Separate test and example for Irisawa hexlet

Put shared code in the conditionally compiled `engine::irisawa` module.

README.md

@@ -17,51 +17,3 @@ Note that currently this is just the barest beginnings of the project, more of a
 * 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.
-
-## Prototype
-
-The latest prototype is in the folder `app-proto`. It includes both a user interface and a numerical constraint-solving engine.
-
-### Install the prerequisites
-
-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)
-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
-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/)
-5. Call `cargo install trunk` to install the [Trunk](https://trunkrs.dev/) web-build tool
-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
-   * On POSIX systems, the search path is stored in the `PATH` environment variable
-
-### Play with the prototype
-
-1. Go into the `app-proto` folder
-2. Call `trunk serve --release` to build and serve the prototype
-   * *The crates the prototype depends on will be downloaded and served automatically*
-   * *For a faster build, at the expense of a much slower prototype, you can call `trunk serve` without the `--release` flag*
-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*
-4. Press *ctrl+C* in the shell where Trunk is running to stop serving the prototype
-
-### Run the engine on some example problems
-
-1. Go into the `app-proto` folder
-2. Call `./run-examples`
-   * *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*
-     
-     ```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*
-
-### Run the automated tests
-
-1. Go into the `app-proto` folder
-2. Call `cargo test`

app-proto/Cargo.toml

@@ -6,7 +6,7 @@ edition = "2021"
 
 [features]
 default = ["console_error_panic_hook"]
-dev = []
+irisawa = []
 
 [dependencies]
 itertools = "0.13.0"
@@ -26,7 +26,6 @@ console_error_panic_hook = { version = "0.1.7", optional = true }
 [dependencies.web-sys]
 version = "0.3.69"
 features = [
-  'DomRect',
   'HtmlCanvasElement',
   'HtmlInputElement',
   'Performance',
@@ -43,7 +42,7 @@ features = [
 #   https://github.com/rust-lang/cargo/issues/2911#issuecomment-1483256987
 #
 [dev-dependencies]
-dyna3 = { path = ".", default-features = false, features = ["dev"] }
+dyna3 = { path = ".", default-features = false, features = ["irisawa"] }
 wasm-bindgen-test = "0.3.34"
 
 [profile.release]

app-proto/examples/irisawa-hexlet.rs

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

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

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

app-proto/examples/three-spheres.rs

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

app-proto/main.css

@@ -1,19 +1,7 @@
-:root {
-  --text: #fcfcfc; /* almost white */
-  --text-bright: white;
-  --text-invalid: #f58fc2; /* bright pink */
-  --border: #555; /* light gray */
-  --border-focus: #aaa; /* bright gray */
-  --border-invalid: #70495c; /* dusky pink */
-  --selection-highlight: #444; /* medium gray */
-  --page-background: #222; /* dark gray */
-  --display-background: #020202; /* almost black */
-}
-
 body {
   margin: 0px;
-  color: var(--text);
-  background-color: var(--page-background);
+  color: #fcfcfc;
+  background-color: #222;
   font-family: 'Fira Sans', sans-serif;
 }
 
@@ -29,7 +17,7 @@ body {
   padding: 0px;
   border-width: 0px 1px 0px 0px;
   border-style: solid;
-  border-color: var(--border);
+  border-color: #555;
 }
 
 /* add-remove */
@@ -47,10 +35,6 @@ body {
 }
 
 /* KLUDGE */
-/*
-  for convenience, we're using emoji as temporary icons for some buttons. these
-  buttons need to be displayed in an emoji font
-*/
 #add-remove > button.emoji {
   font-family: 'Noto Emoji', sans-serif;
 }
@@ -73,49 +57,49 @@ summary {
 }
 
 summary.selected {
-  color: var(--text-bright);
-  background-color: var(--selection-highlight);
+  color: #fff;
+  background-color: #444;
 }
 
-summary > div, .constraint {
+summary > div, .cst {
   padding-top: 4px;
   padding-bottom: 4px;
 }
 
-.element, .constraint {
+.elt, .cst {
   display: flex;
   flex-grow: 1;
   padding-left: 8px;
   padding-right: 8px;
 }
 
-.element-switch {
+.elt-switch {
   width: 18px;
   padding-left: 2px;
   text-align: center;
 }
 
-details:has(li) .element-switch::after {
+details:has(li) .elt-switch::after {
   content: '▸';
 }
 
-details[open]:has(li) .element-switch::after {
+details[open]:has(li) .elt-switch::after {
   content: '▾';
 }
 
-.element-label {
+.elt-label {
   flex-grow: 1;
 }
 
-.constraint-label {
+.cst-label {
   flex-grow: 1;
 }
 
-.element-representation {
+.elt-rep {
   display: flex;
 }
 
-.element-representation > div {
+.elt-rep > div {
   padding: 2px 0px 0px 0px;
   font-size: 10pt;
   font-variant-numeric: tabular-nums;
@@ -123,27 +107,27 @@ details[open]:has(li) .element-switch::after {
   width: 56px;
 }
 
-.constraint {
+.cst {
   font-style: italic;
 }
 
-.constraint.invalid {
-  color: var(--text-invalid);
+.cst.invalid {
+  color: #f58fc2;
 }
 
-.constraint > input[type=checkbox] {
+.cst > input[type=checkbox] {
   margin: 0px 8px 0px 0px;
 }
 
-.constraint > input[type=text] {
+.cst > input[type=text] {
   color: inherit;
   background-color: inherit;
-  border: 1px solid var(--border);
+  border: 1px solid #555;
   border-radius: 2px;
 }
 
-.constraint.invalid > input[type=text] {
-  border-color: var(--border-invalid);
+.cst.invalid > input[type=text] {
+  border-color: #70495c;
 }
 
 .status {
@@ -156,7 +140,7 @@ details[open]:has(li) .element-switch::after {
 
 .invalid > .status::after, details:has(.invalid):not([open]) .status::after {
   content: '⚠';
-  color: var(--text-invalid);
+  color: #f58fc2;
 }
 
 /* display */
@@ -165,11 +149,11 @@ canvas {
   float: left;
   margin-left: 20px;
   margin-top: 20px;
-  background-color: var(--display-background);
-  border: 1px solid var(--border);
+  background-color: #020202;
+  border: 1px solid #555;
   border-radius: 16px;
 }
 
 canvas:focus {
-  border-color: var(--border-focus);
+  border-color: #aaa;
 }

app-proto/run-examples

@@ -1,5 +1,3 @@
-#!/bin/sh
-
 # run all Cargo examples, as described here:
 #
 #   Karol Kuczmarski. "Add examples to your Rust libraries"
@@ -8,4 +6,4 @@
 
 cargo run --example irisawa-hexlet
 cargo run --example three-spheres
-cargo run --example point-on-sphere
+cargo run --example point-on-sphere

app-proto/src/add_remove.rs

@@ -4,8 +4,6 @@ use web_sys::{console, wasm_bindgen::JsValue};
 use crate::{engine, AppState, assembly::{Assembly, Constraint, Element}};
 
 /* DEBUG */
-// load an example assembly for testing. this code will be removed once we've
-// built a more formal test assembly system
 fn load_gen_assemb(assembly: &Assembly) {
     let _ = assembly.try_insert_element(
         Element::new(
@@ -58,8 +56,6 @@ fn load_gen_assemb(assembly: &Assembly) {
 }
 
 /* DEBUG */
-// load an example assembly for testing. this code will be removed once we've
-// built a more formal test assembly system
 fn load_low_curv_assemb(assembly: &Assembly) {
