.0, 1.0)
        )
    );
    let _ = assembly.try_insert_element(
@ -48,7 +48,7 @@ fn load_general(assembly: &Assembly) {
            String::from("ursa_major"),
            String::from("Ursa major"),
            [0.25_f32, 0.00_f32, 1.00_f32],
-            engine::sphere(-0.5, 0.5, 0.0, 0.75),
+            engine::sphere(-0.5, 0.5, 0.0, 0.75)
        )
    );
    let _ = assembly.try_insert_element(
@ -56,7 +56,7 @@ fn load_general(assembly: &Assembly) {
            String::from("ursa_minor"),
            String::from("Ursa minor"),
            [0.25_f32, 1.00_f32, 0.00_f32],
-            engine::sphere(0.5, -0.5, 0.0, 0.5),
+            engine::sphere(0.5, -0.5, 0.0, 0.5)
        )
    );
    let _ = assembly.try_insert_element(
@ -64,7 +64,7 @@ fn load_general(assembly: &Assembly) {
            String::from("moon_deimos"),
            String::from("Deimos"),
            [0.75_f32, 0.75_f32, 0.00_f32],
-            engine::sphere(0.0, 0.15, 1.0, 0.25),
+            engine::sphere(0.0, 0.15, 1.0, 0.25)
        )
    );
    let _ = assembly.try_insert_element(
@ -72,12 +72,12 @@ fn load_general(assembly: &Assembly) {
            String::from("moon_phobos"),
            String::from("Phobos"),
            [0.00_f32, 0.75_f32, 0.50_f32],
-            engine::sphere(0.0, -0.15, -1.0, 0.25),
+            engine::sphere(0.0, -0.15, -1.0, 0.25)
        )
    );
 }
-fn load_low_curvature(assembly: &Assembly) {
+fn load_low_curv_assemb(assembly: &Assembly) {
    // create the spheres
    let a = 0.75_f64.sqrt();
    let _ = assembly.try_insert_element(
@ -85,7 +85,7 @@ fn load_low_curvature(assembly: &Assembly) {
            "central".to_string(),
            "Central".to_string(),
            [0.75_f32, 0.75_f32, 0.75_f32],
-            engine::sphere(0.0, 0.0, 0.0, 1.0),
+            engine::sphere(0.0, 0.0, 0.0, 1.0)
        )
    );
    let _ = assembly.try_insert_element(
@ -93,7 +93,7 @@ fn load_low_curvature(assembly: &Assembly) {
            "assemb_plane".to_string(),
            "Assembly plane".to_string(),
            [0.75_f32, 0.75_f32, 0.75_f32],
-            engine::sphere_with_offset(0.0, 0.0, 1.0, 0.0, 0.0),
+            engine::sphere_with_offset(0.0, 0.0, 1.0, 0.0, 0.0)
        )
    );
    let _ = assembly.try_insert_element(
@ -101,7 +101,7 @@ fn load_low_curvature(assembly: &Assembly) {
            "side1".to_string(),
            "Side 1".to_string(),
            [1.00_f32, 0.00_f32, 0.25_f32],
-            engine::sphere_with_offset(1.0, 0.0, 0.0, 1.0, 0.0),
+            engine::sphere_with_offset(1.0, 0.0, 0.0, 1.0, 0.0)
        )
    );
    let _ = assembly.try_insert_element(
@ -109,7 +109,7 @@ fn load_low_curvature(assembly: &Assembly) {
            "side2".to_string(),
            "Side 2".to_string(),
            [0.25_f32, 1.00_f32, 0.00_f32],
-            engine::sphere_with_offset(-0.5, a, 0.0, 1.0, 0.0),
+            engine::sphere_with_offset(-0.5, a, 0.0, 1.0, 0.0)
        )
    );
    let _ = assembly.try_insert_element(
@ -117,7 +117,7 @@ fn load_low_curvature(assembly: &Assembly) {
            "side3".to_string(),
            "Side 3".to_string(),
            [0.00_f32, 0.25_f32, 1.00_f32],
-            engine::sphere_with_offset(-0.5, -a, 0.0, 1.0, 0.0),
+            engine::sphere_with_offset(-0.5, -a, 0.0, 1.0, 0.0)
        )
    );
    let _ = assembly.try_insert_element(
@ -125,7 +125,7 @@ fn load_low_curvature(assembly: &Assembly) {
            "corner1".to_string(),
            "Corner 1".to_string(),
            [0.75_f32, 0.75_f32, 0.75_f32],
-            engine::sphere(-4.0/3.0, 0.0, 0.0, 1.0/3.0),
+            engine::sphere(-4.0/3.0, 0.0, 0.0, 1.0/3.0)
        )
    );
    let _ = assembly.try_insert_element(
@ -133,7 +133,7 @@ fn load_low_curvature(assembly: &Assembly) {
            "corner2".to_string(),
            "Corner 2".to_string(),
            [0.75_f32, 0.75_f32, 0.75_f32],
-            engine::sphere(2.0/3.0, -4.0/3.0 * a, 0.0, 1.0/3.0),
+            engine::sphere(2.0/3.0, -4.0/3.0 * a, 0.0, 1.0/3.0)
        )
    );
    let _ = assembly.try_insert_element(
@ -141,10 +141,10 @@ fn load_low_curvature(assembly: &Assembly) {
            String::from("corner3"),
            String::from("Corner 3"),
            [0.75_f32, 0.75_f32, 0.75_f32],
-            engine::sphere(2.0/3.0, 4.0/3.0 * a, 0.0, 1.0/3.0),
+            engine::sphere(2.0/3.0, 4.0/3.0 * a, 0.0, 1.0/3.0)
        )
    );
-
+    
    // impose the desired tangencies and make the sides planar
    let index_range = 1..=3;
    let [central, assemb_plane] = ["central", "assemb_plane"].map(
@ -196,13 +196,13 @@ fn load_low_curvature(assembly: &Assembly) {
    }
 }
-fn load_pointed(assembly: &Assembly) {
+fn load_pointed_assemb(assembly: &Assembly) {
    let _ = assembly.try_insert_element(
        Point::new(
            format!("point_front"),
            format!("Front point"),
            [0.75_f32, 0.75_f32, 0.75_f32],
-            engine::point(0.0, 0.0, FRAC_1_SQRT_2),
+            engine::point(0.0, 0.0, FRAC_1_SQRT_2)
        )
    );
    let _ = assembly.try_insert_element(
@ -210,29 +210,29 @@ fn load_pointed(assembly: &Assembly) {
            format!("point_back"),
            format!("Back point"),
            [0.75_f32, 0.75_f32, 0.75_f32],
-            engine::point(0.0, 0.0, -FRAC_1_SQRT_2),
+            engine::point(0.0, 0.0, -FRAC_1_SQRT_2)
        )
    );
    for index_x in 0..=1 {
        for index_y in 0..=1 {
            let x = index_x as f64 - 0.5;
            let y = index_y as f64 - 0.5;
-
+            
            let _ = assembly.try_insert_element(
                Sphere::new(
                    format!("sphere{index_x}{index_y}"),
                    format!("Sphere {index_x}{index_y}"),
                    [0.5*(1.0 + x) as f32, 0.5*(1.0 + y) as f32, 0.5*(1.0 - x*y) as f32],
-                    engine::sphere(x, y, 0.0, 1.0),
+                    engine::sphere(x, y, 0.0, 1.0)
                )
            );
-
+            
            let _ = assembly.try_insert_element(
                Point::new(
                    format!("point{index_x}{index_y}"),
                    format!("Point {index_x}{index_y}"),
                    [0.5*(1.0 + x) as f32, 0.5*(1.0 + y) as f32, 0.5*(1.0 - x*y) as f32],
-                    engine::point(x, y, 0.0),
+                    engine::point(x, y, 0.0)
                )
            );
        }
@ -246,7 +246,7 @@ fn load_pointed(assembly: &Assembly) {
 //   B-C     "
 //   C-C     "
 //   A-C   -0.25 * φ^2 = -0.6545084971874737
-fn load_tridiminished_icosahedron(assembly: &Assembly) {
+fn load_tridim_icosahedron_assemb(assembly: &Assembly) {
    // create the vertices
    const COLOR_A: ElementColor = [1.00_f32, 0.25_f32, 0.25_f32];
    const COLOR_B: ElementColor = [0.75_f32, 0.75_f32, 0.75_f32];
@ -256,61 +256,61 @@ fn load_tridiminished_icosahedron(assembly: &Assembly) {
            "a1".to_string(),
            "A₁".to_string(),
            COLOR_A,
-            engine::point(0.25, 0.75, 0.75),
+            engine::point(0.25, 0.75, 0.75)
        ),
        Point::new(
            "a2".to_string(),
            "A₂".to_string(),
            COLOR_A,
-            engine::point(0.75, 0.25, 0.75),
+            engine::point(0.75, 0.25, 0.75)
        ),
        Point::new(
            "a3".to_string(),
            "A₃".to_string(),
            COLOR_A,
-            engine::point(0.75, 0.75, 0.25),
+            engine::point(0.75, 0.75, 0.25)
        ),
        Point::new(
            "b1".to_string(),
            "B₁".to_string(),
            COLOR_B,
-            engine::point(0.75, -0.25, -0.25),
+            engine::point(0.75, -0.25, -0.25)
        ),
        Point::new(
            "b2".to_string(),
            "B₂".to_string(),
            COLOR_B,
-            engine::point(-0.25, 0.75, -0.25),
+            engine::point(-0.25, 0.75, -0.25)
        ),
        Point::new(
            "b3".to_string(),
            "B₃".to_string(),
            COLOR_B,
-            engine::point(-0.25, -0.25, 0.75),
+            engine::point(-0.25, -0.25, 0.75)
        ),
        Point::new(
            "c1".to_string(),
            "C₁".to_string(),
            COLOR_C,
-            engine::point(0.0, -1.0, -1.0),
+            engine::point(0.0, -1.0, -1.0)
        ),
        Point::new(
            "c2".to_string(),
            "C₂".to_string(),
            COLOR_C,
-            engine::point(-1.0, 0.0, -1.0),
+            engine::point(-1.0, 0.0, -1.0)
        ),
        Point::new(
            "c3".to_string(),
            "C₃".to_string(),
            COLOR_C,
-            engine::point(-1.0, -1.0, 0.0),
+            engine::point(-1.0, -1.0, 0.0)
-        ),
+        )
    ];
    for vertex in vertices {
        let _ = assembly.try_insert_element(vertex);
    }
-
+    
    // create the faces
    const COLOR_FACE: ElementColor = [0.75_f32, 0.75_f32, 0.75_f32];
    let frac_1_sqrt_6 = 1.0 / 6.0_f64.sqrt();
@ -320,26 +320,26 @@ fn load_tridiminished_icosahedron(assembly: &Assembly) {
            "face1".to_string(),
            "Face 1".to_string(),
            COLOR_FACE,
-            engine::sphere_with_offset(frac_2_sqrt_6, -frac_1_sqrt_6, -frac_1_sqrt_6, -frac_1_sqrt_6, 0.0),
+            engine::sphere_with_offset(frac_2_sqrt_6, -frac_1_sqrt_6, -frac_1_sqrt_6, -frac_1_sqrt_6, 0.0)
        ),
        Sphere::new(
            "face2".to_string(),
            "Face 2".to_string(),
            COLOR_FACE,
-            engine::sphere_with_offset(-frac_1_sqrt_6, frac_2_sqrt_6, -frac_1_sqrt_6, -frac_1_sqrt_6, 0.0),
