chore: wrap all code at 80 characters

.forgejo/setup-trunk/action.yaml

@@ -10,7 +10,7 @@ runs:
   using: "composite"
   steps:
     - run: rustup target add wasm32-unknown-unknown
-    
+
     # install the Trunk binary to `ci-bin` within the workspace directory, which
     # is determined by the `github.workspace` label and reflected in the
     # `GITHUB_WORKSPACE` environment variable. then, make the `trunk` command

.forgejo/workflows/continuous-integration.yaml

@@ -24,6 +24,6 @@ jobs:
       # workspace directory (action variable `github.workspace`, environment
       # variable `$GITHUB_WORKSPACE`):
       - uses: https://code.forgejo.org/actions/checkout@v4
-      
+
       - uses: ./.forgejo/setup-trunk
-      - run: RUSTFLAGS='-D warnings' cargo test
+      - run: RUSTFLAGS='-D warnings' cargo test

README.md

@@ -52,20 +52,20 @@ The latest prototype is in the folder `app-proto`. It includes both a user inter
 1. Use `sh` to run the script `tools/run-examples.sh`.
    - The script is location-independent, so you can do this from anywhere in the dyna3 repository.
    - The call from the top level of the repository is:
-     
+
      ```bash
      sh tools/run-examples.sh
      ```
    - For each example problem, the engine will print the value of the loss function at each optimization step.
    - The first example that prints is the same as the Irisawa hexlet example from the Julia version of the engine prototype. If you go into `engine-proto/gram-test`, launch Julia, and then execute
-     
+
      ```julia
      include("irisawa-hexlet.jl")
      for (step, scaled_loss) in enumerate(history_alt.scaled_loss)
        println(rpad(step-1, 4), " | ", scaled_loss)
      end
      ```
-     
+
      you should see that it prints basically the same loss history until the last few steps, when the lower default precision of the Rust engine really starts to show.
 
 ### Run the automated tests

app-proto/examples/irisawa-hexlet.rs

@@ -15,9 +15,9 @@ fn main() {
         for k in 4..9 {
             println!("  {} sun", 1.0 / config[(3, k)]);
         }
-        
+
         // print the completed Gram matrix
         print::gram_matrix(&config);
     }
     print::loss_history(&realization.history);
-}
+}

app-proto/examples/kaleidocycle.rs

@@ -14,7 +14,7 @@ fn main() {
         // print the completed Gram matrix and the realized configuration
         print::gram_matrix(&config);
         print::config(&config);
-        
+
         // find the kaleidocycle's twist motion by projecting onto the tangent
         // space
         const N_POINTS: usize = 12;
@@ -29,4 +29,4 @@ fn main() {
         let normalization = 5.0 / twist_motion[(2, 0)];
         println!("\nTwist motion:{}", (normalization * twist_motion).to_string().trim_end());
     }
-}
+}

app-proto/index.html

@@ -6,7 +6,7 @@
     <link data-trunk rel="css" href="main.css"/>
     <link href="https://fonts.bunny.net/css?family=fira-sans:ital,wght@0,400;1,400&display=swap" rel="stylesheet">
     <link href="https://fonts.bunny.net/css?family=noto-emoji:wght@400&text=%f0%9f%94%97%e2%9a%a0&display=swap" rel="stylesheet">
-    
+
     <!--
       the Charming visualization crate, which we use to show engine diagnostics,
       depends the ECharts JavaScript package

app-proto/src/assembly.rs

@@ -261,7 +261,8 @@ impl ProblemPoser for Sphere {
         let index = self.column_index().expect(
             indexing_error("Sphere", &self.id, "it").as_str());
         problem.gram.push_sym(index, index, 1.0);
-        problem.guess.set_column(index, &self.representation.get_clone_untracked());
+        problem.guess.set_column(
+            index, &self.representation.get_clone_untracked());
     }
 }
 
@@ -367,7 +368,8 @@ impl ProblemPoser for Point {
             indexing_error("Point", &self.id, "it").as_str());
         problem.gram.push_sym(index, index, 0.0);
         problem.frozen.push(Self::WEIGHT_COMPONENT, index, 0.5);
-        problem.guess.set_column(index, &self.representation.get_clone_untracked());
+        problem.guess.set_column(
+            index, &self.representation.get_clone_untracked());
     }
 }
 
