Add kaleidocycle example

The engine successfully captures the kaleidocycle's twisting motion.
However, nudging doesn't work quite the way we want. This is probably to
be expected, since nudges don't commute with Euclidean motions in our
current implementation.

.forgejo/setup-trunk/action.yaml

@@ -1,22 +0,0 @@
-# set up the Trunk web build system
-#
-#   https://trunkrs.dev
-#
-# the `curl` call is based on David Tolnay's `rust-toolchain` action
-#
-#   https://github.com/dtolnay/rust-toolchain
-#
-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
-    # available by placing the fully qualified path to `ci-bin` on the
-    # workflow's search path
-    - run: mkdir -p ci-bin
-    - run: curl --output - --proto '=https' --tlsv1.2 --retry 10 --retry-connrefused --location --silent --show-error --fail 'https://github.com/trunk-rs/trunk/releases/download/v0.21.12/trunk-x86_64-unknown-linux-gnu.tar.gz' | tar --gunzip --extract --file -
-      working-directory: ci-bin
-    - run: echo "${{ github.workspace }}/ci-bin" >> $GITHUB_PATH

.forgejo/workflows/continuous-integration.yaml

@@ -1,29 +0,0 @@
-on:
-  pull_request:
-  push:
-    branches: [main]
-jobs:
-  # run the automated tests, reporting success if the tests pass and were built
-  # without warnings. the examples are run as tests, because we've configured
-  # each example target with `test = true` and `harness = false` in Cargo.toml.
-  # Trunk build failures caused by problems outside the Rust source code, like
-  # missing assets, should be caught by `trunk_build_test`
-  test:
-    runs-on: docker
-    container:
-      image: cimg/rust:1.86-node
-    defaults:
-      run:
-        # set the default working directory for each `run` step, relative to the
-        # workspace directory. this default only affects `run` steps (and if we
-        # tried to set the `working-directory` label for any other kind of step,
-        # it wouldn't be recognized anyway)
-        working-directory: app-proto
-    steps:
-      # Check out the repository so that its top-level directory is the
-      # 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

.gitignore

@@ -1,2 +1,8 @@
-ci-bin
+node_modules
+site
+docbuild
+__tests__
+coverage
+dyna3.zip
+tmpproj
 *~

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. Go into the `app-proto` folder
-   - The crates the prototype depends on will be downloaded and served automatically.
+2. Call `trunk serve --release` to build and serve the prototype
-   - For a faster build, at the expense of a much slower prototype, you can call `trunk serve` without the `--release` flag.
+   * *The crates the prototype depends on will be downloaded and served automatically*
-   - If you want to stay in the top-level folder, you can call `trunk serve --config app-proto [--release]` from there instead.
+   * *For a faster build, at the expense of a much slower prototype, you can call `trunk serve` without the `--release` flag*
-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.

app-proto/Cargo.toml

@@ -3,23 +3,19 @@ name = "dyna3"
 version = "0.1.0"
 authors = ["Aaron Fenyes", "Glen Whitney"]
 edition = "2021"
-rust-version = "1.86"
 
 [features]
 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"
 nalgebra = "0.33.0"
-readonly = "0.2.12"
+rustc-hash = "2.0.0"
-sycamore = "0.9.1"
+slab = "0.4.9"
-
+sycamore = "0.9.0-beta.3"
-# We use Charming to help display engine diagnostics
-charming = { version = "0.5.1", features = ["wasm"] }
 
 # The `console_error_panic_hook` crate provides better debugging of panics by
 # logging them with `console.error`. This is great for development, but requires
@@ -50,33 +46,6 @@ features = [
 dyna3 = { path = ".", default-features = false, features = ["dev"] }
 wasm-bindgen-test = "0.3.34"
 
-# turn off spurious warnings about the custom config that Sycamore uses
-#
-#   https://sycamore.dev/book/troubleshooting#unexpected-cfg-condition-name--sycamore-force-ssr
-#
-[lints.rust]
-unexpected_cfgs = { level = "warn", check-cfg = ["cfg(sycamore_force_ssr)"] }
-
 [profile.release]
 opt-level = "s" # optimize for small code size
 debug = true # include debug symbols
-
-[[example]]
-name = "irisawa-hexlet"
-test = true
-harness = false
-
-[[example]]
-name = "kaleidocycle"
-test = true
-harness = false
-
-[[example]]
-name = "point-on-sphere"
-test = true
-harness = false
-
-[[example]]
-name = "three-spheres"
-test = true
-harness = false

app-proto/Trunk.toml

@@ -1,2 +0,0 @@
-[build]
-public_url = "./"

app-proto/examples/common/print.rs

@@ -1,36 +0,0 @@
-#![allow(dead_code)]
-
-use nalgebra::DMatrix;
-
-use dyna3::engine::{Q, DescentHistory, Realization};
-
-pub fn title(title: &str) {
-    println!("─── {title} ───");
-}
-
-pub fn realization_diagnostics(realization: &Realization) {
-    let Realization { result, history } = realization;
-    println!();
-    if let Err(ref message) = result {
-        println!("❌️ {message}");
-    } else {
-        println!("✅️ Target accuracy achieved!");
-    }
-    println!("Steps: {}", history.scaled_loss.len() - 1);
-    println!("Loss: {}", history.scaled_loss.last().unwrap());
-}
-
-pub fn gram_matrix(config: &DMatrix<f64>) {
-    println!("\nCompleted Gram matrix:{}", (config.tr_mul(&*Q) * config).to_string().trim_end());
-}
-
-pub fn config(config: &DMatrix<f64>) {
-    println!("\nConfiguration:{}", config.to_string().trim_end());
-}
-
-pub fn loss_history(history: &DescentHistory) {
-    println!("\nStep │ Loss\n─────┼────────────────────────────────");
-    for (step, scaled_loss) in history.scaled_loss.iter().enumerate() {
-        println!("{:<4} │ {}", step, scaled_loss);
-    }
-}

app-proto/examples/irisawa-hexlet.rs

@@ -1,23 +1,25 @@
-#[path = "common/print.rs"]
+use dyna3::engine::{Q, irisawa::realize_irisawa_hexlet};
-mod print;
-
-use dyna3::engine::{ConfigNeighborhood, examples::realize_irisawa_hexlet};
 
 fn main() {
     const SCALED_TOL: f64 = 1.0e-12;
-    let realization = realize_irisawa_hexlet(SCALED_TOL);
+    let (config, _, success, history) = realize_irisawa_hexlet(SCALED_TOL);
-    print::title("Irisawa hexlet");
+    print!("\nCompleted Gram matrix:{}", config.tr_mul(&*Q) * &config);
-    print::realization_diagnostics(&realization);
+    if success {
-    if let Ok(ConfigNeighborhood { config, .. }) = realization.result {
+        println!("Target accuracy achieved!");
-        // print the diameters of the chain spheres
+    } else {
+        println!("Failed to reach target accuracy");
+    }
+    println!("Steps: {}", history.scaled_loss.len() - 1);
+    println!("Loss: {}", history.scaled_loss.last().unwrap());
+    if success {
         println!("\nChain diameters:");
         println!("  {} sun (given)", 1.0 / config[(3, 3)]);
         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);
+    println!("\nStep │ Loss\n─────┼────────────────────────────────");
-}
+    for (step, scaled_loss) in history.scaled_loss.into_iter().enumerate() {
+        println!("{:<4} │ {}", step, scaled_loss);
+    }
+}

app-proto/examples/kaleidocycle.rs

@@ -1,32 +1,81 @@
-#[path = "common/print.rs"]
+use nalgebra::DMatrix;
-mod print;
+use std::{array, f64::consts::PI};
 
-use nalgebra::{DMatrix, DVector};
+use dyna3::engine::{Q, point, realize_gram, PartialMatrix};
-
-use dyna3::engine::{ConfigNeighborhood, examples::realize_kaleidocycle};
 
 fn main() {
-    const SCALED_TOL: f64 = 1.0e-12;
+    // set up a kaleidocycle, made of points with fixed distances between them,
-    let realization = realize_kaleidocycle(SCALED_TOL);
+    // and find its tangent space
-    print::title("Kaleidocycle");
+    const N_POINTS: usize = 12;
-    print::realization_diagnostics(&realization);
+    let gram = {
-    if let Ok(ConfigNeighborhood { config, nbhd: tangent }) = realization.result {
+        let mut gram_to_be = PartialMatrix::new();
-        // print the completed Gram matrix and the realized configuration
+        for block in (0..N_POINTS).step_by(2) {
-        print::gram_matrix(&config);
+            let block_next = (block + 2) % N_POINTS;
-        print::config(&config);
+            for j in 0..2 {
-
+                // diagonal and hinge edges
-        // find the kaleidocycle's twist motion by projecting onto the tangent
+                for k in j..2 {
-        // space
+                    gram_to_be.push_sym(block + j, block + k, if j == k { 0.0 } else { -0.5 });
-        const N_POINTS: usize = 12;
+                }
-        let up = DVector::from_column_slice(&[0.0, 0.0, 1.0, 0.0]);
+                
-        let down = -&up;
+                // non-hinge edges
-        let twist_motion: DMatrix<_> = (0..N_POINTS).step_by(4).flat_map(
+                for k in 0..2 {
-            |n| [
+                    gram_to_be.push_sym(block + j, block_next + k, -0.625);
-                tangent.proj(&up.as_view(), n),
+                }
-                tangent.proj(&down.as_view(), n+1),
+            }
-            ]
+        }
-        ).sum();
+        gram_to_be
-        let normalization = 5.0 / twist_motion[(2, 0)];
+    };
-        println!("\nTwist motion:{}", (normalization * twist_motion).to_string().trim_end());
+    let guess = {
+        const N_HINGES: usize = 6;
+        let guess_elts = (0..N_HINGES).step_by(2).flat_map(
+            |n| {
+                let ang_hor = (n as f64) * PI/3.0;
+                let ang_vert = ((n + 1) as f64) * PI/3.0;
+                let x_vert = ang_vert.cos();
+                let y_vert = ang_vert.sin();
+                [
+                    point(0.0, 0.0, 0.0),
+                    point(ang_hor.cos(), ang_hor.sin(), 0.0),
+                    point(x_vert, y_vert, -0.5),
+                    point(x_vert, y_vert, 0.5)
+                ]
+            }
+        ).collect::<Vec<_>>();
+        DMatrix::from_columns(&guess_elts)
+    };
+    let frozen: [_; N_POINTS] = array::from_fn(|k| (3, k));
+    let (config, tangent, success, history) = realize_gram(
+        &gram, guess, &frozen,
+        1.0e-12, 0.5, 0.9, 1.1, 200, 110
+    );
+    print!("Completed Gram matrix:{}", config.tr_mul(&*Q) * &config);
+    print!("Configuration:{}", config);
+    if success {
+        println!("Target accuracy achieved!");
+    } else {
+        println!("Failed to reach target accuracy");
     }
-}
+    println!("Steps: {}", history.scaled_loss.len() - 1);
+    println!("Loss: {}\n", history.scaled_loss.last().unwrap());
+    
+    // find the kaleidocycle's twist motion
+    let twist_motion: DMatrix<_> = (0..N_POINTS).step_by(4).flat_map(
+        |n| {
+            let up_field = {
+                DMatrix::from_column_slice(5, 5, &[
+                    0.0, 0.0, 0.0, 0.0, 0.0,
+                    0.0, 0.0, 0.0, 0.0, 0.0,
+                    0.0, 0.0, 0.0, 0.0, 1.0,
+                    0.0, 0.0, 2.0, 0.0, 0.0,
+                    0.0, 0.0, 0.0, 0.0, 0.0
+                ])
+            };
+            [
+                tangent.proj(&(&up_field * config.column(n)).as_view(), n),
+                tangent.proj(&(-&up_field * config.column(n+1)).as_view(), n+1)
+            ]
+        }
+    ).sum();
+    let normalization = 5.0 / twist_motion[(2, 0)];
+    print!("Twist motion:{}", normalization * twist_motion);
+}

app-proto/examples/point-on-sphere.rs

@@ -1,33 +1,38 @@
-#[path = "common/print.rs"]
+use nalgebra::DMatrix;
-mod print;
 
-use dyna3::engine::{
+use dyna3::engine::{Q, point, realize_gram, sphere, PartialMatrix};
-    point,
-    realize_gram,
-    sphere,
-    ConfigNeighborhood,
-    ConstraintProblem,
-};
 
 fn main() {
-    let mut problem = ConstraintProblem::from_guess(&[
+    let gram = {
+        let mut gram_to_be = PartialMatrix::new();
+        for j in 0..2 {
+            for k in j..2 {
+                gram_to_be.push_sym(j, k, if (j, k) == (1, 1) { 1.0 } else { 0.0 });
+            }
+        }
+        gram_to_be
+    };
+    let guess = DMatrix::from_columns(&[
         point(0.0, 0.0, 2.0),
         sphere(0.0, 0.0, 0.0, 1.0)
     ]);
-    for j in 0..2 {
+    let frozen = [(3, 0)];
-        for k in j..2 {
+    println!();
-            problem.gram.push_sym(j, k, if (j, k) == (1, 1) { 1.0 } else { 0.0 });
+    let (config, _, success, history) = realize_gram(
-        }
+        &gram, guess, &frozen,
-    }
+        1.0e-12, 0.5, 0.9, 1.1, 200, 110
-    problem.frozen.push(3, 0, problem.guess[(3, 0)]);
-    let realization = realize_gram(
-        &problem, 1.0e-12, 0.5, 0.9, 1.1, 200, 110
     );
-    print::title("Point on a sphere");
+    print!("\nCompleted Gram matrix:{}", config.tr_mul(&*Q) * &config);
-    print::realization_diagnostics(&realization);
+    print!("Configuration:{}", config);
-    if let Ok(ConfigNeighborhood { config, .. }) = realization.result {
+    if success {
-        print::gram_matrix(&config);
+        println!("Target accuracy achieved!");
-        print::config(&config);
+    } else {
+        println!("Failed to reach target accuracy");
+    }
+    println!("Steps: {}", history.scaled_loss.len() - 1);
+    println!("Loss: {}", history.scaled_loss.last().unwrap());
+    println!("\nStep │ Loss\n─────┼────────────────────────────────");
+    for (step, scaled_loss) in history.scaled_loss.into_iter().enumerate() {
+        println!("{:<4} │ {}", step, scaled_loss);
     }
-    print::loss_history(&realization.history);
 }

app-proto/examples/three-spheres.rs

@@ -1,34 +1,40 @@
-#[path = "common/print.rs"]
+use nalgebra::DMatrix;
-mod print;
 