     let a = 0.75_f64.sqrt();
     let _ = assembly.try_insert_element(
@@ -177,27 +173,27 @@ pub fn AddRemove() -> View {
                 }
             ) { "+" }
             button(
-                class="emoji", /* KLUDGE */ // for convenience, we're using an emoji as a temporary icon for this button
+                class="emoji", /* KLUDGE */
                 disabled={
                     let state = use_context::<AppState>();
                     state.selection.with(|sel| sel.len() != 2)
                 },
                 on:click=|_| {
                     let state = use_context::<AppState>();
-                    let subjects = state.selection.with(
+                    let args = state.selection.with(
                         |sel| {
-                            let subject_vec: Vec<_> = sel.into_iter().collect();
-                            (subject_vec[0].clone(), subject_vec[1].clone())
+                            let arg_vec: Vec<_> = sel.into_iter().collect();
+                            (arg_vec[0].clone(), arg_vec[1].clone())
                         }
                     );
-                    let lorentz_prod = create_signal(0.0);
-                    let lorentz_prod_valid = create_signal(false);
+                    let rep = create_signal(0.0);
+                    let rep_valid = create_signal(false);
                     let active = create_signal(true);
                     state.assembly.insert_constraint(Constraint {
-                        subjects: subjects,
-                        lorentz_prod: lorentz_prod,
-                        lorentz_prod_text: create_signal(String::new()),
-                        lorentz_prod_valid: lorentz_prod_valid,
+                        args: args,
+                        rep: rep,
+                        rep_text: create_signal(String::new()),
+                        rep_valid: rep_valid,
                         active: active,
                     });
                     state.selection.update(|sel| sel.clear());
@@ -209,10 +205,10 @@ pub fn AddRemove() -> View {
                         for (_, cst) in csts.into_iter() {
                             console::log_5(
                                 &JsValue::from(" "),
-                                &JsValue::from(cst.subjects.0),
-                                &JsValue::from(cst.subjects.1),
+                                &JsValue::from(cst.args.0),
+                                &JsValue::from(cst.args.1),
                                 &JsValue::from(":"),
-                                &JsValue::from(cst.lorentz_prod.get_untracked())
+                                &JsValue::from(cst.rep.get_untracked())
                             );
                         }
                     });
@@ -221,19 +217,18 @@ pub fn AddRemove() -> View {
                     // and valid, or is edited while active and valid
                     create_effect(move || {
                         console::log_1(&JsValue::from(
-                            format!("Constraint ({}, {}) updated", subjects.0, subjects.1)
+                            format!("Constraint ({}, {}) updated", args.0, args.1)
                         ));
-                        lorentz_prod.track();
-                        if active.get() && lorentz_prod_valid.get() {
+                        rep.track();
+                        if active.get() && rep_valid.get() {
                             state.assembly.realize();
                         }
                     });
                 }
             ) { "🔗" }
-            select(bind:value=assembly_name) { /* DEBUG */ // example assembly chooser
+            select(bind:value=assembly_name) { /* DEBUG */
                 option(value="general") { "General" }
                 option(value="low-curv") { "Low-curvature" }
-                option(value="empty") { "Empty" }
             }
         }
     }

app-proto/src/assembly.rs

@@ -1,132 +1,52 @@
-use nalgebra::{DMatrix, DVector, DVectorView, Vector3};
+use nalgebra::{DMatrix, DVector};
 use rustc_hash::FxHashMap;
 use slab::Slab;
-use std::{collections::BTreeSet, sync::atomic::{AtomicU64, Ordering}};
+use std::collections::BTreeSet;
 use sycamore::prelude::*;
 use web_sys::{console, wasm_bindgen::JsValue}; /* DEBUG */
 
-use crate::engine::{realize_gram, ConfigSubspace, PartialMatrix, Q};
-
-// the types of the keys we use to access an assembly's elements and constraints
-pub type ElementKey = usize;
-pub type ConstraintKey = usize;
-
-pub type ElementColor = [f32; 3];
-
-/* KLUDGE */
-// we should reconsider this design when we build a system for switching between
-// assemblies. at that point, we might want to switch to hierarchical keys,
-// where each each element has a key that identifies it within its assembly and
-// each assembly has a key that identifies it within the sesssion
-static NEXT_ELEMENT_SERIAL: AtomicU64 = AtomicU64::new(0);
+use crate::engine::{realize_gram, PartialMatrix};
 
 #[derive(Clone, PartialEq)]
 pub struct Element {
     pub id: String,
     pub label: String,
-    pub color: ElementColor,
-    pub representation: Signal<DVector<f64>>,
-    pub constraints: Signal<BTreeSet<ConstraintKey>>,
-
-    // a serial number, assigned by `Element::new`, that uniquely identifies
-    // each element
-    pub serial: u64,
+    pub color: [f32; 3],
+    pub rep: Signal<DVector<f64>>,
+    pub constraints: Signal<BTreeSet<usize>>,
     
-    // the configuration matrix column index that was assigned to this element
-    // last time the assembly was realized, or `None` if the element has never
-    // been through a realization
-    column_index: Option<usize>
+    // internal properties, not reflected in any view
+    pub index: usize
 }
 
 impl Element {
     pub fn new(
         id: String,
         label: String,
-        color: ElementColor,
-        representation: DVector<f64>
+        color: [f32; 3],
+        rep: DVector<f64>
     ) -> Element {
-        // take the next serial number, panicking if that was the last number we
-        // had left. the technique we use to panic on overflow is taken from
-        // _Rust Atomics and Locks_, by Mara Bos
-        //
-        //   https://marabos.nl/atomics/atomics.html#example-handle-overflow
-        //
-        let serial = NEXT_ELEMENT_SERIAL.fetch_update(
-            Ordering::SeqCst, Ordering::SeqCst,
-            |serial| serial.checked_add(1)
-        ).expect("Out of serial numbers for elements");
-        
         Element {
             id: id,
             label: label,
             color: color,
-            representation: create_signal(representation),
+            rep: create_signal(rep),
             constraints: create_signal(BTreeSet::default()),
-            serial: serial,
-            column_index: None
-        }
-    }
-    
-    // the smallest positive depth, represented as a multiple of `dir`, where
-    // the line generated by `dir` hits the element (which is assumed to be a
-    // sphere). returns `None` if the line misses the sphere. this function