@@ -412,7 +414,8 @@ pub struct InversiveDistanceRegulator {
 
 impl InversiveDistanceRegulator {
     pub fn new(subjects: [Rc<dyn Element>; 2]) -> Self {
-        let representations = subjects.each_ref().map(|subj| subj.representation());
+        let representations = subjects.each_ref().map(
+            |subj| subj.representation());
         let measurement = create_memo(move || {
             representations[0].with(|rep_0|
                 representations[1].with(|rep_1|
@@ -518,6 +521,7 @@ impl ProblemPoser for HalfCurvatureRegulator {
 
 #[derive(Clone, Copy, Sequence)]
 pub enum Axis { X = 0, Y = 1, Z = 2 }
+
 impl Axis {
     fn name(&self) -> &'static str {
         match self { Axis::X => "X", Axis::Y => "Y", Axis::Z => "Z" }
@@ -544,7 +548,9 @@ impl PointCoordinateRegulator {
             move |rep| rep[axis as usize]
         );
         let set_point = create_signal(SpecifiedValue::from_empty_spec());
-        Self { subject, axis, measurement, set_point, serial: Self::next_serial() }
+        Self {
+            subject, axis, measurement, set_point, serial: Self::next_serial()
+        }
     }
 }
 
@@ -578,8 +584,8 @@ impl ProblemPoser for PointCoordinateRegulator {
                 }
                 if nset == Axis::CARDINALITY {
                     let [x, y, z] = coords;
-                    problem.frozen.push(
+                    problem.frozen.push(Point::NORM_COMPONENT,
-                        Point::NORM_COMPONENT, col, point(x,y,z)[Point::NORM_COMPONENT]);
+                        col, point(x,y,z)[Point::NORM_COMPONENT]);
                 }
             }
         });
@@ -678,7 +684,8 @@ impl Assembly {
         let id = elt.id().clone();
         let elt_rc = Rc::new(elt);
         self.elements.update(|elts| elts.insert(elt_rc.clone()));
-        self.elements_by_id.update(|elts_by_id| elts_by_id.insert(id, elt_rc.clone()));
+        self.elements_by_id.update(
+            |elts_by_id| elts_by_id.insert(id, elt_rc.clone()));
 
         // create and insert the element's default regulators
         for reg in elt_rc.default_regulators() {
@@ -754,7 +761,8 @@ impl Assembly {
     pub fn load_config(&self, config: &DMatrix<f64>) {
         for elt in self.elements.get_clone_untracked() {
             elt.representation().update(
-                |rep| rep.set_column(0, &config.column(elt.column_index().unwrap()))
+                |rep| rep.set_column(
+                    0, &config.column(elt.column_index().unwrap()))
             );
         }
     }
@@ -899,7 +907,8 @@ impl Assembly {
             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);
+                let mut target_columns =
+                    motion_proj.columns_mut(0, realized_dim);
                 target_columns += self.tangent.with(
                     |tan| tan.proj(&elt_motion.velocity, column_index)
                 );
@@ -907,9 +916,10 @@ impl Assembly {
                 // 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);
-                let unif_to_std = elt_motion.element.representation().with_untracked(
+                let unif_to_std =
-                    |rep| local_unif_to_std(rep.as_view())
+                    elt_motion.element.representation().with_untracked(
-                );
+                        |rep| local_unif_to_std(rep.as_view())
+                    );
                 target_column += unif_to_std * elt_motion.velocity;
             }
         }
@@ -926,7 +936,10 @@ impl Assembly {
                         elt.project_to_normalized(rep);
                     },
                     None => {
-                        console_log!("No velocity to unpack for fresh element \"{}\"", elt.id())
+                        console_log!(
+                            "No velocity to unpack for fresh element \"{}\"",
+                            elt.id()
+                        )
                     },
                 };
             });
@@ -961,13 +974,15 @@ mod tests {
     fn unindexed_subject_test_inversive_distance() {
         let _ = create_root(|| {
             let subjects = [0, 1].map(
-                |k| Rc::new(Sphere::default(format!("sphere{k}"), k)) as Rc<dyn Element>
+                |k| Rc::new(
+                    Sphere::default(format!("sphere{k}"), k)) as Rc<dyn Element>
             );
             subjects[0].set_column_index(0);
             InversiveDistanceRegulator {
                 subjects: subjects,
                 measurement: create_memo(|| 0.0),
-                set_point: create_signal(SpecifiedValue::try_from("0.0".to_string()).unwrap()),
+                set_point: create_signal(
+                    SpecifiedValue::try_from("0.0".to_string()).unwrap()),
                 serial: InversiveDistanceRegulator::next_serial()
             }.pose(&mut ConstraintProblem::new(2));
         });
@@ -996,8 +1011,10 @@ mod tests {
             // nudge the sphere repeatedly along the `z` axis
             const STEP_SIZE: f64 = 0.0025;
             const STEP_CNT: usize = 400;
-            let sphere = assembly.elements_by_id.with(|elts_by_id| elts_by_id[sphere_id].clone());
+            let sphere = assembly.elements_by_id.with(
-            let velocity = DVector::from_column_slice(&[0.0, 0.0, STEP_SIZE, 0.0]);
+                |elts_by_id| elts_by_id[sphere_id].clone());
+            let velocity =
+                DVector::from_column_slice(&[0.0, 0.0, STEP_SIZE, 0.0]);
             for _ in 0..STEP_CNT {
                 assembly.deform(
                     vec![
@@ -1015,7 +1032,8 @@ mod tests {
             let final_half_curv = sphere.representation().with_untracked(
                 |rep| rep[Sphere::CURVATURE_COMPONENT]
             );
-            assert!((final_half_curv / INITIAL_HALF_CURV - 1.0).abs() < DRIFT_TOL);
+            assert!((final_half_curv / INITIAL_HALF_CURV - 1.0).abs()
+                < DRIFT_TOL);
         });
     }
 }

