Switch font to Fira Sans

It has tabular numbers, and it's nice and big too.
Stop Assembly::realize from reacting to itself
2024-11-01 23:58:45 -07:00 · 2024-11-01 20:49:00 -07:00 · 2024-11-01 20:40:25 -07:00 · 2024-11-01 19:11:33 -07:00 · 2024-11-01 19:01:14 -07:00 · 2024-11-01 18:56:11 -07:00
13 changed files with 1144 additions and 302 deletions
--- a/app-proto/Cargo.toml
+++ b/app-proto/Cargo.toml
@ -1,7 +1,7 @@
 [package]
-name = "sketch-outline"
+name = "dyna3"
 version = "0.1.0"
-authors = ["Aaron"]
+authors = ["Aaron Fenyes", "Glen Whitney"]
 edition = "2021"
 [features]
@ -10,6 +10,7 @@ default = ["console_error_panic_hook"]
 [dependencies]
 itertools = "0.13.0"
 js-sys = "0.3.70"
 lazy_static = "1.5.0"
 nalgebra = "0.33.0"
 rustc-hash = "2.0.0"
 slab = "0.4.9"
@ -25,6 +26,7 @@ console_error_panic_hook = { version = "0.1.7", optional = true }
 version = "0.3.69"
 features = [
  'HtmlCanvasElement',
  'HtmlInputElement',
  'Performance',
  'WebGl2RenderingContext',
  'WebGlBuffer',
--- a/app-proto/index.html
+++ b/app-proto/index.html
@ -2,8 +2,10 @@
 <html>
  <head>
    <meta charset="utf-8"/>
-    <title>Sketch outline</title>
+    <title>dyna3</title>
    <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">
  </head>
  <body></body>
 </html>
--- a/app-proto/main.css
+++ b/app-proto/main.css
@ -2,6 +2,7 @@ body {
  margin: 0px;
  color: #fcfcfc;
  background-color: #222;
  font-family: 'Fira Sans', sans-serif;
 }
 /* sidebar */
@ -33,6 +34,11 @@ body {
  font-size: large;
 }
 /* KLUDGE */
 #add-remove > button.emoji {
  font-family: 'Noto Emoji', sans-serif;
 }
 /* outline */
 #outline {
@ -93,10 +99,11 @@ details[open]:has(li) .elt-switch::after {
  display: flex;
 }
-.elt-rep > div, .cst-rep {
+.elt-rep > div {
  padding: 2px 0px 0px 0px;
  font-size: 10pt;
-  text-align: center;
+  font-variant-numeric: tabular-nums;
  text-align: right;
  width: 56px;
 }
@ -104,10 +111,38 @@ details[open]:has(li) .elt-switch::after {
  font-style: italic;
 }
-.cst > input {
+.cst.invalid {
  color: #f58fc2;
 }
 .cst > input[type=checkbox] {
  margin: 0px 8px 0px 0px;
 }
 .cst > input[type=text] {
  color: inherit;
  background-color: inherit;
  border: 1px solid #555;
  border-radius: 2px;
 }
 .cst.invalid > input[type=text] {
  border-color: #70495c;
 }
 .status {
  width: 20px;
  padding-left: 4px;
  text-align: center;
  font-family: 'Noto Emoji';
  font-style: normal;
 }
 .invalid > .status::after, details:has(.invalid):not([open]) .status::after {
  content: '⚠';
  color: #f58fc2;
 }
 /* display */
 canvas {
--- a/app-proto/run-examples
+++ b/app-proto/run-examples
@ -0,0 +1,8 @@
 # based on "Enabling print statements in Cargo tests", by Jon Almeida
 #
 #   https://jonalmeida.com/posts/2015/01/23/print-cargo/
 #
 cargo test -- --nocapture engine::tests::irisawa_hexlet_test
 cargo test -- --nocapture engine::tests::three_spheres_example
 cargo test -- --nocapture engine::tests::point_on_sphere_example
--- a/app-proto/src/add_remove.rs
+++ b/app-proto/src/add_remove.rs
@ -1,4 +1,3 @@
 use std::collections::BTreeSet; /* DEBUG */
 use sycamore::prelude::*;
 use web_sys::{console, wasm_bindgen::JsValue};
@ -7,68 +6,52 @@ use crate::{engine, AppState, assembly::{Assembly, Constraint, Element}};
 /* DEBUG */
 fn load_gen_assemb(assembly: &Assembly) {
    let _ = assembly.try_insert_element(
-        Element {
+        Element::new(
-            id: String::from("gemini_a"),
+            String::from("gemini_a"),
-            label: String::from("Castor"),
+            String::from("Castor"),
-            color: [1.00_f32, 0.25_f32, 0.00_f32],
+            [1.00_f32, 0.25_f32, 0.00_f32],
-            rep: engine::sphere(0.5, 0.5, 0.0, 1.0),
+            engine::sphere(0.5, 0.5, 0.0, 1.0)
-            constraints: BTreeSet::default()
+        )
        }
    );
    let _ = assembly.try_insert_element(
-        Element {
+        Element::new(
-            id: String::from("gemini_b"),
+            String::from("gemini_b"),
-            label: String::from("Pollux"),
+            String::from("Pollux"),
-            color: [0.00_f32, 0.25_f32, 1.00_f32],
+            [0.00_f32, 0.25_f32, 1.00_f32],
-            rep: engine::sphere(-0.5, -0.5, 0.0, 1.0),
+            engine::sphere(-0.5, -0.5, 0.0, 1.0)
-            constraints: BTreeSet::default()
+        )
        }
    );
    let _ = assembly.try_insert_element(
-        Element {
+        Element::new(
-            id: String::from("ursa_major"),
+            String::from("ursa_major"),
-            label: String::from("Ursa major"),
+            String::from("Ursa major"),
-            color: [0.25_f32, 0.00_f32, 1.00_f32],
+            [0.25_f32, 0.00_f32, 1.00_f32],
-            rep: engine::sphere(-0.5, 0.5, 0.0, 0.75),
+            engine::sphere(-0.5, 0.5, 0.0, 0.75)
-            constraints: BTreeSet::default()
+        )
        }
    );
    let _ = assembly.try_insert_element(
-        Element {
+        Element::new(
-            id: String::from("ursa_minor"),
+            String::from("ursa_minor"),
-            label: String::from("Ursa minor"),
+            String::from("Ursa minor"),
-            color: [0.25_f32, 1.00_f32, 0.00_f32],
+            [0.25_f32, 1.00_f32, 0.00_f32],
-            rep: engine::sphere(0.5, -0.5, 0.0, 0.5),
+            engine::sphere(0.5, -0.5, 0.0, 0.5)
-            constraints: BTreeSet::default()
+        )
        }
    );
    let _ = assembly.try_insert_element(
-        Element {
+        Element::new(
-            id: String::from("moon_deimos"),
+            String::from("moon_deimos"),
-            label: String::from("Deimos"),
+            String::from("Deimos"),
-            color: [0.75_f32, 0.75_f32, 0.00_f32],
+            [0.75_f32, 0.75_f32, 0.00_f32],
-            rep: engine::sphere(0.0, 0.15, 1.0, 0.25),
+            engine::sphere(0.0, 0.15, 1.0, 0.25)
-            constraints: BTreeSet::default()
+        )
        }
    );
    let _ = assembly.try_insert_element(
-        Element {
+        Element::new(
-            id: String::from("moon_phobos"),
+            String::from("moon_phobos"),
-            label: String::from("Phobos"),
+            String::from("Phobos"),
-            color: [0.00_f32, 0.75_f32, 0.50_f32],
+            [0.00_f32, 0.75_f32, 0.50_f32],