-use dyna3::engine::{
+use dyna3::engine::{Q, realize_gram, sphere, PartialMatrix};
-    realize_gram,
-    sphere,
-    ConfigNeighborhood,
-    ConstraintProblem,
-};
 
 fn main() {
-    let mut problem = ConstraintProblem::from_guess({
+    let gram = {
+        let mut gram_to_be = PartialMatrix::new();
+        for j in 0..3 {
+            for k in j..3 {
+                gram_to_be.push_sym(j, k, if j == k { 1.0 } else { -1.0 });
+            }
+        }
+        gram_to_be
+    };
+    let guess = {
         let a: f64 = 0.75_f64.sqrt();
-        &[
+        DMatrix::from_columns(&[
             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 {
+    println!();
-        for k in j..3 {
+    let (config, _, success, history) = realize_gram(
-            problem.gram.push_sym(j, k, if j == k { 1.0 } else { -1.0 });
+        &gram, guess, &[],
-        }
+        1.0e-12, 0.5, 0.9, 1.1, 200, 110
-    }
-    let realization = realize_gram(
-        &problem, 1.0e-12, 0.5, 0.9, 1.1, 200, 110
     );
-    print::title("Three spheres");
+    print!("\nCompleted Gram matrix:{}", config.tr_mul(&*Q) * &config);
-    print::realization_diagnostics(&realization);
+    if success {
-    if let Ok(ConfigNeighborhood { config, .. }) = realization.result {
+        println!("Target accuracy achieved!");
-        print::gram_matrix(&config);
+    } else {
+        println!("Failed to reach target accuracy");
+    }
+    println!("Steps: {}", history.scaled_loss.len() - 1);
+    println!("Loss: {}", history.scaled_loss.last().unwrap());
+    println!("\nStep │ Loss\n─────┼────────────────────────────────");
+    for (step, scaled_loss) in history.scaled_loss.into_iter().enumerate() {
+        println!("{:<4} │ {}", step, scaled_loss);
     }
-    print::loss_history(&realization.history);
 }

app-proto/index.html

@@ -6,12 +6,6 @@
     <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
-    -->
-    <script src="https://cdn.jsdelivr.net/npm/echarts@5.5.1/dist/echarts.min.js"></script>
   </head>
   <body></body>
 </html>

app-proto/main.css

@@ -3,8 +3,7 @@
   --text-bright: white;
   --text-invalid: #f58fc2; /* bright pink */
   --border: #555; /* light gray */
-  --border-focus-dark: #aaa; /* bright gray */
+  --border-focus: #aaa; /* bright gray */
-  --border-focus-light: white;
   --border-invalid: #70495c; /* dusky pink */
   --selection-highlight: #444; /* medium gray */
   --page-background: #222; /* dark gray */
@@ -18,24 +17,13 @@ body {
   font-family: 'Fira Sans', sans-serif;
 }
 
-.invalid {
-  color: var(--text-invalid);
-}
-
-.status {
-  width: 20px;
-  text-align: center;
-  font-family: 'Noto Emoji';
-  font-style: normal;
-}
-
 /* sidebar */
 
 #sidebar {
   display: flex;
   flex-direction: column;
   float: left;
-  width: 500px;
+  width: 450px;
   height: 100vh;
   margin: 0px;
   padding: 0px;
@@ -53,7 +41,9 @@ body {
 }
 
 #add-remove > button {
+  width: 32px;
   height: 32px;
+  font-size: large;
 }
 
 /* KLUDGE */
@@ -62,9 +52,7 @@ body {
   buttons need to be displayed in an emoji font
 */
 #add-remove > button.emoji {
-  width: 32px;
   font-family: 'Noto Emoji', sans-serif;
-  font-size: large;
 }
 
 /* outline */
@@ -89,22 +77,18 @@ summary.selected {
   background-color: var(--selection-highlight);
 }
 
-summary > div, .regulator {
+summary > div, .constraint {
   padding-top: 4px;
   padding-bottom: 4px;
 }
 
-.element, .regulator {
+.element, .constraint {
   display: flex;
   flex-grow: 1;
   padding-left: 8px;
   padding-right: 8px;
 }
 
-.element > input {
-  margin-left: 8px;
-}
-
 .element-switch {
   width: 18px;
   padding-left: 2px;
@@ -123,7 +107,7 @@ details[open]:has(li) .element-switch::after {
   flex-grow: 1;
 }
 
-.regulator-label {
+.constraint-label {
   flex-grow: 1;
 }
 
@@ -139,97 +123,45 @@ details[open]:has(li) .element-switch::after {
   width: 56px;
 }
 
-.regulator {
+.constraint {
   font-style: italic;
 }
 
-.regulator-type {
+.constraint.invalid {
-  padding: 2px 8px 0px 8px;
+  color: var(--text-invalid);
-  font-size: 10pt;
 }
 
-.regulator-input {
+.constraint > input[type=checkbox] {
-  margin-right: 4px;
+  margin: 0px 8px 0px 0px;
+}
+
+.constraint > input[type=text] {
   color: inherit;
   background-color: inherit;
   border: 1px solid var(--border);
   border-radius: 2px;
 }
 
-.regulator-input::placeholder {
+.constraint.invalid > input[type=text] {
-  color: inherit;
-  opacity: 54%;
-  font-style: italic;
-}
-
-.regulator-input.constraint {
-  background-color: var(--display-background);
-}
-
-.regulator-input.invalid {
-  color: var(--text-invalid);
   border-color: var(--border-invalid);
 }
 
-.regulator-input.invalid + .status::after, details:has(.invalid):not([open]) .status::after {
+.status {
+  width: 20px;
+  padding-left: 4px;
+  text-align: center;
+  font-family: 'Noto Emoji';
+  font-style: normal;
+}
+
+.invalid > .status::after, details:has(.invalid):not([open]) .status::after {
   content: '⚠';
   color: var(--text-invalid);
 }
 
-/* diagnostics */
-
-#diagnostics {
-  margin: 10px;
-}
-
-#diagnostics-bar {
-  display: flex;
-  gap: 8px;
-}
-
-#realization-status {
-  display: flex;
-  flex-grow: 1;
-}
-
-#realization-status .status {
-  margin-right: 4px;
-}
-
-#realization-status :not(.status) {
-  flex-grow: 1;
-}
-
-#realization-status .status::after {
-  content: '✓';
-}
-
-#realization-status.invalid .status::after {
-  content: '⚠';
-}
-
-#step-input > label {
-  padding-right: 4px;
-}
-
-#step-input > input {
-  width: 45px;
-}
-
-.diagnostics-panel {
-  margin-top: 10px;
-  min-height: 180px;
-}
-
-.diagnostics-chart {
-  background-color: var(--display-background);
-  border: 1px solid var(--border);
-  border-radius: 8px;
-}
-
 /* display */
 
-#display {
+canvas {
   float: left;
   margin-left: 20px;
   margin-top: 20px;
@@ -238,12 +170,6 @@ details[open]:has(li) .element-switch::after {
   border-radius: 16px;
 }
 
-#display:focus {
+canvas:focus {
-  border-color: var(--border-focus-dark);
+  border-color: var(--border-focus);
-  outline: none;
-}
-
-input:focus {
-  border-color: var(--border-focus-light);
-  outline: none;
 }

app-proto/run-examples

@@ -0,0 +1,12 @@
+#!/bin/sh
+
+# run all Cargo examples, as described here:
+#
+#   Karol Kuczmarski. "Add examples to your Rust libraries"
+#   http://xion.io/post/code/rust-examples.html
+#
+
+cargo run --example irisawa-hexlet
+cargo run --example three-spheres
+cargo run --example point-on-sphere
+cargo run --example kaleidocycle

app-proto/src/add_remove.rs

@@ -0,0 +1,240 @@
+use sycamore::prelude::*;
+use web_sys::{console, wasm_bindgen::JsValue};
+
+use crate::{engine, AppState, assembly::{Assembly, Constraint, Element}};
+
+/* DEBUG */
+// load an example assembly for testing. this code will be removed once we've
+// built a more formal test assembly system
+fn load_gen_assemb(assembly: &Assembly) {
+    let _ = assembly.try_insert_element(
+        Element::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)
+        )
+    );
+    let _ = assembly.try_insert_element(
+        Element::new(
+            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)
+        )
+    );
+    let _ = assembly.try_insert_element(
+        Element::new(
+            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)
+        )
+    );
+    let _ = assembly.try_insert_element(
+        Element::new(
+            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)
+        )
+    );
+    let _ = assembly.try_insert_element(
+        Element::new(
+            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)
+        )
+    );
+    let _ = assembly.try_insert_element(
+        Element::new(
+            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)
+        )
+    );
+}
+
+/* DEBUG */
+// load an example assembly for testing. this code will be removed once we've
+// built a more formal test assembly system
+fn load_low_curv_assemb(assembly: &Assembly) {
+    let a = 0.75_f64.sqrt();
+    let _ = assembly.try_insert_element(
+        Element::new(
+            "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)
+        )
+    );
+    let _ = assembly.try_insert_element(
+        Element::new(
+            "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)
+        )
+    );
+    let _ = assembly.try_insert_element(
+        Element::new(
+            "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)
+        )
+    );
+    let _ = assembly.try_insert_element(
+        Element::new(
+            "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)
+        )
+    );
+    let _ = assembly.try_insert_element(
+        Element::new(
+            "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)
+        )
+    );
+    let _ = assembly.try_insert_element(
+        Element::new(
+            "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)
+        )
+    );
+    let _ = assembly.try_insert_element(
+        Element::new(
+            "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)
+        )
+    );
+    let _ = assembly.try_insert_element(
+        Element::new(
+            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)
+        )
+    );
+}
+
+#[component]
+pub fn AddRemove() -> View {
+    /* DEBUG */
+    let assembly_name = create_signal("general".to_string());
+    create_effect(move || {
+        // get name of chosen assembly
+        let name = assembly_name.get_clone();
+        console::log_1(
+            &JsValue::from(format!("Showing assembly \"{}\"", name.clone()))
+        );
+        
+        batch(|| {
+            let state = use_context::<AppState>();
+            let assembly = &state.assembly;
+            
+            // clear state
+            assembly.elements.update(|elts| elts.clear());
+            assembly.elements_by_id.update(|elts_by_id| elts_by_id.clear());
+            state.selection.update(|sel| sel.clear());
+            
+            // load assembly
+            match name.as_str() {
+                "general" => load_gen_assemb(assembly),
+                "low-curv" => load_low_curv_assemb(assembly),
+                _ => ()
+            };
+        });
+    });
+    
+    view! {
+        div(id="add-remove") {
+            button(
+                on:click=|_| {
+                    let state = use_context::<AppState>();
+                    state.assembly.insert_new_element();
+                    
+                    /* DEBUG */
+                    // print updated list of elements by identifier
+                    console::log_1(&JsValue::from("elements by identifier:"));
+                    for (id, key) in state.assembly.elements_by_id.get_clone().iter() {
+                        console::log_3(
+                            &JsValue::from(" "),
+                            &JsValue::from(id),
+                            &JsValue::from(*key)
+                        );
+                    }
+                }
+            ) { "+" }
+            button(
+                class="emoji", /* KLUDGE */ // for convenience, we're using an emoji as a temporary icon for this button
+                disabled={
+                    let state = use_context::<AppState>();
+                    state.selection.with(|sel| sel.len() != 2)
+                },
+                on:click=|_| {
+                    let state = use_context::<AppState>();
+                    let subjects = state.selection.with(
+                        |sel| {
+                            let subject_vec: Vec<_> = sel.into_iter().collect();
+                            (subject_vec[0].clone(), subject_vec[1].clone())
+                        }
+                    );
+                    let lorentz_prod = create_signal(0.0);
+                    let lorentz_prod_valid = create_signal(false);
+                    let active = create_signal(true);
+                    state.assembly.insert_constraint(Constraint {
+                        subjects: subjects,
+                        lorentz_prod: lorentz_prod,
+                        lorentz_prod_text: create_signal(String::new()),
+                        lorentz_prod_valid: lorentz_prod_valid,
+                        active: active,
+                    });
+                    state.selection.update(|sel| sel.clear());
+                    
+                    /* DEBUG */
+                    // print updated constraint list
+                    console::log_1(&JsValue::from("Constraints:"));
+                    state.assembly.constraints.with(|csts| {
+                        for (_, cst) in csts.into_iter() {
+                            console::log_5(
+                                &JsValue::from(" "),
+                                &JsValue::from(cst.subjects.0),
+                                &JsValue::from(cst.subjects.1),
+                                &JsValue::from(":"),
+                                &JsValue::from(cst.lorentz_prod.get_untracked())
+                            );
+                        }
+                    });
+                    
+                    // update the realization when the constraint becomes active
+                    // and valid, or is edited while active and valid
+                    create_effect(move || {
+                        console::log_1(&JsValue::from(
+                            format!("Constraint ({}, {}) updated", subjects.0, subjects.1)
+                        ));
+                        lorentz_prod.track();
+                        if active.get() && lorentz_prod_valid.get() {
+                            state.assembly.realize();
+                        }
+                    });
+                }
+            ) { "🔗" }
+            select(bind:value=assembly_name) { /* DEBUG */ // example assembly chooser
+                option(value="general") { "General" }
+                option(value="low-curv") { "Low-curvature" }
+                option(value="empty") { "Empty" }
+            }
+        }
+    }
+}