app-proto/src/components/add_remove.rs

@@ -39,7 +39,9 @@ pub fn AddRemove() -> View {
                 }
             ) { "Add point" }
             button(
-                class = "emoji", /* KLUDGE */ // for convenience, we're using an emoji as a temporary icon for this button
+                /* KLUDGE */ // for convenience, we're using an emoji as an
+                // icon for this button
+                class = "emoji",
                 disabled = {
                     let state = use_context::<AppState>();
                     state.selection.with(|sel| sel.len() != 2)

app-proto/src/components/display.rs

@@ -50,7 +50,8 @@ impl SceneSpheres {
     }
 
     fn len_i32(&self) -> i32 {
-        self.representations.len().try_into().expect("Number of spheres must fit in a 32-bit integer")
+        self.representations.len().try_into().expect(
+            "Number of spheres must fit in a 32-bit integer")
     }
 
     fn push(
@@ -127,8 +128,12 @@ impl DisplayItem for Sphere {
         const HIGHLIGHT: f32 = 0.2;
 
         let representation = self.representation.get_clone_untracked();
-        let color = if selected { self.color.map(|channel| 0.2 + 0.8*channel) } else { self.color };
+        let color =
-        let opacity = if self.ghost.get() { GHOST_OPACITY } else { DEFAULT_OPACITY };
+            if selected { self.color.map(|channel| 0.2 + 0.8*channel) }
+            else { self.color };
+        let opacity =
+            if self.ghost.get() { GHOST_OPACITY }
+            else { DEFAULT_OPACITY };
         let highlight = if selected { 1.0 } else { HIGHLIGHT };
         scene.spheres.push(representation, color, opacity, highlight);
     }
@@ -145,7 +150,8 @@ impl DisplayItem for Sphere {
         // `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 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];
@@ -186,7 +192,9 @@ impl DisplayItem for Point {
         const HIGHLIGHT: f32 = 0.5;
 