+            engine::sphere_with_offset(-frac_1_sqrt_6, frac_2_sqrt_6, -frac_1_sqrt_6, -frac_1_sqrt_6, 0.0)
        ),
        Sphere::new(
            "face3".to_string(),
            "Face 3".to_string(),
            COLOR_FACE,
-            engine::sphere_with_offset(-frac_1_sqrt_6, -frac_1_sqrt_6, frac_2_sqrt_6, -frac_1_sqrt_6, 0.0),
+            engine::sphere_with_offset(-frac_1_sqrt_6, -frac_1_sqrt_6, frac_2_sqrt_6, -frac_1_sqrt_6, 0.0)
-        ),
+        )
    ];
    for face in faces {
        face.ghost().set(true);
        let _ = assembly.try_insert_element(face);
    }
-
+    
    let index_range = 1..=3;
    for j in index_range.clone() {
        // make each face planar
@ -352,7 +352,7 @@ fn load_tridiminished_icosahedron(assembly: &Assembly) {
        curvature_regulator.set_point().set(
            SpecifiedValue::try_from("0".to_string()).unwrap()
        );
-
+        
        // put each A vertex on the face it belongs to
        let vertex_a = assembly.elements_by_id.with_untracked(
            |elts_by_id| elts_by_id[&format!("a{j}")].clone()
@ -360,7 +360,7 @@ fn load_tridiminished_icosahedron(assembly: &Assembly) {
        let incidence_a = InversiveDistanceRegulator::new([face.clone(), vertex_a.clone()]);
        incidence_a.set_point.set(SpecifiedValue::try_from("0".to_string()).unwrap());
        assembly.insert_regulator(Rc::new(incidence_a));
-
+        
        // regulate the B-C vertex distances
        let vertices_bc = ["b", "c"].map(
            |series| assembly.elements_by_id.with_untracked(
@ -370,10 +370,10 @@ fn load_tridiminished_icosahedron(assembly: &Assembly) {
        assembly.insert_regulator(
            Rc::new(InversiveDistanceRegulator::new(vertices_bc))
        );
-
+        
        // get the pair of indices adjacent to `j`
        let adjacent_indices = [j % 3 + 1, (j + 1) % 3 + 1];
-
+        
        for k in adjacent_indices.clone() {
            for series in ["b", "c"] {
                // put each B and C vertex on the faces it belongs to
@ -383,14 +383,14 @@ fn load_tridiminished_icosahedron(assembly: &Assembly) {
                let incidence = InversiveDistanceRegulator::new([face.clone(), vertex.clone()]);
                incidence.set_point.set(SpecifiedValue::try_from("0".to_string()).unwrap());
                assembly.insert_regulator(Rc::new(incidence));
-
+                
                // regulate the A-B and A-C vertex distances
                assembly.insert_regulator(
                    Rc::new(InversiveDistanceRegulator::new([vertex_a.clone(), vertex]))
                );
            }
        }
-
+        
        // regulate the A-A and C-C vertex distances
        let adjacent_pairs = ["a", "c"].map(
            |series| adjacent_indices.map(
@ -409,27 +409,27 @@ fn load_tridiminished_icosahedron(assembly: &Assembly) {
 // to finish describing the dodecahedral circle packing, set the inversive
 // distance regulators to -1. some of the regulators have already been set
-fn load_dodecahedral_packing(assembly: &Assembly) {
+fn load_dodeca_packing_assemb(assembly: &Assembly) {
    // add the substrate
    let _ = assembly.try_insert_element(
        Sphere::new(
            "substrate".to_string(),
            "Substrate".to_string(),
            [0.75_f32, 0.75_f32, 0.75_f32],
-            engine::sphere(0.0, 0.0, 0.0, 1.0),
+            engine::sphere(0.0, 0.0, 0.0, 1.0)
        )
    );
    let substrate = assembly.elements_by_id.with_untracked(
        |elts_by_id| elts_by_id["substrate"].clone()
    );
-
+    
    // fix the substrate's curvature
    substrate.regulators().with_untracked(
        |regs| regs.first().unwrap().clone()
    ).set_point().set(
        SpecifiedValue::try_from("0.5".to_string()).unwrap()
    );
-
+    
    // add the circles to be packed
    const COLOR_A: ElementColor = [1.00_f32, 0.25_f32, 0.00_f32];
    const COLOR_B: ElementColor = [1.00_f32, 0.00_f32, 0.25_f32];
@ -445,10 +445,10 @@ fn load_dodecahedral_packing(assembly: &Assembly) {
        for k in 0..2 {
            let small_coord = face_scales[k] * (2.0*(j as f64) - 1.0);
            let big_coord = face_scales[k] * (2.0*(k as f64) - 1.0) * phi;
-
+            
            let id_num = format!("{j}{k}");
            let label_sub = format!("{}{}", subscripts[j], subscripts[k]);
-
+            
            // add the A face
            let id_a = format!("a{id_num}");
            let _ = assembly.try_insert_element(
@ -456,7 +456,7 @@ fn load_dodecahedral_packing(assembly: &Assembly) {
                    id_a.clone(),
                    format!("A{label_sub}"),
                    COLOR_A,
-                    engine::sphere(0.0, small_coord, big_coord, face_radii[k]),
+                    engine::sphere(0.0, small_coord, big_coord, face_radii[k])
                )
            );
            faces.push(
@ -464,7 +464,7 @@ fn load_dodecahedral_packing(assembly: &Assembly) {
                    |elts_by_id| elts_by_id[&id_a].clone()
                )
            );
-
+            
            // add the B face
            let id_b = format!("b{id_num}");
            let _ = assembly.try_insert_element(
@ -472,7 +472,7 @@ fn load_dodecahedral_packing(assembly: &Assembly) {
                    id_b.clone(),
                    format!("B{label_sub}"),
                    COLOR_B,
-                    engine::sphere(small_coord, big_coord, 0.0, face_radii[k]),
+                    engine::sphere(small_coord, big_coord, 0.0, face_radii[k])
                )
            );
            faces.push(
@ -480,7 +480,7 @@ fn load_dodecahedral_packing(assembly: &Assembly) {
                    |elts_by_id| elts_by_id[&id_b].clone()
                )
            );
-
+            
            // add the C face
            let id_c = format!("c{id_num}");
            let _ = assembly.try_insert_element(
@ -488,7 +488,7 @@ fn load_dodecahedral_packing(assembly: &Assembly) {
                    id_c.clone(),
                    format!("C{label_sub}"),
                    COLOR_C,
-                    engine::sphere(big_coord, 0.0, small_coord, face_radii[k]),
+                    engine::sphere(big_coord, 0.0, small_coord, face_radii[k])
                )
            );
            faces.push(
@ -498,14 +498,14 @@ fn load_dodecahedral_packing(assembly: &Assembly) {
            );
        }
    }
-
+    
    // make each face sphere perpendicular to the substrate
    for face in faces {
        let right_angle = InversiveDistanceRegulator::new([face, substrate.clone()]);
        right_angle.set_point.set(SpecifiedValue::try_from("0".to_string()).unwrap());
        assembly.insert_regulator(Rc::new(right_angle));
    }
-
+    
    // set up the tangencies that define the packing
    for [long_edge_plane, short_edge_plane] in [["a", "b"], ["b", "c"], ["c", "a"]] {
        for k in 0..2 {
@ -524,14 +524,14 @@ fn load_dodecahedral_packing(assembly: &Assembly) {
                    )
                )
            );
-
+            
            // set up the short-edge tangency
            let short_tangency = InversiveDistanceRegulator::new(short_edge.clone());
            if k == 0 {
                short_tangency.set_point.set(SpecifiedValue::try_from("-1".to_string()).unwrap());
            }
            assembly.insert_regulator(Rc::new(short_tangency));
-
+            
            // set up the side tangencies
            for i in 0..2 {
                for j in 0..2 {
@ -550,7 +550,7 @@ fn load_dodecahedral_packing(assembly: &Assembly) {
 // the initial configuration of this test assembly deliberately violates the
 // constraints, so loading the assembly will trigger a non-trivial realization
-fn load_balanced(assembly: &Assembly) {
+fn load_balanced_assemb(assembly: &Assembly) {
    // create the spheres
    const R_OUTER: f64 = 10.0;
    const R_INNER: f64 = 4.0;
@ -559,37 +559,37 @@ fn load_balanced(assembly: &Assembly) {
            "outer".to_string(),
            "Outer".to_string(),
            [0.75_f32, 0.75_f32, 0.75_f32],
-            engine::sphere(0.0, 0.0, 0.0, R_OUTER),
+            engine::sphere(0.0, 0.0, 0.0, R_OUTER)
        ),
        Sphere::new(
            "a".to_string(),
            "A".to_string(),
            [1.00_f32, 0.00_f32, 0.25_f32],
-            engine::sphere(0.0, 4.0, 0.0, R_INNER),
+            engine::sphere(0.0, 4.0, 0.0, R_INNER)
        ),
        Sphere::new(
            "b".to_string(),
            "B".to_string(),
            [0.00_f32, 0.25_f32, 1.00_f32],
-            engine::sphere(0.0, -4.0, 0.0, R_INNER),
+            engine::sphere(0.0, -4.0, 0.0, R_INNER)
        ),
    ];
    for sphere in spheres {
        let _ = assembly.try_insert_element(sphere);
    }
-
+    
    // get references to the spheres
    let [outer, a, b] = ["outer", "a", "b"].map(
        |id| assembly.elements_by_id.with_untracked(
            |elts_by_id| elts_by_id[id].clone()
        )
    );
-
+    
    // fix the diameters of the outer, sun, and moon spheres
    for (sphere, radius) in [
        (outer.clone(), R_OUTER),
        (a.clone(), R_INNER),
-        (b.clone(), R_INNER),
+        (b.clone(), R_INNER)
    ] {
        let curvature_regulator = sphere.regulators().with_untracked(
            |regs| regs.first().unwrap().clone()
@ -599,7 +599,7 @@ fn load_balanced(assembly: &Assembly) {
            SpecifiedValue::try_from(curvature.to_string()).unwrap()
        );
    }
-
+    
    // set the inversive distances between the spheres. as described above, the
    // initial configuration deliberately violates these constraints