app-proto/src/components.rs

@@ -1,5 +0,0 @@
-pub mod add_remove;
-pub mod diagnostics;
-pub mod display;
-pub mod outline;
-pub mod test_assembly_chooser;

app-proto/src/components/add_remove.rs

@@ -1,69 +0,0 @@
-use std::rc::Rc;
-use sycamore::prelude::*;
-
-use super::test_assembly_chooser::TestAssemblyChooser;
-use crate::{
-    AppState,
-    assembly::{InversiveDistanceRegulator, Point, Sphere},
-};
-
-#[component]
-pub fn AddRemove() -> View {
-    view! {
-        div(id = "add-remove") {
-            button(
-                on:click = |_| {
-                    let state = use_context::<AppState>();
-                    batch(|| {
-                        // 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 = |_| {
-                    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
-                disabled = {
-                    let state = use_context::<AppState>();
-                    state.selection.with(|sel| sel.len() != 2)
-                },
-                on:click = |_| {
-                    let state = use_context::<AppState>();
-                    let subjects: [_; 2] = state.selection.with(
-                        // the button is only enabled when two elements are
-                        // selected, so we know the cast to a two-element array
-                        // will succeed
-                        |sel| sel
-                            .clone()
-                            .into_iter()
-                            .collect::<Vec<_>>()
-                            .try_into()
-                            .unwrap()
-                    );
-                    state.assembly.insert_regulator(
-                        Rc::new(InversiveDistanceRegulator::new(subjects))
-                    );
-                    state.selection.update(|sel| sel.clear());
-                }
-            ) { "🔗" }
-            TestAssemblyChooser {}
-        }
-    }
-}

app-proto/src/components/diagnostics.rs

@@ -1,320 +0,0 @@
-use charming::{
-    Chart,
-    WasmRenderer,
-    component::{Axis, DataZoom, Grid},
-    element::{AxisType, Symbol},
-    series::{Line, Scatter},
-};
-use sycamore::prelude::*;
-
-use crate::{AppState, specified::SpecifiedValue};
-
-#[derive(Clone)]
-struct DiagnosticsState {
-    active_tab: Signal<String>,
-}
-
-impl DiagnosticsState {
-    fn new(initial_tab: String) -> Self {
-        Self { active_tab: create_signal(initial_tab) }
-    }
-}
-
-// a realization status indicator
-#[component]
-fn RealizationStatus() -> View {
-    let state = use_context::<AppState>();
-    let realization_status = state.assembly.realization_status;
-    view! {
-        div(
-            id = "realization-status",
-            class = realization_status.with(
-                |status| match status {
-                    Ok(_) => "",
-                    Err(_) => "invalid",
-                }
-            )
-        ) {
-            div(class = "status")
-            div {
-                (realization_status.with(
-                    |status| match status {
-                        Ok(_) => "Target accuracy achieved".to_string(),
-                        Err(message) => message.clone(),
-                    }
-                ))
-            }
-        }
-    }
-}
-
-// 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()) },
-    ]
-}
-
-// the loss history from the last realization
-#[component]
-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
-            let scaled_loss: Vec<_> = state.assembly.descent_history.with(
-                |history| history.scaled_loss
-                    .iter()
-                    .enumerate()
-                    .map(|(step, &loss)| (step, loss))
-                    .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
-            // chart: it instead leads to previous data being re-used
-            let scaled_loss_series = Line::new().data(
-                if scaled_loss.len() > 0 {
-                    scaled_loss
-                } else {
-                    vec![vec![Some(0.0), None::<f64>]]
-                }
-            );
-            let chart = Chart::new()
-                .animation(false)
-                .data_zoom(DataZoom::new().y_axis_index(0).right(40))
-                .x_axis(step_axis)
-                .y_axis(scaled_loss_axis)
-                .grid(Grid::new().top(20).right(80).bottom(30).left(60))
-                .series(scaled_loss_series);
-            renderer.render(CONTAINER_ID, &chart).unwrap();
-        });
-    });
-
-    view! {
-        div(id = CONTAINER_ID, class = "diagnostics-chart")
-    }
-}
-
-// the spectrum of the Hessian during the last realization
-#[component]
-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,
-            ): (Vec<_>, Vec<_>) = state.assembly.descent_history.with(
-                |history| history.hess_eigvals
-                    .iter()
-                    .enumerate()
-                    .map(
-                        |(step, eigvals)| eigvals.iter().map(
-                            move |&val| (step, val)
-                        )
-                    )
-                    .flatten()
-                    .partition(|&(_, val)| val == 0.0)
-            );
-            let zero_level = hess_eigvals_nonzero
-                .iter()
-                .map(|(_, val)| val.abs())
-                .reduce(f64::min)
-                .map(|val| 0.1 * val)
-                .unwrap_or(1.0);
-            let (
-                hess_eigvals_pos,
-                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
-            // chart: it instead leads to previous data being re-used
-            let eigval_series_pos = Scatter::new()
-                .symbol_size(4.5)
-                .data(
-                    if hess_eigvals_pos.len() > 0 {
-                        hess_eigvals_pos
-                            .into_iter()
-                            .map(into_log10_time_point)
-                            .collect()
-                    } else {
-                        vec![vec![Some(0.0), None::<f64>]]
-                    }
-                );
-            let eigval_series_neg = Scatter::new()
-                .symbol(Symbol::Diamond)
-                .symbol_size(6.0)
-                .data(
-                    if hess_eigvals_neg.len() > 0 {
-                        hess_eigvals_neg
-                            .into_iter()
-                            .map(into_log10_time_point)
-                            .collect()
-                    } else {
-                        vec![vec![Some(0.0), None::<f64>]]
-                    }
-                );
-            let eigval_series_zero = Scatter::new()
-                .symbol(Symbol::Triangle)
-                .symbol_size(5.0)
-                .data(
-                    if hess_eigvals_zero.len() > 0 {
-                        hess_eigvals_zero
-                            .into_iter()
-                            .map(|(step, _)| (step, zero_level))
-                            .map(into_log10_time_point)
-                            .collect()
-                    } else {
-                        vec![vec![Some(0.0), None::<f64>]]
-                    }
-                );
-            let chart = Chart::new()
-                .animation(false)
-                .data_zoom(DataZoom::new().y_axis_index(0).right(40))
-                .x_axis(step_axis)
-                .y_axis(eigval_axis)
-                .grid(Grid::new().top(20).right(80).bottom(30).left(60))
-                .series(eigval_series_pos)
-                .series(eigval_series_neg)
-                .series(eigval_series_zero);
-            renderer.render(CONTAINER_ID, &chart).unwrap();
-        });
-    });
-
-    view! {
-        div(id = CONTAINER_ID, class = "diagnostics-chart")
-    }
-}
-
-#[component(inline_props)]
-fn DiagnosticsPanel(name: &'static str, children: Children) -> View {
-    let diagnostics_state = use_context::<DiagnosticsState>();
-    view! {
-        div(
-            class = "diagnostics-panel",
-            "hidden" = diagnostics_state.active_tab.with(
-                |active_tab| {
-                    if active_tab == name {
-                        None
-                    } else {
-                        Some("")
-                    }
-                }
-            )
-        ) {
-            (children)
-        }
-    }
-}
-
-#[component]
-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-bar") {
-                RealizationStatus {}
-                select(bind:value = active_tab) {
-                    option(value = "loss") { "Loss" }
-                    option(value = "spectrum") { "Spectrum" }
-                }
-                StepInput {}
-            }
-            DiagnosticsPanel(name = "loss") { LossHistory {} }
-            DiagnosticsPanel(name = "spectrum") { SpectrumHistory {} }
-        }
-    }
-}