         let representation = self.representation.get_clone_untracked();
-        let color = if selected { self.color.map(|channel| 0.2 + 0.8*channel) } else { self.color };
+        let color =
+            if selected { self.color.map(|channel| 0.2 + 0.8*channel) }
+            else { self.color };
         let opacity = if self.ghost.get() { GHOST_OPACITY } else { 1.0 };
         let highlight = if selected { 1.0 } else { HIGHLIGHT };
         scene.points.push(representation, color, opacity, highlight, selected);
@@ -199,7 +207,8 @@ impl DisplayItem for Point {
         assembly_to_world: &DMatrix<f64>,
         pixel_size: f64,
     ) -> Option<f64> {
-        let rep = self.representation.with_untracked(|rep| assembly_to_world * rep);
+        let rep = self.representation.with_untracked(
+            |rep| assembly_to_world * rep);
         if rep[2] < 0.0 {
             // this constant should be kept synchronized with `point.frag`
             const POINT_RADIUS_PX: f64 = 4.0;
@@ -357,11 +366,12 @@ fn event_dir(event: &MouseEvent) -> (Vector3<f64>, f64) {
     // this constant should be kept synchronized with `spheres.frag` and
     // `point.vert`
     const FOCAL_SLOPE: f64 = 0.3;
-
+    let horizontal = f64::from(event.client_x()) - rect.left();
+    let vertical = rect.bottom() - f64::from(event.client_y());
     (
         Vector3::new(
-            FOCAL_SLOPE * (2.0*(f64::from(event.client_x()) - rect.left()) - width) / shortdim,
+            FOCAL_SLOPE * (2.0*horizontal - width) / shortdim,
-            FOCAL_SLOPE * (2.0*(rect.bottom() - f64::from(event.client_y())) - height) / shortdim,
+            FOCAL_SLOPE * (2.0*vertical - height) / shortdim,
             -1.0,
         ),
         FOCAL_SLOPE * 2.0 / shortdim,
@@ -445,7 +455,8 @@ pub fn Display() -> View {
         let performance = window().unwrap().performance().unwrap();
 
         // get the display canvas
-        let canvas = display.get().unchecked_into::<web_sys::HtmlCanvasElement>();
+        let canvas =
+            display.get().unchecked_into::<web_sys::HtmlCanvasElement>();
         let ctx = canvas
             .get_context("webgl2")
             .unwrap()
@@ -458,7 +469,8 @@ pub fn Display() -> View {
 
         // set blend mode
         ctx.enable(WebGl2RenderingContext::BLEND);
-        ctx.blend_func(WebGl2RenderingContext::SRC_ALPHA, WebGl2RenderingContext::ONE_MINUS_SRC_ALPHA);
+        ctx.blend_func(WebGl2RenderingContext::SRC_ALPHA,
+            WebGl2RenderingContext::ONE_MINUS_SRC_ALPHA);
 
         // set up the sphere rendering program
         let sphere_program = set_up_program(
@@ -487,16 +499,20 @@ pub fn Display() -> View {
         // machine, the the length of a float or genType array seems to be
         // capped at 1024 elements
         console::log_2(
-            &ctx.get_parameter(WebGl2RenderingContext::MAX_FRAGMENT_UNIFORM_VECTORS).unwrap(),
+            &ctx.get_parameter(
+                WebGl2RenderingContext::MAX_FRAGMENT_UNIFORM_VECTORS).unwrap(),
             &JsValue::from("uniform vectors available"),
         );
 
         // find the sphere program's vertex attribute
-        let viewport_position_attr = ctx.get_attrib_location(&sphere_program, "position") as u32;
+        let viewport_position_attr =
+            ctx.get_attrib_location(&sphere_program, "position") as u32;
 
         // find the sphere program's uniforms
         const SPHERE_MAX: usize = 200;
-        let sphere_cnt_loc = ctx.get_uniform_location(&sphere_program, "sphere_cnt");
+        let sphere_cnt_loc = ctx.get_uniform_location(
+            &sphere_program, "sphere_cnt"
+        );
         let sphere_sp_locs = get_uniform_array_locations::<SPHERE_MAX>(
             &ctx, &sphere_program, "sphere_list", Some("sp")
         );
@@ -509,10 +525,18 @@ pub fn Display() -> View {
         let sphere_highlight_locs = get_uniform_array_locations::<SPHERE_MAX>(
             &ctx, &sphere_program, "highlight_list", None
         );
-        let resolution_loc = ctx.get_uniform_location(&sphere_program, "resolution");
+        let resolution_loc = ctx.get_uniform_location(
-        let shortdim_loc = ctx.get_uniform_location(&sphere_program, "shortdim");
+            &sphere_program, "resolution"
-        let layer_threshold_loc = ctx.get_uniform_location(&sphere_program, "layer_threshold");
+        );
-        let debug_mode_loc = ctx.get_uniform_location(&sphere_program, "debug_mode");
+        let shortdim_loc = ctx.get_uniform_location(
+            &sphere_program, "shortdim"
+        );
+        let layer_threshold_loc = ctx.get_uniform_location(
+            &sphere_program, "layer_threshold"
+        );
+        let debug_mode_loc = ctx.get_uniform_location(
+            &sphere_program, "debug_mode"
+        );
 