-            rep: engine::sphere(0.0, -0.15, -1.0, 0.25),
+            engine::sphere(0.0, -0.15, -1.0, 0.25)
-            constraints: BTreeSet::default()
+        )
        }
    );
    assembly.insert_constraint(
        Constraint {
            args: (
                assembly.elements_by_id.with_untracked(|elts_by_id| elts_by_id["gemini_a"]),
                assembly.elements_by_id.with_untracked(|elts_by_id| elts_by_id["gemini_b"])
            ),
            rep: 0.5,
            active: create_signal(true)
        }
    );
 }
@ -76,76 +59,68 @@ fn load_gen_assemb(assembly: &Assembly) {
 fn load_low_curv_assemb(assembly: &Assembly) {
    let a = 0.75_f64.sqrt();
    let _ = assembly.try_insert_element(
-        Element {
+        Element::new(
-            id: "central".to_string(),
+            "central".to_string(),
-            label: "Central".to_string(),
+            "Central".to_string(),
-            color: [0.75_f32, 0.75_f32, 0.75_f32],
+            [0.75_f32, 0.75_f32, 0.75_f32],
-            rep: engine::sphere(0.0, 0.0, 0.0, 1.0),
+            engine::sphere(0.0, 0.0, 0.0, 1.0)
-            constraints: BTreeSet::default()
+        )
        }
    );
    let _ = assembly.try_insert_element(
-        Element {
+        Element::new(
-            id: "assemb_plane".to_string(),
+            "assemb_plane".to_string(),
-            label: "Assembly plane".to_string(),
+            "Assembly plane".to_string(),
-            color: [0.75_f32, 0.75_f32, 0.75_f32],
+            [0.75_f32, 0.75_f32, 0.75_f32],
-            rep: engine::sphere_with_offset(0.0, 0.0, 1.0, 0.0, 0.0),
+            engine::sphere_with_offset(0.0, 0.0, 1.0, 0.0, 0.0)
-            constraints: BTreeSet::default()
+        )
        }
    );
    let _ = assembly.try_insert_element(
-        Element {
+        Element::new(
-            id: "side1".to_string(),
+            "side1".to_string(),
-            label: "Side 1".to_string(),
+            "Side 1".to_string(),
-            color: [1.00_f32, 0.00_f32, 0.25_f32],
+            [1.00_f32, 0.00_f32, 0.25_f32],
-            rep: engine::sphere_with_offset(1.0, 0.0, 0.0, 1.0, 0.0),
+            engine::sphere_with_offset(1.0, 0.0, 0.0, 1.0, 0.0)
-            constraints: BTreeSet::default()
+        )
        }
    );
    let _ = assembly.try_insert_element(
-        Element {
+        Element::new(
-            id: "side2".to_string(),
+            "side2".to_string(),
-            label: "Side 2".to_string(),
+            "Side 2".to_string(),
-            color: [0.25_f32, 1.00_f32, 0.00_f32],
+            [0.25_f32, 1.00_f32, 0.00_f32],
-            rep: engine::sphere_with_offset(-0.5, a, 0.0, 1.0, 0.0),
+            engine::sphere_with_offset(-0.5, a, 0.0, 1.0, 0.0)
-            constraints: BTreeSet::default()
+        )
        }
    );
    let _ = assembly.try_insert_element(
-        Element {
+        Element::new(
-            id: "side3".to_string(),
+            "side3".to_string(),
-            label: "Side 3".to_string(),
+            "Side 3".to_string(),
-            color: [0.00_f32, 0.25_f32, 1.00_f32],
+            [0.00_f32, 0.25_f32, 1.00_f32],
-            rep: engine::sphere_with_offset(-0.5, -a, 0.0, 1.0, 0.0),
+            engine::sphere_with_offset(-0.5, -a, 0.0, 1.0, 0.0)
-            constraints: BTreeSet::default()
+        )
        }
    );
    let _ = assembly.try_insert_element(
-        Element {
+        Element::new(
-            id: "corner1".to_string(),
+            "corner1".to_string(),
-            label: "Corner 1".to_string(),
+            "Corner 1".to_string(),
-            color: [0.75_f32, 0.75_f32, 0.75_f32],
+            [0.75_f32, 0.75_f32, 0.75_f32],
-            rep: engine::sphere(-4.0/3.0, 0.0, 0.0, 1.0/3.0),
+            engine::sphere(-4.0/3.0, 0.0, 0.0, 1.0/3.0)
-            constraints: BTreeSet::default()
+        )
        }
    );
    let _ = assembly.try_insert_element(
-        Element {
+        Element::new(
-            id: "corner2".to_string(),
+            "corner2".to_string(),
-            label: "Corner 2".to_string(),
+            "Corner 2".to_string(),
-            color: [0.75_f32, 0.75_f32, 0.75_f32],
+            [0.75_f32, 0.75_f32, 0.75_f32],
-            rep: engine::sphere(2.0/3.0, -4.0/3.0 * a, 0.0, 1.0/3.0),
+            engine::sphere(2.0/3.0, -4.0/3.0 * a, 0.0, 1.0/3.0)
-            constraints: BTreeSet::default()
+        )
        }
    );
    let _ = assembly.try_insert_element(
-        Element {
+        Element::new(
-            id: String::from("corner3"),
+            String::from("corner3"),
-            label: String::from("Corner 3"),
+            String::from("Corner 3"),
-            color: [0.75_f32, 0.75_f32, 0.75_f32],
+            [0.75_f32, 0.75_f32, 0.75_f32],
-            rep: engine::sphere(2.0/3.0, 4.0/3.0 * a, 0.0, 1.0/3.0),
+            engine::sphere(2.0/3.0, 4.0/3.0 * a, 0.0, 1.0/3.0)
-            constraints: BTreeSet::default()
+        )
        }
    );
 }
@ -198,6 +173,7 @@ pub fn AddRemove() -> View {
                }
            ) { "+" }
            button(
                class="emoji", /* KLUDGE */
                disabled={
                    let state = use_context::<AppState>();
                    state.selection.with(|sel| sel.len() != 2)
@ -210,16 +186,21 @@ pub fn AddRemove() -> View {
                            (arg_vec[0].clone(), arg_vec[1].clone())
                        }
                    );
                    let rep = create_signal(0.0);
                    let rep_valid = create_signal(false);
                    let active = create_signal(true);
                    state.assembly.insert_constraint(Constraint {
                        args: args,
-                        rep: 0.0,
+                        rep: rep,
-                        active: create_signal(true)
+                        rep_text: create_signal(String::new()),
                        rep_valid: rep_valid,
                        active: active,
                    });
                    state.selection.update(|sel| sel.clear());
                    /* DEBUG */
                    // print updated constraint list
-                    console::log_1(&JsValue::from("constraints:"));
+                    console::log_1(&JsValue::from("Constraints:"));
