Change conditional panic to expect

Use `expect` to communicate that every element should have a column index when `pose` is called. Rewrite the panic messages in the style recommended by the `expect` documentation.
Flag regulator update logging as debug
2025-04-21 14:47:26 -07:00 · 2025-04-17 21:31:24 -07:00 · 2025-04-17 21:25:22 -07:00 · 2025-04-17 21:00:24 -07:00 · 2025-04-17 14:40:28 -07:00 · 2025-04-17 14:16:54 -07:00
36 changed files with 1729 additions and 4336 deletions
--- a/.forgejo/setup-trunk/action.yaml
+++ b/.forgejo/setup-trunk/action.yaml
@ -10,7 +10,7 @@ runs:
  using: "composite"
  steps:
    - run: rustup target add wasm32-unknown-unknown
-
+    
    # install the Trunk binary to `ci-bin` within the workspace directory, which
    # is determined by the `github.workspace` label and reflected in the
    # `GITHUB_WORKSPACE` environment variable. then, make the `trunk` command
--- a/.forgejo/workflows/continuous-integration.yaml
+++ b/.forgejo/workflows/continuous-integration.yaml
@ -11,7 +11,7 @@ jobs:
  test:
    runs-on: docker
    container:
-      image: cimg/rust:1.86-node
+      image: cimg/rust:1.85-node
    defaults:
      run:
        # set the default working directory for each `run` step, relative to the
@ -24,6 +24,6 @@ jobs:
      # workspace directory (action variable `github.workspace`, environment
      # variable `$GITHUB_WORKSPACE`):
      - uses: https://code.forgejo.org/actions/checkout@v4
-
+      
      - uses: ./.forgejo/setup-trunk
-      - run: RUSTFLAGS='-D warnings' cargo test
+      - run: RUSTFLAGS='-D warnings' cargo test
--- a/README.md
+++ b/README.md
@ -12,11 +12,11 @@ Note that currently this is just the barest beginnings of the project, more of a
 ### Implementation goals
-* Provide a comfortable, intuitive UI
+* Comfortable, intuitive UI
-* Allow execution in browser (so implemented in WASM-compatible language)
+* Able to run in browser (so implemented in WASM-compatible language)
-* Produce scalable graphics of 3D diagrams, and maybe STL files (or other fabricatable file format) as well
+* Produce scalable graphics of 3D diagrams, and maybe STL files (or other fabricatable file format) as well.
 ## Prototype
@ -24,66 +24,44 @@ The latest prototype is in the folder `app-proto`. It includes both a user inter
 ### Install the prerequisites
-1. Install [`rustup`](https://rust-lang.github.io/rustup/): the officially recommended Rust toolchain manager.
+1. Install [`rustup`](https://rust-lang.github.io/rustup/): the officially recommended Rust toolchain manager
-   - It's available on Ubuntu as a [Snap](https://snapcraft.io/rustup).
+   * It's available on Ubuntu as a [Snap](https://snapcraft.io/rustup)
-2. Call `rustup default stable` to "download the latest stable release of Rust and set it as your default toolchain".
+2. Call `rustup default stable` to "download the latest stable release of Rust and set it as your default toolchain"
-   - If you forget, the `rustup` [help system](https://github.com/rust-lang/rustup/blob/d9b3601c3feb2e88cf3f8ca4f7ab4fdad71441fd/src/errors.rs#L109-L112) will remind you.
+   * If you forget, the `rustup` [help system](https://github.com/rust-lang/rustup/blob/d9b3601c3feb2e88cf3f8ca4f7ab4fdad71441fd/src/errors.rs#L109-L112) will remind you
-3. Call `rustup target add wasm32-unknown-unknown` to add the [most generic 32-bit WebAssembly target](https://doc.rust-lang.org/nightly/rustc/platform-support/wasm32-unknown-unknown.html).
+3. Call `rustup target add wasm32-unknown-unknown` to add the [most generic 32-bit WebAssembly target](https://doc.rust-lang.org/nightly/rustc/platform-support/wasm32-unknown-unknown.html)
-4. Call `cargo install wasm-pack` to install the [WebAssembly toolchain](https://rustwasm.github.io/docs/wasm-pack/).
+4. Call `cargo install wasm-pack` to install the [WebAssembly toolchain](https://rustwasm.github.io/docs/wasm-pack/)
-5. Call `cargo install trunk` to install the [Trunk](https://trunkrs.dev/) web-build tool.
+5. Call `cargo install trunk` to install the [Trunk](https://trunkrs.dev/) web-build tool
   - In the future, `trunk` can be updated with the same command. (You may need the `--locked` flag if your ambient version of `rustc` does not match that required by `trunk`.)
 6. Add the `.cargo/bin` folder in your home directory to your executable search path
-   - This lets you call Trunk, and other tools installed by Cargo, without specifying their paths.
+   * This lets you call Trunk, and other tools installed by Cargo, without specifying their paths
-   - On POSIX systems, the search path is stored in the `PATH` environment variable.
+   * On POSIX systems, the search path is stored in the `PATH` environment variable
   - Alternatively, if you don't want to adjust your `PATH`, you can install `trunk` in another directory `DIR` via `cargo install --root DIR trunk`.
 ### Play with the prototype
-1. From the `app-proto` folder, call `trunk serve --release` to build and serve the prototype.
+1. 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.
--- a/app-proto/Cargo.lock
+++ b/app-proto/Cargo.lock
@ -1,6 +1,6 @@
 # This file is automatically @generated by Cargo.
 # It is not intended for manual editing.
-version = 4
+version = 3
 [[package]]
 name = "ahash"
@ -20,21 +20,6 @@ version = "0.2.18"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "5c6cb57a04249c6480766f7f7cef5467412af1490f8d1e243141daddada3264f"
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@ -50,21 +35,6 @@ version = "1.3.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "0c4b4d0bd25bd0b74681c0ad21497610ce1b7c91b1022cd21c80c6fbdd9476b0"
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@ -98,35 +68,6 @@ version = "1.0.0"
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 checksum = "baf1de4339761588bc0619e3cbc0120ee582ebb74b53b4efbf79117bd2da40fd"
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 "num-traits",
 "serde",
 "windows-link",
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 [[package]]
 name = "console_error_panic_hook"
 version = "0.1.7"
@ -137,130 +78,19 @@ dependencies = [
 "wasm-bindgen",
 ]
 [[package]]
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 version = "0.8.7"
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 "typenum",
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 [[package]]
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 "slab",
 "sycamore",
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@ -272,48 +102,12 @@ version = "1.13.0"
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@ -325,28 +119,6 @@ dependencies = [
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@ -357,12 +129,6 @@ dependencies = [
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@ -372,47 +138,6 @@ dependencies = [
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@ -420,8 +145,7 @@ source = "registry+https://github.com/rust-lang/crates.io-index"
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- "hashbrown 0.14.5",
+ "hashbrown",
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@ -433,12 +157,6 @@ dependencies = [
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@ -476,12 +194,6 @@ dependencies = [
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@ -538,12 +250,6 @@ dependencies = [
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@ -553,21 +259,6 @@ dependencies = [
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@ -600,57 +291,6 @@ version = "1.0.15"
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 version = "2.8.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "db7d01726be8ab66ab32f9df467ae8b1148906685bbe75c82d1e65d7f5b3f841"
 dependencies = [
 "pest",
 "pest_meta",
 "proc-macro2",
 "quote",
 "syn",
 ]
 [[package]]
 name = "pest_meta"
 version = "2.8.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "7f9f832470494906d1fca5329f8ab5791cc60beb230c74815dff541cbd2b5ca0"
 dependencies = [
 "once_cell",
 "pest",
 "sha2",
 ]
 [[package]]
 name = "powerfmt"
 version = "0.2.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "439ee305def115ba05938db6eb1644ff94165c5ab5e9420d1c1bcedbba909391"
 [[package]]
 name = "ppv-lite86"
 version = "0.2.20"
@ -726,10 +366,10 @@ dependencies = [
 ]
 [[package]]
-name = "ryu"
+name = "rustc-hash"
-version = "1.0.20"
+version = "2.0.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "28d3b2b1366ec20994f1fd18c3c594f05c5dd4bc44d8bb0c1c632c8d6829481f"
+checksum = "583034fd73374156e66797ed8e5b0d5690409c9226b22d87cb7f19821c05d152"
 [[package]]
 name = "safe_arch"
@ -755,90 +395,6 @@ version = "1.0.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "e1cf6437eb19a8f4a6cc0f7dca544973b0b78843adbfeb3683d1a94a0024a294"
 [[package]]
 name = "serde"
 version = "1.0.219"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "5f0e2c6ed6606019b4e29e69dbaba95b11854410e5347d525002456dbbb786b6"
 dependencies = [
 "serde_derive",
 ]
 [[package]]
 name = "serde-wasm-bindgen"
 version = "0.6.5"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "8302e169f0eddcc139c70f139d19d6467353af16f9fce27e8c30158036a1e16b"
 dependencies = [
 "js-sys",
 "serde",
 "wasm-bindgen",
 ]
 [[package]]
 name = "serde_derive"
 version = "1.0.219"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "5b0276cf7f2c73365f7157c8123c21cd9a50fbbd844757af28ca1f5925fc2a00"
 dependencies = [
 "proc-macro2",
 "quote",
 "syn",
 ]
 [[package]]
 name = "serde_json"
 version = "1.0.140"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "20068b6e96dc6c9bd23e01df8827e6c7e1f2fddd43c21810382803c136b99373"
 dependencies = [
 "itoa",
 "memchr",
 "ryu",
 "serde",
 ]
 [[package]]
 name = "serde_with"
 version = "3.12.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "d6b6f7f2fcb69f747921f79f3926bd1e203fce4fef62c268dd3abfb6d86029aa"
 dependencies = [
 "base64",
 "chrono",
 "hex",
 "indexmap 1.9.3",
 "indexmap 2.5.0",
 "serde",
 "serde_derive",
 "serde_json",
 "serde_with_macros",
 "time",
 ]
 [[package]]
 name = "serde_with_macros"
 version = "3.12.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "8d00caa5193a3c8362ac2b73be6b9e768aa5a4b2f721d8f4b339600c3cb51f8e"
 dependencies = [
 "darling",
 "proc-macro2",
 "quote",
 "syn",
 ]
 [[package]]
 name = "sha2"
 version = "0.10.9"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "a7507d819769d01a365ab707794a4084392c824f54a7a6a7862f8c3d0892b283"
 dependencies = [
 "cfg-if",
 "cpufeatures",
 "digest",
 ]
 [[package]]
 name = "shlex"
 version = "1.3.0"
@ -858,6 +414,15 @@ dependencies = [
 "wide",
 ]
 [[package]]
 name = "slab"
 version = "0.4.9"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "8f92a496fb766b417c996b9c5e57daf2f7ad3b0bebe1ccfca4856390e3d3bb67"
 dependencies = [
 "autocfg",
 ]
 [[package]]
 name = "slotmap"
 version = "1.0.7"
@ -873,20 +438,14 @@ version = "1.13.2"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "3c5e1a9a646d36c3599cd173a41282daf47c44583ad367b8e6837255952e5c67"
 [[package]]
 name = "strsim"
 version = "0.11.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "7da8b5736845d9f2fcb837ea5d9e2628564b3b043a70948a3f0b778838c5fb4f"
 [[package]]
 name = "sycamore"
-version = "0.9.1"
+version = "0.9.0-beta.3"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "5f38201dcb10aa609e81ca6f7547758a7eb602240a5ff682e668909fd0f7b2cc"