-    // should be kept synchronized with `sphere_cast` in `inversive.frag`, which
-    // does essentially the same thing on the GPU side
-    pub fn cast(&self, dir: Vector3<f64>, assembly_to_world: &DMatrix<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
+            index: 0
         }
     }
 }
+            
 
 #[derive(Clone)]
 pub struct Constraint {
-    pub subjects: (ElementKey, ElementKey),
-    pub lorentz_prod: Signal<f64>,
-    pub lorentz_prod_text: Signal<String>,
-    pub lorentz_prod_valid: Signal<bool>,
+    pub args: (usize, usize),
+    pub rep: Signal<f64>,
+    pub rep_text: Signal<String>,
+    pub rep_valid: Signal<bool>,
     pub active: Signal<bool>
 }
 
-pub struct ElementMotion<'a> {
-    pub key: ElementKey,
-    pub velocity: DVectorView<'a, f64>
-}
-
-type AssemblyMotion<'a> = Vec<ElementMotion<'a>>;
-
 // a complete, view-independent description of an assembly
 #[derive(Clone)]
 pub struct Assembly {
@@ -134,20 +54,8 @@ pub struct Assembly {
     pub elements: Signal<Slab<Element>>,
     pub constraints: Signal<Slab<Constraint>>,
     
-    // solution variety tangent space. the basis vectors are stored in
-    // configuration matrix format, ordered according to the elements' column
-    // indices. when you realize the assembly, every element that's present
-    // during realization gets a column index and is reflected in the tangent
-    // space. since the methods in this module never assign column indices
-    // without later realizing the assembly, we get the following invariant:
-    //
-    //  (1) if an element has a column index, its tangent motions can be found
-    //      in that column of the tangent space basis matrices
-    //
-    pub tangent: Signal<ConfigSubspace>,
-    
     // indexing
-    pub elements_by_id: Signal<FxHashMap<String, ElementKey>>
+    pub elements_by_id: Signal<FxHashMap<String, usize>>
 }
 
 impl Assembly {
@@ -155,7 +63,6 @@ impl Assembly {
         Assembly {
             elements: create_signal(Slab::new()),
             constraints: create_signal(Slab::new()),
-            tangent: create_signal(ConfigSubspace::zero(0)),
             elements_by_id: create_signal(FxHashMap::default())
         }
     }
@@ -204,13 +111,13 @@ impl Assembly {
     }
     
     pub fn insert_constraint(&self, constraint: Constraint) {
-        let subjects = constraint.subjects;
+        let args = constraint.args;
         let key = self.constraints.update(|csts| csts.insert(constraint));
-        let subject_constraints = self.elements.with(
-            |elts| (elts[subjects.0].constraints, elts[subjects.1].constraints)
+        let arg_constraints = self.elements.with(
+            |elts| (elts[args.0].constraints, elts[args.1].constraints)
         );
-        subject_constraints.0.update(|csts| csts.insert(key));
-        subject_constraints.1.update(|csts| csts.insert(key));
+        arg_constraints.0.update(|csts| csts.insert(key));
+        arg_constraints.1.update(|csts| csts.insert(key));
     }
     
     // --- realization ---
@@ -219,7 +126,7 @@ impl Assembly {
         // index the elements
         self.elements.update_silent(|elts| {
             for (index, (_, elt)) in elts.into_iter().enumerate() {
-                elt.column_index = Some(index);
+                elt.index = index;
             }
         });
         
@@ -229,11 +136,11 @@ impl Assembly {
             let mut gram_to_be = PartialMatrix::new();
             self.constraints.with_untracked(|csts| {
                 for (_, cst) in csts {
-                    if cst.active.get_untracked() && cst.lorentz_prod_valid.get_untracked() {
-                        let subjects = cst.subjects;
-                        let row = elts[subjects.0].column_index.unwrap();
-                        let col = elts[subjects.1].column_index.unwrap();
-                        gram_to_be.push_sym(row, col, cst.lorentz_prod.get_untracked());
+                    if cst.active.get_untracked() && cst.rep_valid.get_untracked() {
+                        let args = cst.args;
+                        let row = elts[args.0].index;
+                        let col = elts[args.1].index;
+                        gram_to_be.push_sym(row, col, cst.rep.get_untracked());
                     }
                 }
             });
@@ -242,9 +149,9 @@ impl Assembly {
             // Gram matrix
             let mut guess_to_be = DMatrix::<f64>::zeros(5, elts.len());
             for (_, elt) in elts {
-                let index = elt.column_index.unwrap();
+                let index = elt.index;
                 gram_to_be.push_sym(index, index, 1.0);
-                guess_to_be.set_column(index, &elt.representation.get_clone_untracked());
+                guess_to_be.set_column(index, &elt.rep.get_clone_untracked());
             }
             
             (gram_to_be, guess_to_be)
@@ -267,7 +174,7 @@ impl Assembly {
         }
         
         // look for a configuration with the given Gram matrix
-        let (config, tangent, success, history) = realize_gram(
+        let (config, success, history) = realize_gram(
             &gram, guess, &[],
             1.0e-12, 0.5, 0.9, 1.1, 200, 110
         );
@@ -283,111 +190,14 @@ impl Assembly {
         ));
         console::log_2(&JsValue::from("Steps:"), &JsValue::from(history.scaled_loss.len() - 1));
         console::log_2(&JsValue::from("Loss:"), &JsValue::from(*history.scaled_loss.last().unwrap()));
-        console::log_2(&JsValue::from("Tangent dimension:"), &JsValue::from(tangent.dim()));
         
         if success {
             // read out the solution
             for (_, elt) in self.elements.get_clone_untracked() {
-                elt.representation.update(
-                    |rep| rep.set_column(0, &config.column(elt.column_index.unwrap()))
+                elt.rep.update(
+                    |rep| rep.set_column(0, &config.column(elt.index))
                 );
             }
-            
-            // save the tangent space
-            self.tangent.set_silent(tangent);
         }
     }
-    
-    // --- deformation ---
-    
-    // project the given motion to the tangent space of the solution variety and
-    // move the assembly along it. the implementation is based on invariant (1)
-    // from above and the following additional invariant:
-    //
-    //  (2) if an element is affected by a constraint, it has a column index
-    //
-    // we have this invariant because the assembly gets realized each time you
-    // add a constraint
-    pub fn deform(&self, motion: AssemblyMotion) {
-        /* KLUDGE */
-        // when the tangent space is zero, deformation won't do anything, but
-        // the attempt to deform should be registered in the UI. this console
-        // message will do for now
-        if self.tangent.with(|tan| tan.dim() <= 0 && tan.assembly_dim() > 0) {
-            console::log_1(&JsValue::from("The assembly is rigid"));
-        }
-        
-        // give a column index to each moving element that doesn't have one yet.