                    state.assembly.constraints.with(|csts| {
                        for (_, cst) in csts.into_iter() {
                            console::log_5(
@ -227,10 +208,22 @@ pub fn AddRemove() -> View {
                                &JsValue::from(cst.args.0),
                                &JsValue::from(cst.args.1),
                                &JsValue::from(":"),
-                                &JsValue::from(cst.rep)
+                                &JsValue::from(cst.rep.get_untracked())
                            );
                        }
                    });
                    // update the realization when the constraint becomes active
                    // and valid, or is edited while active and valid
                    create_effect(move || {
                        console::log_1(&JsValue::from(
                            format!("Constraint ({}, {}) updated", args.0, args.1)
                        ));
                        rep.track();
                        if active.get() && rep_valid.get() {
                            state.assembly.realize();
                        }
                    });
                }
            ) { "🔗" }
            select(bind:value=assembly_name) { /* DEBUG */
--- a/app-proto/src/assembly.rs
+++ b/app-proto/src/assembly.rs
@ -1,22 +1,49 @@
-use nalgebra::DVector;
+use nalgebra::{DMatrix, DVector};
 use rustc_hash::FxHashMap;
 use slab::Slab;
 use std::collections::BTreeSet;
 use sycamore::prelude::*;
 use web_sys::{console, wasm_bindgen::JsValue}; /* DEBUG */
 use crate::engine::{realize_gram, PartialMatrix};
 #[derive(Clone, PartialEq)]
 pub struct Element {
    pub id: String,
    pub label: String,
    pub color: [f32; 3],
-    pub rep: DVector<f64>,
+    pub rep: Signal<DVector<f64>>,
-    pub constraints: BTreeSet<usize>
+    pub constraints: Signal<BTreeSet<usize>>,
    // internal properties, not reflected in any view
    pub index: usize
 }
 impl Element {
    pub fn new(
        id: String,
        label: String,
        color: [f32; 3],
        rep: DVector<f64>
    ) -> Element {
        Element {
            id: id,
            label: label,
            color: color,
            rep: create_signal(rep),
            constraints: create_signal(BTreeSet::default()),
            index: 0
        }
    }
 }
 #[derive(Clone)]
 pub struct Constraint {
    pub args: (usize, usize),
-    pub rep: f64,
+    pub rep: Signal<f64>,
    pub rep_text: Signal<String>,
    pub rep_valid: Signal<bool>,
    pub active: Signal<bool>
 }
@ -40,6 +67,8 @@ impl Assembly {
        }
    }
    // --- inserting elements and constraints ---
    // insert an element into the assembly without checking whether we already
    // have an element with the same identifier. any element that does have the
    // same identifier will get kicked out of the `elements_by_id` index
@ -72,22 +101,103 @@ impl Assembly {
        // create and insert a new element
        self.insert_element_unchecked(
-            Element {
+            Element::new(
-                id: id,
+                id,
-                label: format!("Sphere {}", id_num),
+                format!("Sphere {}", id_num),
-                color: [0.75_f32, 0.75_f32, 0.75_f32],
+                [0.75_f32, 0.75_f32, 0.75_f32],
-                rep: DVector::<f64>::from_column_slice(&[0.0, 0.0, 0.0, 0.5, -0.5]),
+                DVector::<f64>::from_column_slice(&[0.0, 0.0, 0.0, 0.5, -0.5])
-                constraints: BTreeSet::default()
+            )
            }
        );
    }
    pub fn insert_constraint(&self, constraint: Constraint) {
        let args = constraint.args;
        let key = self.constraints.update(|csts| csts.insert(constraint));
-        self.elements.update(|elts| {
+        let arg_constraints = self.elements.with(
-            elts[args.0].constraints.insert(key);
+            |elts| (elts[args.0].constraints, elts[args.1].constraints)
-            elts[args.1].constraints.insert(key);
+        );
-        })
+        arg_constraints.0.update(|csts| csts.insert(key));
        arg_constraints.1.update(|csts| csts.insert(key));
    }
    // --- realization ---
    pub fn realize(&self) {
        // index the elements
        self.elements.update_silent(|elts| {
            for (index, (_, elt)) in elts.into_iter().enumerate() {
                elt.index = index;
            }
        });
        // set up the Gram matrix and the initial configuration matrix
        let (gram, guess) = self.elements.with_untracked(|elts| {
            // set up the off-diagonal part of the Gram matrix
            let mut gram_to_be = PartialMatrix::new();
            self.constraints.with_untracked(|csts| {
                for (_, cst) in csts {
                    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());
                    }
                }
            });
            // set up the initial configuration matrix and the diagonal of the
            // Gram matrix
            let mut guess_to_be = DMatrix::<f64>::zeros(5, elts.len());
            for (_, elt) in elts {
                let index = elt.index;
                gram_to_be.push_sym(index, index, 1.0);
                guess_to_be.set_column(index, &elt.rep.get_clone_untracked());
            }
            (gram_to_be, guess_to_be)
        });
        /* DEBUG */
        // log the Gram matrix
        console::log_1(&JsValue::from("Gram matrix:"));
        gram.log_to_console();
        /* DEBUG */
        // log the initial configuration matrix
        console::log_1(&JsValue::from("Old configuration:"));
        for j in 0..guess.nrows() {
            let mut row_str = String::new();
            for k in 0..guess.ncols() {
                row_str.push_str(format!(" {:>8.3}", guess[(j, k)]).as_str());
            }
            console::log_1(&JsValue::from(row_str));
        }
        // look for a configuration with the given Gram matrix
        let (config, success, history) = realize_gram(
            &gram, guess, &[],
            1.0e-12, 0.5, 0.9, 1.1, 200, 110
        );
        /* DEBUG */
        // report the outcome of the search
        console::log_1(&JsValue::from(
            if success {
                "Target accuracy achieved!"