    for inner in [a, b] {
@ -611,14 +611,14 @@ fn load_balanced(assembly: &Assembly) {
 // the initial configuration of this test assembly deliberately violates the
 // constraints, so loading the assembly will trigger a non-trivial realization
-fn load_off_center(assembly: &Assembly) {
+fn load_off_center_assemb(assembly: &Assembly) {
    // create a point almost at the origin and a sphere centered on the origin
    let _ = assembly.try_insert_element(
        Point::new(
            "point".to_string(),
            "Point".to_string(),
            [0.75_f32, 0.75_f32, 0.75_f32],
-            engine::point(1e-9, 0.0, 0.0),
+            engine::point(1e-9, 0.0, 0.0)
        ),
    );
    let _ = assembly.try_insert_element(
@ -626,17 +626,17 @@ fn load_off_center(assembly: &Assembly) {
            "sphere".to_string(),
            "Sphere".to_string(),
            [0.75_f32, 0.75_f32, 0.75_f32],
-            engine::sphere(0.0, 0.0, 0.0, 1.0),
+            engine::sphere(0.0, 0.0, 0.0, 1.0)
        ),
    );
-
+    
    // get references to the elements
    let point_and_sphere = ["point", "sphere"].map(
        |id| assembly.elements_by_id.with_untracked(
            |elts_by_id| elts_by_id[id].clone()
        )
    );
-
+    
    // put the point on the sphere
    let incidence = InversiveDistanceRegulator::new(point_and_sphere);
    incidence.set_point.set(SpecifiedValue::try_from("0".to_string()).unwrap());
@ -648,9 +648,9 @@ fn load_off_center(assembly: &Assembly) {
 // sqrt(1/6) and sqrt(3/2), respectively. to measure those radii, set an
 // inversive distance of -1 between the insphere and each face, and then set an
 // inversive distance of 0 between the circumsphere and each vertex
-fn load_radius_ratio(assembly: &Assembly) {
+fn load_radius_ratio_assemb(assembly: &Assembly) {
    let index_range = 1..=4;
-
+    
    // create the spheres
    const GRAY: ElementColor = [0.75_f32, 0.75_f32, 0.75_f32];
    let spheres = [
@ -658,19 +658,19 @@ fn load_radius_ratio(assembly: &Assembly) {
            "sphere_faces".to_string(),
            "Insphere".to_string(),
            GRAY,
-            engine::sphere(0.0, 0.0, 0.0, 0.5),
+            engine::sphere(0.0, 0.0, 0.0, 0.5)
        ),
        Sphere::new(
            "sphere_vertices".to_string(),
            "Circumsphere".to_string(),
            GRAY,
-            engine::sphere(0.0, 0.0, 0.0, 0.25),
+            engine::sphere(0.0, 0.0, 0.0, 0.25)
-        ),
+        )
    ];
    for sphere in spheres {
        let _ = assembly.try_insert_element(sphere);
    }
-
+    
    // create the vertices
    let vertices = izip!(
        index_range.clone(),
@ -678,13 +678,13 @@ fn load_radius_ratio(assembly: &Assembly) {
            [1.00_f32, 0.50_f32, 0.75_f32],
            [1.00_f32, 0.75_f32, 0.50_f32],
            [1.00_f32, 1.00_f32, 0.50_f32],
-            [0.75_f32, 0.50_f32, 1.00_f32],
+            [0.75_f32, 0.50_f32, 1.00_f32]
        ].into_iter(),
        [
            engine::point(-0.6, -0.8, -0.6),
            engine::point(-0.6, 0.8, 0.6),
            engine::point(0.6, -0.8, 0.6),
-            engine::point(0.6, 0.8, -0.6),
+            engine::point(0.6, 0.8, -0.6)
        ].into_iter()
    ).map(
        |(k, color, representation)| {
@ -692,14 +692,14 @@ fn load_radius_ratio(assembly: &Assembly) {
                format!("v{k}"),
                format!("Vertex {k}"),
                color,
-                representation,
+                representation
            )
        }
    );
    for vertex in vertices {
        let _ = assembly.try_insert_element(vertex);
    }
-
+    
    // create the faces
    let base_dir = Vector3::new(1.0, 0.75, 1.0).normalize();
    let offset = base_dir.dot(&Vector3::new(-0.6, 0.8, 0.6));
@ -709,13 +709,13 @@ fn load_radius_ratio(assembly: &Assembly) {
            [1.00_f32, 0.00_f32, 0.25_f32],
            [1.00_f32, 0.25_f32, 0.00_f32],
            [0.75_f32, 0.75_f32, 0.00_f32],
-            [0.25_f32, 0.00_f32, 1.00_f32],
+            [0.25_f32, 0.00_f32, 1.00_f32]
        ].into_iter(),
        [
            engine::sphere_with_offset(base_dir[0], base_dir[1], base_dir[2], offset, 0.0),
            engine::sphere_with_offset(base_dir[0], -base_dir[1], -base_dir[2], offset, 0.0),
            engine::sphere_with_offset(-base_dir[0], base_dir[1], -base_dir[2], offset, 0.0),
-            engine::sphere_with_offset(-base_dir[0], -base_dir[1], base_dir[2], offset, 0.0),
+            engine::sphere_with_offset(-base_dir[0], -base_dir[1], base_dir[2], offset, 0.0)
        ].into_iter()
    ).map(
        |(k, color, representation)| {
@ -723,7 +723,7 @@ fn load_radius_ratio(assembly: &Assembly) {
                format!("f{k}"),
                format!("Face {k}"),
                color,
-                representation,
+                representation
            )
        }
    );
@ -731,18 +731,18 @@ fn load_radius_ratio(assembly: &Assembly) {
        face.ghost().set(true);
        let _ = assembly.try_insert_element(face);
    }
-
+    
    // impose the constraints
    for j in index_range.clone() {
        let [face_j, vertex_j] = [
            format!("f{j}"),
-            format!("v{j}"),
+            format!("v{j}")
        ].map(
            |id| assembly.elements_by_id.with_untracked(
                |elts_by_id| elts_by_id[&id].clone()
            )
        );
-
+        
        // make the faces planar
        let curvature_regulator = face_j.regulators().with_untracked(
            |regs| regs.first().unwrap().clone()
@ -750,12 +750,12 @@ fn load_radius_ratio(assembly: &Assembly) {
        curvature_regulator.set_point().set(
            SpecifiedValue::try_from("0".to_string()).unwrap()
        );
-
+        
        for k in index_range.clone().filter(|&index| index != j) {
            let vertex_k = assembly.elements_by_id.with_untracked(
                |elts_by_id| elts_by_id[&format!("v{k}")].clone()
            );
-
+            
            // fix the distances between the vertices
            if j < k {
                let distance_regulator = InversiveDistanceRegulator::new(
@ -763,7 +763,7 @@ fn load_radius_ratio(assembly: &Assembly) {
                );
                assembly.insert_regulator(Rc::new(distance_regulator));
            }
-
+            
            // put the vertices on the faces
            let incidence_regulator = InversiveDistanceRegulator::new([face_j.clone(), vertex_k.clone()]);
            incidence_regulator.set_point.set(SpecifiedValue::try_from("0".to_string()).unwrap());
@ -789,7 +789,7 @@ fn load_radius_ratio(assembly: &Assembly) {
 // conditions are exactly representable as floats, unlike the analogous numbers
 // in the scaled-up problem. the inexact representations might break the
 // symmetry that's getting the engine stuck
-fn load_irisawa_hexlet(assembly: &Assembly) {
+fn load_irisawa_hexlet_assemb(assembly: &Assembly) {
    let index_range = 1..=6;
    let colors = [
        [1.00_f32, 0.00_f32, 0.25_f32],
@ -797,28 +797,28 @@ fn load_irisawa_hexlet(assembly: &Assembly) {
        [0.75_f32, 0.75_f32, 0.00_f32],
        [0.25_f32, 1.00_f32, 0.00_f32],
        [0.00_f32, 0.25_f32, 1.00_f32],
-        [0.25_f32, 0.00_f32, 1.00_f32],
+        [0.25_f32, 0.00_f32, 1.00_f32]
    ].into_iter();
-
+    
    // create the spheres
    let spheres = [
        Sphere::new(
            "outer".to_string(),
            "Outer".to_string(),
            [0.5_f32, 0.5_f32, 0.5_f32],
-            engine::sphere(0.0, 0.0, 0.0, 1.5),
+            engine::sphere(0.0, 0.0, 0.0, 1.5)
        ),
        Sphere::new(
            "sun".to_string(),
            "Sun".to_string(),
            [0.75_f32, 0.75_f32, 0.75_f32],
-            engine::sphere(0.0, -0.75, 0.0, 0.75),
+            engine::sphere(0.0, -0.75, 0.0, 0.75)
        ),
        Sphere::new(
            "moon".to_string(),
            "Moon".to_string(),
            [0.25_f32, 0.25_f32, 0.25_f32],
-            engine::sphere(0.0, 0.75, 0.0, 0.75),
+            engine::sphere(0.0, 0.75, 0.0, 0.75)
        ),
    ].into_iter().chain(
        index_range.clone().zip(colors).map(
@ -828,7 +828,7 @@ fn load_irisawa_hexlet(assembly: &Assembly) {
                    format!("chain{k}"),
                    format!("Chain {k}"),
                    color,
-                    engine::sphere(1.0 * ang.sin(), 0.0, 1.0 * ang.cos(), 0.5),
+                    engine::sphere(1.0 * ang.sin(), 0.0, 1.0 * ang.cos(), 0.5)
                )
            }
        )
@ -836,7 +836,7 @@ fn load_irisawa_hexlet(assembly: &Assembly) {
    for sphere in spheres {
        let _ = assembly.try_insert_element(sphere);
    }
-
+    
    // put the outer sphere in ghost mode and fix its curvature
    let outer = assembly.elements_by_id.with_untracked(
        |elts_by_id| elts_by_id["outer"].clone()
@ -848,7 +848,7 @@ fn load_irisawa_hexlet(assembly: &Assembly) {
    outer_curvature_regulator.set_point().set(
        SpecifiedValue::try_from((1.0 / 3.0).to_string()).unwrap()
    );
-
+    
    // impose the desired tangencies
    let [outer, sun, moon] = ["outer", "sun", "moon"].map(
        |id| assembly.elements_by_id.with_untracked(
@ -865,18 +865,18 @@ fn load_irisawa_hexlet(assembly: &Assembly) {
            (outer.clone(), "1"),
            (sun.clone(), "-1"),
            (moon.clone(), "-1"),
-            (chain_sphere_next.clone(), "-1"),
+            (chain_sphere_next.clone(), "-1")
        ] {
            let tangency = InversiveDistanceRegulator::new([chain_sphere.clone(), other_sphere]);