-        // this temporarily breaks invariant (1), but the invariant will be
-        // restored when we realize the assembly at the end of the deformation.
-        // in the process, we find out how many matrix columns we'll need to
-        // hold the deformation
-        let realized_dim = self.tangent.with(|tan| tan.assembly_dim());
-        let motion_dim = self.elements.update_silent(|elts| {
-            let mut next_column_index = realized_dim;
-            for elt_motion in motion.iter() {
-                let moving_elt = &mut elts[elt_motion.key];
-                if moving_elt.column_index.is_none() {
-                    moving_elt.column_index = Some(next_column_index);
-                    next_column_index += 1;
-                }
-            }
-            next_column_index
-        });
-        
-        // project the element motions onto the tangent space of the solution
-        // variety and sum them to get a deformation of the whole assembly. the
-        // matrix `motion_proj` that holds the deformation has extra columns for
-        // any moving elements that aren't reflected in the saved tangent space
-        const ELEMENT_DIM: usize = 5;
-        let mut motion_proj = DMatrix::zeros(ELEMENT_DIM, motion_dim);
-        for elt_motion in motion {
-            // we can unwrap the column index because we know that every moving
-            // element has one at this point
-            let column_index = self.elements.with_untracked(
-                |elts| elts[elt_motion.key].column_index.unwrap()
-            );
-            
-            if column_index < realized_dim {
-                // this element had a column index when we started, so by
-                // invariant (1), it's reflected in the tangent space
-                let mut target_columns = motion_proj.columns_mut(0, realized_dim);
-                target_columns += self.tangent.with(
-                    |tan| tan.proj(&elt_motion.velocity, column_index)
-                );
-            } else {
-                // this element didn't have a column index when we started, so
-                // by invariant (2), it's unconstrained
-                let mut target_column = motion_proj.column_mut(column_index);
-                target_column += elt_motion.velocity;
-            }
-        }
-        
-        // step each element along the mass shell geodesic that matches its
-        // velocity in the deformation found above
-        /* KLUDGE */
-        // since our test assemblies only include spheres, we assume that every
-        // element is on the 1 mass shell
-        for (_, elt) in self.elements.get_clone_untracked() {
-            elt.representation.update_silent(|rep| {
-                match elt.column_index {
-                    Some(column_index) => {
-                        let rep_next = &*rep + motion_proj.column(column_index);
-                        let normalizer = rep_next.dot(&(&*Q * &rep_next));
-                        rep.set_column(0, &(rep_next / normalizer));
-                    },
-                    None => {
-                        console::log_1(&JsValue::from(
-                            format!("No velocity to unpack for fresh element \"{}\"", elt.id)
-                        ))
-                    }
-                };
-            });
-        }
-        
-        // bring the configuration back onto the solution variety. this also
-        // gets the elements' column indices and the saved tangent space back in
-        // sync
-        self.realize();
-    }
 }

app-proto/src/display.rs

@@ -1,12 +1,10 @@
 use core::array;
-use nalgebra::{DMatrix, DVector, Rotation3, Vector3};
+use nalgebra::{DMatrix, Rotation3, Vector3};
 use sycamore::{prelude::*, motion::create_raf};
 use web_sys::{
     console,
     window,
-    Element,
     KeyboardEvent,
-    MouseEvent,
     WebGl2RenderingContext,
     WebGlProgram,
     WebGlShader,
@@ -14,7 +12,7 @@ use web_sys::{
     wasm_bindgen::{JsCast, JsValue}
 };
 
-use crate::{AppState, assembly::{ElementKey, ElementMotion}};
+use crate::AppState;
 
 fn compile_shader(
     context: &WebGl2RenderingContext,
@@ -84,24 +82,6 @@ fn bind_vertex_attrib(
     );
 }
 
-// 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>();
@@ -109,9 +89,6 @@ pub fn Display() -> View {
     // 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);
@@ -123,20 +100,12 @@ pub fn Display() -> View {
     let zoom_out = create_signal(0.0);
     let turntable = create_signal(false); /* BENCHMARKING */
     
-    // manipulation
-    let translate_neg_x = create_signal(0.0);
-    let translate_pos_x = create_signal(0.0);
-    let translate_neg_y = create_signal(0.0);
-    let translate_pos_y = create_signal(0.0);
-    let translate_neg_z = create_signal(0.0);
-    let translate_pos_z = create_signal(0.0);
-    
     // change listener
     let scene_changed = create_signal(true);
     create_effect(move || {
         state.assembly.elements.with(|elts| {
             for (_, elt) in elts {
-                elt.representation.track();
+                elt.rep.track();
             }
         });
         state.selection.track();
@@ -149,7 +118,6 @@ pub fn Display() -> View {
     let mut frames_since_last_sample = 0;
     let mean_frame_interval = create_signal(0.0);
     
-    let assembly_for_raf = state.assembly.clone();
     on_mount(move || {
         // timing
         let mut last_time = 0.0;
@@ -162,9 +130,6 @@ pub fn Display() -> View {
         let mut rotation = DMatrix::<f64>::identity(5, 5);
         let mut location_z: f64 = 5.0;
         
-        // manipulation
-        const TRANSLATION_SPEED: f64 = 0.15; // in length units per second
-        
         // display parameters
         const OPACITY: f32 = 0.5; /* SCAFFOLDING */
         const HIGHLIGHT: f32 = 0.2; /* SCAFFOLDING */
@@ -285,14 +250,6 @@ pub fn Display() -> View {
             let zoom_out_val = zoom_out.get();
             let turntable_val = turntable.get(); /* BENCHMARKING */
             
-            // get the manipulation state
-            let translate_neg_x_val = translate_neg_x.get();
-            let translate_pos_x_val = translate_pos_x.get();
-            let translate_neg_y_val = translate_neg_y.get();
-            let translate_pos_y_val = translate_pos_y.get();
-            let translate_neg_z_val = translate_neg_z.get();
-            let translate_pos_z_val = translate_pos_z.get();
-            
             // update the assembly's orientation
             let ang_vel = {
                 let pitch = pitch_up_val - pitch_down_val;
@@ -318,41 +275,6 @@ pub fn Display() -> View {
             let zoom = zoom_out_val - zoom_in_val;
             location_z *= (time_step * ZOOM_SPEED * zoom).exp();
             
-            // manipulate the assembly
-            if state.selection.with(|sel| sel.len() == 1) {
-                let sel = state.selection.with(