            } else {
                "Failed to reach target accuracy"
            }
        ));
        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()));
        if success {
            // read out the solution
            for (_, elt) in self.elements.get_clone_untracked() {
                elt.rep.update(
                    |rep| rep.set_column(0, &config.column(elt.index))
                );
            }
        }
    }
 }
--- a/app-proto/src/display.rs
+++ b/app-proto/src/display.rs
@ -103,7 +103,11 @@ pub fn Display() -> View {
    // change listener
    let scene_changed = create_signal(true);
    create_effect(move || {
-        state.assembly.elements.track();
+        state.assembly.elements.with(|elts| {
            for (_, elt) in elts {
                elt.rep.track();
            }
        });
        state.selection.track();
        scene_changed.set(true);
    });
@ -295,23 +299,40 @@ pub fn Display() -> View {
                let assembly_to_world = &location * &orientation;
                // get the assembly
-                let elements = state.assembly.elements.get_clone();
+                let (
-                let element_iter = (&elements).into_iter();
+                    elt_cnt,
-                let reps_world: Vec<_> = element_iter.clone().map(|(_, elt)| &assembly_to_world * &elt.rep).collect();
+                    reps_world,
-                let colors: Vec<_> = element_iter.clone().map(|(key, elt)|
+                    colors,
                    highlights
                ) = state.assembly.elements.with(|elts| {
                    (
                        // number of elements
                        elts.len() as i32,
                        // representation vectors in world coordinates
                        elts.iter().map(
                            |(_, elt)| elt.rep.with(|rep| &assembly_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();
+                        }).collect::<Vec<_>>(),
-                let highlights: Vec<_> = element_iter.map(|(key, _)|
+                        
                        // highlight levels
                        elts.iter().map(|(key, _)| {
                            if state.selection.with(|sel| sel.contains(&key)) {
                                1.0_f32
                            } else {
                                HIGHLIGHT
                            }
-                ).collect();
+                        }).collect::<Vec<_>>()
                    )
                });
                // set the resolution
                let width = canvas.width() as f32;
@ -320,7 +341,7 @@ pub fn Display() -> View {
                ctx.uniform1f(shortdim_loc.as_ref(), width.min(height));
                // pass the assembly
-                ctx.uniform1i(sphere_cnt_loc.as_ref(), elements.len() as i32);
+                ctx.uniform1i(sphere_cnt_loc.as_ref(), elt_cnt);
                for n in 0..reps_world.len() {
                    let v = &reps_world[n];
                    ctx.uniform3f(
--- a/app-proto/src/engine.rs
+++ b/app-proto/src/engine.rs
@ -1,4 +1,12 @@
-use nalgebra::DVector;
+use lazy_static::lazy_static;
 use nalgebra::{Const, DMatrix, DVector, Dyn};
 use web_sys::{console, wasm_bindgen::JsValue}; /* DEBUG */
 // --- elements ---
 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)])
 }
 // the sphere with the given center and radius, with inward-pointing normals
 pub fn sphere(center_x: f64, center_y: f64, center_z: f64, radius: f64) -> DVector<f64> {
@ -25,3 +33,470 @@ pub fn sphere_with_offset(dir_x: f64, dir_y: f64, dir_z: f64, off: f64, curv: f6
        off * (1.0 + 0.5 * off * curv)
    ])
 }
 // --- partial matrices ---
 struct MatrixEntry {
    index: (usize, usize),
    value: f64
 }
 pub struct PartialMatrix(Vec<MatrixEntry>);
 impl PartialMatrix {
    pub fn new() -> PartialMatrix {
        PartialMatrix(Vec::<MatrixEntry>::new())
    }
    pub fn push_sym(&mut self, row: usize, col: usize, value: f64) {
        let PartialMatrix(entries) = self;
        entries.push(MatrixEntry { index: (row, col), value: value });
        if row != col {
            entries.push(MatrixEntry { index: (col, row), value: value });
        }
    }
    /* DEBUG */
    pub fn log_to_console(&self) {
        let PartialMatrix(entries) = self;
        for ent in entries {
            let ent_str = format!("  {} {} {}", ent.index.0, ent.index.1, ent.value);
            console::log_1(&JsValue::from(ent_str.as_str()));
        }
    }
    fn proj(&self, a: &DMatrix<f64>) -> DMatrix<f64> {
        let mut result = DMatrix::<f64>::zeros(a.nrows(), a.ncols());
        let PartialMatrix(entries) = self;
        for ent in entries {
            result[ent.index] = a[ent.index];
        }
        result
    }
    fn sub_proj(&self, rhs: &DMatrix<f64>) -> DMatrix<f64> {
        let mut result = DMatrix::<f64>::zeros(rhs.nrows(), rhs.ncols());
        let PartialMatrix(entries) = self;
        for ent in entries {
            result[ent.index] = ent.value - rhs[ent.index];
        }
        result
    }
 }
 // --- descent history ---
 pub struct DescentHistory {
    pub config: Vec<DMatrix<f64>>,
    pub scaled_loss: Vec<f64>,
    pub neg_grad: Vec<DMatrix<f64>>,
    pub min_eigval: Vec<f64>,
    pub base_step: Vec<DMatrix<f64>>,
    pub backoff_steps: Vec<i32>
 }
 impl DescentHistory {
    fn new() -> DescentHistory {
        DescentHistory {
            config: Vec::<DMatrix<f64>>::new(),
            scaled_loss: Vec::<f64>::new(),
            neg_grad: Vec::<DMatrix<f64>>::new(),
            min_eigval: Vec::<f64>::new(),
            base_step: Vec::<DMatrix<f64>>::new(),
            backoff_steps: Vec::<i32>::new(),
        }
    }
 }
 // --- gram matrix realization ---
 // the Lorentz form
 lazy_static! {
    static ref Q: DMatrix<f64> = DMatrix::from_row_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,  0.0,
        0.0, 0.0, 0.0,  0.0, -2.0,
        0.0, 0.0, 0.0, -2.0,  0.0
    ]);
 }
 struct SearchState {
    config: DMatrix<f64>,
    err_proj: DMatrix<f64>,
    loss: f64
 }
 impl SearchState {
    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();
        SearchState {
            config: config,
            err_proj: err_proj,
            loss: loss
        }
    }
 }
 fn basis_matrix(index: (usize, usize), nrows: usize, ncols: usize) -> DMatrix<f64> {
    let mut result = DMatrix::<f64>::zeros(nrows, ncols);
    result[index] = 1.0;
    result
 }
 // use backtracking line search to find a better configuration
 fn seek_better_config(
    gram: &PartialMatrix,
    state: &SearchState,
    base_step: &DMatrix<f64>,
    base_target_improvement: f64,
    min_efficiency: f64,
    backoff: f64,
    max_backoff_steps: i32
 ) -> Option<(SearchState, i32)> {
    let mut rate = 1.0;
    for backoff_steps in 0..max_backoff_steps {
        let trial_config = &state.config + rate * base_step;
        let trial_state = SearchState::from_config(gram, trial_config);
        let improvement = state.loss - trial_state.loss;
        if improvement >= min_efficiency * rate * base_target_improvement {
            return Some((trial_state, backoff_steps));
        }
        rate *= backoff;
    }
    None
 }
 // seek a matrix `config` for which `config' * Q * config` matches the partial
 // matrix `gram`. use gradient descent starting from `guess`
 pub fn realize_gram(
    gram: &PartialMatrix,
    guess: DMatrix<f64>,
    frozen: &[(usize, usize)],
    scaled_tol: f64,
    min_efficiency: f64,
    backoff: f64,
    reg_scale: f64,
    max_descent_steps: i32,
    max_backoff_steps: i32
 ) -> (DMatrix<f64>, bool, DescentHistory) {
    // start the descent history
    let mut history = DescentHistory::new();