+checksum = "dedaf7237c05913604a5b0b2536b613f6c8510c6b213d2583b1294869755cabd"
 dependencies = [
- "hashbrown 0.14.5",
+ "hashbrown",
- "indexmap 2.5.0",
+ "indexmap",
 "paste",
 "sycamore-core",
 "sycamore-macro",
@ -898,20 +457,20 @@ dependencies = [
 [[package]]
 name = "sycamore-core"
-version = "0.9.1"
+version = "0.9.0-beta.3"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "41dc04bf0de321c6486356b2be751fac82fabb06c992d25b6748587561bba187"
+checksum = "e5ddddc3d1bcb38c04ad55d2d1ab4f6a358e4daaeae0a0436892f1fade9fb31a"
 dependencies = [
- "hashbrown 0.14.5",
+ "hashbrown",
 "paste",
 "sycamore-reactive",
 ]
 [[package]]
 name = "sycamore-macro"
-version = "0.9.1"
+version = "0.9.0-beta.3"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "a0c1d2eddc94db6d03e67eb832df5512b967e81053a573cd01bf3e1c3db00137"
+checksum = "77181c27cb753e86065308901871ccc7456fb19527b6a4ffacad3b63175ed014"
 dependencies = [
 "once_cell",
 "proc-macro2",
@ -923,21 +482,20 @@ dependencies = [
 [[package]]
 name = "sycamore-reactive"
-version = "0.9.1"
+version = "0.9.0-beta.3"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "f2bacf810535efc2701187a716a5652197ad241d620d5b00fb12caa6dfa23add"
+checksum = "7aa6870203507c07e850687c0ccf528eb0f04240e3596bac9137007ffb6c50b1"
 dependencies = [
 "paste",
 "slotmap",
 "smallvec",
 "wasm-bindgen",
 ]
 [[package]]
 name = "sycamore-view-parser"
-version = "0.9.1"
+version = "0.9.0-beta.3"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "6c22875843db83cd4d49c0123a195e433bdc74e13ed0fff4ace0e77bb0a67033"
+checksum = "a6144640af2eafffc68a92f3aacbbfaa21f7fd31906e2336fe304fd100fe226b"
 dependencies = [
 "proc-macro2",
 "quote",
@ -946,9 +504,9 @@ dependencies = [
 [[package]]
 name = "sycamore-web"
-version = "0.9.1"
+version = "0.9.0-beta.3"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "4b17aa5875f59f541cdf6fb58751ec702a6ed9801f30dd2b4d5f2279025b98bd"
+checksum = "bca93dcf1b1830bf1aac93508ed51babcda92c1d32d96067ab416d94e4b7c475"
 dependencies = [
 "html-escape",
 "js-sys",
@ -964,78 +522,21 @@ dependencies = [
 [[package]]
 name = "syn"
-version = "2.0.87"
+version = "2.0.77"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "25aa4ce346d03a6dcd68dd8b4010bcb74e54e62c90c573f394c46eae99aba32d"
+checksum = "9f35bcdf61fd8e7be6caf75f429fdca8beb3ed76584befb503b1569faee373ed"
 dependencies = [
 "proc-macro2",
 "quote",
 "unicode-ident",
 ]
 [[package]]
 name = "thiserror"
 version = "2.0.12"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "567b8a2dae586314f7be2a752ec7474332959c6460e02bde30d702a66d488708"
 dependencies = [
 "thiserror-impl",
 ]
 [[package]]
 name = "thiserror-impl"
 version = "2.0.12"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "7f7cf42b4507d8ea322120659672cf1b9dbb93f8f2d4ecfd6e51350ff5b17a1d"
 dependencies = [
 "proc-macro2",
 "quote",
 "syn",
 ]
 [[package]]
 name = "time"
 version = "0.3.41"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "8a7619e19bc266e0f9c5e6686659d394bc57973859340060a69221e57dbc0c40"
 dependencies = [
 "deranged",
 "itoa",
 "num-conv",
 "powerfmt",
 "serde",
 "time-core",
 "time-macros",
 ]
 [[package]]
 name = "time-core"
 version = "0.1.4"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "c9e9a38711f559d9e3ce1cdb06dd7c5b8ea546bc90052da6d06bb76da74bb07c"
 [[package]]
 name = "time-macros"
 version = "0.2.22"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "3526739392ec93fd8b359c8e98514cb3e8e021beb4e5f597b00a0221f8ed8a49"
 dependencies = [
 "num-conv",
 "time-core",
 ]
 [[package]]
 name = "typenum"
 version = "1.17.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "42ff0bf0c66b8238c6f3b578df37d0b7848e55df8577b3f74f92a69acceeb825"
 [[package]]
 name = "ucd-trie"
 version = "0.1.7"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "2896d95c02a80c6d6a5d6e953d479f5ddf2dfdb6a244441010e373ac0fb88971"
 [[package]]
 name = "unicode-ident"
 version = "1.0.13"
@ -1192,65 +693,6 @@ dependencies = [
 "windows-sys",
 ]
 [[package]]
 name = "windows-core"
 version = "0.61.2"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "c0fdd3ddb90610c7638aa2b3a3ab2904fb9e5cdbecc643ddb3647212781c4ae3"
 dependencies = [
 "windows-implement",
 "windows-interface",
 "windows-link",
 "windows-result",
 "windows-strings",
 ]
 [[package]]
 name = "windows-implement"
 version = "0.60.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "a47fddd13af08290e67f4acabf4b459f647552718f683a7b415d290ac744a836"
 dependencies = [
 "proc-macro2",
 "quote",
 "syn",
 ]
 [[package]]
 name = "windows-interface"
 version = "0.59.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "bd9211b69f8dcdfa817bfd14bf1c97c9188afa36f4750130fcdf3f400eca9fa8"
 dependencies = [
 "proc-macro2",
 "quote",
 "syn",
 ]
 [[package]]
 name = "windows-link"
 version = "0.1.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "76840935b766e1b0a05c0066835fb9ec80071d4c09a16f6bd5f7e655e3c14c38"
 [[package]]
 name = "windows-result"
 version = "0.3.4"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "56f42bd332cc6c8eac5af113fc0c1fd6a8fd2aa08a0119358686e5160d0586c6"
 dependencies = [
 "windows-link",
 ]
 [[package]]
 name = "windows-strings"
 version = "0.4.2"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "56e6c93f3a0c3b36176cb1327a4958a0353d5d166c2a35cb268ace15e91d3b57"
 dependencies = [
 "windows-link",
 ]
 [[package]]
 name = "windows-sys"
 version = "0.59.0"
--- a/app-proto/Cargo.toml
+++ b/app-proto/Cargo.toml
@ -3,23 +3,20 @@ 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"
-sycamore = "0.9.1"
+rustc-hash = "2.0.0"
-
+slab = "0.4.9"
-# We use Charming to help display engine diagnostics
+sycamore = "0.9.0-beta.3"
 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
@ -50,13 +47,6 @@ 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
--- a/app-proto/Trunk.toml
+++ b/app-proto/Trunk.toml
@ -1,2 +0,0 @@
 [build]
 public_url = "./"
--- a/app-proto/examples/common/print.rs
+++ b/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);
    }
 }
--- a/app-proto/examples/irisawa-hexlet.rs
+++ b/app-proto/examples/irisawa-hexlet.rs
@ -1,23 +1,25 @@
-#[path = "common/print.rs"]
+use dyna3::engine::{Q, examples::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);
    }
 }
--- a/app-proto/examples/kaleidocycle.rs
+++ b/app-proto/examples/kaleidocycle.rs
@ -1,32 +1,30 @@
 #[path = "common/print.rs"]
 mod print;
 use nalgebra::{DMatrix, DVector};
-use dyna3::engine::{ConfigNeighborhood, examples::realize_kaleidocycle};
+use dyna3::engine::{Q, examples::realize_kaleidocycle};
 fn main() {
    const SCALED_TOL: f64 = 1.0e-12;
-    let realization = realize_kaleidocycle(SCALED_TOL);
+    let (config, tangent, success, history) = realize_kaleidocycle(SCALED_TOL);
-    print::title("Kaleidocycle");
+    print!("Completed Gram matrix:{}", config.tr_mul(&*Q) * &config);
-    print::realization_diagnostics(&realization);
+    print!("Configuration:{}", config);
-    if let Ok(ConfigNeighborhood { config, nbhd: tangent }) = realization.result {
+    if success {
-        // print the completed Gram matrix and the realized configuration
+        println!("Target accuracy achieved!");
-        print::gram_matrix(&config);
+    } else {
-        print::config(&config);
+        println!("Failed to reach target accuracy");
        // find the kaleidocycle's twist motion by projecting onto the tangent
        // space
        const N_POINTS: usize = 12;
        let up = DVector::from_column_slice(&[0.0, 0.0, 1.0, 0.0]);
        let down = -&up;
        let twist_motion: DMatrix<_> = (0..N_POINTS).step_by(4).flat_map(
            |n| [
                tangent.proj(&up.as_view(), n),
                tangent.proj(&down.as_view(), n+1),
            ]
        ).sum();
        let normalization = 5.0 / twist_motion[(2, 0)];
        println!("\nTwist motion:{}", (normalization * twist_motion).to_string().trim_end());
    }
-}
+    println!("Steps: {}", history.scaled_loss.len() - 1);
    println!("Loss: {}\n", history.scaled_loss.last().unwrap());
    // find the kaleidocycle's twist motion by projecting onto the tangent space
    const N_POINTS: usize = 12;
    let up = DVector::from_column_slice(&[0.0, 0.0, 1.0, 0.0]);
    let down = -&up;
    let twist_motion: DMatrix<_> = (0..N_POINTS).step_by(4).flat_map(
        |n| [
            tangent.proj(&up.as_view(), n),
            tangent.proj(&down.as_view(), n+1)
        ]
    ).sum();
    let normalization = 5.0 / twist_motion[(2, 0)];
    print!("Twist motion:{}", normalization * twist_motion);
 }
--- a/app-proto/examples/point-on-sphere.rs
+++ b/app-proto/examples/point-on-sphere.rs
@ -1,13 +1,4 @@
-#[path = "common/print.rs"]
+use dyna3::engine::{Q, point, realize_gram, sphere, ConstraintProblem};
 mod print;
 use dyna3::engine::{
    point,
    realize_gram,
    sphere,
    ConfigNeighborhood,
    ConstraintProblem,
 };
 fn main() {
    let mut problem = ConstraintProblem::from_guess(&[
@ -20,14 +11,21 @@ fn main() {
        }
    }
    problem.frozen.push(3, 0, problem.guess[(3, 0)]);
-    let realization = realize_gram(
+    println!();
    let (config, _, success, history) = 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);
 }
--- a/app-proto/examples/three-spheres.rs
+++ b/app-proto/examples/three-spheres.rs
@ -1,12 +1,4 @@
-#[path = "common/print.rs"]
+use dyna3::engine::{Q, realize_gram, sphere, ConstraintProblem};
 mod print;
 use dyna3::engine::{
    realize_gram,
    sphere,
    ConfigNeighborhood,
    ConstraintProblem,
 };
 fn main() {
    let mut problem = ConstraintProblem::from_guess({
@ -14,7 +6,7 @@ fn main() {
        &[
            sphere(1.0, 0.0, 0.0, 1.0),
            sphere(-0.5, a, 0.0, 1.0),
-            sphere(-0.5, -a, 0.0, 1.0),
+            sphere(-0.5, -a, 0.0, 1.0)
        ]
    });
    for j in 0..3 {
@ -22,13 +14,20 @@ fn main() {
            problem.gram.push_sym(j, k, if j == k { 1.0 } else { -1.0 });
        }
    }
-    let realization = realize_gram(
+    println!();
    let (config, _, success, history) = 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);
 }
--- a/app-proto/index.html
+++ b/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>
--- a/app-proto/main.css
+++ b/app-proto/main.css
@ -18,17 +18,6 @@ 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 {
@ -53,7 +42,9 @@ body {
 }
 #add-remove > button {
  width: 32px;
  height: 32px;
  font-size: large;
 }
 /* KLUDGE */
@ -62,9 +53,7 @@ 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 */
@ -101,10 +90,6 @@ summary > div, .regulator {
  padding-right: 8px;
 }
 .element > input {
  margin-left: 8px;
 }
 .element-switch {
  width: 18px;
  padding-left: 2px;
@ -149,7 +134,6 @@ details[open]:has(li) .element-switch::after {
 }
 .regulator-input {
  margin-right: 4px;
  color: inherit;
  background-color: inherit;
  border: 1px solid var(--border);
@ -171,65 +155,22 @@ details[open]:has(li) .element-switch::after {
  border-color: var(--border-invalid);
 }
 .status {
  width: 20px;
  padding-left: 4px;
  text-align: center;
  font-family: 'Noto Emoji';
  font-style: normal;
 }
 .regulator-input.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;
@ -238,7 +179,7 @@ details[open]:has(li) .element-switch::after {
  border-radius: 16px;
 }
-#display:focus {
+canvas:focus {
  border-color: var(--border-focus-dark);