-                    |sel| *sel.into_iter().next().unwrap()
-                );
-                let rep = state.assembly.elements.with_untracked(
-                    |elts| elts[sel].representation.get_clone_untracked()
-                );
-                let translate_x = translate_pos_x_val - translate_neg_x_val;
-                let translate_y = translate_pos_y_val - translate_neg_y_val;
-                let translate_z = translate_pos_z_val - translate_neg_z_val;
-                if translate_x != 0.0 || translate_y != 0.0 || translate_z != 0.0 {
-                    let vel_field = {
-                        let u = Vector3::new(translate_x, translate_y, translate_z).normalize();
-                        DMatrix::from_column_slice(5, 5, &[
-                                 0.0,      0.0,      0.0, 0.0, u[0],
-                                 0.0,      0.0,      0.0, 0.0, u[1],
-                                 0.0,      0.0,      0.0, 0.0, u[2],
-                            2.0*u[0], 2.0*u[1], 2.0*u[2], 0.0,  0.0,
-                                 0.0,      0.0,      0.0, 0.0,  0.0
-                        ])
-                    };
-                    let elt_motion: DVector<f64> = time_step * TRANSLATION_SPEED * vel_field * rep;
-                    assembly_for_raf.deform(
-                        vec![
-                            ElementMotion {
-                                key: sel,
-                                velocity: elt_motion.as_view()
-                            }
-                        ]
-                    );
-                    scene_changed.set(true);
-                }
-            }
-            
             if scene_changed.get() {
                 /* INSTRUMENTS */
                 // measure mean frame interval
@@ -374,7 +296,7 @@ pub fn Display() -> View {
                         0.0, 0.0,   0.0, 0.0, 1.0
                     ])
                 };
-                let asm_to_world = &location * &orientation;
+                let assembly_to_world = &location * &orientation;
                 
                 // get the assembly
                 let (
@@ -389,7 +311,7 @@ pub fn Display() -> View {
                         
                         // representation vectors in world coordinates
                         elts.iter().map(
-                            |(_, elt)| elt.representation.with(|rep| &asm_to_world * rep)
+                            |(_, elt)| elt.rep.with(|rep| &assembly_to_world * rep)
                         ).collect::<Vec<_>>(),
                         
                         // colors
@@ -448,9 +370,6 @@ pub fn Display() -> View {
                 // 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
@@ -471,7 +390,7 @@ pub fn Display() -> View {
         start_animation_loop();
     });
     
-    let set_nav_signal = move |event: &KeyboardEvent, value: f64| {
+    let set_nav_signal = move |event: KeyboardEvent, value: f64| {
         let mut navigating = true;
         let shift = event.shift_key();
         match event.key().as_str() {
@@ -491,23 +410,6 @@ pub fn Display() -> View {
         }
     };
     
-    let set_manip_signal = move |event: &KeyboardEvent, value: f64| {
-        let mut manipulating = true;
-        let shift = event.shift_key();
-        match event.key().as_str() {
-            "d" | "D" => translate_pos_x.set(value),
-            "a" | "A" => translate_neg_x.set(value),
-            "w" | "W" if shift => translate_neg_z.set(value),
-            "s" | "S" if shift => translate_pos_z.set(value),
-            "w" | "W" => translate_pos_y.set(value),
-            "s" | "S" => translate_neg_y.set(value),
-            _ => manipulating = false
-        };
-        if manipulating {
-            event.prevent_default();
-        }
-    };
-    
     view! {
         /* TO DO */
         // switch back to integer-valued parameters when that becomes possible
@@ -519,7 +421,6 @@ pub fn Display() -> View {
             tabindex="0",
             on:keydown=move |event: KeyboardEvent| {
                 if event.key() == "Shift" {
-                    // swap navigation inputs
                     roll_cw.set(yaw_right.get());
                     roll_ccw.set(yaw_left.get());
                     zoom_in.set(pitch_up.get());
@@ -528,24 +429,16 @@ pub fn Display() -> View {
                     yaw_left.set(0.0);
                     pitch_up.set(0.0);
                     pitch_down.set(0.0);
-                    
-                    // swap manipulation inputs
-                    translate_pos_z.set(translate_neg_y.get());
-                    translate_neg_z.set(translate_pos_y.get());
-                    translate_pos_y.set(0.0);
-                    translate_neg_y.set(0.0);
                 } else {
                     if event.key() == "Enter" { /* BENCHMARKING */
                         turntable.set_fn(|turn| !turn);
                         scene_changed.set(true);
                     }
-                    set_nav_signal(&event, 1.0);
-                    set_manip_signal(&event, 1.0);
+                    set_nav_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());
@@ -554,15 +447,8 @@ pub fn Display() -> View {
                     roll_ccw.set(0.0);
                     zoom_in.set(0.0);
                     zoom_out.set(0.0);
-                    
-                    // swap manipulation inputs
-                    translate_pos_y.set(translate_neg_z.get());
-                    translate_neg_y.set(translate_pos_z.get());
-                    translate_pos_z.set(0.0);
-                    translate_neg_z.set(0.0);
                 } else {
-                    set_nav_signal(&event, 0.0);
-                    set_manip_signal(&event, 0.0);
+                    set_nav_signal(event, 0.0);
                 }
             },
             on:blur=move |_| {
@@ -572,31 +458,6 @@ pub fn Display() -> View {
                 yaw_left.set(0.0);
                 roll_ccw.set(0.0);
                 roll_cw.set(0.0);
-            },
-            on:click=move |event: MouseEvent| {
-                // find the nearest element along the pointer direction
-                let dir = event_dir(&event);
-                console::log_1(&JsValue::from(dir.to_string()));
-                let mut clicked: Option<(ElementKey, f64)> = None;
-                for (key, elt) in state.assembly.elements.get_clone_untracked() {
-                    match assembly_to_world.with(|asm_to_world| elt.cast(dir, asm_to_world)) {
-                        Some(depth) => match clicked {
-                            Some((_, best_depth)) => {
-                                if depth < best_depth {
-                                    clicked = Some((key, depth))
-                                }
-                            },
-                            None => clicked = Some((key, depth))
-                        }