         // load the viewport vertex positions into a new vertex buffer object
         const VERTEX_CNT: usize = 6;
@@ -526,13 +550,18 @@ pub fn Display() -> View {
              1.0,  1.0, 0.0,
              1.0, -1.0, 0.0,
         ];
-        let viewport_position_buffer = load_new_buffer(&ctx, &viewport_positions);
+        let viewport_position_buffer =
+            load_new_buffer(&ctx, &viewport_positions);
 
         // find the point program's vertex attributes
-        let point_position_attr = ctx.get_attrib_location(&point_program, "position") as u32;
+        let point_position_attr =
-        let point_color_attr = ctx.get_attrib_location(&point_program, "color") as u32;
+            ctx.get_attrib_location(&point_program, "position") as u32;
-        let point_highlight_attr = ctx.get_attrib_location(&point_program, "highlight") as u32;
+        let point_color_attr =
-        let point_selection_attr = ctx.get_attrib_location(&point_program, "selected") as u32;
+            ctx.get_attrib_location(&point_program, "color") as u32;
+        let point_highlight_attr =
+            ctx.get_attrib_location(&point_program, "highlight") as u32;
+        let point_selection_attr =
+            ctx.get_attrib_location(&point_program, "selected") as u32;
 
         // set up a repainting routine
         let (_, start_animation_loop, _) = create_raf(move || {
@@ -596,7 +625,8 @@ pub fn Display() -> View {
             let realization_successful = state.assembly.realization_status.with(
                 |status| status.is_ok()
             );
-            let step_val = state.assembly.step.with_untracked(|step| step.value);
+            let step_val =
+                state.assembly.step.with_untracked(|step| step.value);
             let on_init_step = step_val.is_some_and(|n| n == 0.0);
             let on_last_step = step_val.is_some_and(
                 |n| state.assembly.descent_history.with_untracked(
@@ -606,7 +636,8 @@ pub fn Display() -> View {
             let on_manipulable_step =
                 !realization_successful && on_init_step
                 || realization_successful && on_last_step;
-            if on_manipulable_step && state.selection.with(|sel| sel.len() == 1) {
+            if on_manipulable_step
+                   && state.selection.with(|sel| sel.len() == 1) {
                 let sel = state.selection.with(
                     |sel| sel.into_iter().next().unwrap().clone()
                 );
@@ -651,7 +682,8 @@ pub fn Display() -> View {
                 // measure mean frame interval
                 frames_since_last_sample += 1;
                 if frames_since_last_sample >= SAMPLE_PERIOD {
-                    mean_frame_interval.set((time - last_sample_time) / (SAMPLE_PERIOD as f64));
+                    mean_frame_interval.set(
+                        (time - last_sample_time) / (SAMPLE_PERIOD as f64));
                     last_sample_time = time;
                     frames_since_last_sample = 0;
                 }
@@ -676,7 +708,8 @@ pub fn Display() -> View {
                 // set up the scene
                 state.assembly.elements.with_untracked(
                     |elts| for elt in elts {
-                        let selected = state.selection.with(|sel| sel.contains(elt));
+                        let selected =
+                            state.selection.with(|sel| sel.contains(elt));
                         elt.show(&mut scene, selected);
                     }
                 );
@@ -691,9 +724,10 @@ pub fn Display() -> View {
                 ctx.enable_vertex_attrib_array(viewport_position_attr);
 
                 // write the spheres in world coordinates
-                let sphere_reps_world: Vec<_> = scene.spheres.representations.into_iter().map(
+                let sphere_reps_world: Vec<_> =
-                    |rep| (&asm_to_world * rep).cast::<f32>()
+                    scene.spheres.representations.into_iter().map(
-                ).collect();
+                        |rep| (&asm_to_world * rep).cast::<f32>()
+                    ).collect();
 
                 // set the resolution
                 let width = canvas.width() as f32;
@@ -729,10 +763,12 @@ pub fn Display() -> View {
 