  outline: none;
 }
--- a/app-proto/run-examples
+++ b/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
--- a/app-proto/src/add_remove.rs
+++ b/app-proto/src/add_remove.rs
@ -0,0 +1,205 @@
 use sycamore::prelude::*;
 use web_sys::{console, wasm_bindgen::JsValue};
 use crate::{
    engine,
    AppState,
    assembly::{Assembly, Element, InversiveDistanceRegulator}
 };
 /* 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_sphere(
        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_sphere(
        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_sphere(
        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_sphere(
        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_sphere(
        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_sphere(
        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_sphere(
        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_sphere(
        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_sphere(
        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_sphere(
        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_sphere(
        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_sphere(
        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_sphere(
        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_sphere(
        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.regulators.update(|regs| regs.clear());
            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_sphere();
                }
            ) { "+" }
            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(
                        InversiveDistanceRegulator::new(subjects, &state.assembly)
                    );
                    state.selection.update(|sel| sel.clear());
                }
            ) { "🔗" }
            select(bind:value=assembly_name) { /* DEBUG */ // example assembly chooser
                option(value="general") { "General" }
                option(value="low-curv") { "Low-curvature" }
                option(value="empty") { "Empty" }
            }
        }
    }
 }
--- a/app-proto/src/assembly.rs
+++ b/app-proto/src/assembly.rs
--- a/app-proto/src/components.rs
+++ b/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;
--- a/app-proto/src/components/add_remove.rs
+++ b/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 {}
        }
    }
 }
--- a/app-proto/src/components/diagnostics.rs
+++ b/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 {} }
        }
    }
 }
--- a/app-proto/src/components/display.rs
+++ b/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()),
                };
            },
        )
    }
 }
--- a/app-proto/src/components/point.frag
+++ b/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;
 }
--- a/app-proto/src/components/point.vert
+++ b/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;
 }
--- a/app-proto/src/components/test_assembly_chooser.rs
+++ b/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" }
        }
    }
 }
--- a/app-proto/src/display.rs
+++ b/app-proto/src/display.rs
@ -0,0 +1,613 @@
 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);
    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();
            }
        });
        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 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();
            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
            if state.selection.with(|sel| sel.len() == 1) {
                let sel = state.selection.with(
                    |sel| *sel.into_iter().next().unwrap()
                );
                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 {
                                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),
            "]" | "}" => 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,
            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())
                };
            }
        )
    }
 }
--- a/app-proto/src/engine.rs
+++ b/app-proto/src/engine.rs
@ -1,9 +1,10 @@
 use lazy_static::lazy_static;
 use nalgebra::{Const, DMatrix, DVector, DVectorView, Dyn, SymmetricEigen};
-use std::fmt::{Display, Error, Formatter};
+use web_sys::{console, wasm_bindgen::JsValue}; /* DEBUG */
 // --- elements ---
 #[cfg(feature = "dev")]
 pub fn point(x: f64, y: f64, z: f64) -> DVector<f64> {
    DVector::from_column_slice(&[x, y, z, 0.5, 0.5*(x*x + y*y + z*z)])
 }
@ -16,7 +17,7 @@ pub fn sphere(center_x: f64, center_y: f64, center_z: f64, radius: f64) -> DVect
        center_y / radius,
        center_z / radius,
        0.5 / radius,
-        0.5 * (center_norm_sq / radius - radius),
+        0.5 * (center_norm_sq / radius - radius)
    ])
 }
@ -30,51 +31,79 @@ pub fn sphere_with_offset(dir_x: f64, dir_y: f64, dir_z: f64, off: f64, curv: f6
        norm_sp * dir_y,
        norm_sp * dir_z,
        0.5 * curv,
-        off * (1.0 + 0.5 * off * curv),
+        off * (1.0 + 0.5 * off * curv)
    ])
 }
-// project a sphere's representation vector to the normalization variety by
+// given a sphere's representation vector, change the sphere's half-curvature to
-// contracting toward the last coordinate axis
+// `half-curv` and then restore normalization by contracting the representation
-pub fn project_sphere_to_normalized(rep: &mut DVector<f64>) {
+// vector toward the curvature axis
-    let q_sp = rep.fixed_rows::<3>(0).norm_squared();
+pub fn change_half_curvature(rep: &mut DVector<f64>, half_curv: f64) {
-    let half_q_lt = -2.0 * rep[3] * rep[4];
+    // set the sphere's half-curvature to the desired value
    rep[3] = half_curv;
    // restore normalization by contracting toward the curvature axis
    const SIZE_THRESHOLD: f64 = 1e-9;
    let half_q_lt = -2.0 * half_curv * rep[4];
    let half_q_lt_sq = half_q_lt * half_q_lt;
-    let scaling = half_q_lt + (q_sp + half_q_lt_sq).sqrt();
+    let mut spatial = rep.fixed_rows_mut::<3>(0);
-    rep.fixed_rows_mut::<4>(0).scale_mut(1.0 / scaling);
+    let q_sp = spatial.norm_squared();
-}
+    if q_sp < SIZE_THRESHOLD && half_q_lt_sq < SIZE_THRESHOLD {
-
+        spatial.copy_from_slice(
-// normalize a point's representation vector by scaling
+            &[0.0, 0.0, (1.0 - 2.0 * half_q_lt).sqrt()]
-pub fn project_point_to_normalized(rep: &mut DVector<f64>) {
+        );
-    rep.scale_mut(0.5 / rep[3]);
+    } else {
        let scaling = half_q_lt + (q_sp + half_q_lt_sq).sqrt();
        spatial.scale_mut(1.0 / scaling);
        rep[4] /= scaling;
    }
    /* DEBUG */
    // verify normalization
    let rep_for_debug = rep.clone();
    console::log_1(&JsValue::from(
        format!(
            "Sphere self-product after curvature change: {}",
            rep_for_debug.dot(&(&*Q * &rep_for_debug))
        )
    ));
 }
 // --- partial matrices ---
 pub struct MatrixEntry {
-    pub index: (usize, usize),
+    index: (usize, usize),
-    pub value: f64,
+    value: f64
 }
 pub struct PartialMatrix(Vec<MatrixEntry>);
 impl PartialMatrix {
-    pub fn new() -> Self {
+    pub fn new() -> PartialMatrix {
-        Self(Vec::<MatrixEntry>::new())
+        PartialMatrix(Vec::<MatrixEntry>::new())
    }
-
+    
    pub fn push(&mut self, row: usize, col: usize, value: f64) {
-        let Self(entries) = self;
+        let PartialMatrix(entries) = self;
-        entries.push(MatrixEntry { index: (row, col), value });
+        entries.push(MatrixEntry { index: (row, col), value: value });
    }
-
+    
    pub fn push_sym(&mut self, row: usize, col: usize, value: f64) {
        self.push(row, col, value);
        if row != col {
            self.push(col, row, value);
        }
    }
-
+    
    /* DEBUG */
    pub fn log_to_console(&self) {
        for &MatrixEntry { index: (row, col), value } in self {
            console::log_1(&JsValue::from(
                format!("  {} {} {}", row, col, value)
            ));
        }
    }
    fn freeze(&self, a: &DMatrix<f64>) -> DMatrix<f64> {
        let mut result = a.clone();
        for &MatrixEntry { index, value } in self {
@ -82,7 +111,7 @@ impl PartialMatrix {
        }
        result
    }
-
+    
    fn proj(&self, a: &DMatrix<f64>) -> DMatrix<f64> {
        let mut result = DMatrix::<f64>::zeros(a.nrows(), a.ncols());
        for &MatrixEntry { index, .. } in self {
@ -90,7 +119,7 @@ impl PartialMatrix {
        }
        result
    }
-
+    
    fn sub_proj(&self, rhs: &DMatrix<f64>) -> DMatrix<f64> {
        let mut result = DMatrix::<f64>::zeros(rhs.nrows(), rhs.ncols());
        for &MatrixEntry { index, value } in self {
@ -100,21 +129,12 @@ impl PartialMatrix {
    }
 }
 impl Display for PartialMatrix {
    fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error> {
        for &MatrixEntry { index: (row, col), value } in self {
            writeln!(f, "  {row} {col} {value}")?;
        }
        Ok(())
    }
 }
 impl IntoIterator for PartialMatrix {
    type Item = MatrixEntry;
    type IntoIter = std::vec::IntoIter<Self::Item>;
-
+    
    fn into_iter(self) -> Self::IntoIter {
-        let Self(entries) = self;
+        let PartialMatrix(entries) = self;
        entries.into_iter()
    }
 }
@ -122,7 +142,7 @@ impl IntoIterator for PartialMatrix {
 impl<'a> IntoIterator for &'a PartialMatrix {
    type Item = &'a MatrixEntry;
    type IntoIter = std::slice::Iter<'a, MatrixEntry>;
-
+    
    fn into_iter(self) -> Self::IntoIter {
        let PartialMatrix(entries) = self;
        entries.into_iter()
@ -135,26 +155,22 @@ impl<'a> IntoIterator for &'a PartialMatrix {
 pub struct ConfigSubspace {
    assembly_dim: usize,
    basis_std: Vec<DMatrix<f64>>,
-    basis_proj: Vec<DMatrix<f64>>,
+    basis_proj: Vec<DMatrix<f64>>
 }
 impl ConfigSubspace {
-    pub fn zero(assembly_dim: usize) -> Self {
+    pub fn zero(assembly_dim: usize) -> ConfigSubspace {
-        Self {
+        ConfigSubspace {
-            assembly_dim,
+            assembly_dim: assembly_dim,
            basis_proj: Vec::new(),
-            basis_std: Vec::new(),
+            basis_std: Vec::new()
        }
    }
-
+    
    // approximate the kernel of a symmetric endomorphism of the configuration
    // space for `assembly_dim` elements. we consider an eigenvector to be part
    // of the kernel if its eigenvalue is smaller than the constant `THRESHOLD`
-    fn symmetric_kernel(
+    fn symmetric_kernel(a: DMatrix<f64>, proj_to_std: DMatrix<f64>, assembly_dim: usize) -> ConfigSubspace {
        a: DMatrix<f64>,
        proj_to_std: DMatrix<f64>,
        assembly_dim: usize,
    ) -> Self {
        // find a basis for the kernel. the basis is expressed in the projection
        // coordinates, and it's orthonormal with respect to the projection
        // inner product
@ -167,14 +183,21 @@ impl ConfigSubspace {
                |(λ, v)| (λ.abs() < THRESHOLD).then_some(v)
            ).collect::<Vec<_>>().as_slice()
        );
-
+        
        /* DEBUG */
        // print the eigenvalues
        #[cfg(all(target_family = "wasm", target_os = "unknown"))]
        console::log_1(&JsValue::from(
            format!("Eigenvalues used to find kernel:{}", eig.eigenvalues)
        ));
        // express the basis in the standard coordinates