-                        None => ()
-                    };
-                }
-                
-                // if we clicked something, select it
-                match clicked {
-                    Some((key, _)) => state.select(key, event.shift_key()),
-                    None => state.selection.update(|sel| sel.clear())
-                };
             }
         )
     }

app-proto/src/engine.rs

@@ -1,10 +1,9 @@
 use lazy_static::lazy_static;
-use nalgebra::{Const, DMatrix, DVector, DVectorView, Dyn, SymmetricEigen};
+use nalgebra::{Const, DMatrix, DVector, Dyn};
 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)])
 }
@@ -85,75 +84,6 @@ impl PartialMatrix {
     }
 }
 
-// --- configuration subspaces ---
-
-#[derive(Clone)]
-pub struct ConfigSubspace {
-    assembly_dim: usize,
-    basis: Vec<DMatrix<f64>>
-}
-
-impl ConfigSubspace {
-    pub fn zero(assembly_dim: usize) -> ConfigSubspace {
-        ConfigSubspace {
-            assembly_dim: assembly_dim,
-            basis: Vec::new()
-        }
-    }
-    
-    // approximate the kernel of a symmetric endomorphism of the configuration
-    // space for `assembly_dim` elements. we consider an eigenvector to be part
-    // of the kernel if its eigenvalue is smaller than the constant `THRESHOLD`
-    fn symmetric_kernel(a: DMatrix<f64>, assembly_dim: usize) -> ConfigSubspace {
-        const ELEMENT_DIM: usize = 5;
-        const THRESHOLD: f64 = 1.0e-4;
-        let eig = SymmetricEigen::new(a);
-        let eig_vecs = eig.eigenvectors.column_iter();
-        let eig_pairs = eig.eigenvalues.iter().zip(eig_vecs);
-        let basis = eig_pairs.filter_map(
-            |(λ, v)| (λ.abs() < THRESHOLD).then_some(
-                Into::<DMatrix<f64>>::into(
-                    v.reshape_generic(Dyn(ELEMENT_DIM), Dyn(assembly_dim))
-                )
-            )
-        );
-        
-        /* DEBUG */
-        // print the eigenvalues
-        #[cfg(all(target_family = "wasm", target_os = "unknown"))]
-        console::log_1(&JsValue::from(
-            format!("Eigenvalues used to find kernel:{}", eig.eigenvalues)
-        ));
-        
-        ConfigSubspace {
-            assembly_dim: assembly_dim,
-            basis: basis.collect()
-        }
-    }
-    
-    pub fn dim(&self) -> usize {
-        self.basis.len()
-    }
-    
-    pub fn assembly_dim(&self) -> usize {
-        self.assembly_dim
-    }
-    
-    // find the projection onto this subspace, with respect to the Euclidean
-    // inner product, of the motion where the element with the given column
-    // index has velocity `v`
-    pub fn proj(&self, v: &DVectorView<f64>, column_index: usize) -> DMatrix<f64> {
-        if self.dim() == 0 {
-            const ELEMENT_DIM: usize = 5;
-            DMatrix::zeros(ELEMENT_DIM, self.assembly_dim)
-        } else {
-            self.basis.iter().map(
-                |b| b.column(column_index).dot(&v) * b
-            ).sum()
-        }
-    }
-}
-
 // --- descent history ---
 
 pub struct DescentHistory {
@@ -250,7 +180,7 @@ pub fn realize_gram(
     reg_scale: f64,
     max_descent_steps: i32,
     max_backoff_steps: i32
-) -> (DMatrix<f64>, ConfigSubspace, bool, DescentHistory) {
+) -> (DMatrix<f64>, bool, DescentHistory) {
     // start the descent history
     let mut history = DescentHistory::new();
     
@@ -270,8 +200,12 @@ pub fn realize_gram(
     
     // use Newton's method with backtracking and gradient descent backup
     let mut state = SearchState::from_config(gram, guess);
-    let mut hess = DMatrix::zeros(element_dim, assembly_dim);
     for _ in 0..max_descent_steps {
+        // stop if the loss is tolerably low
+        history.config.push(state.config.clone());
+        history.scaled_loss.push(state.loss / scale_adjustment);
+        if state.loss < tol { break; }
+        
         // find the negative gradient of the loss function
         let neg_grad = 4.0 * &*Q * &state.config * &state.err_proj;
         let mut neg_grad_stacked = neg_grad.clone().reshape_generic(Dyn(total_dim), Const::<1>);
@@ -294,7 +228,7 @@ pub fn realize_gram(
                 hess_cols.push(deriv_grad.reshape_generic(Dyn(total_dim), Const::<1>));
             }
         }
-        hess = DMatrix::from_columns(hess_cols.as_slice());
+        let mut hess = DMatrix::from_columns(hess_cols.as_slice());
         
         // regularize the Hessian
         let min_eigval = hess.symmetric_eigenvalues().min();
@@ -314,11 +248,6 @@ pub fn realize_gram(
             hess[(k, k)] = 1.0;
         }
         
-        // stop if the loss is tolerably low
-        history.config.push(state.config.clone());
-        history.scaled_loss.push(state.loss / scale_adjustment);
-        if state.loss < tol { break; }
-        
         // compute the Newton step
         /*
           we need to either handle or eliminate the case where the minimum
@@ -326,7 +255,7 @@ pub fn realize_gram(
           singular. right now, this causes the Cholesky decomposition to return
           `None`, leading to a panic when we unrap
         */
-        let base_step_stacked = hess.clone().cholesky().unwrap().solve(&neg_grad_stacked);
+        let base_step_stacked = hess.cholesky().unwrap().solve(&neg_grad_stacked);
         let base_step = base_step_stacked.reshape_generic(Dyn(element_dim), Dyn(assembly_dim));
         history.base_step.push(base_step.clone());
         
@@ -339,16 +268,10 @@ pub fn realize_gram(
                 state = better_state;
                 history.backoff_steps.push(backoff_steps);
             },
-            None => return (state.config, ConfigSubspace::zero(assembly_dim), false, history)
+            None => return (state.config, false, history)
         };
     }
-    let success = state.loss < tol;
-    let tangent = if success {
-        ConfigSubspace::symmetric_kernel(hess, assembly_dim)
-    } else {
-        ConfigSubspace::zero(assembly_dim)
-    };
-    (state.config, tangent, success, history)
+    (state.config, state.loss < tol, history)
 }
 
 // --- tests ---
@@ -361,13 +284,13 @@ pub fn realize_gram(
 //   "Japan's 'Wasan' Mathematical Tradition", by Abe Haruki
 //   https://www.nippon.com/en/japan-topics/c12801/
 //
-#[cfg(feature = "dev")]
+#[cfg(feature = "irisawa")]
 pub mod irisawa {
     use std::{array, f64::consts::PI};
     
     use super::*;
     
-    pub fn realize_irisawa_hexlet(scaled_tol: f64) -> (DMatrix<f64>, ConfigSubspace, bool, DescentHistory) {
+    pub fn realize_irisawa_hexlet(scaled_tol: f64) -> (DMatrix<f64>, bool, DescentHistory) {
         let gram = {
             let mut gram_to_be = PartialMatrix::new();
             for s in 0..9 {
@@ -475,7 +398,7 @@ mod tests {
     fn irisawa_hexlet_test() {
         // solve Irisawa's problem
         const SCALED_TOL: f64 = 1.0e-12;
-        let (config, _, _, _) = realize_irisawa_hexlet(SCALED_TOL);
+        let (config, _, _) = realize_irisawa_hexlet(SCALED_TOL);
         