            tangency.set_point.set(SpecifiedValue::try_from(inversive_distance.to_string()).unwrap());
            assembly.insert_regulator(Rc::new(tangency));
        }
    }
-
+    
    let outer_sun_tangency = InversiveDistanceRegulator::new([outer.clone(), sun]);
    outer_sun_tangency.set_point.set(SpecifiedValue::try_from("1".to_string()).unwrap());
    assembly.insert_regulator(Rc::new(outer_sun_tangency));
-
+    
    let outer_moon_tangency = InversiveDistanceRegulator::new([outer.clone(), moon]);
    outer_moon_tangency.set_point.set(SpecifiedValue::try_from("1".to_string()).unwrap());
    assembly.insert_regulator(Rc::new(outer_moon_tangency));
@ -895,47 +895,53 @@ pub fn TestAssemblyChooser() -> View {
        console::log_1(
            &JsValue::from(format!("Showing assembly \"{}\"", name.clone()))
        );
-
+        
        batch(|| {
            let state = use_context::<AppState>();
            let assembly = &state.assembly;
-
+            
            // pause realization
            assembly.keep_realized.set(false);
            // clear state
            assembly.regulators.update(|regs| regs.clear());
            assembly.elements.update(|elts| elts.clear());
            assembly.elements_by_id.update(|elts_by_id| elts_by_id.clear());
            assembly.descent_history.set(DescentHistory::new());
            state.selection.update(|sel| sel.clear());
-
+            
            // load assembly
            match name.as_str() {
-                "general" => load_general(assembly),
+                "general" => load_gen_assemb(assembly),
-                "low-curvature" => load_low_curvature(assembly),
+                "low-curv" => load_low_curv_assemb(assembly),
-                "pointed" => load_pointed(assembly),
+                "pointed" => load_pointed_assemb(assembly),
-                "tridiminished-icosahedron" => load_tridiminished_icosahedron(assembly),
+                "tridim-icosahedron" => load_tridim_icosahedron_assemb(assembly),
-                "dodecahedral-packing" => load_dodecahedral_packing(assembly),
+                "dodeca-packing" => load_dodeca_packing_assemb(assembly),
-                "balanced" => load_balanced(assembly),
+                "balanced" => load_balanced_assemb(assembly),
-                "off-center" => load_off_center(assembly),
+                "off-center" => load_off_center_assemb(assembly),
-                "radius-ratio" => load_radius_ratio(assembly),
+                "radius-ratio" => load_radius_ratio_assemb(assembly),
-                "irisawa-hexlet" => load_irisawa_hexlet(assembly),
+                "irisawa-hexlet" => load_irisawa_hexlet_assemb(assembly),
-                _ => (),
+                _ => ()
            };
            // resume realization
            assembly.keep_realized.set(true);
        });
    });
-
+    
    // build the chooser
    view! {
-        select(bind:value = assembly_name) {
+        select(bind:value=assembly_name) {
-            option(value = "general") { "General" }
+            option(value="general") { "General" }
-            option(value = "low-curvature") { "Low-curvature" }
+            option(value="low-curv") { "Low-curvature" }
-            option(value = "pointed") { "Pointed" }
+            option(value="pointed") { "Pointed" }
-            option(value = "tridiminished-icosahedron") { "Tridiminished icosahedron" }
+            option(value="tridim-icosahedron") { "Tridiminished icosahedron" }
-            option(value = "dodecahedral-packing") { "Dodecahedral packing" }
+            option(value="dodeca-packing") { "Dodecahedral packing" }
-            option(value = "balanced") { "Balanced" }
+            option(value="balanced") { "Balanced" }
-            option(value = "off-center") { "Off-center" }
+            option(value="off-center") { "Off-center" }
-            option(value = "radius-ratio") { "Radius ratio" }
+            option(value="radius-ratio") { "Radius ratio" }
-            option(value = "irisawa-hexlet") { "Irisawa hexlet" }
+            option(value="irisawa-hexlet") { "Irisawa hexlet" }
-            option(value = "empty") { "Empty" }
+            option(value="empty") { "Empty" }
        }
    }
-}
+}
--- a/app-proto/src/engine.rs
+++ b/app-proto/src/engine.rs
@ -1,6 +1,7 @@
 use lazy_static::lazy_static;
 use nalgebra::{Const, DMatrix, DVector, DVectorView, Dyn, SymmetricEigen};
 use std::fmt::{Display, Error, Formatter};
 use web_sys::{console, wasm_bindgen::JsValue}; /* DEBUG */
 // --- elements ---
@ -16,7 +17,7 @@ pub fn sphere(center_x: f64, center_y: f64, center_z: f64, radius: f64) -> DVect
        center_y / radius,
        center_z / radius,
        0.5 / radius,
-        0.5 * (center_norm_sq / radius - radius),
+        0.5 * (center_norm_sq / radius - radius)
    ])
 }
@ -30,7 +31,7 @@ pub fn sphere_with_offset(dir_x: f64, dir_y: f64, dir_z: f64, off: f64, curv: f6
        norm_sp * dir_y,
        norm_sp * dir_z,
        0.5 * curv,
-        off * (1.0 + 0.5 * off * curv),
+        off * (1.0 + 0.5 * off * curv)
    ])
 }
@ -49,32 +50,66 @@ pub fn project_point_to_normalized(rep: &mut DVector<f64>) {
    rep.scale_mut(0.5 / rep[3]);
 }
 // given a sphere's representation vector, change the sphere's half-curvature to
 // `half-curv` and then restore normalization by contracting the representation
 // vector toward the curvature axis
 pub fn change_half_curvature(rep: &mut DVector<f64>, half_curv: f64) {
    // set the sphere's half-curvature to the desired value
    rep[3] = half_curv;
    // restore normalization by contracting toward the curvature axis
    const SIZE_THRESHOLD: f64 = 1e-9;
    let half_q_lt = -2.0 * half_curv * rep[4];
    let half_q_lt_sq = half_q_lt * half_q_lt;
    let mut spatial = rep.fixed_rows_mut::<3>(0);
    let q_sp = spatial.norm_squared();
    if q_sp < SIZE_THRESHOLD && half_q_lt_sq < SIZE_THRESHOLD {
        spatial.copy_from_slice(
            &[0.0, 0.0, (1.0 - 2.0 * half_q_lt).sqrt()]
        );
    } else {
        let scaling = half_q_lt + (q_sp + half_q_lt_sq).sqrt();
        spatial.scale_mut(1.0 / scaling);
        rep[4] /= scaling;
    }
    /* DEBUG */
    // verify normalization
    let rep_for_debug = rep.clone();
    console::log_1(&JsValue::from(
        format!(
            "Sphere self-product after curvature change: {}",
            rep_for_debug.dot(&(&*Q * &rep_for_debug))
        )
    ));
 }
 // --- partial matrices ---
 pub struct MatrixEntry {
-    pub index: (usize, usize),
+    index: (usize, usize),
-    pub value: f64,
+    value: f64
 }
 pub struct PartialMatrix(Vec<MatrixEntry>);
 impl PartialMatrix {
-    pub fn new() -> Self {
+    pub fn new() -> PartialMatrix {
-        Self(Vec::<MatrixEntry>::new())
+        PartialMatrix(Vec::<MatrixEntry>::new())
    }
-
+    
    pub fn push(&mut self, row: usize, col: usize, value: f64) {
-        let Self(entries) = self;
+        let PartialMatrix(entries) = self;
-        entries.push(MatrixEntry { index: (row, col), value });
+        entries.push(MatrixEntry { index: (row, col), value: value });
    }
-
+    
    pub fn push_sym(&mut self, row: usize, col: usize, value: f64) {
        self.push(row, col, value);
        if row != col {
            self.push(col, row, value);
        }
    }
-
+    
    fn freeze(&self, a: &DMatrix<f64>) -> DMatrix<f64> {
        let mut result = a.clone();
        for &MatrixEntry { index, value } in self {
@ -82,7 +117,7 @@ impl PartialMatrix {
        }
        result
    }
-
+    
    fn proj(&self, a: &DMatrix<f64>) -> DMatrix<f64> {
        let mut result = DMatrix::<f64>::zeros(a.nrows(), a.ncols());
        for &MatrixEntry { index, .. } in self {
@ -90,7 +125,7 @@ impl PartialMatrix {
        }
        result
    }
-
+    
    fn sub_proj(&self, rhs: &DMatrix<f64>) -> DMatrix<f64> {
        let mut result = DMatrix::<f64>::zeros(rhs.nrows(), rhs.ncols());
        for &MatrixEntry { index, value } in self {
@ -112,9 +147,9 @@ impl Display for PartialMatrix {
 impl IntoIterator for PartialMatrix {
    type Item = MatrixEntry;
    type IntoIter = std::vec::IntoIter<Self::Item>;
-
+    
    fn into_iter(self) -> Self::IntoIter {
-        let Self(entries) = self;
+        let PartialMatrix(entries) = self;
        entries.into_iter()
    }
 }
@ -122,7 +157,7 @@ impl IntoIterator for PartialMatrix {
 impl<'a> IntoIterator for &'a PartialMatrix {
    type Item = &'a MatrixEntry;
    type IntoIter = std::slice::Iter<'a, MatrixEntry>;
-
+    
    fn into_iter(self) -> Self::IntoIter {
        let PartialMatrix(entries) = self;
        entries.into_iter()
@ -135,26 +170,22 @@ impl<'a> IntoIterator for &'a PartialMatrix {
 pub struct ConfigSubspace {
    assembly_dim: usize,
    basis_std: Vec<DMatrix<f64>>,
-    basis_proj: Vec<DMatrix<f64>>,
+    basis_proj: Vec<DMatrix<f64>>
 }
 impl ConfigSubspace {
-    pub fn zero(assembly_dim: usize) -> Self {
+    pub fn zero(assembly_dim: usize) -> ConfigSubspace {
-        Self {
+        ConfigSubspace {
-            assembly_dim,
+            assembly_dim: assembly_dim,
            basis_proj: Vec::new(),
-            basis_std: Vec::new(),
+            basis_std: 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(
+    fn symmetric_kernel(a: DMatrix<f64>, proj_to_std: DMatrix<f64>, assembly_dim: usize) -> ConfigSubspace {
        a: DMatrix<f64>,
        proj_to_std: DMatrix<f64>,
        assembly_dim: usize,
    ) -> Self {
        // find a basis for the kernel. the basis is expressed in the projection
        // coordinates, and it's orthonormal with respect to the projection