                 // bind the viewport vertex position buffer to the position
                 // attribute in the vertex shader
-                bind_to_attribute(&ctx, viewport_position_attr, SPACE_DIM as i32, &viewport_position_buffer);
+                bind_to_attribute(&ctx, viewport_position_attr,
+                    SPACE_DIM as i32, &viewport_position_buffer);
 
                 // draw the scene
-                ctx.draw_arrays(WebGl2RenderingContext::TRIANGLES, 0, VERTEX_CNT as i32);
+                ctx.draw_arrays(WebGl2RenderingContext::TRIANGLES, 0,
+                    VERTEX_CNT as i32);
 
                 // disable the sphere program's vertex attribute
                 ctx.disable_vertex_attrib_array(viewport_position_attr);
@@ -760,13 +796,19 @@ pub fn Display() -> View {
                     // load the point positions and colors into new buffers and
                     // bind them to the corresponding attributes in the vertex
                     // shader
-                    bind_new_buffer_to_attribute(&ctx, point_position_attr, SPACE_DIM as i32, point_positions.as_slice());
+                    bind_new_buffer_to_attribute(&ctx, point_position_attr,
-                    bind_new_buffer_to_attribute(&ctx, point_color_attr, (COLOR_SIZE + 1) as i32, scene.points.colors_with_opacity.concat().as_slice());
+                        SPACE_DIM as i32, point_positions.as_slice());
-                    bind_new_buffer_to_attribute(&ctx, point_highlight_attr, 1 as i32, scene.points.highlights.as_slice());
+                    bind_new_buffer_to_attribute(&ctx, point_color_attr,
-                    bind_new_buffer_to_attribute(&ctx, point_selection_attr, 1 as i32, scene.points.selections.as_slice());
+                        (COLOR_SIZE + 1) as i32,
+                        scene.points.colors_with_opacity.concat().as_slice());
+                    bind_new_buffer_to_attribute(&ctx, point_highlight_attr,
+                        1i32, scene.points.highlights.as_slice());
+                    bind_new_buffer_to_attribute(&ctx, point_selection_attr,
+                        1i32, scene.points.selections.as_slice());
 
                     // draw the scene
-                    ctx.draw_arrays(WebGl2RenderingContext::POINTS, 0, point_positions.ncols() as i32);
+                    ctx.draw_arrays(WebGl2RenderingContext::POINTS, 0,
+                        point_positions.ncols() as i32);
 
                     // disable the point program's vertex attributes
                     ctx.disable_vertex_attrib_array(point_position_attr);
@@ -915,7 +957,9 @@ pub fn Display() -> View {
                     .into_iter()
                     .filter(|elt| !elt.ghost().get());
                 for elt in tangible_elts {
-                    match assembly_to_world.with(|asm_to_world| elt.cast(dir, asm_to_world, pixel_size)) {
+                    let target = assembly_to_world.with(
+                        |asm_to_world| elt.cast(dir, asm_to_world, pixel_size));
+                    match target {
                         Some(depth) => match clicked {
                             Some((_, best_depth)) => {
                                 if depth < best_depth {

app-proto/src/components/outline.rs

@@ -63,8 +63,10 @@ fn RegulatorInput(regulator: Rc<dyn Regulator>) -> View {
             placeholder = measurement.with(|result| result.to_string()),
             bind:value = value,
             on:change = move |_| {
+                let specification =
+                    SpecifiedValue::try_from(value.get_clone_untracked());
                 valid.set(
-                    match SpecifiedValue::try_from(value.get_clone_untracked()) {
+                    match specification {
                         Ok(set_pt) => {
                             set_point.set(set_pt);
                             true
@@ -141,7 +143,9 @@ fn ElementOutlineItem(element: Rc<dyn Element>) -> View {
     let class = {
         let element_for_class = element.clone();
         state.selection.map(
-            move |sel| if sel.contains(&element_for_class) { "selected" } else { "" }
+            move |sel|
+                if sel.contains(&element_for_class) { "selected" }
+                else { "" }
         )
     };
     let label = element.label().clone();
@@ -175,7 +179,8 @@ fn ElementOutlineItem(element: Rc<dyn Element>) -> View {
                         move |event: KeyboardEvent| {
                             match event.key().as_str() {
                                 "Enter" => {
-                                    state.select(&element_for_handler, event.shift_key());
+                                    state.select(&element_for_handler,
+                                        event.shift_key());
                                     event.prevent_default();
                                 },
                                 "ArrowRight" if regulated.get() => {
@@ -205,18 +210,22 @@ fn ElementOutlineItem(element: Rc<dyn Element>) -> View {
                             let state_for_handler = state.clone();
                             let element_for_handler = element.clone();
                             move |event: MouseEvent| {
-                                state_for_handler.select(&element_for_handler, event.shift_key());
+                                state_for_handler.select(&element_for_handler,
+                                    event.shift_key());
                                 event.stop_propagation();
                                 event.prevent_default();
                             }
                         }
                     ) {
                         div(class = "element-label") { (label) }
-                        div(class = "element-representation") { (rep_components) }
+                        div(class = "element-representation") {
+                            (rep_components)
+                        }
                         input(
                             r#type = "checkbox",
                             bind:checked = element.ghost(),
-                            on:click = |event: MouseEvent| event.stop_propagation()
+                            on:click =
+                                |event: MouseEvent| event.stop_propagation()
                         )
                     }
                 }