app-proto/src/components/display.rs

@@ -1,939 +0,0 @@
-use core::array;
-use nalgebra::{DMatrix, DVector, Rotation3, Vector3};
-use std::rc::Rc;
-use sycamore::{prelude::*, motion::create_raf};
-use web_sys::{
-    console,
-    window,
-    KeyboardEvent,
-    MouseEvent,
-    WebGl2RenderingContext,
-    WebGlBuffer,
-    WebGlProgram,
-    WebGlShader,
-    WebGlUniformLocation,
-    wasm_bindgen::{JsCast, JsValue},
-};
-
-use crate::{
-    AppState,
-    assembly::{Element, ElementColor, ElementMotion, Point, Sphere},
-};
-
-// --- color ---
-
-const COLOR_SIZE: usize = 3;
-type ColorWithOpacity = [f32; COLOR_SIZE + 1];
-
-fn combine_channels(color: ElementColor, opacity: f32) -> ColorWithOpacity {
-    let mut color_with_opacity = [0.0; COLOR_SIZE + 1];
-    color_with_opacity[..COLOR_SIZE].copy_from_slice(&color);
-    color_with_opacity[COLOR_SIZE] = opacity;
-    color_with_opacity
-}
-
-// --- scene data ---
-
-struct SceneSpheres {
-    representations: Vec<DVector<f64>>,
-    colors_with_opacity: Vec<ColorWithOpacity>,
-    highlights: Vec<f32>,
-}
-
-impl SceneSpheres {
-    fn new() -> Self {
-        Self {
-            representations: Vec::new(),
-            colors_with_opacity: 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(
-        &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);
-    }
-}
-
-struct ScenePoints {
-    representations: Vec<DVector<f64>>,
-    colors_with_opacity: Vec<ColorWithOpacity>,
-    highlights: Vec<f32>,
-    selections: Vec<f32>,
-}
-
-impl ScenePoints {
-    fn new() -> Self {
-        Self {
-            representations: Vec::new(),
-            colors_with_opacity: Vec::new(),
-            highlights: Vec::new(),
-            selections: Vec::new(),
-        }
-    }
-
-    fn push(
-        &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);
-        self.selections.push(if selected { 1.0 } else { 0.0 });
-    }
-}
-
-pub struct Scene {
-    spheres: SceneSpheres,
-    points: ScenePoints,
-}
-
-impl Scene {
-    fn new() -> Self {
-        Self {
-            spheres: SceneSpheres::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(
-        &self,
-        dir: Vector3<f64>,
-        assembly_to_world: &DMatrix<f64>,
-        pixel_size: f64,
-    ) -> Option<f64>;
-}
-
-impl DisplayItem for Sphere {
-    fn show(&self, scene: &mut Scene, selected: bool) {
-        /* SCAFFOLDING */
-        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(
-        &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
-            //
-            //   a*u^2 + b*u + c
-            //
-            // at `u = 0` will reach zero at a finite depth `u_lin`. the root of
-            // the quadratic adjacent to `u_lin` is stored in `lin_root`. if
-            // both roots have the same sign, `lin_root` will be the one closer
-            // to `u = 0`
-            let square_rect_ratio = 1.0 + (1.0 - adjust).sqrt();
-            let lin_root = -(2.0*c)/b / square_rect_ratio;
-            if a.abs() > DEG_THRESHOLD * b.abs() {
-                if lin_root > 0.0 {
-                    Some(lin_root)
-                } else {
-                    let other_root = -b/(2.*a) * square_rect_ratio;
-                    (other_root > 0.0).then_some(other_root)
-                }
-            } else {
-                (lin_root > 0.0).then_some(lin_root)
-            }
-        } else {
-            // the line through `dir` misses the sphere completely
-            None
-        }
-    }
-}
-
-impl DisplayItem for Point {
-    fn show(&self, scene: &mut Scene, selected: bool) {
-        /* 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(
-        &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])
-            } else {
-                None
-            }
-        } else {
-            None
-        }
-    }
-}
-
-// --- WebGL utilities ---
-
-fn compile_shader(
-    context: &WebGl2RenderingContext,
-    shader_type: u32,
-    source: &str,
-) -> WebGlShader {
-    let shader = context.create_shader(shader_type).unwrap();
-    context.shader_source(&shader, source);
-    context.compile_shader(&shader);
-    shader
-}
-
-fn set_up_program(
-    context: &WebGl2RenderingContext,
-    vertex_shader_source: &str,
-    fragment_shader_source: &str,
-) -> WebGlProgram {
-    // compile the shaders
-    let vertex_shader = compile_shader(
-        &context,
-        WebGl2RenderingContext::VERTEX_SHADER,
-        vertex_shader_source,
-    );
-    let fragment_shader = compile_shader(
-        &context,
-        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
-        .get_program_parameter(&program, WebGl2RenderingContext::LINK_STATUS)
-        .as_bool()
-        .unwrap();
-    let link_msg = if link_status {
-        "Linked successfully"
-    } else {
-        "Linking failed"
-    };
-    console::log_1(&JsValue::from(link_msg));
-
-    program
-}
-
-fn get_uniform_array_locations<const N: usize>(
-    context: &WebGl2RenderingContext,
-    program: &WebGlProgram,
-    var_name: &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}]"),
-        };
-        context.get_uniform_location(&program, name.as_str())
-    })
-}
-
-// bind the given vertex buffer object to the given vertex attribute
-fn bind_to_attribute(
-    context: &WebGl2RenderingContext,
-    attr_index: u32,
-    attr_size: i32,
-    buffer: &Option<WebGlBuffer>,
-) {
-    context.bind_buffer(WebGl2RenderingContext::ARRAY_BUFFER, buffer.as_ref());
-    context.vertex_attrib_pointer_with_i32(
-        attr_index,
-        attr_size,
-        WebGl2RenderingContext::FLOAT,
-        false, // don't normalize
-        0, // zero stride
-        0, // zero offset
-    );
-}
-
-// load the given data into a new vertex buffer object
-fn load_new_buffer(
-    context: &WebGl2RenderingContext,
-    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
-    // buffer, invalidating the view, so we have to make sure we don't allocate
-    // any memory until the view is dropped. we're okay here because the view is
-    // used as soon as it's created
-    unsafe {
-        context.buffer_data_with_array_buffer_view(
-            WebGl2RenderingContext::ARRAY_BUFFER,
-            &js_sys::Float32Array::view(&data),
-            WebGl2RenderingContext::STATIC_DRAW,
-        );
-    }
-
-    buffer
-}
-
-fn bind_new_buffer_to_attribute(
-    context: &WebGl2RenderingContext,
-    attr_index: u32,
-    attr_size: i32,
-    data: &[f32],
-) {
-    let buffer = load_new_buffer(context, data);
-    bind_to_attribute(context, attr_index, attr_size, &buffer);
-}
-
-// the direction in camera space that a mouse event is pointing along
-fn event_dir(event: &MouseEvent) -> (Vector3<f64>, f64) {
-    let target: web_sys::Element = event.target().unwrap().unchecked_into();
-    let rect = target.get_bounding_client_rect();
-    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,
-        ),
-        FOCAL_SLOPE * 2.0 / shortdim,
-    )
-}
-
-// --- display component ---
-
-#[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);
-    let yaw_right = create_signal(0.0);
-    let yaw_left = create_signal(0.0);
-    let roll_ccw = create_signal(0.0);
-    let roll_cw = create_signal(0.0);
-    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);
-    let translate_neg_y = create_signal(0.0);
-    let translate_pos_y = create_signal(0.0);
-    let translate_neg_z = create_signal(0.0);
-    let translate_pos_z = create_signal(0.0);
-    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 || {
-        state.assembly.elements.with(|elts| {
-            for elt in elts {
-                elt.representation().track();
-                elt.ghost().track();
-            }
-        });
-        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
-        const TURNTABLE_SPEED: f64 = 0.1; /* BENCHMARKING */
-        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
-            .get_context("webgl2")
-            .unwrap()
-            .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"),
-        );
-
-        // set up the point rendering program
-        let point_program = set_up_program(
-            &ctx,
-            include_str!("point.vert"),
-            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
-        // requires this maximum to be at least 224, as discussed in the
-        // documentation of the GL_MAX_FRAGMENT_UNIFORM_VECTORS parameter
-        // here:
-        //
-        //   https://registry.khronos.org/OpenGL-Refpages/es3.0/html/glGet.xhtml
-        //
-        // there are also other size limits. for example, on Aaron's
-        // machine, the the length of a float or genType array seems to be
-        // capped at 1024 elements
-        console::log_2(
-            &ctx.get_parameter(WebGl2RenderingContext::MAX_FRAGMENT_UNIFORM_VECTORS).unwrap(),
-            &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");
-        let sphere_sp_locs = get_uniform_array_locations::<SPHERE_MAX>(
-            &ctx, &sphere_program, "sphere_list", Some("sp")
-        );
-        let sphere_lt_locs = get_uniform_array_locations::<SPHERE_MAX>(
-            &ctx, &sphere_program, "sphere_list", Some("lt")
-        );
-        let sphere_color_locs = get_uniform_array_locations::<SPHERE_MAX>(
-            &ctx, &sphere_program, "color_list", None
-        );
-        let sphere_highlight_locs = get_uniform_array_locations::<SPHERE_MAX>(
-            &ctx, &sphere_program, "highlight_list", None
-        );
-        let resolution_loc = ctx.get_uniform_location(&sphere_program, "resolution");
-        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] = [
-            // northwest triangle
-            -1.0, -1.0, 0.0,
-            -1.0,  1.0, 0.0,
-             1.0,  1.0, 0.0,
-            // southeast triangle
-            -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();
-            let yaw_right_val = yaw_right.get();
-            let yaw_left_val = yaw_left.get();
-            let roll_ccw_val = roll_ccw.get();
-            let roll_cw_val = roll_cw.get();
-            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();
-            let translate_neg_y_val = translate_neg_y.get();
-            let translate_pos_y_val = translate_pos_y.get();
-            let translate_neg_z_val = translate_neg_z.get();
-            let translate_pos_z_val = translate_pos_z.get();
-            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;
-                let yaw = yaw_right_val - yaw_left_val;
-                let roll = roll_ccw_val - roll_cw_val;
-                if pitch != 0.0 || yaw != 0.0 || roll != 0.0 {
-                    ROT_SPEED * Vector3::new(-pitch, yaw, roll).normalize()
-                } else {
-                    Vector3::zeros()
-                }
-            } /* BENCHMARKING */ + if turntable_val {
-                Vector3::new(0.0, TURNTABLE_SPEED, 0.0)
-            } else {
-                Vector3::zeros()
-            };
-            let mut rotation_sp = rotation.fixed_view_mut::<3, 3>(0, 0);
-            rotation_sp.copy_from(
-                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 */
-            // 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()
-                );
-                let translate_x = translate_pos_x_val - translate_neg_x_val;
-                let translate_y = translate_pos_y_val - translate_neg_y_val;
-                let translate_z = translate_pos_z_val - translate_neg_z_val;
-                let shrink = shrink_pos_val - shrink_neg_val;
-                let translating =
-                    translate_x != 0.0
-                    || translate_y != 0.0
-                    || translate_z != 0.0;
-                if translating || shrink != 0.0 {
-                    let elt_motion = {
-                        let u = if translating {
-                            TRANSLATION_SPEED * Vector3::new(
-                                translate_x, translate_y, translate_z
-                            ).normalize()
-                        } else {
-                            Vector3::zeros()
-                        };
-                        time_step * DVector::from_column_slice(
-                            &[u[0], u[1], u[2], SHRINKING_SPEED * shrink]
-                        )
-                    };
-                    assembly_for_raf.deform(
-                        vec![
-                            ElementMotion {
-                                element: sel,
-                                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;
-                if frames_since_last_sample >= SAMPLE_PERIOD {
-                    mean_frame_interval.set((time - last_sample_time) / (SAMPLE_PERIOD as f64));
-                    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;
-                    DMatrix::from_column_slice(5, 5, &[
-                        1.0, 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,   u,
-                        0.0, 0.0, 2.0*u, 1.0, u*u,
-                        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 {
-                        let selected = state.selection.with(|sel| sel.contains(elt));
-                        elt.show(&mut scene, selected);
-                    }
-                );
-                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(),
-                    );
-                    ctx.uniform2fv_with_f32_array(
-                        sphere_lt_locs[n].as_ref(),
-                        v.rows(3, 2).as_slice(),
-                    );
-                    ctx.uniform4fv_with_f32_array(
-                        sphere_color_locs[n].as_ref(),
-                        &scene.spheres.colors_with_opacity[n],
-                    );
-                    ctx.uniform1f(
-                        sphere_highlight_locs[n].as_ref(),
-                        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(
-                        &scene.points.representations.into_iter().map(
-                            |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
-                    bind_new_buffer_to_attribute(&ctx, point_position_attr, SPACE_DIM as i32, point_positions.as_slice());
-                    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
-                    || pitch_down_val != 0.0
-                    || yaw_left_val != 0.0
-                    || yaw_right_val != 0.0
-                    || roll_cw_val != 0.0
-                    || roll_ccw_val != 0.0
-                    || zoom_in_val != 0.0
-                    || zoom_out_val != 0.0
-                    || turntable_val /* BENCHMARKING */
-                );
-            } else {
-                frames_since_last_sample = 0;
-                mean_frame_interval.set(-1.0);
-            }
-        });
-        start_animation_loop();
-    });
-
-    let set_nav_signal = move |event: &KeyboardEvent, value: f64| {
-        let mut navigating = true;
-        let shift = event.shift_key();
-        match event.key().as_str() {
-            "ArrowUp" if shift => zoom_in.set(value),
-            "ArrowDown" if shift => zoom_out.set(value),
-            "ArrowUp" => pitch_up.set(value),
-            "ArrowDown" => pitch_down.set(value),
-            "ArrowRight" if shift => roll_cw.set(value),
-            "ArrowLeft" if shift => roll_ccw.set(value),
-            "ArrowRight" => yaw_right.set(value),
-            "ArrowLeft" => yaw_left.set(value),
-            _ => 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();
-        match event.key().as_str() {
-            "d" | "D" => translate_pos_x.set(value),
-            "a" | "A" => translate_neg_x.set(value),
-            "w" | "W" if shift => translate_neg_z.set(value),
-            "s" | "S" if shift => translate_pos_z.set(value),
-            "w" | "W" => translate_pos_y.set(value),
-            "s" | "S" => translate_neg_y.set(value),
-            "]" | "}" => shrink_neg.set(value),
-            "[" | "{" => shrink_pos.set(value),
-            _ => manipulating = false,
-        };
-        if manipulating {
-            event.prevent_default();
-        }
-    };
-
-    view! {
-        /* TO DO */
-        // switch back to integer-valued parameters when that becomes possible
-        // again
-        canvas(
-            ref = display,
-            id = "display",
-            width = "600",
-            height = "600",
-            tabindex = "0",
-            on:keydown = move |event: KeyboardEvent| {
-                if event.key() == "Shift" {
-                    // swap navigation inputs
-                    roll_cw.set(yaw_right.get());
-                    roll_ccw.set(yaw_left.get());
-                    zoom_in.set(pitch_up.get());
-                    zoom_out.set(pitch_down.get());
-                    yaw_right.set(0.0);
-                    yaw_left.set(0.0);
-                    pitch_up.set(0.0);
-                    pitch_down.set(0.0);
-
-                    // swap manipulation inputs
-                    translate_pos_z.set(translate_neg_y.get());
-                    translate_neg_z.set(translate_pos_y.get());
-                    translate_pos_y.set(0.0);
-                    translate_neg_y.set(0.0);
-                } else {
-                    if event.key() == "Enter" { /* BENCHMARKING */
-                        turntable.set_fn(|turn| !turn);
-                        scene_changed.set(true);
-                    }
-                    set_nav_signal(&event, 1.0);
-                    set_manip_signal(&event, 1.0);
-                }
-            },
-            on:keyup = move |event: KeyboardEvent| {
-                if event.key() == "Shift" {
-                    // swap navigation inputs
-                    yaw_right.set(roll_cw.get());
-                    yaw_left.set(roll_ccw.get());
-                    pitch_up.set(zoom_in.get());
-                    pitch_down.set(zoom_out.get());
-                    roll_cw.set(0.0);
-                    roll_ccw.set(0.0);
-                    zoom_in.set(0.0);
-                    zoom_out.set(0.0);
-
-                    // swap manipulation inputs
-                    translate_pos_y.set(translate_neg_z.get());
-                    translate_neg_y.set(translate_pos_z.get());
-                    translate_pos_z.set(0.0);
-                    translate_neg_z.set(0.0);
-                } else {
-                    set_nav_signal(&event, 0.0);
-                    set_manip_signal(&event, 0.0);
-                }
-            },
-            on:blur = move |_| {
-                pitch_up.set(0.0);
-                pitch_down.set(0.0);
-                yaw_right.set(0.0);
-                yaw_left.set(0.0);
-                roll_ccw.set(0.0);
-                roll_cw.set(0.0);
-            },
-            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()));
-                let mut clicked: Option<(Rc<dyn Element>, f64)> = None;
-                let tangible_elts = state.assembly.elements
-                    .get_clone_untracked()
-                    .into_iter()
-                    .filter(|elt| !elt.ghost().get());
-                for elt in tangible_elts {
-                    match assembly_to_world.with(|asm_to_world| elt.cast(dir, asm_to_world, pixel_size)) {
-                        Some(depth) => match clicked {
-                            Some((_, best_depth)) => {
-                                if depth < best_depth {
-                                    clicked = Some((elt, depth))
-                                }
-                            },
-                            None => clicked = Some((elt, depth)),
-                        },
-                        None => (),
-                    };
-                }
-
-                // if we clicked something, select it
-                match clicked {
-                    Some((elt, _)) => state.select(&elt, event.shift_key()),
-                    None => state.selection.update(|sel| sel.clear()),
-                };
-            },
-        )
-    }
-}