        // inner product
@ -167,14 +198,21 @@ impl ConfigSubspace {
                |(λ, v)| (λ.abs() < THRESHOLD).then_some(v)
            ).collect::<Vec<_>>().as_slice()
        );
-
+        
        /* 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)
        ));
        // express the basis in the standard coordinates
        let basis_std = proj_to_std * &basis_proj;
-
+        
        const ELEMENT_DIM: usize = 5;
        const UNIFORM_DIM: usize = 4;
-        Self {
+        ConfigSubspace {
-            assembly_dim,
+            assembly_dim: assembly_dim,
            basis_std: basis_std.column_iter().map(
                |v| Into::<DMatrix<f64>>::into(
                    v.reshape_generic(Dyn(ELEMENT_DIM), Dyn(assembly_dim))
@ -184,18 +222,18 @@ impl ConfigSubspace {
                |v| Into::<DMatrix<f64>>::into(
                    v.reshape_generic(Dyn(UNIFORM_DIM), Dyn(assembly_dim))
                )
-            ).collect(),
+            ).collect()
        }
    }
-
+    
    pub fn dim(&self) -> usize {
        self.basis_std.len()
    }
-
+    
    pub fn assembly_dim(&self) -> usize {
        self.assembly_dim
    }
-
+    
    // find the projection onto this subspace of the motion where the element
    // with the given column index has velocity `v`. the velocity is given in
    // projection coordinates, and the projection is done with respect to the
@ -218,14 +256,14 @@ pub struct DescentHistory {
    pub config: Vec<DMatrix<f64>>,
    pub scaled_loss: Vec<f64>,
    pub neg_grad: Vec<DMatrix<f64>>,
-    pub hess_eigvals: Vec<DVector<f64>>,
+    pub hess_eigvals: Vec::<DVector<f64>>,
    pub base_step: Vec<DMatrix<f64>>,
-    pub backoff_steps: Vec<i32>,
+    pub backoff_steps: Vec<i32>
 }
 impl DescentHistory {
-    pub fn new() -> Self {
+    pub fn new() -> DescentHistory {
-        Self {
+        DescentHistory {
            config: Vec::<DMatrix<f64>>::new(),
            scaled_loss: Vec::<f64>::new(),
            neg_grad: Vec::<DMatrix<f64>>::new(),
@ -245,21 +283,21 @@ pub struct ConstraintProblem {
 }
 impl ConstraintProblem {
-    pub fn new(element_count: usize) -> Self {
+    pub fn new(element_count: usize) -> ConstraintProblem {
        const ELEMENT_DIM: usize = 5;
-        Self {
+        ConstraintProblem {
            gram: PartialMatrix::new(),
            frozen: PartialMatrix::new(),
-            guess: DMatrix::<f64>::zeros(ELEMENT_DIM, element_count),
+            guess: DMatrix::<f64>::zeros(ELEMENT_DIM, element_count)
        }
    }
-
+    
    #[cfg(feature = "dev")]
-    pub fn from_guess(guess_columns: &[DVector<f64>]) -> Self {
+    pub fn from_guess(guess_columns: &[DVector<f64>]) -> ConstraintProblem {
-        Self {
+        ConstraintProblem {
            gram: PartialMatrix::new(),
            frozen: PartialMatrix::new(),
-            guess: DMatrix::from_columns(guess_columns),
+            guess: DMatrix::from_columns(guess_columns)
        }
    }
 }
@ -273,21 +311,25 @@ lazy_static! {
        0.0, 1.0, 0.0,  0.0,  0.0,
        0.0, 0.0, 1.0,  0.0,  0.0,
        0.0, 0.0, 0.0,  0.0, -2.0,
-        0.0, 0.0, 0.0, -2.0,  0.0,
+        0.0, 0.0, 0.0, -2.0,  0.0
    ]);
 }
 struct SearchState {
    config: DMatrix<f64>,
    err_proj: DMatrix<f64>,
-    loss: f64,
+    loss: f64
 }
 impl SearchState {
-    fn from_config(gram: &PartialMatrix, config: DMatrix<f64>) -> Self {
+    fn from_config(gram: &PartialMatrix, config: DMatrix<f64>) -> SearchState {
        let err_proj = gram.sub_proj(&(config.tr_mul(&*Q) * &config));
        let loss = err_proj.norm_squared();
-        Self { config, err_proj, loss }
+        SearchState {
            config: config,
            err_proj: err_proj,
            loss: loss
        }
    }
 }
@ -314,7 +356,7 @@ pub fn local_unif_to_std(v: DVectorView<f64>) -> DMatrix<f64> {
            curv,  0.0,  0.0,  0.0, v[0],
             0.0, curv,  0.0,  0.0, v[1],
             0.0,  0.0, curv,  0.0, v[2],
-             0.0,  0.0,  0.0,  0.0,  1.0,
+             0.0,  0.0,  0.0,  0.0,  1.0
        ])
    } else {
        // `v` represents a sphere. the normalization condition says that the
@ -323,7 +365,7 @@ pub fn local_unif_to_std(v: DVectorView<f64>) -> DMatrix<f64> {
                 curv,       0.0,       0.0,       0.0,            v[0],
                  0.0,      curv,       0.0,       0.0,            v[1],
                  0.0,       0.0,      curv,       0.0,            v[2],
-            curv*v[0], curv*v[1], curv*v[2], curv*v[3], curv*v[4] + 1.0,
+            curv*v[0], curv*v[1], curv*v[2], curv*v[3], curv*v[4] + 1.0
        ])
    }
 }
@ -336,7 +378,7 @@ fn seek_better_config(
    base_target_improvement: f64,
    min_efficiency: f64,
    backoff: f64,
-    max_backoff_steps: i32,
+    max_backoff_steps: i32
 ) -> Option<(SearchState, i32)> {
    let mut rate = 1.0;
    for backoff_steps in 0..max_backoff_steps {
@ -353,13 +395,13 @@ fn seek_better_config(
 // a first-order neighborhood of a configuration
 pub struct ConfigNeighborhood {
-    #[cfg(feature = "dev")] pub config: DMatrix<f64>,
+    pub config: DMatrix<f64>,
-    pub nbhd: ConfigSubspace,
+    pub nbhd: ConfigSubspace
 }
 pub struct Realization {
    pub result: Result<ConfigNeighborhood, String>,
-    pub history: DescentHistory,
+    pub history: DescentHistory
 }
 // seek a matrix `config` that matches the partial matrix `problem.frozen` and
@ -373,41 +415,30 @@ pub fn realize_gram(
    backoff: f64,
    reg_scale: f64,
    max_descent_steps: i32,
-    max_backoff_steps: i32,
+    max_backoff_steps: i32
 ) -> Realization {
    // destructure the problem data
-    let ConstraintProblem { gram, guess, frozen } = problem;
+    let ConstraintProblem {
-
+        gram, guess, frozen
    } = problem;
    // start the descent history
    let mut history = DescentHistory::new();
-
+    
    // handle the case where the assembly is empty. our general realization
    // routine can't handle this case because it builds the Hessian using
    // `DMatrix::from_columns`, which panics when the list of columns is empty
    let assembly_dim = guess.ncols();
    if assembly_dim == 0 {
        let result = Ok(
            ConfigNeighborhood {
                #[cfg(feature = "dev")] config: guess.clone(),
                nbhd: ConfigSubspace::zero(0),
            }
        );
        return Realization { result, history };
    }
    // find the dimension of the search space
    let element_dim = guess.nrows();
    let assembly_dim = guess.ncols();
    let total_dim = element_dim * assembly_dim;
-
+    
    // scale the tolerance
    let scale_adjustment = (gram.0.len() as f64).sqrt();
    let tol = scale_adjustment * scaled_tol;
-
+    
    // convert the frozen indices to stacked format
    let frozen_stacked: Vec<usize> = frozen.into_iter().map(
        |MatrixEntry { index: (row, col), .. }| col*element_dim + row
    ).collect();
-
+    
    // use a regularized Newton's method with backtracking
    let mut state = SearchState::from_config(gram, frozen.freeze(guess));
    let mut hess = DMatrix::zeros(element_dim, assembly_dim);
@ -416,7 +447,7 @@ pub fn realize_gram(
        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>);
        history.neg_grad.push(neg_grad.clone());
-
+        
        // find the negative Hessian of the loss function
        let mut hess_cols = Vec::<DVector<f64>>::with_capacity(total_dim);
        for col in 0..assembly_dim {
@ -435,7 +466,7 @@ pub fn realize_gram(
            }
        }
        hess = DMatrix::from_columns(hess_cols.as_slice());
-
+        
        // regularize the Hessian
        let hess_eigvals = hess.symmetric_eigenvalues();
        let min_eigval = hess_eigvals.min();
@ -443,7 +474,7 @@ pub fn realize_gram(
            hess -= reg_scale * min_eigval * DMatrix::identity(total_dim, total_dim);
        }
        history.hess_eigvals.push(hess_eigvals);
-
+        
        // project the negative gradient and negative Hessian onto the
        // orthogonal complement of the frozen subspace
        let zero_col = DVector::zeros(total_dim);
@ -454,12 +485,12 @@ pub fn realize_gram(
            hess.set_column(k, &zero_col);
            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
        /* TO DO */
        /*
@ -473,26 +504,26 @@ pub fn realize_gram(
            Some(cholesky) => cholesky,
            None => return Realization {
                result: Err("Cholesky decomposition failed".to_string()),
-                history,
+                history
-            },
+            }
        };
        let base_step_stacked = hess_cholesky.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());
-
+        
        // use backtracking line search to find a better configuration
        if let Some((better_state, backoff_steps)) = seek_better_config(
            gram, &state, &base_step, neg_grad.dot(&base_step),
-            min_efficiency, backoff, max_backoff_steps,
+            min_efficiency, backoff, max_backoff_steps
        ) {
            state = better_state;
            history.backoff_steps.push(backoff_steps);
        } else {
            return Realization {
                result: Err("Line search failed".to_string()),
-                history,
+                history
-            };
+            }
-        }
+        };
    }
    let result = if state.loss < tol {
        // express the uniform basis in the standard basis
@ -505,11 +536,11 @@ pub fn realize_gram(
                .view_mut(block_start, (element_dim, UNIFORM_DIM))
                .copy_from(&local_unif_to_std(state.config.column(n)));