    // 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(
        |index| index.1*element_dim + index.0
    ).collect();
    // use Newton's method with backtracking and gradient descent backup
    let mut state = SearchState::from_config(gram, guess);
    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>);
        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 {
            for row in 0..element_dim {
                let index = (row, col);
                let basis_mat = basis_matrix(index, element_dim, assembly_dim);
                let neg_d_err =
                    basis_mat.tr_mul(&*Q) * &state.config
                    + state.config.tr_mul(&*Q) * &basis_mat;
                let neg_d_err_proj = gram.proj(&neg_d_err);
                let deriv_grad = 4.0 * &*Q * (
                    -&basis_mat * &state.err_proj
                    + &state.config * &neg_d_err_proj
                );
                hess_cols.push(deriv_grad.reshape_generic(Dyn(total_dim), Const::<1>));
            }
        }
        let mut hess = DMatrix::from_columns(hess_cols.as_slice());
        // regularize the Hessian
        let min_eigval = hess.symmetric_eigenvalues().min();
        if min_eigval <= 0.0 {
            hess -= reg_scale * min_eigval * DMatrix::identity(total_dim, total_dim);
        }
        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);
        let zero_row = zero_col.transpose();
        for &k in &frozen_stacked {
            neg_grad_stacked[k] = 0.0;
            hess.set_row(k, &zero_row);
            hess.set_column(k, &zero_col);
            hess[(k, k)] = 1.0;
        }
        // compute the Newton step
        /*
          we need to either handle or eliminate the case where the minimum
          eigenvalue of the Hessian is zero, so the regularized Hessian is
          singular. right now, this causes the Cholesky decomposition to return
          `None`, leading to a panic when we unrap
        */
        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());
        // use backtracking line search to find a better configuration
        match seek_better_config(
            gram, &state, &base_step, neg_grad.dot(&base_step),
            min_efficiency, backoff, max_backoff_steps
        ) {
            Some((better_state, backoff_steps)) => {
                state = better_state;
                history.backoff_steps.push(backoff_steps);
            },
            None => return (state.config, false, history)
        };
    }
    (state.config, state.loss < tol, history)
 }
 // --- tests ---
 #[cfg(test)]
 mod tests {
    use std::{array, f64::consts::PI};
    use super::*;
    #[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 }
        ]);
        let attempt = DMatrix::<f64>::from_row_slice(2, 3, &[
            1.0, 2.0, 3.0,
            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
        ]);
        assert_eq!(target.sub_proj(&attempt), expected_result);
    }
    #[test]
    fn zero_loss_test() {
        let gram = PartialMatrix({
            let mut entries = Vec::<MatrixEntry>::new();
            for j in 0..3 {
                for k in 0..3 {
                    entries.push(MatrixEntry {
                        index: (j, k),
                        value: if j == k { 1.0 } else { -1.0 }
                    });
                }
            }
            entries
        });
        let config = {
            let a: f64 = 0.75_f64.sqrt();
            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)
            ])
        };
        let state = SearchState::from_config(&gram, config);
        assert!(state.loss.abs() < f64::EPSILON);
    }
    // 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
    // Present_)
    //
    //   "Japan's 'Wasan' Mathematical Tradition", by Abe Haruki
    //   https://www.nippon.com/en/japan-topics/c12801/
    //
    #[test]
    fn irisawa_hexlet_test() {
        let gram = PartialMatrix({
            let mut entries = Vec::<MatrixEntry>::new();
            for s in 0..9 {
                // each sphere is represented by a spacelike vector
                entries.push(MatrixEntry { index: (s, s), value: 1.0 });
                // the circumscribing sphere is tangent to all of the other
                // spheres, with matching orientation
                if s > 0 {
                    entries.push(MatrixEntry { index: (0, s), value: 1.0 });
                    entries.push(MatrixEntry { index: (s, 0), value: 1.0 });
                }
                if s > 2 {
                    // each chain sphere is tangent to the "sun" and "moon"
                    // spheres, with opposing orientation
                    for n in 1..3 {
                        entries.push(MatrixEntry { index: (s, n), value: -1.0 });
                        entries.push(MatrixEntry { index: (n, s), value: -1.0 });
                    }
                    // each chain sphere is tangent to the next chain sphere,
                    // with opposing orientation
                    let s_next = 3 + (s-2) % 6;
                    entries.push(MatrixEntry { index: (s, s_next), value: -1.0 });
                    entries.push(MatrixEntry { index: (s_next, s), value: -1.0 });
                }
            }
            entries
        });
        let guess = DMatrix::from_columns(
            [
                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)
            ].into_iter().chain(
                (1..=6).map(
                    |k| {
                        let ang = (k as f64) * PI/3.0;
                        sphere(9.0 * ang.cos(), 9.0 * ang.sin(), 0.0, 2.5)
                    }
                )
            ).collect::<Vec<_>>().as_slice()
        );
        let frozen: [(usize, usize); 4] = array::from_fn(|k| (3, k));
        const SCALED_TOL: f64 = 1.0e-12;
        let (config, success, history) = realize_gram(
            &gram, guess, &frozen,
            SCALED_TOL, 0.5, 0.9, 1.1, 200, 110
        );
        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];
        for (k, diam) in solution_diams.into_iter().enumerate() {
            assert!((config[(3, k)] - 1.0 / diam).abs() < entry_tol);
        }
        print!("\nCompleted Gram matrix:{}", config.tr_mul(&*Q) * &config);
        if success {
            println!("Target accuracy achieved!");
        } 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)]);
            }
        }
        println!("\nStep │ Loss\n─────┼────────────────────────────────");
        for (step, scaled_loss) in history.scaled_loss.into_iter().enumerate() {
            println!("{:<4} │ {}", step, scaled_loss);
        }
    }
    // --- process inspection examples ---
    // these tests are meant for human inspection, not automated use. run them
    // one at a time in `--nocapture` mode and read through the results and
    // optimization histories that they print out. the `run-examples` script
    // will run all of them
    #[test]
    fn three_spheres_example() {
        let gram = PartialMatrix({
            let mut entries = Vec::<MatrixEntry>::new();
            for j in 0..3 {
                for k in 0..3 {
                    entries.push(MatrixEntry {
                        index: (j, k),
                        value: if j == k { 1.0 } else { -1.0 }
                    });
                }
            }
            entries
        });
        let guess = {
            let a: f64 = 0.75_f64.sqrt();
            DMatrix::from_columns(&[
                sphere(1.0, 0.0, 0.0, 1.0),
                sphere(-0.5, a, 0.0, 1.0),
                sphere(-0.5, -a, 0.0, 1.0)
            ])
        };
        println!();
        let (config, success, history) = realize_gram(