app-proto/src/components/outline.rs

@@ -1,275 +0,0 @@
-use itertools::Itertools;
-use std::rc::Rc;
-use sycamore::prelude::*;
-use web_sys::{KeyboardEvent, MouseEvent, wasm_bindgen::JsCast};
-
-use crate::{
-    AppState,
-    assembly::{
-        Element,
-        HalfCurvatureRegulator,
-        InversiveDistanceRegulator,
-        PointCoordinateRegulator,
-        Regulator,
-    },
-    specified::SpecifiedValue
-};
-
-// an editable view of a regulator
-#[component(inline_props)]
-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 || {
-        batch(|| {
-            valid.set(true);
-            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",
-            class = move || {
-                if valid.get() {
-                    set_point.with(|set_pt| {
-                        if set_pt.is_present() {
-                            "regulator-input constraint"
-                        } else {
-                            "regulator-input"
-                        }
-                    })
-                } else {
-                    "regulator-input invalid"
-                }
-            },
-            placeholder = measurement.with(|result| result.to_string()),
-            bind:value = value,
-            on:change = move |_| {
-                valid.set(
-                    match SpecifiedValue::try_from(value.get_clone_untracked()) {
-                        Ok(set_pt) => {
-                            set_point.set(set_pt);
-                            true
-                        },
-                        Err(_) => false,
-                    }
-                )
-            },
-            on:keydown = {
-                move |event: KeyboardEvent| {
-                    match event.key().as_str() {
-                        "Escape" => reset_value(),
-                        _ => (),
-                    }
-                }
-            },
-        )
-    }
-}
-
-pub trait OutlineItem {
-    fn outline_item(self: Rc<Self>, element: &Rc<dyn Element>) -> View;
-}
-
-impl OutlineItem for InversiveDistanceRegulator {
-    fn outline_item(self: Rc<Self>, element: &Rc<dyn Element>) -> View {
-        let other_subject_label = if self.subjects[0] == element.clone() {
-            self.subjects[1].label()
-        } else {
-            self.subjects[0].label()
-        }.clone();
-        view! {
-            li(class = "regulator") {
-                div(class = "regulator-label") { (other_subject_label) }
-                div(class = "regulator-type") { "Inversive distance" }
-                RegulatorInput(regulator = self)
-                div(class = "status")
-            }
-        }
-    }
-}
-
-impl OutlineItem for HalfCurvatureRegulator {
-    fn outline_item(self: Rc<Self>, _element: &Rc<dyn Element>) -> View {
-        view! {
-            li(class = "regulator") {
-                div(class = "regulator-label") // for spacing
-                div(class = "regulator-type") { "Half-curvature" }
-                RegulatorInput(regulator = self)
-                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")
-            }
-        }
-    }
-}
-
-// a list item that shows an element in an outline view of an assembly
-#[component(inline_props)]
-fn ElementOutlineItem(element: Rc<dyn Element>) -> View {
-    let state = use_context::<AppState>();
-    let class = {
-        let element_for_class = element.clone();
-        state.selection.map(
-            move |sel| if sel.contains(&element_for_class) { "selected" } else { "" }
-        )
-    };
-    let label = element.label().clone();
-    let representation = element.representation().clone();
-    let rep_components = move || {
-        representation.with(
-            |rep| rep.iter().map(
-                |u| {
-                    let u_str = format!("{:.3}", u).replace("-", "\u{2212}");
-                    view! { div { (u_str) } }
-                }
-            ).collect::<Vec<_>>()
-        )
-    };
-    let regulated = element.regulators().map(|regs| regs.len() > 0);
-    let regulator_list = element.regulators().map(
-        |regs| regs
-            .clone()
-            .into_iter()
-            .sorted_by_key(|reg| reg.subjects().len())
-            .collect::<Vec<_>>()
-    );
-    let details_node = create_node_ref();
-    view! {
-        li {
-            details(ref = details_node) {
-                summary(
-                    class = class.get(),
-                    on:keydown = {
-                        let element_for_handler = element.clone();
-                        move |event: KeyboardEvent| {
-                            match event.key().as_str() {
-                                "Enter" => {
-                                    state.select(&element_for_handler, event.shift_key());
-                                    event.prevent_default();
-                                },
-                                "ArrowRight" if regulated.get() => {
-                                    let _ = details_node
-                                        .get()
-                                        .unchecked_into::<web_sys::Element>()
-                                        .set_attribute("open", "");
-                                },
-                                "ArrowLeft" => {
-                                    let _ = details_node
-                                        .get()
-                                        .unchecked_into::<web_sys::Element>()
-                                        .remove_attribute("open");
-                                },
-                                _ => (),
-                            }
-                        }
-                    }
-                ) {
-                    div(
-                        class = "element-switch",
-                        on:click = |event: MouseEvent| event.stop_propagation()
-                    )
-                    div(
-                        class = "element",
-                        on:click = {
-                            let state_for_handler = state.clone();
-                            let element_for_handler = element.clone();
-                            move |event: MouseEvent| {
-                                state_for_handler.select(&element_for_handler, event.shift_key());
-                                event.stop_propagation();
-                                event.prevent_default();
-                            }
-                        }
-                    ) {
-                        div(class = "element-label") { (label) }
-                        div(class = "element-representation") { (rep_components) }
-                        input(
-                            r#type = "checkbox",
-                            bind:checked = element.ghost(),
-                            on:click = |event: MouseEvent| event.stop_propagation()
-                        )
-                    }
-                }
-                ul(class = "regulators") {
-                    Keyed(
-                        list = regulator_list,
-                        view = move |reg| reg.outline_item(&element),
-                        key = |reg| reg.serial()
-                    )
-                }
-            }
-        }
-    }
-}
-
-// a component that lists the elements of the current assembly, showing each
-// element's regulators in a collapsible sub-list. its implementation is based
-// on Kate Morley's HTML + CSS tree views:
-//
-//   https://iamkate.com/code/tree-views/
-//
-#[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
-    // ever wanted to sort by ID, we could do that more simply using the
-    // `elements_by_id` index
-    let element_list = state.assembly.elements.map(
-        |elts| elts
-            .clone()
-            .into_iter()
-            .sorted_by_key(|elt| elt.id().clone())
-            .collect::<Vec<_>>()
-    );
-
-    view! {
-        ul(
-            id = "outline",
-            on:click = {
-                let state = use_context::<AppState>();
-                move |_| state.selection.update(|sel| sel.clear())
-            }
-        ) {
-            Keyed(
-                list = element_list,
-                view = |elt| view! {
-                    ElementOutlineItem(element = elt)
-                },
-                key = |elt| elt.serial()
-            )
-        }
-    }
-}

app-proto/src/components/point.frag

@@ -1,19 +0,0 @@
-#version 300 es
-
-precision highp float;
-
-in vec4 point_color;
-in float point_highlight;
-in float total_radius;
-
-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;
-}

app-proto/src/components/point.vert

@@ -1,24 +0,0 @@
-#version 300 es
-
-in vec4 position;
-in vec4 color;
-in float highlight;
-in float selected;
-
-out vec4 point_color;
-out float point_highlight;
-out float total_radius;
-
-// camera
-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;
-}