        }
-
+        
        // find the kernel of the Hessian. give it the uniform inner product
        let tangent = ConfigSubspace::symmetric_kernel(hess, unif_to_std, assembly_dim);
-
+        
-        Ok(ConfigNeighborhood { #[cfg(feature = "dev")] config: state.config, nbhd: tangent })
+        Ok(ConfigNeighborhood { config: state.config, nbhd: tangent })
    } else {
        Err("Failed to reach target accuracy".to_string())
    };
@ -521,9 +552,9 @@ pub fn realize_gram(
 #[cfg(feature = "dev")]
 pub mod examples {
    use std::f64::consts::PI;
-
+    
    use super::*;
-
+    
    // this problem is from a sangaku by Irisawa Shintarō Hiroatsu. the article
    // below includes a nice translation of the problem statement, which was
    // recorded in Uchida Itsumi's book _Kokon sankan_ (_Mathematics, Past and
@ -537,7 +568,7 @@ pub mod examples {
            [
                sphere(0.0, 0.0, 0.0, 15.0),
                sphere(0.0, 0.0, -9.0, 5.0),
-                sphere(0.0, 0.0, 11.0, 3.0),
+                sphere(0.0, 0.0, 11.0, 3.0)
            ].into_iter().chain(
                (1..=6).map(
                    |k| {
@ -547,40 +578,40 @@ pub mod examples {
                )
            ).collect::<Vec<_>>().as_slice()
        );
-
+        
        for s in 0..9 {
            // each sphere is represented by a spacelike vector
            problem.gram.push_sym(s, s, 1.0);
-
+            
            // the circumscribing sphere is tangent to all of the other
            // spheres, with matching orientation
            if s > 0 {
                problem.gram.push_sym(0, s, 1.0);
            }
-
+            
            if s > 2 {
                // each chain sphere is tangent to the "sun" and "moon"
                // spheres, with opposing orientation
                for n in 1..3 {
                    problem.gram.push_sym(s, n, -1.0);
                }
-
+                
                // each chain sphere is tangent to the next chain sphere,
                // with opposing orientation
                let s_next = 3 + (s-2) % 6;
                problem.gram.push_sym(s, s_next, -1.0);
            }
        }
-
+        
        // the frozen entries fix the radii of the circumscribing sphere, the
        // "sun" and "moon" spheres, and one of the chain spheres
        for k in 0..4 {
            problem.frozen.push(3, k, problem.guess[(3, k)]);
        }
-
+        
        realize_gram(&problem, scaled_tol, 0.5, 0.9, 1.1, 200, 110)
    }
-
+    
    // set up a kaleidocycle, made of points with fixed distances between them,
    // and find its tangent space
    pub fn realize_kaleidocycle(scaled_tol: f64) -> Realization {
@ -596,12 +627,12 @@ pub mod examples {
                        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),
+                        point(x_vert, y_vert, 0.5)
                    ]
                }
            ).collect::<Vec<_>>().as_slice()
        );
-
+        
        const N_POINTS: usize = 2 * N_HINGES;
        for block in (0..N_POINTS).step_by(2) {
            let block_next = (block + 2) % N_POINTS;
@ -610,18 +641,18 @@ pub mod examples {
                for k in j..2 {
                    problem.gram.push_sym(block + j, block + k, if j == k { 0.0 } else { -0.5 });
                }
-
+                
                // non-hinge edges
                for k in 0..2 {
                    problem.gram.push_sym(block + j, block_next + k, -0.625);
                }
            }
        }
-
+        
        for k in 0..N_POINTS {
            problem.frozen.push(3, k, problem.guess[(3, k)])
        }
-
+        
        realize_gram(&problem, scaled_tol, 0.5, 0.9, 1.1, 200, 110)
    }
 }
@ -630,47 +661,47 @@ pub mod examples {
 mod tests {
    use nalgebra::Vector3;
    use std::{f64::consts::{FRAC_1_SQRT_2, PI}, iter};
-
+    
    use super::{*, examples::*};
-
+    
    #[test]
    fn freeze_test() {
        let frozen = PartialMatrix(vec![
            MatrixEntry { index: (0, 0), value: 14.0 },
            MatrixEntry { index: (0, 2), value: 28.0 },
            MatrixEntry { index: (1, 1), value: 42.0 },
-            MatrixEntry { index: (1, 2), value: 49.0 },
+            MatrixEntry { index: (1, 2), value: 49.0 }
        ]);
        let config = DMatrix::<f64>::from_row_slice(2, 3, &[
            1.0, 2.0, 3.0,
-            4.0, 5.0, 6.0,
+            4.0, 5.0, 6.0
        ]);
        let expected_result = DMatrix::<f64>::from_row_slice(2, 3, &[
            14.0, 2.0, 28.0,
-            4.0, 42.0, 49.0,
+            4.0, 42.0, 49.0
        ]);
        assert_eq!(frozen.freeze(&config), expected_result);
    }
-
+    
    #[test]
    fn sub_proj_test() {
        let target = PartialMatrix(vec![
            MatrixEntry { index: (0, 0), value: 19.0 },
            MatrixEntry { index: (0, 2), value: 39.0 },
            MatrixEntry { index: (1, 1), value: 59.0 },
-            MatrixEntry { index: (1, 2), value: 69.0 },
+            MatrixEntry { index: (1, 2), value: 69.0 }
        ]);
        let attempt = DMatrix::<f64>::from_row_slice(2, 3, &[
            1.0, 2.0, 3.0,
-            4.0, 5.0, 6.0,
+            4.0, 5.0, 6.0
        ]);
        let expected_result = DMatrix::<f64>::from_row_slice(2, 3, &[
            18.0, 0.0, 36.0,
-            0.0, 54.0, 63.0,
+            0.0, 54.0, 63.0
        ]);
        assert_eq!(target.sub_proj(&attempt), expected_result);
    }
-
+    
    #[test]
    fn zero_loss_test() {
        let mut gram = PartialMatrix::new();
@ -684,13 +715,13 @@ mod tests {
            DMatrix::from_columns(&[
                sphere(1.0, 0.0, 0.0, a),
                sphere(-0.5, a, 0.0, a),
-                sphere(-0.5, -a, 0.0, a),
+                sphere(-0.5, -a, 0.0, a)
            ])
        };
        let state = SearchState::from_config(&gram, config);
        assert!(state.loss.abs() < f64::EPSILON);
    }
-
+    
    /* TO DO */
    // at the frozen indices, the optimization steps should have exact zeros,
    // and the realized configuration should have the desired values
@ -698,7 +729,7 @@ mod tests {
    fn frozen_entry_test() {
        let mut problem = ConstraintProblem::from_guess(&[
            point(0.0, 0.0, 2.0),
-            sphere(0.0, 0.0, 0.0, 0.95),
+            sphere(0.0, 0.0, 0.0, 0.95)
        ]);
        for j in 0..2 {
            for k in j..2 {
@ -720,13 +751,13 @@ mod tests {
            assert_eq!(config[index], value);
        }
    }
-
+    
    #[test]
    fn irisawa_hexlet_test() {
        // solve Irisawa's problem
        const SCALED_TOL: f64 = 1.0e-12;
        let config = realize_irisawa_hexlet(SCALED_TOL).result.unwrap().config;
-
+        
        // check against Irisawa's solution
        let entry_tol = SCALED_TOL.sqrt();
        let solution_diams = [30.0, 10.0, 6.0, 5.0, 15.0, 10.0, 3.75, 2.5, 2.0 + 8.0/11.0];
@ -734,7 +765,7 @@ mod tests {
            assert!((config[(3, k)] - 1.0 / diam).abs() < entry_tol);
        }
    }
-
+    
    #[test]
    fn tangent_test_three_spheres() {
        const SCALED_TOL: f64 = 1.0e-12;
@ -742,7 +773,7 @@ mod tests {
        let mut problem = ConstraintProblem::from_guess(&[
            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),
+            sphere(0.0, 0.0, -1.0, 1.0)
        ]);
        for j in 0..3 {
            for k in j..3 {
@ -758,7 +789,7 @@ mod tests {
        let ConfigNeighborhood { config, nbhd: tangent } = result.unwrap();
        assert_eq!(config, problem.guess);
        assert_eq!(history.scaled_loss.len(), 1);
-
+        
        // list some motions that should form a basis for the tangent space of
        // the solution variety
        const UNIFORM_DIM: usize = 4;
@ -772,8 +803,8 @@ mod tests {
            DMatrix::<f64>::from_column_slice(UNIFORM_DIM, assembly_dim, &[
                0.0, 0.0,  0.0,  0.0,
                0.0, 0.0, -0.5, -0.5,
-                0.0, 0.0, -0.5,  0.5,
+                0.0, 0.0, -0.5,  0.5
-            ]),
+            ])
        ];
        let tangent_motions_std = vec![
            basis_matrix((0, 1), element_dim, assembly_dim),
@ -783,14 +814,14 @@ mod tests {
            DMatrix::<f64>::from_column_slice(element_dim, assembly_dim, &[
                0.0, 0.0,  0.0,  0.00,  0.0,
                0.0, 0.0, -1.0, -0.25, -1.0,
-                0.0, 0.0, -1.0,  0.25,  1.0,
+                0.0, 0.0, -1.0,  0.25,  1.0
-            ]),
+            ])
        ];
-
+        
        // confirm that the dimension of the tangent space is no greater than
        // expected
        assert_eq!(tangent.basis_std.len(), tangent_motions_std.len());
-
+        
        // 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
@ -802,13 +833,13 @@ mod tests {
            assert!((motion_std - motion_proj).norm_squared() < tol_sq);
        }
    }
-
+    
    fn translation_motion_unif(vel: &Vector3<f64>, assembly_dim: usize) -> Vec<DVector<f64>> {
        let mut elt_motion = DVector::zeros(4);
        elt_motion.fixed_rows_mut::<3>(0).copy_from(vel);
        iter::repeat(elt_motion).take(assembly_dim).collect()
    }
-
+    
    fn rotation_motion_unif(ang_vel: &Vector3<f64>, points: Vec<DVectorView<f64>>) -> Vec<DVector<f64>> {
        points.into_iter().map(
            |pt| {
@ -819,7 +850,7 @@ mod tests {
            }
        ).collect()
    }
-
+    
    #[test]
    fn tangent_test_kaleidocycle() {
        // set up a kaleidocycle and find its tangent space
@ -827,7 +858,7 @@ mod tests {
        let Realization { result, history } = realize_kaleidocycle(SCALED_TOL);