app-proto/src/components/spheres.frag

@@ -175,8 +175,9 @@ void main() {
     if (debug_mode) {
         // at the bottom of the screen, show the color scale instead of the
         // layer count
-        if (gl_FragCoord.y < 10.) layer_cnt = int(16. * gl_FragCoord.x / resolution.x);
+        if (gl_FragCoord.y < 10.) {
-
+            layer_cnt = int(16. * gl_FragCoord.x / resolution.x);
+        }
         // convert number to color
         ivec3 bits = layer_cnt / ivec3(1, 2, 4);
         vec3 color = mod(vec3(bits), 2.);
@@ -217,14 +218,17 @@ void main() {
         // highlight intersections
         float ixn_dist = intersection_dist(frag, frag_next);
         float max_highlight = max(highlight, highlight_next);
-        float ixn_highlight = 0.5 * max_highlight * (1. - smoothstep(2./3.*ixn_threshold, 1.5*ixn_threshold, ixn_dist));
+        float ixn_highlight = 0.5 * max_highlight * (1. - smoothstep(
+            2./3.*ixn_threshold, 1.5*ixn_threshold, ixn_dist));
         frag.color = mix(frag.color, vec4(1.), ixn_highlight);
         frag_next.color = mix(frag_next.color, vec4(1.), ixn_highlight);
 
         // highlight cusps
         float cusp_cos = abs(dot(dir, frag.normal));
-        float cusp_threshold = 2.*sqrt(ixn_threshold * sphere_list[hit.id].lt.s);
+        float cusp_threshold = 2.*sqrt(
-        float cusp_highlight = highlight * (1. - smoothstep(2./3.*cusp_threshold, 1.5*cusp_threshold, cusp_cos));
+            ixn_threshold * sphere_list[hit.id].lt.s);
+        float cusp_highlight = highlight * (1. - smoothstep(
+            2./3.*cusp_threshold, 1.5*cusp_threshold, cusp_cos));
         frag.color = mix(frag.color, vec4(1.), cusp_highlight);
 