            &gram, guess, &[],
            1.0e-12, 0.5, 0.9, 1.1, 200, 110
        );
        print!("\nCompleted Gram matrix:{}", config.tr_mul(&*Q) * &config);
        if success {
            println!("Target accuracy achieved!");
        } 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);
        }
    }
    #[test]
    fn point_on_sphere_example() {
        let gram = PartialMatrix({
            let mut entries = Vec::<MatrixEntry>::new();
            for j in 0..2 {
                for k in 0..2 {
                    entries.push(MatrixEntry {
                        index: (j, k),
                        value: if (j, k) == (1, 1) { 1.0 } else { 0.0 }
                    });
                }
            }
            entries
        });
        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)];
        println!();
        let (config, success, history) = realize_gram(
            &gram, guess, &frozen,
            1.0e-12, 0.5, 0.9, 1.1, 200, 110
        );
        print!("\nCompleted Gram matrix:{}", config.tr_mul(&*Q) * &config);
        print!("Configuration:{}", config);
        if success {
            println!("Target accuracy achieved!");
        } else {
            println!("Failed to reach target accuracy");
        }
        println!("Steps: {}", history.scaled_loss.len() - 1);
        println!("Loss: {}", 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);
        }
    }
 }
--- a/app-proto/src/outline.rs
+++ b/app-proto/src/outline.rs
@ -1,58 +1,80 @@
 use itertools::Itertools;
-use sycamore::{prelude::*, web::tags::div};
+use sycamore::prelude::*;
-use web_sys::{Element, KeyboardEvent, MouseEvent, wasm_bindgen::JsCast};
+use web_sys::{
    Event,
    HtmlInputElement,
    KeyboardEvent,
    MouseEvent,
    wasm_bindgen::JsCast
 };
-use crate::AppState;
+use crate::{AppState, assembly, assembly::Constraint};
 // this component lists the elements of the assembly, showing the constraints
 // on each element as a collapsible sub-list. its implementation is based on
 // Kate Morley's HTML + CSS tree views:
 //
 //   https://iamkate.com/code/tree-views/
 //
 #[component]
 pub fn Outline() -> View {
    // sort the elements alphabetically by ID
    let elements_sorted = create_memo(|| {
        let state = use_context::<AppState>();
        state.assembly.elements
            .get_clone()
            .into_iter()
            .sorted_by_key(|(_, elt)| elt.id.clone())
            .collect()
    });
 // an editable view of the Lorentz product representing a constraint
 #[component(inline_props)]
 fn LorentzProductInput(constraint: Constraint) -> View {
    view! {
-        ul(
+        input(
-            id="outline",
+            r#type="text",
-            on:click={
+            bind:value=constraint.rep_text,
-                let state = use_context::<AppState>();
+            on:change=move |event: Event| {
-                move |_| state.selection.update(|sel| sel.clear())
+                let target: HtmlInputElement = event.target().unwrap().unchecked_into();
                match target.value().parse::<f64>() {
                    Ok(rep) => batch(|| {
                        constraint.rep.set(rep);
                        constraint.rep_valid.set(true);
                    }),
                    Err(_) => constraint.rep_valid.set(false)
                };
            }
-        ) {
+        )
-            Keyed(
+    }
-                list=elements_sorted,
+}
-                view=|(key, elt)| {
+
 // a list item that shows a constraint in an outline view of an element
 #[component(inline_props)]
 fn ConstraintOutlineItem(constraint_key: usize, element_key: usize) -> View {
    let state = use_context::<AppState>();
-                    let class = create_memo({
+    let assembly = &state.assembly;
-                        move || {
+    let constraint = assembly.constraints.with(|csts| csts[constraint_key].clone());
-                            if state.selection.with(|sel| sel.contains(&key)) {
+    let other_arg = if constraint.args.0 == element_key {
-                                "selected"
+        constraint.args.1
    } else {
-                                ""
+        constraint.args.0
    };
    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="cst-label") { (other_arg_label) }
            LorentzProductInput(constraint=constraint)
            div(class="status")
        }
    }
-                    });
+}
-                    let label = elt.label.clone();
+
-                    let rep_components = elt.rep.iter().map(|u| {
+// a list item that shows an element in an outline view of an assembly
-                        let u_coord = u.to_string().replace("-", "\u{2212}");
+#[component(inline_props)]
-                        View::from(div().children(u_coord))
+fn ElementOutlineItem(key: usize, element: assembly::Element) -> View {
-                    }).collect::<Vec<_>>();
+    let state = use_context::<AppState>();
-                    let constrained = elt.constraints.len() > 0;
+    let class = state.selection.map(
        move |sel| if sel.contains(&key) { "selected" } else { "" }
    );
    let label = element.label.clone();
    let rep_components = element.rep.map(
        |rep| rep.iter().map(
            |u| format!("{:.3}", u).replace("-", "\u{2212}")
        ).collect()
    );
    let constrained = element.constraints.map(|csts| csts.len() > 0);
    let constraint_list = element.constraints.map(
        |csts| csts.clone().into_iter().collect()
    );
    let details_node = create_node_ref();
    view! {
                        /* [TO DO] switch to integer-valued parameters whenever
                        that becomes possible again */
        li {
            details(ref=details_node) {
                summary(
@ -75,16 +97,16 @@ pub fn Outline() -> View {
                                    }
                                    event.prevent_default();
                                },
-                                                "ArrowRight" if constrained => {
+                                "ArrowRight" if constrained.get() => {
                                    let _ = details_node
                                        .get()
-                                                        .unchecked_into::<Element>()
+                                        .unchecked_into::<web_sys::Element>()
                                        .set_attribute("open", "");
                                },
                                "ArrowLeft" => {
                                    let _ = details_node
                                        .get()
-                                                        .unchecked_into::<Element>()
+                                        .unchecked_into::<web_sys::Element>()
                                        .remove_attribute("open");
                                },
                                _ => ()
@ -118,43 +140,67 @@ pub fn Outline() -> View {
                        }
                    ) {
                        div(class="elt-label") { (label) }
-                                        div(class="elt-rep") { (rep_components) }
+                        div(class="elt-rep") {
                            Indexed(
                                list=rep_components,
                                view=|coord_str| view! {
                                    div { (coord_str) }
                                }
                            )
                        }
                        div(class="status")
                    }
                }
                ul(class="constraints") {
                    Keyed(
-                                        list=elt.constraints.into_iter().collect::<Vec<_>>(),