        let ConfigNeighborhood { config, nbhd: tangent } = result.unwrap();
        assert_eq!(history.scaled_loss.len(), 1);
-
+        
        // list some motions that should form a basis for the tangent space of
        // the solution variety
        const N_HINGES: usize = 6;
@ -838,12 +869,12 @@ mod tests {
            translation_motion_unif(&Vector3::new(1.0, 0.0, 0.0), assembly_dim),
            translation_motion_unif(&Vector3::new(0.0, 1.0, 0.0), assembly_dim),
            translation_motion_unif(&Vector3::new(0.0, 0.0, 1.0), assembly_dim),
-
+            
            // the rotations about the coordinate axes
            rotation_motion_unif(&Vector3::new(1.0, 0.0, 0.0), config.column_iter().collect()),
            rotation_motion_unif(&Vector3::new(0.0, 1.0, 0.0), config.column_iter().collect()),
            rotation_motion_unif(&Vector3::new(0.0, 0.0, 1.0), config.column_iter().collect()),
-
+            
            // the twist motion. more precisely: a motion that keeps the center
            // of mass stationary and preserves the distances between the
            // vertices to first order. this has to be the twist as long as:
@ -860,10 +891,10 @@ mod tests {
                        DVector::from_column_slice(&[0.0, 0.0, 5.0, 0.0]),
                        DVector::from_column_slice(&[0.0, 0.0, 1.0, 0.0]),
                        DVector::from_column_slice(&[-vel_vert_x, -vel_vert_y, -3.0, 0.0]),
-                        DVector::from_column_slice(&[vel_vert_x, vel_vert_y, -3.0, 0.0]),
+                        DVector::from_column_slice(&[vel_vert_x, vel_vert_y, -3.0, 0.0])
                    ]
                }
-            ).collect::<Vec<_>>(),
+            ).collect::<Vec<_>>()
        ];
        let tangent_motions_std = tangent_motions_unif.iter().map(
            |motion| DMatrix::from_columns(
@ -872,11 +903,11 @@ mod tests {
                ).collect::<Vec<_>>()
            )
        ).collect::<Vec<_>>();
-
+        
        // confirm that the dimension of the tangent space is no greater than
        // expected
        assert_eq!(tangent.basis_std.len(), tangent_motions_unif.len());
-
+        
        // 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
@ -888,7 +919,7 @@ mod tests {
            assert!((motion_std - motion_proj).norm_squared() < tol_sq);
        }
    }
-
+    
    fn translation(dis: Vector3<f64>) -> DMatrix<f64> {
        const ELEMENT_DIM: usize = 5;
        DMatrix::from_column_slice(ELEMENT_DIM, ELEMENT_DIM, &[
@ -896,10 +927,10 @@ mod tests {
                   0.0,        1.0,        0.0, 0.0,             dis[1],
                   0.0,        0.0,        1.0, 0.0,             dis[2],
            2.0*dis[0], 2.0*dis[1], 2.0*dis[2], 1.0, dis.norm_squared(),
-                   0.0,        0.0,        0.0, 0.0,                1.0,
+                   0.0,        0.0,        0.0, 0.0,                1.0
        ])
    }
-
+    
    // confirm that projection onto a configuration subspace is equivariant with
    // respect to Euclidean motions
    #[test]
@ -908,7 +939,7 @@ mod tests {
        const SCALED_TOL: f64 = 1.0e-12;
        let mut problem_orig = ConstraintProblem::from_guess(&[
            sphere(0.0, 0.0, 0.5, 1.0),
-            sphere(0.0, 0.0, -0.5, 1.0),
+            sphere(0.0, 0.0, -0.5, 1.0)
        ]);
        problem_orig.gram.push_sym(0, 0, 1.0);
        problem_orig.gram.push_sym(1, 1, 1.0);
@ -919,20 +950,20 @@ mod tests {
        let ConfigNeighborhood { config: config_orig, nbhd: tangent_orig } = result_orig.unwrap();
        assert_eq!(config_orig, problem_orig.guess);
        assert_eq!(history_orig.scaled_loss.len(), 1);
-
+        
        // find another pair of spheres that meet at 120°. we'll think of this
        // solution as a transformed version of the original one
        let guess_tfm = {
            let a = 0.5 * FRAC_1_SQRT_2;
            DMatrix::from_columns(&[
                sphere(a, 0.0, 7.0 + a, 1.0),
-                sphere(-a, 0.0, 7.0 - a, 1.0),
+                sphere(-a, 0.0, 7.0 - a, 1.0)
            ])
        };
        let problem_tfm = ConstraintProblem {
            gram: problem_orig.gram,
            frozen: problem_orig.frozen,
            guess: guess_tfm,
            frozen: problem_orig.frozen
        };
        let Realization { result: result_tfm, history: history_tfm } = realize_gram(
            &problem_tfm, SCALED_TOL, 0.5, 0.9, 1.1, 200, 110
@ -940,17 +971,17 @@ mod tests {
        let ConfigNeighborhood { config: config_tfm, nbhd: tangent_tfm } = result_tfm.unwrap();
        assert_eq!(config_tfm, problem_tfm.guess);
        assert_eq!(history_tfm.scaled_loss.len(), 1);
-
+        
        // project a nudge to the tangent space of the solution variety at the
        // original solution
        let motion_orig = DVector::from_column_slice(&[0.0, 0.0, 1.0, 0.0]);
        let motion_orig_proj = tangent_orig.proj(&motion_orig.as_view(), 0);
-
+        
        // project the equivalent nudge to the tangent space of the solution
        // variety at the transformed solution
        let motion_tfm = DVector::from_column_slice(&[FRAC_1_SQRT_2, 0.0, FRAC_1_SQRT_2, 0.0]);
        let motion_tfm_proj = tangent_tfm.proj(&motion_tfm.as_view(), 0);
-
+        
        // take the transformation that sends the original solution to the
        // transformed solution and apply it to the motion that the original
        // solution makes in response to the nudge
@ -960,11 +991,11 @@ mod tests {
                      0.0, 1.0,            0.0, 0.0, 0.0,
            FRAC_1_SQRT_2, 0.0,  FRAC_1_SQRT_2, 0.0, 0.0,
                      0.0, 0.0,            0.0, 1.0, 0.0,
-                      0.0, 0.0,            0.0, 0.0, 1.0,
+                      0.0, 0.0,            0.0, 0.0, 1.0
        ]);
        let transl = translation(Vector3::new(0.0, 0.0, 7.0));
        let motion_proj_tfm = transl * rot * motion_orig_proj;
-
+        
        // confirm that the projection of the nudge is equivariant. we loosen
        // the comparison tolerance because the transformation seems to
        // introduce some numerical error
@ -972,4 +1003,4 @@ mod tests {
        let tol_sq = ((problem_orig.guess.nrows() * problem_orig.guess.ncols()) as f64) * SCALED_TOL_TFM * SCALED_TOL_TFM;
        assert!((motion_proj_tfm - motion_tfm_proj).norm_squared() < tol_sq);
    }
-}
+}
--- a/app-proto/src/main.rs
+++ b/app-proto/src/main.rs
@ -14,23 +14,23 @@ use components::{
    add_remove::AddRemove,
    diagnostics::Diagnostics,
    display::Display,
-    outline::Outline,
+    outline::Outline
 };
 #[derive(Clone)]
 struct AppState {
    assembly: Assembly,
-    selection: Signal<BTreeSet<Rc<dyn Element>>>,
+    selection: Signal<BTreeSet<Rc<dyn Element>>>
 }
 impl AppState {
-    fn new() -> Self {
+    fn new() -> AppState {
-        Self {
+        AppState {
            assembly: Assembly::new(),
-            selection: create_signal(BTreeSet::default()),
+            selection: create_signal(BTreeSet::default())
        }
    }
-
+    
    // in single-selection mode, select the given element. in multiple-selection
    // mode, toggle whether the given element is selected
    fn select(&self, element: &Rc<dyn Element>, multi: bool) {
@ -53,12 +53,12 @@ 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());
-
+        
        view! {
-            div(id = "sidebar") {
+            div(id="sidebar") {
                AddRemove {}
                Outline {}
                Diagnostics {}
@ -66,4 +66,4 @@ fn main() {
            Display {}
        }
    });
-}
+}
--- a/app-proto/src/specified.rs
+++ b/app-proto/src/specified.rs
@ -13,43 +13,32 @@ use std::num::ParseFloatError;
 #[readonly::make]
 pub struct SpecifiedValue {
    pub spec: String,
-    pub value: Option<f64>,
+    pub value: Option<f64>
 }
 impl SpecifiedValue {
-    pub fn from_empty_spec() -> Self {
+    pub fn from_empty_spec() -> SpecifiedValue {
-        Self { spec: String::new(), value: None }
+        SpecifiedValue { spec: String::new(), value: None }
    }
-
+    
    pub fn is_present(&self) -> bool {
        matches!(self.value, Some(_))
    }
 }
 // a `SpecifiedValue` can be constructed from a floating-point option, which is
 // given a canonical specification
 impl From<Option<f64>> for SpecifiedValue {
    fn from(value: Option<f64>) -> Self {
        match value {
            Some(x) => SpecifiedValue{ spec: x.to_string(), value },
            None => SpecifiedValue::from_empty_spec(),
        }
    }
 }
 // a `SpecifiedValue` can be constructed from a specification string, formatted
 // as described in the comment on the structure definition. the result is `Ok`
 // if the specification is properly formatted, and `Error` if not
 impl TryFrom<String> for SpecifiedValue {
    type Error = ParseFloatError;
-
+    
    fn try_from(spec: String) -> Result<Self, Self::Error> {
        if spec.is_empty() {
-            Ok(Self::from_empty_spec())
+            Ok(SpecifiedValue::from_empty_spec())
        } else {
            spec.parse::<f64>().map(
-                |value| Self { spec, value: Some(value) }
+                |value| SpecifiedValue { spec: spec, value: Some(value) }
            )
        }
    }
-}
+}
--- a/deploy/.gitignore
+++ b/deploy/.gitignore
@ -1,5 +0,0 @@
 /dyna3.zip
 /dyna3/index.html
 /dyna3/dyna3-*.js
 /dyna3/dyna3-*.wasm
 /dyna3/main-*.css
--- a/notes/inversive.md
+++ b/notes/inversive.md
@ -33,7 +33,7 @@ The unification of spheres/planes is indeed attractive for a project like Dyna3.