         // check against Irisawa's solution
         let entry_tol = SCALED_TOL.sqrt();
@@ -484,93 +407,4 @@ mod tests {
             assert!((config[(3, k)] - 1.0 / diam).abs() < entry_tol);
         }
     }
-    
-    #[test]
-    fn tangent_test() {
-        const SCALED_TOL: f64 = 1.0e-12;
-        const ELEMENT_DIM: usize = 5;
-        const ASSEMBLY_DIM: usize = 3;
-        let gram = {
-            let mut gram_to_be = PartialMatrix::new();
-            for j in 0..3 {
-                for k in j..3 {
-                    gram_to_be.push_sym(j, k, if j == k { 1.0 } else { -1.0 });
-                }
-            }
-            gram_to_be
-        };
-        let guess = DMatrix::from_columns(&[
-            sphere(0.0, 0.0, 0.0, -2.0),
-            sphere(0.0, 0.0, 1.0, 1.0),
-            sphere(0.0, 0.0, -1.0, 1.0)
-        ]);
-        let frozen: [_; 5] = std::array::from_fn(|k| (k, 0));
-        let (config, tangent, success, history) = realize_gram(
-            &gram, guess.clone(), &frozen,
-            SCALED_TOL, 0.5, 0.9, 1.1, 200, 110
-        );
-        assert_eq!(config, guess);
-        assert_eq!(success, true);
-        assert_eq!(history.scaled_loss.len(), 1);
-        
-        // confirm that the tangent space has dimension five or less
-        let ConfigSubspace(ref tangent_basis) = tangent;
-        assert_eq!(tangent_basis.len(), 5);
-        
-        // confirm that the tangent space contains all the motions we expect it
-        // to. since we've already bounded the dimension of the tangent space,
-        // this confirms that the tangent space is what we expect it to be
-        let tangent_motions = vec![
-            basis_matrix((0, 1), ELEMENT_DIM, ASSEMBLY_DIM),
-            basis_matrix((1, 1), ELEMENT_DIM, ASSEMBLY_DIM),
-            basis_matrix((0, 2), ELEMENT_DIM, ASSEMBLY_DIM),
-            basis_matrix((1, 2), ELEMENT_DIM, ASSEMBLY_DIM),
-            DMatrix::<f64>::from_column_slice(ELEMENT_DIM, 3, &[
-                0.0, 0.0, 0.0, 0.0, 0.0,
-                0.0, 0.0, -1.0, -0.25, -1.0,
-                0.0, 0.0, -1.0, 0.25, 1.0
-            ])
-        ];
-        let tol_sq = ((ELEMENT_DIM * ASSEMBLY_DIM) as f64) * SCALED_TOL * SCALED_TOL;
-        for motion in tangent_motions {
-            let motion_proj: DMatrix<_> = motion.column_iter().enumerate().map(
-                |(k, v)| tangent.proj(&v, k)
-            ).sum();
-            assert!((motion - motion_proj).norm_squared() < tol_sq);
-        }
-    }
-    
-    // at the frozen indices, the optimization steps should have exact zeros,
-    // and the realized configuration should match the initial guess
-    #[test]
-    fn frozen_entry_test() {
-        let gram = {
-            let mut gram_to_be = PartialMatrix::new();
-            for j in 0..2 {
-                for k in j..2 {
-                    gram_to_be.push_sym(j, k, if (j, k) == (1, 1) { 1.0 } else { 0.0 });
-                }
-            }
-            gram_to_be
-        };
-        let guess = DMatrix::from_columns(&[
-            point(0.0, 0.0, 2.0),
-            sphere(0.0, 0.0, 0.0, 1.0)
-        ]);
-        let frozen = [(3, 0), (3, 1)];
-        println!();
-        let (config, _, success, history) = realize_gram(
-            &gram, guess.clone(), &frozen,
-            1.0e-12, 0.5, 0.9, 1.1, 200, 110
-        );
-        assert_eq!(success, true);
-        for base_step in history.base_step.into_iter() {
-            for index in frozen {
-                assert_eq!(base_step[index], 0.0);
-            }
-        }
-        for index in frozen {
-            assert_eq!(config[index], guess[index]);
-        }
-    }
 }

app-proto/src/main.rs

@@ -8,14 +8,14 @@ use rustc_hash::FxHashSet;
 use sycamore::prelude::*;
 
 use add_remove::AddRemove;
-use assembly::{Assembly, ElementKey};
+use assembly::Assembly;
 use display::Display;
 use outline::Outline;
 
 #[derive(Clone)]
 struct AppState {
     assembly: Assembly,
-    selection: Signal<FxHashSet<ElementKey>>
+    selection: Signal<FxHashSet<usize>>
 }
 
 impl AppState {
@@ -25,31 +25,9 @@ impl AppState {
             selection: create_signal(FxHashSet::default())
         }
     }
-    
-    // in single-selection mode, select the element with the given key. in
-    // multiple-selection mode, toggle whether the element with the given key
-    // is selected
-    fn select(&self, key: ElementKey, multi: bool) {
-        if multi {
-            self.selection.update(|sel| {
-                if !sel.remove(&key) {
-                    sel.insert(key);
-                }
-            });
-        } else {
-            self.selection.update(|sel| {
-                sel.clear();
-                sel.insert(key);
-            });
-        }
-    }
 }
 
 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());
         

app-proto/src/outline.rs

@@ -8,7 +8,7 @@ use web_sys::{
     wasm_bindgen::JsCast
 };
 
-use crate::{AppState, assembly, assembly::{Constraint, ConstraintKey, ElementKey}};
+use crate::{AppState, assembly, assembly::Constraint};
 
 // an editable view of the Lorentz product representing a constraint
 #[component(inline_props)]
@@ -16,15 +16,15 @@ fn LorentzProductInput(constraint: Constraint) -> View {
     view! {
         input(
             r#type="text",
-            bind:value=constraint.lorentz_prod_text,
+            bind:value=constraint.rep_text,
             on:change=move |event: Event| {
                 let target: HtmlInputElement = event.target().unwrap().unchecked_into();
                 match target.value().parse::<f64>() {
-                    Ok(lorentz_prod) => batch(|| {
-                        constraint.lorentz_prod.set(lorentz_prod);
-                        constraint.lorentz_prod_valid.set(true);
+                    Ok(rep) => batch(|| {
+                        constraint.rep.set(rep);
+                        constraint.rep_valid.set(true);
                     }),
-                    Err(_) => constraint.lorentz_prod_valid.set(false)
+                    Err(_) => constraint.rep_valid.set(false)
                 };
             }
         )
@@ -33,23 +33,23 @@ fn LorentzProductInput(constraint: Constraint) -> View {
 
 // a list item that shows a constraint in an outline view of an element
 #[component(inline_props)]
-fn ConstraintOutlineItem(constraint_key: ConstraintKey, element_key: ElementKey) -> View {
+fn ConstraintOutlineItem(constraint_key: usize, element_key: usize) -> View {
     let state = use_context::<AppState>();
     let assembly = &state.assembly;
     let constraint = assembly.constraints.with(|csts| csts[constraint_key].clone());
-    let other_subject = if constraint.subjects.0 == element_key {
-        constraint.subjects.1
+    let other_arg = if constraint.args.0 == element_key {
+        constraint.args.1
     } else {
-        constraint.subjects.0
+        constraint.args.0
     };