app-proto/src/components/test_assembly_chooser.rs

@@ -1,941 +0,0 @@
-use itertools::izip;
-use std::{f64::consts::{FRAC_1_SQRT_2, PI}, rc::Rc};
-use nalgebra::Vector3;
-use sycamore::prelude::*;
-use web_sys::{console, wasm_bindgen::JsValue};
-
-use crate::{
-    AppState,
-    assembly::{
-        Assembly,
-        Element,
-        ElementColor,
-        InversiveDistanceRegulator,
-        Point,
-        Sphere,
-    },
-    engine,
-    engine::DescentHistory,
-    specified::SpecifiedValue,
-};
-
-// --- loaders ---
-
-/* DEBUG */
-// each of these functions loads an example assembly for testing. once we've
-// 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) {
-    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),
-        )
-    );
-    let _ = assembly.try_insert_element(
-        Sphere::new(
-            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),
-        )
-    );
-    let _ = assembly.try_insert_element(
-        Sphere::new(
-            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),
-        )
-    );
-    let _ = assembly.try_insert_element(
-        Sphere::new(
-            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),
-        )
-    );
-    let _ = assembly.try_insert_element(
-        Sphere::new(
-            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),
-        )
-    );
-    let _ = assembly.try_insert_element(
-        Sphere::new(
-            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),
-        )
-    );
-}
-
-fn load_low_curvature(assembly: &Assembly) {
-    // create the spheres
-    let a = 0.75_f64.sqrt();
-    let _ = assembly.try_insert_element(
-        Sphere::new(
-            "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),
-        )
-    );
-    let _ = assembly.try_insert_element(
-        Sphere::new(
-            "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),
-        )
-    );
-    let _ = assembly.try_insert_element(
-        Sphere::new(
-            "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),
-        )
-    );
-    let _ = assembly.try_insert_element(
-        Sphere::new(
-            "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),
-        )
-    );
-    let _ = assembly.try_insert_element(
-        Sphere::new(
-            "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),
-        )
-    );
-    let _ = assembly.try_insert_element(
-        Sphere::new(
-            "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),
-        )
-    );
-    let _ = assembly.try_insert_element(
-        Sphere::new(
-            "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),
-        )
-    );
-    let _ = assembly.try_insert_element(
-        Sphere::new(
-            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),
-        )
-    );
-
-    // impose the desired tangencies and make the sides planar
-    let index_range = 1..=3;
-    let [central, assemb_plane] = ["central", "assemb_plane"].map(
-        |id| assembly.elements_by_id.with_untracked(
-            |elts_by_id| elts_by_id[id].clone()
-        )
-    );
-    let sides = index_range.clone().map(
-        |k| assembly.elements_by_id.with_untracked(
-            |elts_by_id| elts_by_id[&format!("side{k}")].clone()
-        )
-    );
-    let corners = index_range.map(
-        |k| assembly.elements_by_id.with_untracked(
-            |elts_by_id| elts_by_id[&format!("corner{k}")].clone()
-        )
-    );
-    for plane in [assemb_plane.clone()].into_iter().chain(sides.clone()) {
-        // fix the curvature of each plane
-        let curvature = plane.regulators().with_untracked(
-            |regs| regs.first().unwrap().clone()
-        );
-        curvature.set_point().set(SpecifiedValue::try_from("0".to_string()).unwrap());
-    }
-    let all_perpendicular = [central.clone()].into_iter()
-        .chain(sides.clone())
-        .chain(corners.clone());
-    for sphere in all_perpendicular {
-        // make each side and packed sphere perpendicular to the assembly plane
-        let right_angle = InversiveDistanceRegulator::new([sphere, assemb_plane.clone()]);
-        right_angle.set_point.set(SpecifiedValue::try_from("0".to_string()).unwrap());
-        assembly.insert_regulator(Rc::new(right_angle));
-    }
-    for sphere in sides.clone().chain(corners.clone()) {
-        // make each side and corner sphere tangent to the central sphere
-        let tangency = InversiveDistanceRegulator::new([sphere.clone(), central.clone()]);
-        tangency.set_point.set(SpecifiedValue::try_from("-1".to_string()).unwrap());
-        assembly.insert_regulator(Rc::new(tangency));
-    }
-    for (side_index, side) in sides.enumerate() {
-        // make each side tangent to the two adjacent corner spheres
-        for (corner_index, corner) in corners.clone().enumerate() {
-            if side_index != corner_index {
-                let tangency = InversiveDistanceRegulator::new([side.clone(), corner]);
-                tangency.set_point.set(SpecifiedValue::try_from("-1".to_string()).unwrap());
-                assembly.insert_regulator(Rc::new(tangency));
-            }
-        }
-    }
-}
-
-fn load_pointed(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),
-        )
-    );
-    let _ = assembly.try_insert_element(
-        Point::new(
-            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),
-        )
-    );
-    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),
-                )
-            );
-
-            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),
-                )
-            );
-        }
-    }
-}
-
-// to finish describing the tridiminished icosahedron, set the inversive
-// distance regulators as follows:
-//   A-A   -0.25
-//   A-B     "
-//   B-C     "
-//   C-C     "
-//   A-C   -0.25 * φ^2 = -0.6545084971874737
-fn load_tridiminished_icosahedron(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];
-    const COLOR_C: ElementColor = [0.25_f32, 0.50_f32, 1.00_f32];
-    let vertices = [
-        Point::new(
-            "a1".to_string(),
-            "A₁".to_string(),
-            COLOR_A,
-            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),
-        ),
-        Point::new(
-            "a3".to_string(),
-            "A₃".to_string(),
-            COLOR_A,
-            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),
-        ),
-        Point::new(
-            "b2".to_string(),
-            "B₂".to_string(),
-            COLOR_B,
-            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),
-        ),
-        Point::new(
-            "c1".to_string(),
-            "C₁".to_string(),
-            COLOR_C,
-            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),
-        ),
-        Point::new(
-            "c3".to_string(),
-            "C₃".to_string(),
-            COLOR_C,
-            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();
-    let frac_2_sqrt_6 = 2.0 * frac_1_sqrt_6;
-    let faces = [
-        Sphere::new(
-            "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),
-        ),
-        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),
-        ),
-        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),
-        ),
-    ];
-    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
-        let face = assembly.elements_by_id.with_untracked(
-            |elts_by_id| elts_by_id[&format!("face{j}")].clone()
-        );
-        let curvature_regulator = face.regulators().with_untracked(
-            |regs| regs.first().unwrap().clone()
-        );
-        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()
-        );
-        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(
-                |elts_by_id| elts_by_id[&format!("{series}{j}")].clone()
-            )
-        );
-        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
-                let vertex = assembly.elements_by_id.with_untracked(
-                    |elts_by_id| elts_by_id[&format!("{series}{k}")].clone()
-                );
-                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(
-                |index| assembly.elements_by_id.with_untracked(
-                    |elts_by_id| elts_by_id[&format!("{series}{index}")].clone()
-                )
-            )
-        );
-        for pair in adjacent_pairs {
-            assembly.insert_regulator(
-                Rc::new(InversiveDistanceRegulator::new(pair))
-            );
-        }
-    }
-}
-
-// 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) {
-    // 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),
-        )
-    );
-    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];
-    const COLOR_C: ElementColor = [0.25_f32, 0.00_f32, 1.00_f32];
-    let phi = 0.5 + 1.25_f64.sqrt(); /* TO DO */ // replace with std::f64::consts::PHI when that gets stabilized
-    let phi_inv = 1.0 / phi;
-    let coord_scale = (phi + 2.0).sqrt();
-    let face_scales = [phi_inv, (13.0 / 12.0) / coord_scale];
-    let face_radii = [phi_inv, 5.0 / 12.0];
-    let mut faces = Vec::<Rc<dyn Element>>::new();
-    let subscripts = ["₀", "₁"];
-    for j in 0..2 {
-        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(
-                Sphere::new(
-                    id_a.clone(),
-                    format!("A{label_sub}"),
-                    COLOR_A,
-                    engine::sphere(0.0, small_coord, big_coord, face_radii[k]),
-                )
-            );
-            faces.push(
-                assembly.elements_by_id.with_untracked(
-                    |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(
-                Sphere::new(
-                    id_b.clone(),
-                    format!("B{label_sub}"),
-                    COLOR_B,
-                    engine::sphere(small_coord, big_coord, 0.0, face_radii[k]),
-                )
-            );
-            faces.push(
-                assembly.elements_by_id.with_untracked(
-                    |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(
-                Sphere::new(
-                    id_c.clone(),
-                    format!("C{label_sub}"),
-                    COLOR_C,
-                    engine::sphere(big_coord, 0.0, small_coord, face_radii[k]),
-                )
-            );
-            faces.push(
-                assembly.elements_by_id.with_untracked(
-                    |elts_by_id| elts_by_id[&id_c].clone()
-                )
-            );
-        }
-    }
-
-    // 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 {
-            let long_edge_ids = [
-                format!("{long_edge_plane}{k}0"),
-                format!("{long_edge_plane}{k}1")
-            ];
-            let short_edge_ids = [
-                format!("{short_edge_plane}0{k}"),
-                format!("{short_edge_plane}1{k}")
-            ];
-            let [long_edge, short_edge] = [long_edge_ids, short_edge_ids].map(
-                |edge_ids| edge_ids.map(
-                    |id| assembly.elements_by_id.with_untracked(
-                        |elts_by_id| elts_by_id[&id].clone()
-                    )
-                )
-            );
-
-            // 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 {
-                    let side_tangency = InversiveDistanceRegulator::new(
-                        [long_edge[i].clone(), short_edge[j].clone()]
-                    );
-                    if i == 0 && k == 0 {
-                        side_tangency.set_point.set(SpecifiedValue::try_from("-1".to_string()).unwrap());
-                    }
-                    assembly.insert_regulator(Rc::new(side_tangency));
-                }
-            }
-        }
-    }
-}
-
-// 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) {
-    // create the spheres
-    const R_OUTER: f64 = 10.0;
-    const R_INNER: f64 = 4.0;
-    let spheres = [
-        Sphere::new(
-            "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),
-        ),
-        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),
-        ),
-        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),
-        ),
-    ];
-    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),
-    ] {
-        let curvature_regulator = sphere.regulators().with_untracked(
-            |regs| regs.first().unwrap().clone()
-        );
-        let curvature = 0.5 / radius;
-        curvature_regulator.set_point().set(
-            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] {
-        let tangency = InversiveDistanceRegulator::new([outer.clone(), inner]);
-        tangency.set_point.set(SpecifiedValue::try_from("1".to_string()).unwrap());
-        assembly.insert_regulator(Rc::new(tangency));
-    }
-}
-
-// 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) {
-    // 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),
-        ),
-    );
-    let _ = assembly.try_insert_element(
-        Sphere::new(
-            "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),
-        ),
-    );
-
-    // 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());
-    assembly.insert_regulator(Rc::new(incidence));
-}
-
-// setting the inversive distances between the vertices to -2 gives a regular
-// tetrahedron with side length 1, whose insphere and circumsphere have radii
-// 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) {
-    let index_range = 1..=4;
-
-    // create the spheres
-    const GRAY: ElementColor = [0.75_f32, 0.75_f32, 0.75_f32];
-    let spheres = [
-        Sphere::new(
-            "sphere_faces".to_string(),
-            "Insphere".to_string(),
-            GRAY,
-            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),
-        ),
-    ];
-    for sphere in spheres {
-        let _ = assembly.try_insert_element(sphere);
-    }
-
-    // create the vertices
-    let vertices = izip!(
-        index_range.clone(),
-        [
-            [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],
-        ].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),
-        ].into_iter()
-    ).map(
-        |(k, color, representation)| {
-            Point::new(
-                format!("v{k}"),
-                format!("Vertex {k}"),
-                color,
-                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));
-    let faces = izip!(
-        index_range.clone(),
-        [
-            [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],
-        ].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),
-        ].into_iter()
-    ).map(
-        |(k, color, representation)| {
-            Sphere::new(
-                format!("f{k}"),
-                format!("Face {k}"),
-                color,
-                representation,
-            )
-        }
-    );
-    for face in faces {
-        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}"),
-        ].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()
-        );
-        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(
-                    [vertex_j.clone(), vertex_k.clone()]
-                );
-                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());
-            assembly.insert_regulator(Rc::new(incidence_regulator));
-        }
-    }
-}
-
-// to finish setting up the problem, fix the following curvatures:
-//   sun      1
-//   moon     5/3 = 1.666666666666666...
-//   chain1   2
-// a tiny `x` or `z` nudge of the outer sphere reliably prevents realization
-// failures before they happen, or resolves them after they happen. the result
-// depends sensitively on the translation direction, suggesting that realization
-// is failing because the engine is having trouble breaking a symmetry
-// /* TO DO */
-// the engine's performance on this problem is scale-dependent! with the current
-// initial conditions, realization fails for any order of imposing the remaining
-// curvature constraints. scaling everything up by a factor of ten, as done in
-// the original problem, makes realization succeed reliably. one potentially
-// relevant difference is that a lot of the numbers in the current initial
-// 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) {
-    let index_range = 1..=6;
-    let colors = [
-        [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, 1.00_f32, 0.00_f32],
-        [0.00_f32, 0.25_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),
-        ),
-        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),
-        ),
-        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),
-        ),
-    ].into_iter().chain(
-        index_range.clone().zip(colors).map(
-            |(k, color)| {
-                let ang = (k as f64) * PI/3.0;
-                Sphere::new(
-                    format!("chain{k}"),
-                    format!("Chain {k}"),
-                    color,
-                    engine::sphere(1.0 * ang.sin(), 0.0, 1.0 * ang.cos(), 0.5),
-                )
-            }
-        )
-    );
-    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()
-    );
-    outer.ghost().set(true);
-    let outer_curvature_regulator = outer.regulators().with_untracked(
-        |regs| regs.first().unwrap().clone()
-    );
-    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(
-            |elts_by_id| elts_by_id[id].clone()
-        )
-    );
-    let chain = index_range.map(
-        |k| assembly.elements_by_id.with_untracked(
-            |elts_by_id| elts_by_id[&format!("chain{k}")].clone()
-        )
-    );
-    for (chain_sphere, chain_sphere_next) in chain.clone().zip(chain.cycle().skip(1)) {
-        for (other_sphere, inversive_distance) in [
-            (outer.clone(), "1"),
-            (sun.clone(), "-1"),
-            (moon.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));
-}
-
-// --- chooser ---
-
-/* DEBUG */
-#[component]
-pub fn TestAssemblyChooser() -> View {
-    // create an effect that loads the selected test assembly
-    let assembly_name = create_signal("general".to_string());
-    create_effect(move || {
-        // get name of chosen assembly
-        let name = assembly_name.get_clone();
-        console::log_1(
-            &JsValue::from(format!("Showing assembly \"{}\"", name.clone()))
-        );
-
-        batch(|| {
-            let state = use_context::<AppState>();
-            let assembly = &state.assembly;
-
-            // 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),
-                "low-curvature" => load_low_curvature(assembly),
-                "pointed" => load_pointed(assembly),
-                "tridiminished-icosahedron" => load_tridiminished_icosahedron(assembly),
-                "dodecahedral-packing" => load_dodecahedral_packing(assembly),
-                "balanced" => load_balanced(assembly),
-                "off-center" => load_off_center(assembly),
-                "radius-ratio" => load_radius_ratio(assembly),
-                "irisawa-hexlet" => load_irisawa_hexlet(assembly),
-                _ => (),
-            };
-        });
-    });
-
-    // build the chooser
-    view! {
-        select(bind:value = assembly_name) {
-            option(value = "general") { "General" }
-            option(value = "low-curvature") { "Low-curvature" }
-            option(value = "pointed") { "Pointed" }
-            option(value = "tridiminished-icosahedron") { "Tridiminished icosahedron" }
-            option(value = "dodecahedral-packing") { "Dodecahedral packing" }
-            option(value = "balanced") { "Balanced" }
-            option(value = "off-center") { "Off-center" }
-            option(value = "radius-ratio") { "Radius ratio" }
-            option(value = "irisawa-hexlet") { "Irisawa hexlet" }
-            option(value = "empty") { "Empty" }
-        }
-    }
-}