 Discussed coordinates with Alex Kontorovich. He was suggesting "inversive coordinates" -- for a sphere, that's 1/coradius, 1/radius, center/radius (where coradius is radius of sphere inverted in the unit sphere.) The advantage is tangent to and perpendicular to are linear in these coordinates (in the sense that if one is known, the condition of being tangent to or perpendicular to that one are linear). Planes have 1/radius = 0, and in fact, you can take the coordinates to be (2s, 0, x, y, z) where s is the distance to the origin and x,y,z are the normal direction. (Note the normal direction is only determined up to a scalar multiple. So could always scale so that the first non-zero coordinate is 1, or if you like only allow x, y to vary and let z be determined as sqrt(1-x^2^-y^2^). ) Points can be given by (r^2,1,x,y,z) where x,y,z are the coordinates and r is the distance to the origin. Quadratic form that tells you if something is a sphere/plane, or in the boundary, or up in the hyperbolic plane above. There are some details, but not quite explicit for modeling R^3, at http://sites.math.rutgers.edu/~alexk/files/LetterToDuke.pdf -- all this emphasize need to be agnostic with respect to geometric model so that we can experiment. Not really sure exactly how this relates or not to conformal geometric algebra, and whether it can be combined with geometric algebra. As formulated, there are clear-ish reps for planes/spheres and for points, but not as clear for lines. Have to see how to compute distance and/or specify a given distance. To combine inversive coordinates and geometric algebra, maybe think dually; there should be a lift from a normal vector and distance from origin to the five-vector; bivectors would rep circles/lines; trivectors would rep point pairs/points. What is the signature of this algebra, i.e. how many coordinates square to +1, -1, or 0? But it doesn't seem worth it for three dimensions, because there is a natural representation of points, as follows:
 The signature of Q will be (1,4), and in fact Q(I1,I2) = 1/2(ab+ba) - E1\dot E2, where a is the "first" or "coradius" coordinate, "b" is the "second" or "radius" coordinate, and E is the Euclidean part (x,y,z). Then the inversive coordinates of a sphere with center (x,y,z) and radius r will be I = (1/\hat{r},1/r,x/r,y/r,z/r) where \hat{r} = r/(|E|^2 -r^2). These coordinates satisfy Q(I,I) = -1. For this to make sense, of course r > 0, but we get planes by letting the radius of a tangent sphere to the plane go to infinity, and we get I = (2s, 0, x0, y0, z0) where (x0,y0,z0) is the unit normal to the plane and s is the perpendicular distance from the plane to the origin. Still Q(I,I) = -1.
-Since r>0, we can't represent individual points this way. Instead we will use some coordinates J for which Q(J,J) = 0. In particular, if you take for the Euclidean point E = (u,v,w) the coordinates J = (`|E|`^2,1,u,v,w) then Q(J,J) = 0 and moreover it comes out that Q(I,J) = 0
+Since r>0, we can't represent individual points this way. Instead we will use some coordinates J for which Q(J,J) = 0. In particular, if you take for the Euclidean point E = (u,v,w) the coordinates J = (`|E|`^2,1,u,v,w) then Q(J,J) = 0 and moreover it comes out that Q(I,J) = 0 
 whenever E lies on the sphere or plane described by some I with Q(I,I) = -1.
 The condition that two spheres I1 and I2 are tangent seems to be that Q(I1,I2) = 1. So given a fixed sphere, the condition that another sphere be tangent to it is linear in the coordinates of that other sphere.
 This system does seem promising for encoding points, spheres, and planes, and doing basic computations with them. I guess I would just encode a circle as the intersection of the concentric sphere and the containing plane, and a line as either a pair of points or a pair of planes (modulo some equivalence relation, since I can't see any canonical choice of either two planes or two points). Or actually as described below, there is a more canonical choice.
@ -62,4 +62,4 @@ In the engine's coordinate conventions, a sphere with radius $r > 0$ centered on
 $$I'_s = \left(\frac{P_x}{r}, \frac{P_y}{r}, \frac{P_z}{r}, \frac1{2r}, \frac{\|P\|^2 - r^2}{2r}\right),$$
 which has the normalization $Q'(I'_s, I'_s) = 1$. The point $P$ is represented by the vector
 $$I'_P = \left(P_x, P_y, P_z, \frac{1}{2}, \frac{\|P\|^2}{2}\right).$$
-In the `engine` module, these formulas are encoded in the `sphere` and `point` functions.
+In the `engine` module, these formulas are encoded in the `sphere` and `point` functions.
--- a/notes/theory.md
+++ b/notes/theory.md
@ -24,7 +24,7 @@ His final mathematical advice was reasonably encouraging, however:
 "But still I would consider it all more or less doable. One should very precisely think about a doable scope.
 I think three things are essential for the math no matter what you exactly plan.
-1. Think projectively.
+1. Think projectively, 
   Use Projective Geometry, Homogeneous Coordinates (or to a certain extent Quaternions, and Clifford Algebras, which are more or less an elegant way to merge Complex numbers with projective concepts.)
 2. Consider ambient complex spaces.
   The true nature of the objects can only be understood if embedded into a complex ambient space.
@ -37,8 +37,10 @@ I think three things are essential for the math no matter what you exactly plan.
 It would be nice to see how Jürgen handled some of these issues in a 2D system that he designed. Unfortunately, Cinderella was and remains closed-source; it was distributed for profit for some stretch of time. However, (a part of?) it was reimplemented in JavaScript as CindyJS, which is open source. I took a relatively quick look at that source code at one point, and these were my observations:
-CindyJS uses very concrete basic objects: 2D points are represented via projective geometry as a list of three floating-point numbers, and everything is done numerically.  There are no symbolic representations or exact algebraic numbers. (Not sure how a point on a circle or line is handled, that would take further investigation.)
+CindyJS uses very concrete basic objects: 2D points are represented via projective geometry as a list of three floating-point numbers, and everything is done numerically.  There are no symbolic representations or exact algebraic numbers. (Not sure how a point on a circle or line is handled, that would take further investigation.) 
 Lines are given by explicit coordinates as well (not sure of the internal details/exact coordinatization, or of how a "LineThrough" is represented).
 Was unclear to me how the complex parametrization for preserving continuity was handled in the code, even though Jürgen harps on complex ambient spaces; where are the complex numbers? Perhaps that part of Cinderella was never re-implemented?
--- a/src/index.html
+++ b/src/index.html
@ -7,3 +7,5 @@
  <body><script type="module" src="dyna3.js"></script>
  </body>
 </html>
--- a/tools/package-for-deployment.sh
+++ b/tools/package-for-deployment.sh
@ -1,16 +0,0 @@
 # set paths. this technique for getting the script location comes from
 # `mklement0` on Stack Overflow
 #
 #   https://stackoverflow.com/a/24114056
 #
 TOOLS=$(dirname -- $0)
 SRC="$TOOLS/../app-proto/dist"
 DEST="$TOOLS/../deploy/dyna3"
 # remove the old hash-named files
 [ -e "$DEST"/dyna3-*.js ] && rm "$DEST"/dyna3-*.js
 [ -e "$DEST"/dyna3-*.wasm ] && rm "$DEST"/dyna3-*.wasm
 [ -e "$DEST"/main-*.css ] && rm "$DEST"/main-*.css
 # copy the distribution
 cp -r "$SRC/." "$DEST"
Author	SHA1	Message	Date
Aaron Fenyes	5233d8eb93	Move the components into their own module All checks were successful / test (pull_request) Successful in 3m36s Details This makes the module tree more reflective of module use patterns. In particular, it restores the condition that every top-level module is used in top-level code, which was broken by the addition of the `test_assembly_chooser` module in commit `91e4e1f`.	2025-07-22 13:28:48 -07:00
Aaron Fenyes	91e4e1f414	Make the test assembly chooser its own component All checks were successful / test (pull_request) Successful in 3m32s Details	2025-07-21 12:16:16 -07:00
Aaron Fenyes	4e5cd6e4a4	Add a dodecahedral circle packing test assembly All checks were successful / test (pull_request) Successful in 3m33s Details	2025-07-20 23:27:10 -07:00
Aaron Fenyes	97d61e154a	Add a tridiminished icosahedron test assembly	2025-07-20 23:27:10 -07:00
Aaron Fenyes	9c22eebb46	Add an off-center test assembly This test assembly should provide a simple example where the loss function is saddle-shaped near its manifold of minima.	2025-07-20 23:27:10 -07:00
Aaron Fenyes	27a8cbfd69	Add a balanced test assembly This test assembly reveals one way that the engine can stall, indicated by a long plateau in the loss history. You can make the plateau even longer by shrinking the inner spheres.	2025-07-20 23:27:10 -07:00
Aaron Fenyes	fae3f4531e	Add an Irisawa hexlet test assembly This partial setup of the Irisawa hexlet problem is from the summer 2025 tech demo.	2025-07-20 23:27:10 -07:00
Aaron Fenyes	543bc4020f	Add a tetrahedron radius ratio test assembly This partial setup of the tetrahedron radius ratio problem is from the summer 2025 tech demo.	2025-07-20 23:27:10 -07:00
Aaron Fenyes	40d665d8ac	Pause realization while loading assemblies This avoids redundant realizations as we set an assembly's regulators during loading. Adding some regulators to the low-curvature assembly confirms that the feature is working as intended.	2025-07-20 23:27:10 -07:00