        let basis_std = proj_to_std * &basis_proj;
-
+        
        const ELEMENT_DIM: usize = 5;
        const UNIFORM_DIM: usize = 4;
-        Self {
+        ConfigSubspace {
-            assembly_dim,
+            assembly_dim: assembly_dim,
            basis_std: basis_std.column_iter().map(
                |v| Into::<DMatrix<f64>>::into(
                    v.reshape_generic(Dyn(ELEMENT_DIM), Dyn(assembly_dim))
@ -184,18 +207,18 @@ impl ConfigSubspace {
                |v| Into::<DMatrix<f64>>::into(
                    v.reshape_generic(Dyn(UNIFORM_DIM), Dyn(assembly_dim))
                )
-            ).collect(),
+            ).collect()
        }
    }
-
+    
    pub fn dim(&self) -> usize {
        self.basis_std.len()
    }
-
+    
    pub fn assembly_dim(&self) -> usize {
        self.assembly_dim
    }
-
+    
    // find the projection onto this subspace of the motion where the element
    // with the given column index has velocity `v`. the velocity is given in
    // projection coordinates, and the projection is done with respect to the
@ -218,18 +241,18 @@ pub struct DescentHistory {
    pub config: Vec<DMatrix<f64>>,
    pub scaled_loss: Vec<f64>,
    pub neg_grad: Vec<DMatrix<f64>>,
-    pub hess_eigvals: Vec<DVector<f64>>,
+    pub min_eigval: Vec<f64>,
    pub base_step: Vec<DMatrix<f64>>,
-    pub backoff_steps: Vec<i32>,
+    pub backoff_steps: Vec<i32>
 }
 impl DescentHistory {
-    pub fn new() -> Self {
+    fn new() -> DescentHistory {
-        Self {
+        DescentHistory {
            config: Vec::<DMatrix<f64>>::new(),
            scaled_loss: Vec::<f64>::new(),
            neg_grad: Vec::<DMatrix<f64>>::new(),
-            hess_eigvals: Vec::<DVector<f64>>::new(),
+            min_eigval: Vec::<f64>::new(),
            base_step: Vec::<DMatrix<f64>>::new(),
            backoff_steps: Vec::<i32>::new(),
        }
@ -245,21 +268,21 @@ pub struct ConstraintProblem {
 }
 impl ConstraintProblem {
-    pub fn new(element_count: usize) -> Self {
+    pub fn new(element_count: usize) -> ConstraintProblem {
        const ELEMENT_DIM: usize = 5;
-        Self {
+        ConstraintProblem {
            gram: PartialMatrix::new(),
            frozen: PartialMatrix::new(),
-            guess: DMatrix::<f64>::zeros(ELEMENT_DIM, element_count),
+            guess: DMatrix::<f64>::zeros(ELEMENT_DIM, element_count)
        }
    }
-
+    
    #[cfg(feature = "dev")]
-    pub fn from_guess(guess_columns: &[DVector<f64>]) -> Self {
+    pub fn from_guess(guess_columns: &[DVector<f64>]) -> ConstraintProblem {
-        Self {
+        ConstraintProblem {
            gram: PartialMatrix::new(),
            frozen: PartialMatrix::new(),
-            guess: DMatrix::from_columns(guess_columns),
+            guess: DMatrix::from_columns(guess_columns)
        }
    }
 }
@ -273,21 +296,25 @@ lazy_static! {
        0.0, 1.0, 0.0,  0.0,  0.0,
        0.0, 0.0, 1.0,  0.0,  0.0,
        0.0, 0.0, 0.0,  0.0, -2.0,
-        0.0, 0.0, 0.0, -2.0,  0.0,
+        0.0, 0.0, 0.0, -2.0,  0.0
    ]);
 }
 struct SearchState {
    config: DMatrix<f64>,
    err_proj: DMatrix<f64>,
-    loss: f64,
+    loss: f64
 }
 impl SearchState {
-    fn from_config(gram: &PartialMatrix, config: DMatrix<f64>) -> Self {
+    fn from_config(gram: &PartialMatrix, config: DMatrix<f64>) -> SearchState {
        let err_proj = gram.sub_proj(&(config.tr_mul(&*Q) * &config));
        let loss = err_proj.norm_squared();
-        Self { config, err_proj, loss }
+        SearchState {
            config: config,
            err_proj: err_proj,
            loss: loss
        }
    }
 }
@ -314,7 +341,7 @@ pub fn local_unif_to_std(v: DVectorView<f64>) -> DMatrix<f64> {
            curv,  0.0,  0.0,  0.0, v[0],
             0.0, curv,  0.0,  0.0, v[1],
             0.0,  0.0, curv,  0.0, v[2],
-             0.0,  0.0,  0.0,  0.0,  1.0,
+             0.0,  0.0,  0.0,  0.0,  1.0
        ])
    } else {
        // `v` represents a sphere. the normalization condition says that the
@ -323,7 +350,7 @@ pub fn local_unif_to_std(v: DVectorView<f64>) -> DMatrix<f64> {
                 curv,       0.0,       0.0,       0.0,            v[0],
                  0.0,      curv,       0.0,       0.0,            v[1],
                  0.0,       0.0,      curv,       0.0,            v[2],
-            curv*v[0], curv*v[1], curv*v[2], curv*v[3], curv*v[4] + 1.0,
+            curv*v[0], curv*v[1], curv*v[2], curv*v[3], curv*v[4] + 1.0
        ])
    }
 }
@ -336,7 +363,7 @@ fn seek_better_config(
    base_target_improvement: f64,
    min_efficiency: f64,
    backoff: f64,
-    max_backoff_steps: i32,
+    max_backoff_steps: i32
 ) -> Option<(SearchState, i32)> {
    let mut rate = 1.0;
    for backoff_steps in 0..max_backoff_steps {
@ -351,17 +378,6 @@ fn seek_better_config(
    None
 }
 // a first-order neighborhood of a configuration
 pub struct ConfigNeighborhood {
    #[cfg(feature = "dev")] pub config: DMatrix<f64>,
    pub nbhd: ConfigSubspace,
 }
 pub struct Realization {
    pub result: Result<ConfigNeighborhood, String>,
    pub history: DescentHistory,
 }
 // seek a matrix `config` that matches the partial matrix `problem.frozen` and
 // has `config' * Q * config` matching the partial matrix `problem.gram`. start
 // at `problem.guess`, set the frozen entries to their desired values, and then
@ -373,41 +389,30 @@ pub fn realize_gram(
    backoff: f64,
    reg_scale: f64,
    max_descent_steps: i32,
-    max_backoff_steps: i32,
+    max_backoff_steps: i32
-) -> Realization {
+) -> (DMatrix<f64>, ConfigSubspace, bool, DescentHistory) {
    // destructure the problem data
-    let ConstraintProblem { gram, guess, frozen } = problem;
+    let ConstraintProblem {
-
+        gram, guess, frozen
    } = problem;
    // start the descent history
    let mut history = DescentHistory::new();
-
+    
    // handle the case where the assembly is empty. our general realization
    // routine can't handle this case because it builds the Hessian using
    // `DMatrix::from_columns`, which panics when the list of columns is empty
    let assembly_dim = guess.ncols();
    if assembly_dim == 0 {
        let result = Ok(
            ConfigNeighborhood {
                #[cfg(feature = "dev")] config: guess.clone(),
                nbhd: ConfigSubspace::zero(0),
            }
        );
        return Realization { result, history };
    }
    // find the dimension of the search space
    let element_dim = guess.nrows();
    let assembly_dim = guess.ncols();
    let total_dim = element_dim * assembly_dim;
-
+    
    // scale the tolerance
    let scale_adjustment = (gram.0.len() as f64).sqrt();
    let tol = scale_adjustment * scaled_tol;
-
+    
    // convert the frozen indices to stacked format
    let frozen_stacked: Vec<usize> = frozen.into_iter().map(
        |MatrixEntry { index: (row, col), .. }| col*element_dim + row
    ).collect();
-
+    
    // use a regularized Newton's method with backtracking
    let mut state = SearchState::from_config(gram, frozen.freeze(guess));
    let mut hess = DMatrix::zeros(element_dim, assembly_dim);
@ -416,7 +421,7 @@ pub fn realize_gram(
        let neg_grad = 4.0 * &*Q * &state.config * &state.err_proj;
        let mut neg_grad_stacked = neg_grad.clone().reshape_generic(Dyn(total_dim), Const::<1>);
        history.neg_grad.push(neg_grad.clone());
-
+        
        // find the negative Hessian of the loss function
        let mut hess_cols = Vec::<DVector<f64>>::with_capacity(total_dim);
        for col in 0..assembly_dim {
@ -435,15 +440,14 @@ pub fn realize_gram(
            }
        }
        hess = DMatrix::from_columns(hess_cols.as_slice());
-
+        
        // regularize the Hessian
-        let hess_eigvals = hess.symmetric_eigenvalues();
+        let min_eigval = hess.symmetric_eigenvalues().min();
        let min_eigval = hess_eigvals.min();
        if min_eigval <= 0.0 {
            hess -= reg_scale * min_eigval * DMatrix::identity(total_dim, total_dim);
        }
-        history.hess_eigvals.push(hess_eigvals);
+        history.min_eigval.push(min_eigval);
-
+        
        // project the negative gradient and negative Hessian onto the
        // orthogonal complement of the frozen subspace
        let zero_col = DVector::zeros(total_dim);
@ -454,47 +458,37 @@ pub fn realize_gram(
            hess.set_column(k, &zero_col);
            hess[(k, k)] = 1.0;
        }
-
+        
        // stop if the loss is tolerably low
        history.config.push(state.config.clone());
        history.scaled_loss.push(state.loss / scale_adjustment);
        if state.loss < tol { break; }
-
+        
        // compute the Newton step
        /* TO DO */
        /*
-          we should change our regularization to ensure that the Hessian is
+          we need to either handle or eliminate the case where the minimum
-          is positive-definite, rather than just positive-semidefinite. ideally,
+          eigenvalue of the Hessian is zero, so the regularized Hessian is
-          that would guarantee the success of the Cholesky decomposition---
+          singular. right now, this causes the Cholesky decomposition to return
-          although we'd still need the error-handling routine in case of
+          `None`, leading to a panic when we unrap
          numerical hiccups
        */
-        let hess_cholesky = match hess.clone().cholesky() {
+        let base_step_stacked = hess.clone().cholesky().unwrap().solve(&neg_grad_stacked);
            Some(cholesky) => cholesky,
            None => return Realization {
                result: Err("Cholesky decomposition failed".to_string()),
                history,
            },
        };
        let base_step_stacked = hess_cholesky.solve(&neg_grad_stacked);
        let base_step = base_step_stacked.reshape_generic(Dyn(element_dim), Dyn(assembly_dim));
        history.base_step.push(base_step.clone());
-
+        
        // use backtracking line search to find a better configuration
-        if let Some((better_state, backoff_steps)) = seek_better_config(
+        match seek_better_config(
            gram, &state, &base_step, neg_grad.dot(&base_step),
-            min_efficiency, backoff, max_backoff_steps,
+            min_efficiency, backoff, max_backoff_steps
        ) {
-            state = better_state;
+            Some((better_state, backoff_steps)) => {
-            history.backoff_steps.push(backoff_steps);
+                state = better_state;
-        } else {
+                history.backoff_steps.push(backoff_steps);
-            return Realization {
+            },
-                result: Err("Line search failed".to_string()),
+            None => return (state.config, ConfigSubspace::zero(assembly_dim), false, history)
-                history,
+        };
            };
        }
    }
-    let result = if state.loss < tol {
+    let success = state.loss < tol;
    let tangent = if success {
        // express the uniform basis in the standard basis
        const UNIFORM_DIM: usize = 4;
        let total_dim_unif = UNIFORM_DIM * assembly_dim;
@ -505,15 +499,13 @@ pub fn realize_gram(
                .view_mut(block_start, (element_dim, UNIFORM_DIM))
                .copy_from(&local_unif_to_std(state.config.column(n)));