app-proto/src/display.rs

@@ -0,0 +1,603 @@
+use core::array;
+use nalgebra::{DMatrix, DVector, Rotation3, Vector3};
+use sycamore::{prelude::*, motion::create_raf};
+use web_sys::{
+    console,
+    window,
+    Element,
+    KeyboardEvent,
+    MouseEvent,
+    WebGl2RenderingContext,
+    WebGlProgram,
+    WebGlShader,
+    WebGlUniformLocation,
+    wasm_bindgen::{JsCast, JsValue}
+};
+
+use crate::{AppState, assembly::{ElementKey, ElementMotion}};
+
+fn compile_shader(
+    context: &WebGl2RenderingContext,
+    shader_type: u32,
+    source: &str,
+) -> WebGlShader {
+    let shader = context.create_shader(shader_type).unwrap();
+    context.shader_source(&shader, source);
+    context.compile_shader(&shader);
+    shader
+}
+
+fn get_uniform_array_locations<const N: usize>(
+    context: &WebGl2RenderingContext,
+    program: &WebGlProgram,
+    var_name: &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}]")
+        };
+        context.get_uniform_location(&program, name.as_str())
+    })
+}
+
+// load the given data into the vertex input of the given name
+fn bind_vertex_attrib(
+    context: &WebGl2RenderingContext,
+    index: u32,
+    size: i32,
+    data: &[f32]
+) {
+    // create a data buffer and bind it to ARRAY_BUFFER
+    let buffer = context.create_buffer().unwrap();
+    context.bind_buffer(WebGl2RenderingContext::ARRAY_BUFFER, Some(&buffer));
+    
+    // load the given data into the buffer. the function `Float32Array::view`
+    // creates a raw view into our module's `WebAssembly.Memory` buffer.
+    // allocating more memory will change the buffer, invalidating the view.
+    // that means we have to make sure we don't allocate any memory until the
+    // view is dropped
+    unsafe {
+        context.buffer_data_with_array_buffer_view(
+            WebGl2RenderingContext::ARRAY_BUFFER,
+            &js_sys::Float32Array::view(&data),
+            WebGl2RenderingContext::STATIC_DRAW,
+        );
+    }
+    
+    // allow the target attribute to be used
+    context.enable_vertex_attrib_array(index);
+    
+    // take whatever's bound to ARRAY_BUFFER---here, the data buffer created
+    // above---and bind it to the target attribute
+    //
+    //   https://developer.mozilla.org/en-US/docs/Web/API/WebGLRenderingContext/vertexAttribPointer
+    //
+    context.vertex_attrib_pointer_with_i32(
+        index,
+        size,
+        WebGl2RenderingContext::FLOAT,
+        false, // don't normalize
+        0, // zero stride
+        0, // zero offset
+    );
+}
+
+// the direction in camera space that a mouse event is pointing along
+fn event_dir(event: &MouseEvent) -> Vector3<f64> {
+    let target: Element = event.target().unwrap().unchecked_into();
+    let rect = target.get_bounding_client_rect();
+    let width = rect.width();
+    let height = rect.height();
+    let shortdim = width.min(height);
+    
+    // this constant should be kept synchronized with `inversive.frag`
+    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
+    )
+}
+
+#[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);
+    let yaw_right = create_signal(0.0);
+    let yaw_left = create_signal(0.0);
+    let roll_ccw = create_signal(0.0);
+    let roll_cw = create_signal(0.0);
+    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);
+    let translate_neg_y = create_signal(0.0);
+    let translate_pos_y = create_signal(0.0);
+    let translate_neg_z = create_signal(0.0);
+    let translate_pos_z = create_signal(0.0);
+    
+    // change listener
+    let scene_changed = create_signal(true);
+    create_effect(move || {
+        state.assembly.elements.with(|elts| {
+            for (_, elt) in elts {
+                elt.representation.track();
+            }
+        });
+        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
+        const TURNTABLE_SPEED: f64 = 0.1; /* BENCHMARKING */
+        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
+        
+        // display parameters
+        const OPACITY: f32 = 0.5; /* SCAFFOLDING */
+        const HIGHLIGHT: f32 = 0.2; /* SCAFFOLDING */
+        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
+            .get_context("webgl2")
+            .unwrap()
+            .unwrap()
+            .dyn_into::<WebGl2RenderingContext>()
+            .unwrap();
+        
+        // compile and attach the vertex and fragment shaders
+        let vertex_shader = compile_shader(
+            &ctx,
+            WebGl2RenderingContext::VERTEX_SHADER,
+            include_str!("identity.vert"),
+        );
+        let fragment_shader = compile_shader(
+            &ctx,
+            WebGl2RenderingContext::FRAGMENT_SHADER,
+            include_str!("inversive.frag"),
+        );
+        let program = ctx.create_program().unwrap();
+        ctx.attach_shader(&program, &vertex_shader);
+        ctx.attach_shader(&program, &fragment_shader);
+        ctx.link_program(&program);
+        let link_status = ctx
+            .get_program_parameter(&program, WebGl2RenderingContext::LINK_STATUS)
+            .as_bool()
+            .unwrap();
+        let link_msg = if link_status {
+            "Linked successfully"
+        } else {
+            "Linking failed"
+        };
+        console::log_1(&JsValue::from(link_msg));
+        ctx.use_program(Some(&program));
+        
+        /* DEBUG */
+        // print the maximum number of vectors that can be passed as
+        // uniforms to a fragment shader. the OpenGL ES 3.0 standard
+        // requires this maximum to be at least 224, as discussed in the
+        // documentation of the GL_MAX_FRAGMENT_UNIFORM_VECTORS parameter
+        // here:
+        //
+        //   https://registry.khronos.org/OpenGL-Refpages/es3.0/html/glGet.xhtml
+        //
+        // there are also other size limits. for example, on Aaron's
+        // machine, the the length of a float or genType array seems to be
+        // capped at 1024 elements
+        console::log_2(
+            &ctx.get_parameter(WebGl2RenderingContext::MAX_FRAGMENT_UNIFORM_VECTORS).unwrap(),
+            &JsValue::from("uniform vectors available")
+        );
+        
+        // find indices of vertex attributes and uniforms
+        const SPHERE_MAX: usize = 200;
+        let position_index = ctx.get_attrib_location(&program, "position") as u32;
+        let sphere_cnt_loc = ctx.get_uniform_location(&program, "sphere_cnt");
+        let sphere_sp_locs = get_uniform_array_locations::<SPHERE_MAX>(
+            &ctx, &program, "sphere_list", Some("sp")
+        );
+        let sphere_lt_locs = get_uniform_array_locations::<SPHERE_MAX>(
+            &ctx, &program, "sphere_list", Some("lt")
+        );
+        let color_locs = get_uniform_array_locations::<SPHERE_MAX>(
+            &ctx, &program, "color_list", None
+        );
+        let highlight_locs = get_uniform_array_locations::<SPHERE_MAX>(
+            &ctx, &program, "highlight_list", None
+        );
+        let resolution_loc = ctx.get_uniform_location(&program, "resolution");
+        let shortdim_loc = ctx.get_uniform_location(&program, "shortdim");
+        let opacity_loc = ctx.get_uniform_location(&program, "opacity");
+        let layer_threshold_loc = ctx.get_uniform_location(&program, "layer_threshold");
+        let debug_mode_loc = ctx.get_uniform_location(&program, "debug_mode");
+        
+        // create a vertex array and bind it to the graphics context
+        let vertex_array = ctx.create_vertex_array().unwrap();
+        ctx.bind_vertex_array(Some(&vertex_array));
+        
+        // set the vertex positions
+        const VERTEX_CNT: usize = 6;
+        let positions: [f32; 3*VERTEX_CNT] = [
+            // northwest triangle
+            -1.0, -1.0, 0.0,
+            -1.0,  1.0, 0.0,
+             1.0,  1.0, 0.0,
+            // southeast triangle
+            -1.0, -1.0, 0.0,
+             1.0,  1.0, 0.0,
+             1.0, -1.0, 0.0
+        ];
+        bind_vertex_attrib(&ctx, position_index, 3, &positions);
+        
+        // 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();
+            let yaw_right_val = yaw_right.get();
+            let yaw_left_val = yaw_left.get();
+            let roll_ccw_val = roll_ccw.get();
+            let roll_cw_val = roll_cw.get();
+            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();
+            let translate_neg_y_val = translate_neg_y.get();
+            let translate_pos_y_val = translate_pos_y.get();
+            let translate_neg_z_val = translate_neg_z.get();
+            let translate_pos_z_val = translate_pos_z.get();
+            
+            // update the assembly's orientation
+            let ang_vel = {
+                let pitch = pitch_up_val - pitch_down_val;
+                let yaw = yaw_right_val - yaw_left_val;
+                let roll = roll_ccw_val - roll_cw_val;
+                if pitch != 0.0 || yaw != 0.0 || roll != 0.0 {
+                    ROT_SPEED * Vector3::new(-pitch, yaw, roll).normalize()
+                } else {
+                    Vector3::zeros()
+                }
+            } /* BENCHMARKING */ + if turntable_val {
+                Vector3::new(0.0, TURNTABLE_SPEED, 0.0)
+            } else {
+                Vector3::zeros()
+            };
+            let mut rotation_sp = rotation.fixed_view_mut::<3, 3>(0, 0);
+            rotation_sp.copy_from(
+                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
+            if state.selection.with(|sel| sel.len() == 1) {
+                let sel = state.selection.with(
+                    |sel| *sel.into_iter().next().unwrap()
+                );
+                let rep = state.assembly.elements.with_untracked(
+                    |elts| elts[sel].representation.get_clone_untracked()
+                );
+                let translate_x = translate_pos_x_val - translate_neg_x_val;
+                let translate_y = translate_pos_y_val - translate_neg_y_val;
+                let translate_z = translate_pos_z_val - translate_neg_z_val;
+                if translate_x != 0.0 || translate_y != 0.0 || translate_z != 0.0 {
+                    let vel_field = {
+                        let u = Vector3::new(translate_x, translate_y, translate_z).normalize();
+                        DMatrix::from_column_slice(5, 5, &[
+                                 0.0,      0.0,      0.0, 0.0, u[0],
+                                 0.0,      0.0,      0.0, 0.0, u[1],
+                                 0.0,      0.0,      0.0, 0.0, u[2],
+                            2.0*u[0], 2.0*u[1], 2.0*u[2], 0.0,  0.0,
+                                 0.0,      0.0,      0.0, 0.0,  0.0
+                        ])
+                    };
+                    let elt_motion: DVector<f64> = time_step * TRANSLATION_SPEED * vel_field * rep;
+                    assembly_for_raf.deform(
+                        vec![
+                            ElementMotion {
+                                key: sel,
+                                velocity: elt_motion.as_view()
+                            }
+                        ]
+                    );
+                    scene_changed.set(true);
+                }
+            }
+            
+            if scene_changed.get() {
+                /* INSTRUMENTS */
+                // measure mean frame interval
+                frames_since_last_sample += 1;
+                if frames_since_last_sample >= SAMPLE_PERIOD {
+                    mean_frame_interval.set((time - last_sample_time) / (SAMPLE_PERIOD as f64));
+                    last_sample_time = time;
+                    frames_since_last_sample = 0;
+                }
+                
+                // find the map from assembly space to world space
+                let location = {
+                    let u = -location_z;
+                    DMatrix::from_column_slice(5, 5, &[
+                        1.0, 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,   u,
+                        0.0, 0.0, 2.0*u, 1.0, u*u,
+                        0.0, 0.0,   0.0, 0.0, 1.0
+                    ])
+                };
+                let asm_to_world = &location * &orientation;
+                
+                // get the assembly
+                let (
+                    elt_cnt,
+                    reps_world,
+                    colors,
+                    highlights
+                ) = state.assembly.elements.with(|elts| {
+                    (
+                        // number of elements
+                        elts.len() as i32,
+                        
+                        // representation vectors in world coordinates
+                        elts.iter().map(
+                            |(_, elt)| elt.representation.with(|rep| &asm_to_world * rep)
+                        ).collect::<Vec<_>>(),
+                        
+                        // colors
+                        elts.iter().map(|(key, elt)| {
+                            if state.selection.with(|sel| sel.contains(&key)) {
+                                elt.color.map(|ch| 0.2 + 0.8*ch)
+                            } else {
+                                elt.color
+                            }
+                        }).collect::<Vec<_>>(),
+                        
+                        // highlight levels
+                        elts.iter().map(|(key, _)| {
+                            if state.selection.with(|sel| sel.contains(&key)) {
+                                1.0_f32
+                            } else {
+                                HIGHLIGHT
+                            }
+                        }).collect::<Vec<_>>()
+                    )
+                });
+                
+                // 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 assembly
+                ctx.uniform1i(sphere_cnt_loc.as_ref(), elt_cnt);
+                for n in 0..reps_world.len() {
+                    let v = &reps_world[n];
+                    ctx.uniform3f(
+                        sphere_sp_locs[n].as_ref(),
+                        v[0] as f32, v[1] as f32, v[2] as f32
+                    );
+                    ctx.uniform2f(
+                        sphere_lt_locs[n].as_ref(),
+                        v[3] as f32, v[4] as f32
+                    );
+                    ctx.uniform3fv_with_f32_array(
+                        color_locs[n].as_ref(),
+                        &colors[n]
+                    );
+                    ctx.uniform1f(
+                        highlight_locs[n].as_ref(),
+                        highlights[n]
+                    );
+                }
+                
+                // pass the display parameters
+                ctx.uniform1f(opacity_loc.as_ref(), OPACITY);
+                ctx.uniform1i(layer_threshold_loc.as_ref(), LAYER_THRESHOLD);
+                ctx.uniform1i(debug_mode_loc.as_ref(), DEBUG_MODE);
+                
+                // draw the scene
+                ctx.draw_arrays(WebGl2RenderingContext::TRIANGLES, 0, VERTEX_CNT as i32);
+                
+                // update the viewpoint
+                assembly_to_world.set(asm_to_world);
+                
+                // clear the scene change flag
+                scene_changed.set(
+                    pitch_up_val != 0.0
+                    || pitch_down_val != 0.0
+                    || yaw_left_val != 0.0
+                    || yaw_right_val != 0.0
+                    || roll_cw_val != 0.0
+                    || roll_ccw_val != 0.0
+                    || zoom_in_val != 0.0
+                    || zoom_out_val != 0.0
+                    || turntable_val /* BENCHMARKING */
+                );
+            } else {
+                frames_since_last_sample = 0;
+                mean_frame_interval.set(-1.0);
+            }
+        });
+        start_animation_loop();
+    });
+    
+    let set_nav_signal = move |event: &KeyboardEvent, value: f64| {
+        let mut navigating = true;
+        let shift = event.shift_key();
+        match event.key().as_str() {
+            "ArrowUp" if shift => zoom_in.set(value),
+            "ArrowDown" if shift => zoom_out.set(value),
+            "ArrowUp" => pitch_up.set(value),
+            "ArrowDown" => pitch_down.set(value),
+            "ArrowRight" if shift => roll_cw.set(value),
+            "ArrowLeft" if shift => roll_ccw.set(value),
+            "ArrowRight" => yaw_right.set(value),
+            "ArrowLeft" => yaw_left.set(value),
+            _ => 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();
+        match event.key().as_str() {
+            "d" | "D" => translate_pos_x.set(value),
+            "a" | "A" => translate_neg_x.set(value),
+            "w" | "W" if shift => translate_neg_z.set(value),
+            "s" | "S" if shift => translate_pos_z.set(value),
+            "w" | "W" => translate_pos_y.set(value),
+            "s" | "S" => translate_neg_y.set(value),
+            _ => manipulating = false
+        };
+        if manipulating {
+            event.prevent_default();
+        }
+    };
+    
+    view! {
+        /* TO DO */
+        // switch back to integer-valued parameters when that becomes possible
+        // again
+        canvas(
+            ref=display,
+            width="600",
+            height="600",
+            tabindex="0",
+            on:keydown=move |event: KeyboardEvent| {
+                if event.key() == "Shift" {
+                    // swap navigation inputs
+                    roll_cw.set(yaw_right.get());
+                    roll_ccw.set(yaw_left.get());
+                    zoom_in.set(pitch_up.get());
+                    zoom_out.set(pitch_down.get());
+                    yaw_right.set(0.0);
+                    yaw_left.set(0.0);
+                    pitch_up.set(0.0);
+                    pitch_down.set(0.0);
+                    
+                    // swap manipulation inputs
+                    translate_pos_z.set(translate_neg_y.get());
+                    translate_neg_z.set(translate_pos_y.get());
+                    translate_pos_y.set(0.0);
+                    translate_neg_y.set(0.0);
+                } else {
+                    if event.key() == "Enter" { /* BENCHMARKING */
+                        turntable.set_fn(|turn| !turn);
+                        scene_changed.set(true);
+                    }
+                    set_nav_signal(&event, 1.0);
+                    set_manip_signal(&event, 1.0);
+                }
+            },
+            on:keyup=move |event: KeyboardEvent| {
+                if event.key() == "Shift" {
+                    // swap navigation inputs
+                    yaw_right.set(roll_cw.get());
+                    yaw_left.set(roll_ccw.get());
+                    pitch_up.set(zoom_in.get());
+                    pitch_down.set(zoom_out.get());
+                    roll_cw.set(0.0);
+                    roll_ccw.set(0.0);
+                    zoom_in.set(0.0);
+                    zoom_out.set(0.0);
+                    
+                    // swap manipulation inputs
+                    translate_pos_y.set(translate_neg_z.get());
+                    translate_neg_y.set(translate_pos_z.get());
+                    translate_pos_z.set(0.0);
+                    translate_neg_z.set(0.0);
+                } else {
+                    set_nav_signal(&event, 0.0);
+                    set_manip_signal(&event, 0.0);
+                }
+            },
+            on:blur=move |_| {
+                pitch_up.set(0.0);
+                pitch_down.set(0.0);
+                yaw_right.set(0.0);
+                yaw_left.set(0.0);
+                roll_ccw.set(0.0);
+                roll_cw.set(0.0);
+            },
+            on:click=move |event: MouseEvent| {
+                // find the nearest element along the pointer direction
+                let dir = event_dir(&event);
+                console::log_1(&JsValue::from(dir.to_string()));
+                let mut clicked: Option<(ElementKey, f64)> = None;
+                for (key, elt) in state.assembly.elements.get_clone_untracked() {
+                    match assembly_to_world.with(|asm_to_world| elt.cast(dir, asm_to_world)) {
+                        Some(depth) => match clicked {
+                            Some((_, best_depth)) => {
+                                if depth < best_depth {
+                                    clicked = Some((key, depth))
+                                }
+                            },
+                            None => clicked = Some((key, depth))
+                        }
+                        None => ()
+                    };
+                }
+                
+                // if we clicked something, select it
+                match clicked {
+                    Some((key, _)) => state.select(key, event.shift_key()),
+                    None => state.selection.update(|sel| sel.clear())
+                };
+            }
+        )
+    }
+}

app-proto/src/inversive.frag

@@ -17,7 +17,7 @@ struct vecInv {
 const int SPHERE_MAX = 200;
 uniform int sphere_cnt;
 uniform vecInv sphere_list[SPHERE_MAX];
-uniform vec4 color_list[SPHERE_MAX];
+uniform vec3 color_list[SPHERE_MAX];
 uniform float highlight_list[SPHERE_MAX];
 