+                        list=constraint_list,
-                                        view=move |c_key: usize| {
+                        view=move |cst_key| view! {
-                                            let c_state = use_context::<AppState>();
+                            ConstraintOutlineItem(
-                                            let assembly = &c_state.assembly;
+                                constraint_key=cst_key,
-                                            let cst = assembly.constraints.with(|csts| csts[c_key].clone());
+                                element_key=key
-                                            let other_arg = if cst.args.0 == key {
+                            )
-                                                cst.args.1
+                        },
-                                            } else {
+                        key=|cst_key| cst_key.clone()
-                                                cst.args.0
+                    )
-                                            };
+                }
-                                            let other_arg_label = assembly.elements.with(|elts| elts[other_arg].label.clone());
+            }
        }
    }
 }
 // a component that lists the elements of the current assembly, showing the
 // constraints on each element as a collapsible sub-list. its implementation
 // is based on Kate Morley's HTML + CSS tree views:
 //
 //   https://iamkate.com/code/tree-views/
 //
 #[component]
 pub fn Outline() -> View {
    let state = use_context::<AppState>();
    // list the elements alphabetically by ID
    let element_list = state.assembly.elements.map(
        |elts| elts
            .clone()
            .into_iter()
            .sorted_by_key(|(_, elt)| elt.id.clone())
            .collect()
    );
    view! {
-                                                li(class="cst") {
+        ul(
-                                                    input(r#type="checkbox", bind:checked=cst.active)
+            id="outline",
-                                                    div(class="cst-label") { (other_arg_label) }
+            on:click={
-                                                    div(class="cst-rep") { (cst.rep) }
+                let state = use_context::<AppState>();
-                                                }
+                move |_| state.selection.update(|sel| sel.clear())
            }
        ) {
            Keyed(
                list=element_list,
                view=|(key, elt)| view! {
                    ElementOutlineItem(key=key, element=elt)
                },
-                                        key=|c_key| c_key.clone()
+                key=|(key, _)| key.clone()
                                    )
                                }
                            }
                        }
                    }
                },
                key=|(key, elt)| (
                    key.clone(),
                    elt.id.clone(),
                    elt.label.clone(),
                    elt.constraints.clone()
                )
            )
        }
    }
--- a/engine-proto/gram-test/Engine.jl
+++ b/engine-proto/gram-test/Engine.jl
@ -8,7 +8,8 @@ using Optim
 export
  rand_on_shell, Q, DescentHistory,
-  realize_gram_gradient, realize_gram_newton, realize_gram_optim, realize_gram
+  realize_gram_gradient, realize_gram_newton, realize_gram_optim,
  realize_gram_alt_proj, realize_gram
 # === guessing ===
@ -143,7 +144,7 @@ function realize_gram_gradient(
      break
    end
-    # find negative gradient of loss function
+    # find the negative gradient of the loss function
    neg_grad = 4*Q*L*Δ_proj
    slope = norm(neg_grad)
    dir = neg_grad / slope
@ -232,7 +233,7 @@ function realize_gram_newton(
      break
    end
-    # find the negative gradient of loss function
+    # find the negative gradient of the loss function
    neg_grad = 4*Q*L*Δ_proj
    # find the negative Hessian of the loss function
@ -313,6 +314,129 @@ function realize_gram_optim(
  )
 end
 # seek a matrix `L` for which `L'QL` matches the sparse matrix `gram` at every
 # explicit entry of `gram`. use gradient descent starting from `guess`, with an
 # alternate technique for finding the projected base step from the unprojected
 # Hessian
 function realize_gram_alt_proj(
  gram::SparseMatrixCSC{T, <:Any},
  guess::Matrix{T},
  frozen = CartesianIndex[];
  scaled_tol = 1e-30,
  min_efficiency = 0.5,
  backoff = 0.9,
  reg_scale = 1.1,
  max_descent_steps = 200,
  max_backoff_steps = 110
 ) where T <: Number
  # start history
  history = DescentHistory{T}()
  # find the dimension of the search space
  dims = size(guess)
  element_dim, construction_dim = dims
  total_dim = element_dim * construction_dim
  # list the constrained entries of the gram matrix
  J, K, _ = findnz(gram)
  constrained = zip(J, K)
  # scale the tolerance
  scale_adjustment = sqrt(T(length(constrained)))
  tol = scale_adjustment * scaled_tol
  # convert the frozen indices to stacked format
  frozen_stacked = [(index[2]-1)*element_dim + index[1] for index in frozen]
  # initialize search state
  L = copy(guess)
  Δ_proj = proj_diff(gram, L'*Q*L)
  loss = dot(Δ_proj, Δ_proj)
  # use Newton's method with backtracking and gradient descent backup
  for step in 1:max_descent_steps
    # stop if the loss is tolerably low
    if loss < tol
      break
    end
    # find the negative gradient of the loss function
    neg_grad = 4*Q*L*Δ_proj
    # find the negative Hessian of the loss function
    hess = Matrix{T}(undef, total_dim, total_dim)
    indices = [(j, k) for k in 1:construction_dim for j in 1:element_dim]
    for (j, k) in indices
      basis_mat = basis_matrix(T, j, k, dims)
      neg_dΔ = basis_mat'*Q*L + L'*Q*basis_mat
      neg_dΔ_proj = proj_to_entries(neg_dΔ, constrained)
      deriv_grad = 4*Q*(-basis_mat*Δ_proj + L*neg_dΔ_proj)
      hess[:, (k-1)*element_dim + j] = reshape(deriv_grad, total_dim)
    end
    hess_sym = Hermitian(hess)
    push!(history.hess, hess_sym)
    # regularize the Hessian
    min_eigval = minimum(eigvals(hess_sym))
    push!(history.positive, min_eigval > 0)
    if min_eigval <= 0
      hess -= reg_scale * min_eigval * I
    end
    # compute the Newton step
    neg_grad_stacked = reshape(neg_grad, total_dim)
    for k in frozen_stacked
      neg_grad_stacked[k] = 0
      hess[k, :] .= 0
      hess[:, k] .= 0
      hess[k, k] = 1
    end
    base_step_stacked = Hermitian(hess) \ neg_grad_stacked
    base_step = reshape(base_step_stacked, dims)
    push!(history.base_step, base_step)
    # store the current position, loss, and slope
    L_last = L
    loss_last = loss
    push!(history.scaled_loss, loss / scale_adjustment)
    push!(history.neg_grad, neg_grad)
    push!(history.slope, norm(neg_grad))
    # find a good step size using backtracking line search
    push!(history.stepsize, 0)
    push!(history.backoff_steps, max_backoff_steps)
    empty!(history.last_line_L)
    empty!(history.last_line_loss)
    rate = one(T)
    step_success = false
    base_target_improvement = dot(neg_grad, base_step)
    for backoff_steps in 0:max_backoff_steps
      history.stepsize[end] = rate
      L = L_last + rate * base_step
      Δ_proj = proj_diff(gram, L'*Q*L)
      loss = dot(Δ_proj, Δ_proj)
      improvement = loss_last - loss
      push!(history.last_line_L, L)
      push!(history.last_line_loss, loss / scale_adjustment)
      if improvement >= min_efficiency * rate * base_target_improvement
        history.backoff_steps[end] = backoff_steps
        step_success = true
        break
      end
      rate *= backoff
    end
    # if we've hit a wall, quit
    if !step_success