        }
-
+        
        // find the kernel of the Hessian. give it the uniform inner product
-        let tangent = ConfigSubspace::symmetric_kernel(hess, unif_to_std, assembly_dim);
+        ConfigSubspace::symmetric_kernel(hess, unif_to_std, assembly_dim)
        Ok(ConfigNeighborhood { #[cfg(feature = "dev")] config: state.config, nbhd: tangent })
    } else {
-        Err("Failed to reach target accuracy".to_string())
+        ConfigSubspace::zero(assembly_dim)
    };
-    Realization { result, history }
+    (state.config, tangent, success, history)
 }
 // --- tests ---
@ -521,9 +513,9 @@ pub fn realize_gram(
 #[cfg(feature = "dev")]
 pub mod examples {
    use std::f64::consts::PI;
-
+    
    use super::*;
-
+    
    // this problem is from a sangaku by Irisawa Shintarō Hiroatsu. the article
    // below includes a nice translation of the problem statement, which was
    // recorded in Uchida Itsumi's book _Kokon sankan_ (_Mathematics, Past and
@ -532,12 +524,12 @@ pub mod examples {
    //   "Japan's 'Wasan' Mathematical Tradition", by Abe Haruki
    //   https://www.nippon.com/en/japan-topics/c12801/
    //
-    pub fn realize_irisawa_hexlet(scaled_tol: f64) -> Realization {
+    pub fn realize_irisawa_hexlet(scaled_tol: f64) -> (DMatrix<f64>, ConfigSubspace, bool, DescentHistory) {
        let mut problem = ConstraintProblem::from_guess(
            [
                sphere(0.0, 0.0, 0.0, 15.0),
                sphere(0.0, 0.0, -9.0, 5.0),
-                sphere(0.0, 0.0, 11.0, 3.0),
+                sphere(0.0, 0.0, 11.0, 3.0)
            ].into_iter().chain(
                (1..=6).map(
                    |k| {
@ -547,43 +539,43 @@ pub mod examples {
                )
            ).collect::<Vec<_>>().as_slice()
        );
-
+        
        for s in 0..9 {
            // each sphere is represented by a spacelike vector
            problem.gram.push_sym(s, s, 1.0);
-
+            
            // the circumscribing sphere is tangent to all of the other
            // spheres, with matching orientation
            if s > 0 {
                problem.gram.push_sym(0, s, 1.0);
            }
-
+            
            if s > 2 {
                // each chain sphere is tangent to the "sun" and "moon"
                // spheres, with opposing orientation
                for n in 1..3 {
                    problem.gram.push_sym(s, n, -1.0);
                }
-
+                
                // each chain sphere is tangent to the next chain sphere,
                // with opposing orientation
                let s_next = 3 + (s-2) % 6;
                problem.gram.push_sym(s, s_next, -1.0);
            }
        }
-
+        
        // the frozen entries fix the radii of the circumscribing sphere, the
        // "sun" and "moon" spheres, and one of the chain spheres
        for k in 0..4 {
            problem.frozen.push(3, k, problem.guess[(3, k)]);
        }
-
+        
        realize_gram(&problem, scaled_tol, 0.5, 0.9, 1.1, 200, 110)
    }
-
+    
    // set up a kaleidocycle, made of points with fixed distances between them,
    // and find its tangent space
-    pub fn realize_kaleidocycle(scaled_tol: f64) -> Realization {
+    pub fn realize_kaleidocycle(scaled_tol: f64) -> (DMatrix<f64>, ConfigSubspace, bool, DescentHistory) {
        const N_HINGES: usize = 6;
        let mut problem = ConstraintProblem::from_guess(
            (0..N_HINGES).step_by(2).flat_map(
@ -596,12 +588,12 @@ pub mod examples {
                        point(0.0, 0.0, 0.0),
                        point(ang_hor.cos(), ang_hor.sin(), 0.0),
                        point(x_vert, y_vert, -0.5),
-                        point(x_vert, y_vert, 0.5),
+                        point(x_vert, y_vert, 0.5)
                    ]
                }
            ).collect::<Vec<_>>().as_slice()
        );
-
+        
        const N_POINTS: usize = 2 * N_HINGES;
        for block in (0..N_POINTS).step_by(2) {
            let block_next = (block + 2) % N_POINTS;
@ -610,18 +602,18 @@ pub mod examples {
                for k in j..2 {
                    problem.gram.push_sym(block + j, block + k, if j == k { 0.0 } else { -0.5 });
                }
-
+                
                // non-hinge edges
                for k in 0..2 {
                    problem.gram.push_sym(block + j, block_next + k, -0.625);
                }
            }
        }
-
+        
        for k in 0..N_POINTS {
            problem.frozen.push(3, k, problem.guess[(3, k)])
        }
-
+        
        realize_gram(&problem, scaled_tol, 0.5, 0.9, 1.1, 200, 110)
    }
 }
@ -630,47 +622,47 @@ pub mod examples {
 mod tests {
    use nalgebra::Vector3;
    use std::{f64::consts::{FRAC_1_SQRT_2, PI}, iter};
-
+    
    use super::{*, examples::*};
-
+    
    #[test]
    fn freeze_test() {
        let frozen = PartialMatrix(vec![
            MatrixEntry { index: (0, 0), value: 14.0 },
            MatrixEntry { index: (0, 2), value: 28.0 },
            MatrixEntry { index: (1, 1), value: 42.0 },
-            MatrixEntry { index: (1, 2), value: 49.0 },
+            MatrixEntry { index: (1, 2), value: 49.0 }
        ]);
        let config = DMatrix::<f64>::from_row_slice(2, 3, &[
            1.0, 2.0, 3.0,
-            4.0, 5.0, 6.0,
+            4.0, 5.0, 6.0
        ]);
        let expected_result = DMatrix::<f64>::from_row_slice(2, 3, &[
            14.0, 2.0, 28.0,
-            4.0, 42.0, 49.0,
+            4.0, 42.0, 49.0
        ]);
        assert_eq!(frozen.freeze(&config), expected_result);
    }
-
+    
    #[test]
    fn sub_proj_test() {
        let target = PartialMatrix(vec![
            MatrixEntry { index: (0, 0), value: 19.0 },
            MatrixEntry { index: (0, 2), value: 39.0 },
            MatrixEntry { index: (1, 1), value: 59.0 },
-            MatrixEntry { index: (1, 2), value: 69.0 },
+            MatrixEntry { index: (1, 2), value: 69.0 }
        ]);
        let attempt = DMatrix::<f64>::from_row_slice(2, 3, &[
            1.0, 2.0, 3.0,
-            4.0, 5.0, 6.0,
+            4.0, 5.0, 6.0
        ]);
        let expected_result = DMatrix::<f64>::from_row_slice(2, 3, &[
            18.0, 0.0, 36.0,
-            0.0, 54.0, 63.0,
+            0.0, 54.0, 63.0
        ]);
        assert_eq!(target.sub_proj(&attempt), expected_result);
    }
-
+    
    #[test]
    fn zero_loss_test() {
        let mut gram = PartialMatrix::new();
@ -684,13 +676,13 @@ mod tests {
            DMatrix::from_columns(&[
                sphere(1.0, 0.0, 0.0, a),
                sphere(-0.5, a, 0.0, a),
-                sphere(-0.5, -a, 0.0, a),
+                sphere(-0.5, -a, 0.0, a)
            ])
        };
        let state = SearchState::from_config(&gram, config);
        assert!(state.loss.abs() < f64::EPSILON);
    }
-
+    
    /* TO DO */
    // at the frozen indices, the optimization steps should have exact zeros,
    // and the realized configuration should have the desired values
@ -698,7 +690,7 @@ mod tests {
    fn frozen_entry_test() {
        let mut problem = ConstraintProblem::from_guess(&[
            point(0.0, 0.0, 2.0),
-            sphere(0.0, 0.0, 0.0, 0.95),
+            sphere(0.0, 0.0, 0.0, 0.95)
        ]);
        for j in 0..2 {
            for k in j..2 {
@ -707,10 +699,10 @@ mod tests {
        }
        problem.frozen.push(3, 0, problem.guess[(3, 0)]);
        problem.frozen.push(3, 1, 0.5);
-        let Realization { result, history } = realize_gram(
+        let (config, _, success, history) = realize_gram(
            &problem, 1.0e-12, 0.5, 0.9, 1.1, 200, 110
        );
-        let config = result.unwrap().config;
+        assert_eq!(success, true);
        for base_step in history.base_step.into_iter() {
            for &MatrixEntry { index, .. } in &problem.frozen {
                assert_eq!(base_step[index], 0.0);
@ -720,13 +712,13 @@ mod tests {
            assert_eq!(config[index], value);
        }
    }
-
+    
    #[test]
    fn irisawa_hexlet_test() {
        // solve Irisawa's problem
        const SCALED_TOL: f64 = 1.0e-12;
-        let config = realize_irisawa_hexlet(SCALED_TOL).result.unwrap().config;
+        let (config, _, _, _) = realize_irisawa_hexlet(SCALED_TOL);
-
+        
        // check against Irisawa's solution
        let entry_tol = SCALED_TOL.sqrt();
        let solution_diams = [30.0, 10.0, 6.0, 5.0, 15.0, 10.0, 3.75, 2.5, 2.0 + 8.0/11.0];
@ -734,7 +726,7 @@ mod tests {
            assert!((config[(3, k)] - 1.0 / diam).abs() < entry_tol);
        }
    }
-
+    
    #[test]
    fn tangent_test_three_spheres() {
        const SCALED_TOL: f64 = 1.0e-12;
@ -742,7 +734,7 @@ mod tests {
        let mut problem = ConstraintProblem::from_guess(&[
            sphere(0.0, 0.0, 0.0, -2.0),
            sphere(0.0, 0.0, 1.0, 1.0),
-            sphere(0.0, 0.0, -1.0, 1.0),
+            sphere(0.0, 0.0, -1.0, 1.0)
        ]);
        for j in 0..3 {
            for k in j..3 {
@ -752,13 +744,13 @@ mod tests {
        for n in 0..ELEMENT_DIM {
            problem.frozen.push(n, 0, problem.guess[(n, 0)]);
        }
-        let Realization { result, history } = realize_gram(
+        let (config, tangent, success, history) = realize_gram(
            &problem, SCALED_TOL, 0.5, 0.9, 1.1, 200, 110
        );
        let ConfigNeighborhood { config, nbhd: tangent } = result.unwrap();
        assert_eq!(config, problem.guess);
        assert_eq!(success, true);
        assert_eq!(history.scaled_loss.len(), 1);
-
+        
        // list some motions that should form a basis for the tangent space of
        // the solution variety
        const UNIFORM_DIM: usize = 4;
@ -772,8 +764,8 @@ mod tests {
            DMatrix::<f64>::from_column_slice(UNIFORM_DIM, assembly_dim, &[
                0.0, 0.0,  0.0,  0.0,
                0.0, 0.0, -0.5, -0.5,
-                0.0, 0.0, -0.5,  0.5,
+                0.0, 0.0, -0.5,  0.5
-            ]),
+            ])
        ];
        let tangent_motions_std = vec![
            basis_matrix((0, 1), element_dim, assembly_dim),
@ -783,14 +775,14 @@ mod tests {
            DMatrix::<f64>::from_column_slice(element_dim, assembly_dim, &[
                0.0, 0.0,  0.0,  0.00,  0.0,
                0.0, 0.0, -1.0, -0.25, -1.0,
-                0.0, 0.0, -1.0,  0.25,  1.0,
+                0.0, 0.0, -1.0,  0.25,  1.0
-            ]),
+            ])
        ];
-
+        
        // confirm that the dimension of the tangent space is no greater than
        // expected
        assert_eq!(tangent.basis_std.len(), tangent_motions_std.len());
-
+        
        // confirm that the tangent space contains all the motions we expect it
        // to. since we've already bounded the dimension of the tangent space,
        // this confirms that the tangent space is what we expect it to be
@ -802,13 +794,13 @@ mod tests {
            assert!((motion_std - motion_proj).norm_squared() < tol_sq);
        }
    }
-
+    
    fn translation_motion_unif(vel: &Vector3<f64>, assembly_dim: usize) -> Vec<DVector<f64>> {
        let mut elt_motion = DVector::zeros(4);
        elt_motion.fixed_rows_mut::<3>(0).copy_from(vel);
        iter::repeat(elt_motion).take(assembly_dim).collect()
    }
-
+    