-    let other_subject_label = assembly.elements.with(|elts| elts[other_subject].label.clone());
-    let class = constraint.lorentz_prod_valid.map(
-        |&lorentz_prod_valid| if lorentz_prod_valid { "constraint" } else { "constraint invalid" }
+    let other_arg_label = assembly.elements.with(|elts| elts[other_arg].label.clone());
+    let class = constraint.rep_valid.map(
+        |&rep_valid| if rep_valid { "cst" } else { "cst invalid" }
     );
     view! {
         li(class=class.get()) {
             input(r#type="checkbox", bind:checked=constraint.active)
-            div(class="constraint-label") { (other_subject_label) }
+            div(class="cst-label") { (other_arg_label) }
             LorentzProductInput(constraint=constraint)
             div(class="status")
         }
@@ -58,13 +58,13 @@ fn ConstraintOutlineItem(constraint_key: ConstraintKey, element_key: ElementKey)
 
 // a list item that shows an element in an outline view of an assembly
 #[component(inline_props)]
-fn ElementOutlineItem(key: ElementKey, element: assembly::Element) -> View {
+fn ElementOutlineItem(key: usize, element: assembly::Element) -> View {
     let state = use_context::<AppState>();
     let class = state.selection.map(
         move |sel| if sel.contains(&key) { "selected" } else { "" }
     );
     let label = element.label.clone();
-    let rep_components = element.representation.map(
+    let rep_components = element.rep.map(
         |rep| rep.iter().map(
             |u| format!("{:.3}", u).replace("-", "\u{2212}")
         ).collect()
@@ -83,7 +83,18 @@ fn ElementOutlineItem(key: ElementKey, element: assembly::Element) -> View {
                         move |event: KeyboardEvent| {
                             match event.key().as_str() {
                                 "Enter" => {
-                                    state.select(key, 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.prevent_default();
                                 },
                                 "ArrowRight" if constrained.get() => {
@@ -104,11 +115,11 @@ fn ElementOutlineItem(key: ElementKey, element: assembly::Element) -> View {
                     }
                 ) {
                     div(
-                        class="element-switch",
+                        class="elt-switch",
                         on:click=|event: MouseEvent| event.stop_propagation()
                     )
                     div(
-                        class="element",
+                        class="elt",
                         on:click={
                             move |event: MouseEvent| {
                                 if event.shift_key() {
@@ -128,8 +139,8 @@ fn ElementOutlineItem(key: ElementKey, element: assembly::Element) -> View {
                             }
                         }
                     ) {
-                        div(class="element-label") { (label) }
-                        div(class="element-representation") {
+                        div(class="elt-label") { (label) }
+                        div(class="elt-rep") {
                             Indexed(
                                 list=rep_components,
                                 view=|coord_str| view! {
@@ -189,7 +200,7 @@ pub fn Outline() -> View {
                 view=|(key, elt)| view! {
                     ElementOutlineItem(key=key, element=elt)
                 },
-                key=|(_, elt)| elt.serial
+                key=|(key, _)| key.clone()
             )
         }
     }

notes/inversive.md

@@ -41,25 +41,3 @@ I will have to work out formulas for the Euclidean distance between two entities
 In this vein, it seems as though if J1 and J2 are the reps of two points, then Q(J1,J2) = d^2/2. So then the sphere centered at J1 through J2 is (J1-(2Q(J1,J2),0,0,0,0))/sqrt(2Q(J1,J2)). Ugh has a sqrt in it. Similarly for sphere centered at J3 through J2, (J3-(2Q(J3,J2),0000))/sqrt(2Q(J3,J2)). J1,J2,J3 are collinear if these spheres are tangent, i.e. if those vectors have Q-inner-product 1, which is to say Q(J1,J3) - Q(J1,J2) - Q(J3,J2) = 2sqrt(Q(J1,J2)Q(J2,J3)). But maybe that's not the simplest way of putting it. After all, we can just say that the cross-product of the two differences is 0; that has no square roots in it.
 
 One conceivable way to canonicalize lines is to use the *perpendicular* plane that goes through the origin, that's uniquely defined, and anyway just amounts to I = (0,0,d) where d is the ordinary direction vector of the line; and a point J in that plane that the line goes through, which just amounts to J=(r^2,1,E) with Q(I,J) = 0, i.e. E\dot d = 0. It's also the point on the line closest to the origin. The reason that we don't usually use that point as the companion to the direction vector is that the resulting set of six coordinates is not homogeneous. But here that's not an issue, since we have our standard point coordinates and plane coordinates; and for a plane through the origin, only two of the direction coordinates are really free, and then we have the one dot-product relation, so only two of the point coordinates are really free, giving us the correct dimensionality of 4 for the set of lines. So in some sense this says that we could take naively as coordinates for a line the projection of the unit direction vector to the xy plane and the projection of the line's closest point to the origin to the xy plane. That doesn't seem to have any weird gimbal locks or discontinuities or anything. And with these coordinates, you can test if the point E=x,y,z is on the line (dx,dy,cx,cy) by extending (dx,dy) to d via dz = sqrt(1-dx^2 - dy^2), extending (cx,cy) to c by determining cz via d\dot c = 0, and then checking if d\cross(E-c) = 0. And you can see if two lines are parallel just by checking if they have the same direction vector, and if not, you can see if they are coplanar by projecting both of their closest points perpendicularly onto the line in the direction of the cross product of their directions, and if the projections match they are coplanar.
-
-#### Engine Conventions
-
-The coordinate conventions used in the engine are different from the ones used in these notes. Marking the engine vectors and coordinates with $'$, we have
-$$I' = (x', y', z', b', c'),$$
-where
-$$
-\begin{align*}
-x' & = x & b' & = b/2 \\
-y' & = y & c' & = c/2. \\
-z' & = z
-\end{align*}
-$$
-The engine uses the quadratic form $Q' = -Q$, which is expressed in engine coordinates as
-$$Q'(I'_1, I'_2) = x'_1 x'_2 + y'_1 y'_2 + z'_1 z'_2 - 2(b'_1c'_2 + c'_1 b'_2).$$
-In the `engine` module, the matrix of $Q'$ is encoded in the lazy static variable `Q`.
-
-In the engine's coordinate conventions, a sphere with radius $r > 0$ centered on $P = (P_x, P_y, P_z)$ is represented by the vector
-$$I'_s = \left(\frac{P_x}{r}, \frac{P_y}{r}, \frac{P_z}{r}, \frac1{2r}, \frac{\|P\|^2 - r^2}{2r}\right),$$
-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.