 // view
@@ -25,6 +25,7 @@ uniform vec2 resolution;
 uniform float shortdim;
 
 // controls
+uniform float opacity;
 uniform int layer_threshold;
 uniform bool debug_mode;
 
@@ -68,17 +69,17 @@ struct Fragment {
     vec4 color;
 };
 
-Fragment sphere_shading(vecInv v, vec3 pt, vec4 base_color) {
+Fragment sphere_shading(vecInv v, vec3 pt, vec3 base_color) {
     // the expression for normal needs to be checked. it's supposed to give the
     // negative gradient of the lorentz product between the impact point vector
     // and the sphere vector with respect to the coordinates of the impact
     // 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));
+    return Fragment(pt, normal, vec4(illum * base_color, opacity));
 }
 
 float intersection_dist(Fragment a, Fragment b) {
@@ -110,7 +111,7 @@ 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 +137,7 @@ 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 +145,7 @@ 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 +170,14 @@ 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.);
@@ -186,16 +187,15 @@ void main() {
         outColor = vec4(color, 1.);
         return;
     }
-
+    
     // composite the sphere fragments
     vec3 color = vec3(0.);
     int layer = layer_cnt - 1;
     TaggedDepth hit = top_hits[layer];
-    vec4 sphere_color = color_list[hit.id];
     Fragment frag_next = sphere_shading(
         sphere_list[hit.id],
         hit.depth * dir,
-        vec4(hit.dimming * sphere_color.rgb, sphere_color.a)
+        hit.dimming * color_list[hit.id]
     );
     float highlight_next = highlight_list[hit.id];
     --layer;
@@ -203,33 +203,32 @@ 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];
         frag_next = sphere_shading(
             sphere_list[hit.id],
             hit.depth * dir,
-            vec4(hit.dimming * sphere_color.rgb, sphere_color.a)
+            hit.dimming * color_list[hit.id]
         );
         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.);
-}
+}

app-proto/src/main.rs

@@ -1,49 +1,45 @@
+mod add_remove;
 mod assembly;
-mod components;
+mod display;
 mod engine;
-mod specified;
+mod outline;
 
-#[cfg(test)]
+use rustc_hash::FxHashSet;
-mod tests;
-
-use std::{collections::BTreeSet, rc::Rc};
 use sycamore::prelude::*;
 
-use assembly::{Assembly, Element};
+use add_remove::AddRemove;
-use components::{
+use assembly::{Assembly, ElementKey};
-    add_remove::AddRemove,
+use display::Display;
-    diagnostics::Diagnostics,
+use outline::Outline;
-    display::Display,
-    outline::Outline,
-};
 
 #[derive(Clone)]
 struct AppState {
     assembly: Assembly,
-    selection: Signal<BTreeSet<Rc<dyn Element>>>,
+    selection: Signal<FxHashSet<ElementKey>>
 }
 
 impl AppState {
-    fn new() -> Self {
+    fn new() -> AppState {
-        Self {
+        AppState {
             assembly: Assembly::new(),
-            selection: create_signal(BTreeSet::default()),
+            selection: create_signal(FxHashSet::default())
         }
     }
-
+    
-    // in single-selection mode, select the given element. in multiple-selection
+    // in single-selection mode, select the element with the given key. in
-    // mode, toggle whether the given element is selected
+    // multiple-selection mode, toggle whether the element with the given key
-    fn select(&self, element: &Rc<dyn Element>, multi: bool) {
+    // is selected
+    fn select(&self, key: ElementKey, multi: bool) {
         if multi {
             self.selection.update(|sel| {
-                if !sel.remove(element) {
+                if !sel.remove(&key) {
-                    sel.insert(element.clone());
+                    sel.insert(key);
                 }
             });
         } else {
             self.selection.update(|sel| {
                 sel.clear();
-                sel.insert(element.clone());
+                sel.insert(key);
             });
         }
     }
@@ -53,17 +49,16 @@ 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 {}
             }
             Display {}
         }
     });
-}
+}

app-proto/src/outline.rs

@@ -0,0 +1,196 @@
+use itertools::Itertools;
+use sycamore::prelude::*;
+use web_sys::{
+    Event,
+    HtmlInputElement,
+    KeyboardEvent,
+    MouseEvent,
+    wasm_bindgen::JsCast
+};
+
+use crate::{AppState, assembly, assembly::{Constraint, ConstraintKey, ElementKey}};
+
+// an editable view of the Lorentz product representing a constraint
+#[component(inline_props)]
+fn LorentzProductInput(constraint: Constraint) -> View {
+    view! {
+        input(
+            r#type="text",
+            bind:value=constraint.lorentz_prod_text,
+            on:change=move |event: Event| {
+                let target: HtmlInputElement = event.target().unwrap().unchecked_into();
+                match target.value().parse::<f64>() {
+                    Ok(lorentz_prod) => batch(|| {
+                        constraint.lorentz_prod.set(lorentz_prod);
+                        constraint.lorentz_prod_valid.set(true);
+                    }),
+                    Err(_) => constraint.lorentz_prod_valid.set(false)
+                };
+            }
+        )
+    }
+}
+
+// a list item that shows a constraint in an outline view of an element
+#[component(inline_props)]
+fn ConstraintOutlineItem(constraint_key: ConstraintKey, element_key: ElementKey) -> View {
+    let state = use_context::<AppState>();
+    let assembly = &state.assembly;
+    let constraint = assembly.constraints.with(|csts| csts[constraint_key].clone());
+    let other_subject = if constraint.subjects.0 == element_key {
+        constraint.subjects.1
+    } else {
+        constraint.subjects.0
+    };
+    let other_subject_label = assembly.elements.with(|elts| elts[other_subject].label.clone());
+    let class = constraint.lorentz_prod_valid.map(
+        |&lorentz_prod_valid| if lorentz_prod_valid { "constraint" } else { "constraint invalid" }
+    );
+    view! {
+        li(class=class.get()) {
+            input(r#type="checkbox", bind:checked=constraint.active)
+            div(class="constraint-label") { (other_subject_label) }
+            LorentzProductInput(constraint=constraint)
+            div(class="status")
+        }
+    }
+}
+
+// a list item that shows an element in an outline view of an assembly
+#[component(inline_props)]
+fn ElementOutlineItem(key: ElementKey, element: assembly::Element) -> View {
+    let state = use_context::<AppState>();
+    let class = state.selection.map(
+        move |sel| if sel.contains(&key) { "selected" } else { "" }
+    );
+    let label = element.label.clone();
+    let rep_components = element.representation.map(
+        |rep| rep.iter().map(
+            |u| format!("{:.3}", u).replace("-", "\u{2212}")
+        ).collect()
+    );
+    let constrained = element.constraints.map(|csts| csts.len() > 0);
+    let constraint_list = element.constraints.map(
+        |csts| csts.clone().into_iter().collect()
+    );
+    let details_node = create_node_ref();
+    view! {
+        li {
+            details(ref=details_node) {
+                summary(
+                    class=class.get(),
+                    on:keydown={
+                        move |event: KeyboardEvent| {
+                            match event.key().as_str() {
+                                "Enter" => {
+                                    state.select(key, event.shift_key());
+                                    event.prevent_default();
+                                },
+                                "ArrowRight" if constrained.get() => {
+                                    let _ = details_node
+                                        .get()
+                                        .unchecked_into::<web_sys::Element>()
+                                        .set_attribute("open", "");
+                                },
+                                "ArrowLeft" => {
+                                    let _ = details_node
+                                        .get()
+                                        .unchecked_into::<web_sys::Element>()
+                                        .remove_attribute("open");
+                                },
+                                _ => ()
+                            }
+                        }
+                    }
+                ) {
+                    div(
+                        class="element-switch",
+                        on:click=|event: MouseEvent| event.stop_propagation()
+                    )
+                    div(
+                        class="element",
+                        on:click={
+                            move |event: MouseEvent| {
+                                if event.shift_key() {
+                                    state.selection.update(|sel| {
+                                        if !sel.remove(&key) {
+                                            sel.insert(key);
+                                        }
+                                    });
+                                } else {
+                                    state.selection.update(|sel| {
+                                        sel.clear();
+                                        sel.insert(key);
+                                    });
+                                }
+                                event.stop_propagation();
+                                event.prevent_default();
+                            }
+                        }
+                    ) {
+                        div(class="element-label") { (label) }
+                        div(class="element-representation") {
+                            Indexed(
+                                list=rep_components,
+                                view=|coord_str| view! {
+                                    div { (coord_str) }
+                                }
+                            )
+                        }
+                        div(class="status")
+                    }
+                }
+                ul(class="constraints") {
+                    Keyed(
+                        list=constraint_list,
+                        view=move |cst_key| view! {
+                            ConstraintOutlineItem(
+                                constraint_key=cst_key,
+                                element_key=key
+                            )
+                        },
+                        key=|cst_key| cst_key.clone()
+                    )
+                }
+            }
+        }
+    }
+}
+
+// a component that lists the elements of the current assembly, showing the
+// constraints on each element as a collapsible sub-list. its implementation
+// is based on Kate Morley's HTML + CSS tree views:
+//
+//   https://iamkate.com/code/tree-views/
+//
+#[component]
+pub fn Outline() -> View {
+    let state = use_context::<AppState>();
+    
+    // list the elements alphabetically by ID
+    let element_list = state.assembly.elements.map(
+        |elts| elts
+            .clone()
+            .into_iter()
+            .sorted_by_key(|(_, elt)| elt.id.clone())
+            .collect()
+    );
+    
+    view! {
+        ul(
+            id="outline",
+            on:click={
+                let state = use_context::<AppState>();
+                move |_| state.selection.update(|sel| sel.clear())
+            }
+        ) {
+            Keyed(
+                list=element_list,
+                view=|(key, elt)| view! {
+                    ElementOutlineItem(key=key, element=elt)
+                },
+                key=|(_, elt)| elt.serial
+            )
+        }
+    }
+}

app-proto/src/specified.rs

@@ -1,55 +0,0 @@
-use std::num::ParseFloatError;
-
-// a real number described by a specification string. since the structure is
-// read-only, we can guarantee that `spec` always specifies `value` in the
-// following format
-//   ┌──────────────────────────────────────────────────────┬───────────┐
-//   │ `spec`                                               │ `value`   │
-//   ┝━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┿━━━━━━━━━━━┥
-//   │ a string that parses to the floating-point value `x` │ `Some(x)` │
-//   ├──────────────────────────────────────────────────────┼───────────┤
-//   │ the empty string                                     │ `None`    │
-//   └──────────────────────────────────────────────────────┴───────────┘
-#[readonly::make]
-pub struct SpecifiedValue {
-    pub spec: String,
-    pub value: Option<f64>,
-}
-
-impl SpecifiedValue {
-    pub fn from_empty_spec() -> Self {
-        Self { 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())
-        } else {
-            spec.parse::<f64>().map(
-                |value| Self { spec, value: Some(value) }
-            )
-        }
-    }
-}

app-proto/src/tests.rs

@@ -1,14 +0,0 @@
-use std::process::Command;
-
-// build and bundle the application, reporting success if there are no errors or
-// warnings. to see this test fail while others succeed, try moving `index.html`
-// or one of the assets that it links to
-#[test]
-fn trunk_build_test() {
-    let build_status = Command::new("trunk")
-        .arg("build")
-        .env("RUSTFLAGS", "-D warnings")
-        .status()
-        .expect("Call to Trunk failed");
-    assert!(build_status.success());
-}

deploy/.gitignore

@@ -1,5 +0,0 @@
-/dyna3.zip
-/dyna3/index.html
-/dyna3/dyna3-*.js
-/dyna3/dyna3-*.wasm
-/dyna3/main-*.css

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.

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?
+
+

src/index.html

@@ -7,3 +7,5 @@
   <body><script type="module" src="dyna3.js"></script>
   </body>
 </html>
+
+    

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"

tools/run-examples.sh

@@ -1,20 +0,0 @@
-# run all Cargo examples, as described here:
-#
-#   Karol Kuczmarski. "Add examples to your Rust libraries"
-#   http://xion.io/post/code/rust-examples.html
-#
-# you should invoke this script by calling `sh` or another interpreter, rather
-# than calling `souce`, to ensure that the script can find the manifest file for
-# the application prototype
-
-# find the manifest file for the application prototype
-MANIFEST="$(dirname -- $0)/../app-proto/Cargo.toml"
-
-# set up the command that runs each example
-RUN_EXAMPLE="cargo run --manifest-path $MANIFEST --example"
-
-# run the examples
-$RUN_EXAMPLE irisawa-hexlet; echo
-$RUN_EXAMPLE three-spheres; echo
-$RUN_EXAMPLE point-on-sphere; echo
-$RUN_EXAMPLE kaleidocycle