    fn rotation_motion_unif(ang_vel: &Vector3<f64>, points: Vec<DVectorView<f64>>) -> Vec<DVector<f64>> {
        points.into_iter().map(
            |pt| {
@ -819,15 +811,15 @@ mod tests {
            }
        ).collect()
    }
-
+    
    #[test]
    fn tangent_test_kaleidocycle() {
        // set up a kaleidocycle and find its tangent space
        const SCALED_TOL: f64 = 1.0e-12;
-        let Realization { result, history } = realize_kaleidocycle(SCALED_TOL);
+        let (config, tangent, success, history) = realize_kaleidocycle(SCALED_TOL);
-        let ConfigNeighborhood { config, nbhd: tangent } = result.unwrap();
+        assert_eq!(success, true);
        assert_eq!(history.scaled_loss.len(), 1);
-
+        
        // list some motions that should form a basis for the tangent space of
        // the solution variety
        const N_HINGES: usize = 6;
@ -838,12 +830,12 @@ mod tests {
            translation_motion_unif(&Vector3::new(1.0, 0.0, 0.0), assembly_dim),
            translation_motion_unif(&Vector3::new(0.0, 1.0, 0.0), assembly_dim),
            translation_motion_unif(&Vector3::new(0.0, 0.0, 1.0), assembly_dim),
-
+            
            // the rotations about the coordinate axes
            rotation_motion_unif(&Vector3::new(1.0, 0.0, 0.0), config.column_iter().collect()),
            rotation_motion_unif(&Vector3::new(0.0, 1.0, 0.0), config.column_iter().collect()),
            rotation_motion_unif(&Vector3::new(0.0, 0.0, 1.0), config.column_iter().collect()),
-
+            
            // the twist motion. more precisely: a motion that keeps the center
            // of mass stationary and preserves the distances between the
            // vertices to first order. this has to be the twist as long as:
@ -860,10 +852,10 @@ mod tests {
                        DVector::from_column_slice(&[0.0, 0.0, 5.0, 0.0]),
                        DVector::from_column_slice(&[0.0, 0.0, 1.0, 0.0]),
                        DVector::from_column_slice(&[-vel_vert_x, -vel_vert_y, -3.0, 0.0]),
-                        DVector::from_column_slice(&[vel_vert_x, vel_vert_y, -3.0, 0.0]),
+                        DVector::from_column_slice(&[vel_vert_x, vel_vert_y, -3.0, 0.0])
                    ]
                }
-            ).collect::<Vec<_>>(),
+            ).collect::<Vec<_>>()
        ];
        let tangent_motions_std = tangent_motions_unif.iter().map(
            |motion| DMatrix::from_columns(
@ -872,11 +864,11 @@ mod tests {
                ).collect::<Vec<_>>()
            )
        ).collect::<Vec<_>>();
-
+        
        // confirm that the dimension of the tangent space is no greater than
        // expected
        assert_eq!(tangent.basis_std.len(), tangent_motions_unif.len());
-
+        
        // confirm that the tangent space contains all the motions we expect it
        // to. since we've already bounded the dimension of the tangent space,
        // this confirms that the tangent space is what we expect it to be
@ -888,7 +880,7 @@ mod tests {
            assert!((motion_std - motion_proj).norm_squared() < tol_sq);
        }
    }
-
+    
    fn translation(dis: Vector3<f64>) -> DMatrix<f64> {
        const ELEMENT_DIM: usize = 5;
        DMatrix::from_column_slice(ELEMENT_DIM, ELEMENT_DIM, &[
@ -896,10 +888,10 @@ mod tests {
                   0.0,        1.0,        0.0, 0.0,             dis[1],
                   0.0,        0.0,        1.0, 0.0,             dis[2],
            2.0*dis[0], 2.0*dis[1], 2.0*dis[2], 1.0, dis.norm_squared(),
-                   0.0,        0.0,        0.0, 0.0,                1.0,
+                   0.0,        0.0,        0.0, 0.0,                1.0
        ])
    }
-
+    
    // confirm that projection onto a configuration subspace is equivariant with
    // respect to Euclidean motions
    #[test]
@ -908,49 +900,49 @@ mod tests {
        const SCALED_TOL: f64 = 1.0e-12;
        let mut problem_orig = ConstraintProblem::from_guess(&[
            sphere(0.0, 0.0, 0.5, 1.0),
-            sphere(0.0, 0.0, -0.5, 1.0),
+            sphere(0.0, 0.0, -0.5, 1.0)
        ]);
        problem_orig.gram.push_sym(0, 0, 1.0);
        problem_orig.gram.push_sym(1, 1, 1.0);
        problem_orig.gram.push_sym(0, 1, 0.5);
-        let Realization { result: result_orig, history: history_orig } = realize_gram(
+        let (config_orig, tangent_orig, success_orig, history_orig) = realize_gram(
            &problem_orig, SCALED_TOL, 0.5, 0.9, 1.1, 200, 110
        );
        let ConfigNeighborhood { config: config_orig, nbhd: tangent_orig } = result_orig.unwrap();
        assert_eq!(config_orig, problem_orig.guess);
        assert_eq!(success_orig, true);
        assert_eq!(history_orig.scaled_loss.len(), 1);
-
+        
        // find another pair of spheres that meet at 120°. we'll think of this
        // solution as a transformed version of the original one
        let guess_tfm = {
            let a = 0.5 * FRAC_1_SQRT_2;
            DMatrix::from_columns(&[
                sphere(a, 0.0, 7.0 + a, 1.0),
-                sphere(-a, 0.0, 7.0 - a, 1.0),
+                sphere(-a, 0.0, 7.0 - a, 1.0)
            ])
        };
        let problem_tfm = ConstraintProblem {
            gram: problem_orig.gram,
            frozen: problem_orig.frozen,
            guess: guess_tfm,
            frozen: problem_orig.frozen
        };
-        let Realization { result: result_tfm, history: history_tfm } = realize_gram(
+        let (config_tfm, tangent_tfm, success_tfm, history_tfm) = realize_gram(
            &problem_tfm, SCALED_TOL, 0.5, 0.9, 1.1, 200, 110
        );
        let ConfigNeighborhood { config: config_tfm, nbhd: tangent_tfm } = result_tfm.unwrap();
        assert_eq!(config_tfm, problem_tfm.guess);
        assert_eq!(success_tfm, true);
        assert_eq!(history_tfm.scaled_loss.len(), 1);
-
+        
        // project a nudge to the tangent space of the solution variety at the
        // original solution
        let motion_orig = DVector::from_column_slice(&[0.0, 0.0, 1.0, 0.0]);
        let motion_orig_proj = tangent_orig.proj(&motion_orig.as_view(), 0);
-
+        
        // project the equivalent nudge to the tangent space of the solution
        // variety at the transformed solution
        let motion_tfm = DVector::from_column_slice(&[FRAC_1_SQRT_2, 0.0, FRAC_1_SQRT_2, 0.0]);
        let motion_tfm_proj = tangent_tfm.proj(&motion_tfm.as_view(), 0);
-
+        
        // take the transformation that sends the original solution to the
        // transformed solution and apply it to the motion that the original
        // solution makes in response to the nudge
@ -960,11 +952,11 @@ mod tests {
                      0.0, 1.0,            0.0, 0.0, 0.0,
            FRAC_1_SQRT_2, 0.0,  FRAC_1_SQRT_2, 0.0, 0.0,
                      0.0, 0.0,            0.0, 1.0, 0.0,
-                      0.0, 0.0,            0.0, 0.0, 1.0,
+                      0.0, 0.0,            0.0, 0.0, 1.0
        ]);
        let transl = translation(Vector3::new(0.0, 0.0, 7.0));
        let motion_proj_tfm = transl * rot * motion_orig_proj;
-
+        
        // confirm that the projection of the nudge is equivariant. we loosen
        // the comparison tolerance because the transformation seems to
        // introduce some numerical error
@ -972,4 +964,4 @@ mod tests {
        let tol_sq = ((problem_orig.guess.nrows() * problem_orig.guess.ncols()) as f64) * SCALED_TOL_TFM * SCALED_TOL_TFM;
        assert!((motion_proj_tfm - motion_tfm_proj).norm_squared() < tol_sq);
    }
-}
+}
--- a/app-proto/src/components/identity.vert
+++ b/app-proto/src/components/identity.vert
--- a/app-proto/src/components/spheres.frag
+++ b/app-proto/src/components/spheres.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.);
-}
+}
--- a/app-proto/src/main.rs
+++ b/app-proto/src/main.rs
@ -1,49 +1,49 @@
 mod add_remove;
 mod assembly;
-mod components;
+mod display;
 mod engine;
 mod outline;
 mod specified;
 #[cfg(test)]
 mod tests;
-use std::{collections::BTreeSet, rc::Rc};
+use rustc_hash::FxHashSet;
 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 +53,16 @@ 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 {}
        }
    });
-}
+}
--- a/app-proto/src/components/outline.rs
+++ b/app-proto/src/components/outline.rs
@ -1,16 +1,21 @@
 use itertools::Itertools;
 use std::rc::Rc;
 use sycamore::prelude::*;
-use web_sys::{KeyboardEvent, MouseEvent, wasm_bindgen::JsCast};
+use web_sys::{
    KeyboardEvent,
    MouseEvent,
    wasm_bindgen::JsCast
 };
 use crate::{
    AppState,
    assembly,
    assembly::{
-        Element,
+        ElementKey,
        HalfCurvatureRegulator,
        InversiveDistanceRegulator,
        PointCoordinateRegulator,
        Regulator,
        RegulatorKey
    },
    specified::SpecifiedValue
 };
@ -21,16 +26,16 @@ fn RegulatorInput(regulator: Rc<dyn Regulator>) -> View {
    // get the regulator's measurement and set point signals
    let measurement = regulator.measurement();
    let set_point = regulator.set_point();
-
+    
    // the `valid` signal tracks whether the last entered value is a valid set
    // point specification
    let valid = create_signal(true);
-
+    
    // the `value` signal holds the current set point specification
    let value = create_signal(
        set_point.with_untracked(|set_pt| set_pt.spec.clone())
    );
-
+    
    // this `reset_value` closure resets the input value to the regulator's set
    // point specification
    let reset_value = move || {
@ -39,15 +44,15 @@ fn RegulatorInput(regulator: Rc<dyn Regulator>) -> View {
            value.set(set_point.with(|set_pt| set_pt.spec.clone()));
        })
    };
-
+    
    // reset the input value whenever the regulator's set point specification
    // is updated
    create_effect(reset_value);
-
+    
    view! {
        input(
-            r#type = "text",
+            r#type="text",
-            class = move || {
+            class=move || {
                if valid.get() {
                    set_point.with(|set_pt| {
                        if set_pt.is_present() {
@ -60,94 +65,90 @@ fn RegulatorInput(regulator: Rc<dyn Regulator>) -> View {
                    "regulator-input invalid"
                }
            },
-            placeholder = measurement.with(|result| result.to_string()),
+            placeholder=measurement.with(|result| result.to_string()),
-            bind:value = value,
+            bind:value=value,
-            on:change = move |_| {
+            on:change=move |_| {
                valid.set(
                    match SpecifiedValue::try_from(value.get_clone_untracked()) {
                        Ok(set_pt) => {
                            set_point.set(set_pt);
                            true
-                        },
+                        }
-                        Err(_) => false,
+                        Err(_) => false
                    }
                )
            },
-            on:keydown = {
+            on:keydown={
                move |event: KeyboardEvent| {
                    match event.key().as_str() {
                        "Escape" => reset_value(),
-                        _ => (),
+                        _ => ()
                    }
                }
-            },
+            }