      return L_last, false, history
    end
  end
  # return the factorization and its history
  push!(history.scaled_loss, loss / scale_adjustment)
  L, loss < tol, history
 end
 # seek a matrix `L` for which `L'QL` matches the sparse matrix `gram` at every
 # explicit entry of `gram`. use gradient descent starting from `guess`
 function realize_gram(
@ -321,7 +445,6 @@ function realize_gram(
  frozen = nothing;
  scaled_tol = 1e-30,
  min_efficiency = 0.5,
  init_rate = 1.0,
  backoff = 0.9,
  reg_scale = 1.1,
  max_descent_steps = 200,
@ -352,20 +475,19 @@ function realize_gram(
    unfrozen_stacked = reshape(is_unfrozen, total_dim)
  end
-  # initialize variables
+  # initialize search state
  grad_rate = init_rate
  L = copy(guess)
  # use Newton's method with backtracking and gradient descent backup
  Δ_proj = proj_diff(gram, L'*Q*L)
  loss = dot(Δ_proj, Δ_proj)
  # use Newton's method with backtracking and gradient descent backup
  for step in 1:max_descent_steps
    # stop if the loss is tolerably low
    if loss < tol
      break
    end
-    # find the negative gradient of loss function
+    # find the negative gradient of the loss function
    neg_grad = 4*Q*L*Δ_proj
    # find the negative Hessian of the loss function
@ -420,6 +542,7 @@ function realize_gram(
    empty!(history.last_line_loss)
    rate = one(T)
    step_success = false
    base_target_improvement = dot(neg_grad, base_step)
    for backoff_steps in 0:max_backoff_steps
      history.stepsize[end] = rate
      L = L_last + rate * base_step
@ -428,7 +551,7 @@ function realize_gram(
      improvement = loss_last - loss
      push!(history.last_line_L, L)
      push!(history.last_line_loss, loss / scale_adjustment)
-      if improvement >= min_efficiency * rate * dot(neg_grad, base_step)
+      if improvement >= min_efficiency * rate * base_target_improvement
        history.backoff_steps[end] = backoff_steps
        step_success = true
        break
--- a/engine-proto/gram-test/irisawa-hexlet.jl
+++ b/engine-proto/gram-test/irisawa-hexlet.jl
@ -75,3 +75,12 @@ if success
    println("  ", 1 / L[4,k], " sun")
  end
 end
 # test an alternate technique for finding the projected base step from the
 # unprojected Hessian
 L_alt, success_alt, history_alt = Engine.realize_gram_alt_proj(gram, guess, frozen)
 completed_gram_alt = L_alt'*Engine.Q*L_alt
 println("\nDifference in result using alternate projection:\n")
 display(completed_gram_alt - completed_gram)
 println("\nDifference in steps: ", size(history_alt.scaled_loss, 1) - size(history.scaled_loss, 1))
 println("Difference in loss: ", history_alt.scaled_loss[end] - history.scaled_loss[end], "\n")
--- a/engine-proto/gram-test/sphere-in-tetrahedron.jl
+++ b/engine-proto/gram-test/sphere-in-tetrahedron.jl
@ -65,3 +65,12 @@ else
 end
 println("Steps: ", size(history.scaled_loss, 1))
 println("Loss: ", history.scaled_loss[end], "\n")
 # test an alternate technique for finding the projected base step from the
 # unprojected Hessian
 L_alt, success_alt, history_alt = Engine.realize_gram_alt_proj(gram, guess, frozen)
 completed_gram_alt = L_alt'*Engine.Q*L_alt
 println("\nDifference in result using alternate projection:\n")
 display(completed_gram_alt - completed_gram)
 println("\nDifference in steps: ", size(history_alt.scaled_loss, 1) - size(history.scaled_loss, 1))
 println("Difference in loss: ", history_alt.scaled_loss[end] - history.scaled_loss[end], "\n")
--- a/engine-proto/gram-test/tetrahedron-radius-ratio.jl
+++ b/engine-proto/gram-test/tetrahedron-radius-ratio.jl
@ -94,3 +94,12 @@ if success
  radius_ratio = dot(infty, Engine.Q * L[:,5]) / dot(infty, Engine.Q * L[:,6])
  println("\nCircumradius / inradius: ", radius_ratio)
 end
 # test an alternate technique for finding the projected base step from the
 # unprojected Hessian
 L_alt, success_alt, history_alt = Engine.realize_gram_alt_proj(gram, guess, frozen)
 completed_gram_alt = L_alt'*Engine.Q*L_alt
 println("\nDifference in result using alternate projection:\n")
 display(completed_gram_alt - completed_gram)
 println("\nDifference in steps: ", size(history_alt.scaled_loss, 1) - size(history.scaled_loss, 1))
 println("Difference in loss: ", history_alt.scaled_loss[end] - history.scaled_loss[end], "\n")
Author	SHA1	Message	Date
Aaron Fenyes	fc39f2a5f3	Switch font to Fira Sans It has tabular numbers, and it's nice and big too.	2024-11-01 23:58:45 -07:00
Aaron Fenyes	6e42681b71	Stop `Assembly::realize` from reacting to itself Previously, `realize` both tracked and updated the element vectors, so calling it in a reactive context could start a feedback loop.	2024-11-01 20:49:00 -07:00
Aaron Fenyes	327a1267d5	Test representation validity in realization effect	2024-11-01 20:40:25 -07:00
Aaron Fenyes	e12f4332fe	Use tabular numbers for element vectors	2024-11-01 19:11:33 -07:00
Aaron Fenyes	5ce5f855d5	Make element vectors reactive	2024-11-01 19:01:14 -07:00
Aaron Fenyes	e42b8da897	Add an element constructor	2024-11-01 18:56:11 -07:00
Aaron Fenyes	bbeebe4464	Simplify memos	2024-11-01 04:43:30 -07:00
Aaron Fenyes	fb292d8b5b	Render constraint lists dynamically	2024-11-01 04:32:33 -07:00
Aaron Fenyes	a3fce9d298	Correct typo in comment	2024-10-31 01:24:06 -07:00
Aaron Fenyes	5b522c12ee	Include vector representation in element diff key	2024-10-31 01:23:22 -07:00
Aaron Fenyes	1f3a6eea3b	Round element vectors to three decimal places	2024-10-30 23:57:15 -07:00
Aaron Fenyes	35d3e4a6f8	Specify fonts This should help the interface look more consistent across platforms. The font choices are just placeholders: consistency is the main goal.	2024-10-30 23:29:48 -07:00
Aaron Fenyes	0a13c062f4	Flag constraints with invalid input	2024-10-30 21:12:40 -07:00
Aaron Fenyes	9555d8f784	Update title and authors	2024-10-30 16:06:38 -07:00
Aaron Fenyes	df6db983ba	Factor out element outline item	2024-10-30 16:01:19 -07:00
Aaron Fenyes	7f595ff27a	Factor out constraint outline item	2024-10-30 15:49:01 -07:00
Aaron Fenyes	9c191ae586	Polish log messages	2024-10-30 00:27:16 -07:00
Aaron Fenyes	9e31037e17	Spread web-sys imports over multiple lines	2024-10-30 00:19:44 -07:00
Aaron Fenyes	c2e3c64d4a	Remove debug log from Lorentz product input	2024-10-30 00:16:34 -07:00
Aaron Fenyes	76ad4245d5	Factor out Lorentz product input	2024-10-29 23:43:41 -07:00
Aaron Fenyes	a46ef2c8d6	Work around data binding bug in number input Setting `bind:value` or `bind:valueAsNumber` for a number input seems to restrict what you can type in it. We work around this by switching to text inputs for now. We should probably switch back to number inputs if we can, though, because they let us take advantage of the browser's parsing and validation.	2024-10-29 22:53:48 -07:00
Aaron Fenyes	e0880d2ad2	Make constraints editable	2024-10-29 22:32:00 -07:00
Aaron Fenyes	e5f4d523f9	Update the realization when a constraint is activated Sycamore probably has a better way to do this, but this way works for now.	2024-10-29 13:46:15 -07:00
Aaron Fenyes	a37c71153d	Enforce constraints in the editor	2024-10-26 23:51:27 -07:00
Aaron Fenyes	ce33bbf418	Record optimization history	2024-10-26 01:07:17 -07:00
Aaron Fenyes	9f8632efb3	Port the Irisawa hexlet test to Rust In the process, notice that the tolerance scale adjustment was ported wrong, and correct it.	2024-10-25 21:43:53 -07:00
Aaron Fenyes	9fe03264ab	Port the Gram matrix realization routine to Rust Validate with the process inspection example tests, which print out their results and optimization histories when run one at a time in `--nocapture` mode.	2024-10-25 17:34:29 -07:00
Aaron Fenyes	e59d60bf77	Reorganize search state; remove unused variables	2024-10-25 17:17:49 -07:00
Aaron Fenyes	16df161fe7	Test alternate projection technique	2024-10-24 19:51:10 -07:00