        )
    }
 }
 pub trait OutlineItem {
-    fn outline_item(self: Rc<Self>, element: &Rc<dyn Element>) -> View;
+    fn outline_item(self: Rc<Self>, element_key: ElementKey) -> View;
 }
 impl OutlineItem for InversiveDistanceRegulator {
-    fn outline_item(self: Rc<Self>, element: &Rc<dyn Element>) -> View {
+    fn outline_item(self: Rc<Self>, element_key: ElementKey) -> View {
-        let other_subject_label = if self.subjects[0] == element.clone() {
+        let state = use_context::<AppState>();
-            self.subjects[1].label()
+        let other_subject = if self.subjects[0] == element_key {
            self.subjects[1]
        } else {
-            self.subjects[0].label()
+            self.subjects[0]
-        }.clone();
+        };
        let other_subject_label = state.assembly.elements.with(
            |elts| elts[other_subject].label.clone()
        );
        view! {
-            li(class = "regulator") {
+            li(class="regulator") {
-                div(class = "regulator-label") { (other_subject_label) }
+                div(class="regulator-label") { (other_subject_label) }
-                div(class = "regulator-type") { "Inversive distance" }
+                div(class="regulator-type") { "Inversive distance" }
-                RegulatorInput(regulator = self)
+                RegulatorInput(regulator=self)
-                div(class = "status")
+                div(class="status")
            }
        }
    }
 }
 impl OutlineItem for HalfCurvatureRegulator {
-    fn outline_item(self: Rc<Self>, _element: &Rc<dyn Element>) -> View {
+    fn outline_item(self: Rc<Self>, _element_key: ElementKey) -> View {
        view! {
-            li(class = "regulator") {
+            li(class="regulator") {
-                div(class = "regulator-label") // for spacing
+                div(class="regulator-label") // for spacing
-                div(class = "regulator-type") { "Half-curvature" }
+                div(class="regulator-type") { "Half-curvature" }
-                RegulatorInput(regulator = self)
+                RegulatorInput(regulator=self)
-                div(class = "status")
+                div(class="status")
            }
        }
    }
 }
-impl OutlineItem for PointCoordinateRegulator {
+// a list item that shows a regulator in an outline view of an element
-    fn outline_item(self: Rc<Self>, _element: &Rc<dyn Element>) -> View {
+#[component(inline_props)]
-        let name = format!("{} coordinate", self.axis);
+fn RegulatorOutlineItem(regulator_key: RegulatorKey, element_key: ElementKey) -> View {
-        view! {
+    let state = use_context::<AppState>();
-            li(class = "regulator") {
+    let regulator = state.assembly.regulators.with(
-                div(class = "regulator-label") // for spacing
+        |regs| regs[regulator_key].clone()
-                div(class = "regulator-type") { (name) }
+    );
-                RegulatorInput(regulator = self)
+    regulator.outline_item(element_key)
                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 {
+fn ElementOutlineItem(key: ElementKey, element: assembly::Element) -> View {
    let state = use_context::<AppState>();
-    let class = {
+    let class = state.selection.map(
-        let element_for_class = element.clone();
+        move |sel| if sel.contains(&key) { "selected" } else { "" }
-        state.selection.map(
+    );
-            move |sel| if sel.contains(&element_for_class) { "selected" } else { "" }
+    let label = element.label.clone();
        )
    };
    let label = element.label().clone();
    let representation = element.representation().clone();
    let rep_components = move || {
-        representation.with(
+        element.representation.with(
            |rep| rep.iter().map(
                |u| {
                    let u_str = format!("{:.3}", u).replace("-", "\u{2212}");
@ -156,26 +157,29 @@ fn ElementOutlineItem(element: Rc<dyn Element>) -> View {
            ).collect::<Vec<_>>()
        )
    };
-    let regulated = element.regulators().map(|regs| regs.len() > 0);
+    let regulated = element.regulators.map(|regs| regs.len() > 0);
-    let regulator_list = element.regulators().map(
+    let regulator_list = element.regulators.map(
-        |regs| regs
+        move |elt_reg_keys| elt_reg_keys
            .clone()
            .into_iter()
-            .sorted_by_key(|reg| reg.subjects().len())
+            .sorted_by_key(
-            .collect::<Vec<_>>()
+                |&reg_key| state.assembly.regulators.with(
                    |regs| regs[reg_key].subjects().len()
                )
            )
            .collect()
    );
    let details_node = create_node_ref();
    view! {
        li {
-            details(ref = details_node) {
+            details(ref=details_node) {
                summary(
-                    class = class.get(),
+                    class=class.get(),
-                    on:keydown = {
+                    on:keydown={
                        let element_for_handler = element.clone();
                        move |event: KeyboardEvent| {
                            match event.key().as_str() {
                                "Enter" => {
-                                    state.select(&element_for_handler, event.shift_key());
+                                    state.select(key, event.shift_key());
                                    event.prevent_default();
                                },
                                "ArrowRight" if regulated.get() => {
@ -190,41 +194,51 @@ fn ElementOutlineItem(element: Rc<dyn Element>) -> View {
                                        .unchecked_into::<web_sys::Element>()
                                        .remove_attribute("open");
                                },
-                                _ => (),
+                                _ => ()
                            }
                        }
                    }
                ) {
                    div(
-                        class = "element-switch",
+                        class="element-switch",
-                        on:click = |event: MouseEvent| event.stop_propagation()
+                        on:click=|event: MouseEvent| event.stop_propagation()
                    )
                    div(
-                        class = "element",
+                        class="element",
-                        on:click = {
+                        on:click={
                            let state_for_handler = state.clone();
                            let element_for_handler = element.clone();
                            move |event: MouseEvent| {
-                                state_for_handler.select(&element_for_handler, event.shift_key());
+                                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-label") { (label) }
-                        div(class = "element-representation") { (rep_components) }
+                        div(class="element-representation") { (rep_components) }
-                        input(
+                        div(class="status")
                            r#type = "checkbox",
                            bind:checked = element.ghost(),
                            on:click = |event: MouseEvent| event.stop_propagation()
                        )
                    }
                }
-                ul(class = "regulators") {
+                ul(class="regulators") {
                    Keyed(
-                        list = regulator_list,
+                        list=regulator_list,
-                        view = move |reg| reg.outline_item(&element),
+                        view=move |reg_key| view! {
-                        key = |reg| reg.serial()
+                            RegulatorOutlineItem(
                                regulator_key=reg_key,
                                element_key=key
                            )
                        },
                        key=|reg_key| reg_key.clone()
                    )
                }
            }
@ -241,35 +255,31 @@ fn ElementOutlineItem(element: Rc<dyn Element>) -> View {
 #[component]
 pub fn Outline() -> View {
    let state = use_context::<AppState>();
-
+    
    // list the elements alphabetically by ID
    /* TO DO */
    // this code is designed to generalize easily to other sort keys. if we only
    // 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())
+            .sorted_by_key(|(_, elt)| elt.id.clone())
-            .collect::<Vec<_>>()
+            .collect()
    );
-
+    
    view! {
        ul(
-            id = "outline",
+            id="outline",
-            on:click = {
+            on:click={
                let state = use_context::<AppState>();
                move |_| state.selection.update(|sel| sel.clear())
            }
        ) {
            Keyed(
-                list = element_list,
+                list=element_list,
-                view = |elt| view! {
+                view=|(key, elt)| view! {
-                    ElementOutlineItem(element = elt)
+                    ElementOutlineItem(key=key, element=elt)
                },
-                key = |elt| elt.serial()
+                key=|(_, elt)| elt.serial
            )
        }
    }
-}
+}
--- a/app-proto/src/specified.rs
+++ b/app-proto/src/specified.rs
@ -13,43 +13,32 @@ use std::num::ParseFloatError;
 #[readonly::make]
 pub struct SpecifiedValue {
    pub spec: String,
-    pub value: Option<f64>,
+    pub value: Option<f64>
 }
 impl SpecifiedValue {
-    pub fn from_empty_spec() -> Self {
+    pub fn from_empty_spec() -> SpecifiedValue {
-        Self { spec: String::new(), value: None }
+        SpecifiedValue { spec: String::new(), value: None }
    }
-
+    
    pub fn is_present(&self) -> bool {
        matches!(self.value, Some(_))
    }
 }
 // a `SpecifiedValue` can be constructed from a floating-point option, which is
 // given a canonical specification
 impl From<Option<f64>> for SpecifiedValue {
    fn from(value: Option<f64>) -> Self {
        match value {
            Some(x) => SpecifiedValue{ spec: x.to_string(), value },
            None => SpecifiedValue::from_empty_spec(),
        }
    }
 }
 // a `SpecifiedValue` can be constructed from a specification string, formatted
 // as described in the comment on the structure definition. the result is `Ok`
 // if the specification is properly formatted, and `Error` if not
 impl TryFrom<String> for SpecifiedValue {
    type Error = ParseFloatError;
-
+    
    fn try_from(spec: String) -> Result<Self, Self::Error> {
        if spec.is_empty() {
-            Ok(Self::from_empty_spec())
+            Ok(SpecifiedValue::from_empty_spec())
        } else {
            spec.parse::<f64>().map(
-                |value| Self { spec, value: Some(value) }
+                |value| SpecifiedValue { spec: spec, value: Some(value) }
            )
        }
    }
-}
+}
--- a/deploy/.gitignore
+++ b/deploy/.gitignore
@ -1,5 +0,0 @@
 /dyna3.zip
 /dyna3/index.html
 /dyna3/dyna3-*.js
 /dyna3/dyna3-*.wasm
 /dyna3/main-*.css
--- a/notes/inversive.md
+++ b/notes/inversive.md
@ -33,7 +33,7 @@ The unification of spheres/planes is indeed attractive for a project like Dyna3.
 Discussed coordinates with Alex Kontorovich. He was suggesting "inversive coordinates" -- for a sphere, that's 1/coradius, 1/radius, center/radius (where coradius is radius of sphere inverted in the unit sphere.) The advantage is tangent to and perpendicular to are linear in these coordinates (in the sense that if one is known, the condition of being tangent to or perpendicular to that one are linear). Planes have 1/radius = 0, and in fact, you can take the coordinates to be (2s, 0, x, y, z) where s is the distance to the origin and x,y,z are the normal direction. (Note the normal direction is only determined up to a scalar multiple. So could always scale so that the first non-zero coordinate is 1, or if you like only allow x, y to vary and let z be determined as sqrt(1-x^2^-y^2^). ) Points can be given by (r^2,1,x,y,z) where x,y,z are the coordinates and r is the distance to the origin. Quadratic form that tells you if something is a sphere/plane, or in the boundary, or up in the hyperbolic plane above. There are some details, but not quite explicit for modeling R^3, at http://sites.math.rutgers.edu/~alexk/files/LetterToDuke.pdf -- all this emphasize need to be agnostic with respect to geometric model so that we can experiment. Not really sure exactly how this relates or not to conformal geometric algebra, and whether it can be combined with geometric algebra. As formulated, there are clear-ish reps for planes/spheres and for points, but not as clear for lines. Have to see how to compute distance and/or specify a given distance. To combine inversive coordinates and geometric algebra, maybe think dually; there should be a lift from a normal vector and distance from origin to the five-vector; bivectors would rep circles/lines; trivectors would rep point pairs/points. What is the signature of this algebra, i.e. how many coordinates square to +1, -1, or 0? But it doesn't seem worth it for three dimensions, because there is a natural representation of points, as follows:
 The signature of Q will be (1,4), and in fact Q(I1,I2) = 1/2(ab+ba) - E1\dot E2, where a is the "first" or "coradius" coordinate, "b" is the "second" or "radius" coordinate, and E is the Euclidean part (x,y,z). Then the inversive coordinates of a sphere with center (x,y,z) and radius r will be I = (1/\hat{r},1/r,x/r,y/r,z/r) where \hat{r} = r/(|E|^2 -r^2). These coordinates satisfy Q(I,I) = -1. For this to make sense, of course r > 0, but we get planes by letting the radius of a tangent sphere to the plane go to infinity, and we get I = (2s, 0, x0, y0, z0) where (x0,y0,z0) is the unit normal to the plane and s is the perpendicular distance from the plane to the origin. Still Q(I,I) = -1.
-Since r>0, we can't represent individual points this way. Instead we will use some coordinates J for which Q(J,J) = 0. In particular, if you take for the Euclidean point E = (u,v,w) the coordinates J = (`|E|`^2,1,u,v,w) then Q(J,J) = 0 and moreover it comes out that Q(I,J) = 0
+Since r>0, we can't represent individual points this way. Instead we will use some coordinates J for which Q(J,J) = 0. In particular, if you take for the Euclidean point E = (u,v,w) the coordinates J = (`|E|`^2,1,u,v,w) then Q(J,J) = 0 and moreover it comes out that Q(I,J) = 0 
 whenever E lies on the sphere or plane described by some I with Q(I,I) = -1.
 The condition that two spheres I1 and I2 are tangent seems to be that Q(I1,I2) = 1. So given a fixed sphere, the condition that another sphere be tangent to it is linear in the coordinates of that other sphere.
 This system does seem promising for encoding points, spheres, and planes, and doing basic computations with them. I guess I would just encode a circle as the intersection of the concentric sphere and the containing plane, and a line as either a pair of points or a pair of planes (modulo some equivalence relation, since I can't see any canonical choice of either two planes or two points). Or actually as described below, there is a more canonical choice.
@ -62,4 +62,4 @@ In the engine's coordinate conventions, a sphere with radius $r > 0$ centered on
 $$I'_s = \left(\frac{P_x}{r}, \frac{P_y}{r}, \frac{P_z}{r}, \frac1{2r}, \frac{\|P\|^2 - r^2}{2r}\right),$$
 which has the normalization $Q'(I'_s, I'_s) = 1$. The point $P$ is represented by the vector
 $$I'_P = \left(P_x, P_y, P_z, \frac{1}{2}, \frac{\|P\|^2}{2}\right).$$
-In the `engine` module, these formulas are encoded in the `sphere` and `point` functions.
+In the `engine` module, these formulas are encoded in the `sphere` and `point` functions.
--- a/notes/theory.md
+++ b/notes/theory.md
@ -24,7 +24,7 @@ His final mathematical advice was reasonably encouraging, however:
 "But still I would consider it all more or less doable. One should very precisely think about a doable scope.
 I think three things are essential for the math no matter what you exactly plan.
-1. Think projectively.
+1. Think projectively, 
   Use Projective Geometry, Homogeneous Coordinates (or to a certain extent Quaternions, and Clifford Algebras, which are more or less an elegant way to merge Complex numbers with projective concepts.)
 2. Consider ambient complex spaces.
   The true nature of the objects can only be understood if embedded into a complex ambient space.
@ -37,8 +37,10 @@ I think three things are essential for the math no matter what you exactly plan.
 It would be nice to see how Jürgen handled some of these issues in a 2D system that he designed. Unfortunately, Cinderella was and remains closed-source; it was distributed for profit for some stretch of time. However, (a part of?) it was reimplemented in JavaScript as CindyJS, which is open source. I took a relatively quick look at that source code at one point, and these were my observations:
-CindyJS uses very concrete basic objects: 2D points are represented via projective geometry as a list of three floating-point numbers, and everything is done numerically.  There are no symbolic representations or exact algebraic numbers. (Not sure how a point on a circle or line is handled, that would take further investigation.)
+CindyJS uses very concrete basic objects: 2D points are represented via projective geometry as a list of three floating-point numbers, and everything is done numerically.  There are no symbolic representations or exact algebraic numbers. (Not sure how a point on a circle or line is handled, that would take further investigation.) 
 Lines are given by explicit coordinates as well (not sure of the internal details/exact coordinatization, or of how a "LineThrough" is represented).
 Was unclear to me how the complex parametrization for preserving continuity was handled in the code, even though Jürgen harps on complex ambient spaces; where are the complex numbers? Perhaps that part of Cinderella was never re-implemented?
--- a/src/index.html
+++ b/src/index.html
@ -7,3 +7,5 @@
  <body><script type="module" src="dyna3.js"></script>
  </body>
 </html>
--- a/tools/package-for-deployment.sh
+++ b/tools/package-for-deployment.sh
@ -1,16 +0,0 @@
 # set paths. this technique for getting the script location comes from
 # `mklement0` on Stack Overflow
 #
 #   https://stackoverflow.com/a/24114056
 #
 TOOLS=$(dirname -- $0)
 SRC="$TOOLS/../app-proto/dist"
 DEST="$TOOLS/../deploy/dyna3"
 # remove the old hash-named files
 [ -e "$DEST"/dyna3-*.js ] && rm "$DEST"/dyna3-*.js
 [ -e "$DEST"/dyna3-*.wasm ] && rm "$DEST"/dyna3-*.wasm
 [ -e "$DEST"/main-*.css ] && rm "$DEST"/main-*.css
 # copy the distribution
 cp -r "$SRC/." "$DEST"
--- a/tools/run-examples.sh
+++ b/tools/run-examples.sh
@ -1,20 +0,0 @@
 # run all Cargo examples, as described here:
 #
 #   Karol Kuczmarski. "Add examples to your Rust libraries"
 #   http://xion.io/post/code/rust-examples.html
 #
 # you should invoke this script by calling `sh` or another interpreter, rather
 # than calling `souce`, to ensure that the script can find the manifest file for
 # the application prototype
 # find the manifest file for the application prototype
 MANIFEST="$(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
Author	SHA1	Message	Date
Aaron Fenyes	5eeb0935ca	Change conditional panic to `expect` All checks were successful / test (pull_request) Successful in 2m21s Details Use `expect` to communicate that every element should have a column index when `pose` is called. Rewrite the panic messages in the style recommended by the `expect` documentation.	2025-04-21 14:47:26 -07:00
Aaron Fenyes	99a9c3ec55	Flag regulator update logging as debug All checks were successful / test (pull_request) Successful in 2m19s Details	2025-04-17 21:31:24 -07:00
Aaron Fenyes	5506ec1f43	Make regulator activation less redundant	2025-04-17 21:25:22 -07:00
Aaron Fenyes	8dab223f6a	Use field init shorthand in regulator constructors	2025-04-17 21:00:24 -07:00
Aaron Fenyes	620a6be918	Make regulator naming more consistent All checks were successful / test (pull_request) Successful in 2m27s Details Although the inversive distance regulator mostly acts as a general Lorentz product regulator, calling it `InversiveDistanceRegulator` explains how we intend to use it and demonstrates our naming convention.	2025-04-17 14:40:28 -07:00
Aaron Fenyes	7f21e7e999	Centralize the curvature component index constant All checks were successful / test (pull_request) Successful in 2m25s Details	2025-04-17 14:16:54 -07:00
Aaron Fenyes	52d99755f9	Give each regulator a constructor The assembly shouldn't have to know how to construct regulators.	2025-04-17 14:10:07 -07:00
Aaron Fenyes	8f8e806d12	Move pointer creation into `insert_regulator` This will make it easier to give each regulator a constructor instead of an "insert new" method.	2025-04-17 14:02:37 -07:00
Aaron Fenyes	ee8a01b9cb	Let regulators handle their own activation This improves code organization at the cost of a little redundancy: the default implementation of `activate` doesn't do anything, and its implementation for `HalfCurvatureRegulator` redundantly accesses the set point signal and checks whether the regulator is set.	2025-04-17 13:20:50 -07:00
Aaron Fenyes	955220c0bc	Shadow storage variable with builder variable All checks were successful / test (pull_request) Successful in 2m24s Details	2025-04-15 23:49:07 -07:00
Aaron Fenyes	4654bf06bf	Move half-curvature change routine into engine This routine is implemented in a very representation-specific way, so the engine seems like the best place for it.	2025-04-15 23:44:35 -07:00
Aaron Fenyes	e1952d7d52	Clear the regulator list when switching examples All checks were successful / test (pull_request) Successful in 2m21s Details	2025-04-10 12:14:37 -07:00
Aaron Fenyes	81e423fcbe	Give every sphere a curvature regulator All checks were successful / test (pull_request) Successful in 2m24s Details In the process, fix a reactivity bug by removing unintended signal tracking from `insert_regulator`.	2025-04-08 18:49:48 -07:00
Aaron Fenyes	63e3d733ba	Introduce a problem poser trait Elements and regulators use this common interface to write their data into the constraint problem.	2025-04-03 14:13:45 -07:00
Aaron Fenyes	bba0ac3cd6	Add a half-curvature regulator In the process, add the `OutlineItem` trait so that each regulator can implement its own outline item view.	2025-04-03 11:38:18 -07:00
Aaron Fenyes	d57ff59730	Specify the values of the frozen entries Before, a `ConstraintProblem` only specified the indices of the frozen entries. During realization, the frozen entries kept whatever values they had in the initial guess. This commit adds the values of the frozen entries to the `frozen` field of `ConstraintProblem`. The frozen entries of the guess are set to the desired values at the beginning of realization. This commit also improves the `PartialMatrix` structure, which is used to specify the indices and values of the frozen entries.	2025-04-03 11:38:18 -07:00
Aaron Fenyes	96e4a34fa1	Interpolate sphere ID and label, as intended Thanks, Clippy!	2025-04-03 11:38:18 -07:00
Aaron Fenyes	126d4c0cce	Introduce a regulator trait This will provide a common interface for Lorentz product regulators, curvature regulators, and hopefully all the other regulators too.	2025-04-03 11:38:18 -07:00
Aaron Fenyes	00f60b0e90	Store a product regulator's subjects in an array This lets us iterate over subjects. Based on commit 257ce33, with a few updates from 4a9e777.	2025-04-03 11:38:18 -07:00
Aaron Fenyes	7c40d60103	Let the elements and regulators write the problem When we realize an assembly, each element and regulator now writes its own data into the constraint problem.	2025-04-03 11:38:18 -07:00
Aaron Fenyes	bb226c5f45	Encapsulate the constraint problem data This will make it easier for elements and regulators to write themselves into the constraint problem.	2025-04-03 11:38:18 -07:00