         // composite the current fragment

app-proto/src/components/test_assembly_chooser.rs

@@ -167,29 +167,36 @@ fn load_low_curvature(assembly: &Assembly) {
         let curvature = plane.regulators().with_untracked(
             |regs| regs.first().unwrap().clone()
         );
-        curvature.set_point().set(SpecifiedValue::try_from("0".to_string()).unwrap());
+        curvature.set_point().set(
+            SpecifiedValue::try_from("0".to_string()).unwrap());
     }
     let all_perpendicular = [central.clone()].into_iter()
         .chain(sides.clone())
         .chain(corners.clone());
     for sphere in all_perpendicular {
         // make each side and packed sphere perpendicular to the assembly plane
-        let right_angle = InversiveDistanceRegulator::new([sphere, assemb_plane.clone()]);
+        let right_angle = InversiveDistanceRegulator::new(
-        right_angle.set_point.set(SpecifiedValue::try_from("0".to_string()).unwrap());
+            [sphere, assemb_plane.clone()]);
+        right_angle.set_point.set(
+            SpecifiedValue::try_from("0".to_string()).unwrap());
         assembly.insert_regulator(Rc::new(right_angle));
     }
     for sphere in sides.clone().chain(corners.clone()) {
         // make each side and corner sphere tangent to the central sphere
-        let tangency = InversiveDistanceRegulator::new([sphere.clone(), central.clone()]);
+        let tangency = InversiveDistanceRegulator::new(
-        tangency.set_point.set(SpecifiedValue::try_from("-1".to_string()).unwrap());
+            [sphere.clone(), central.clone()]);
+        tangency.set_point.set(
+            SpecifiedValue::try_from("-1".to_string()).unwrap());
         assembly.insert_regulator(Rc::new(tangency));
     }
     for (side_index, side) in sides.enumerate() {
         // make each side tangent to the two adjacent corner spheres
         for (corner_index, corner) in corners.clone().enumerate() {
             if side_index != corner_index {
-                let tangency = InversiveDistanceRegulator::new([side.clone(), corner]);
+                let tangency = InversiveDistanceRegulator::new(
-                tangency.set_point.set(SpecifiedValue::try_from("-1".to_string()).unwrap());
+                    [side.clone(), corner]);
+                tangency.set_point.set(
+                    SpecifiedValue::try_from("-1".to_string()).unwrap());
                 assembly.insert_regulator(Rc::new(tangency));
             }
         }
@@ -217,12 +224,15 @@ fn load_pointed(assembly: &Assembly) {
         for index_y in 0..=1 {
             let x = index_x as f64 - 0.5;
             let y = index_y as f64 - 0.5;
-
+            let x32 = x as f32;
+            let y32 = y as f32;
+            let coords =
+                [0.5*(1.0 + x32), 0.5*(1.0 + y32), 0.5*(1.0 - x32*y32)];
             let _ = assembly.try_insert_element(
                 Sphere::new(
                     format!("sphere{index_x}{index_y}"),
                     format!("Sphere {index_x}{index_y}"),
-                    [0.5*(1.0 + x) as f32, 0.5*(1.0 + y) as f32, 0.5*(1.0 - x*y) as f32],
+                    coords,
                     engine::sphere(x, y, 0.0, 1.0),
                 )
             );
@@ -231,7 +241,7 @@ fn load_pointed(assembly: &Assembly) {
                 Point::new(
                     format!("point{index_x}{index_y}"),
                     format!("Point {index_x}{index_y}"),
-                    [0.5*(1.0 + x) as f32, 0.5*(1.0 + y) as f32, 0.5*(1.0 - x*y) as f32],
+                    coords,
                     engine::point(x, y, 0.0),
                 )
             );
@@ -320,19 +330,25 @@ fn load_tridiminished_icosahedron(assembly: &Assembly) {
             "face1".to_string(),
             "Face 1".to_string(),
             COLOR_FACE,
-            engine::sphere_with_offset(frac_2_sqrt_6, -frac_1_sqrt_6, -frac_1_sqrt_6, -frac_1_sqrt_6, 0.0),
+            engine::sphere_with_offset(
+                frac_2_sqrt_6, -frac_1_sqrt_6, -frac_1_sqrt_6,
+                -frac_1_sqrt_6, 0.0),
         ),
         Sphere::new(
             "face2".to_string(),
             "Face 2".to_string(),
             COLOR_FACE,
-            engine::sphere_with_offset(-frac_1_sqrt_6, frac_2_sqrt_6, -frac_1_sqrt_6, -frac_1_sqrt_6, 0.0),
+            engine::sphere_with_offset(
+                -frac_1_sqrt_6, frac_2_sqrt_6, -frac_1_sqrt_6,
+                -frac_1_sqrt_6, 0.0),
         ),
         Sphere::new(
             "face3".to_string(),
             "Face 3".to_string(),
             COLOR_FACE,
-            engine::sphere_with_offset(-frac_1_sqrt_6, -frac_1_sqrt_6, frac_2_sqrt_6, -frac_1_sqrt_6, 0.0),
+            engine::sphere_with_offset(
+                -frac_1_sqrt_6, -frac_1_sqrt_6, frac_2_sqrt_6,
+                -frac_1_sqrt_6, 0.0),
         ),
     ];
     for face in faces {
@@ -357,8 +373,10 @@ fn load_tridiminished_icosahedron(assembly: &Assembly) {
         let vertex_a = assembly.elements_by_id.with_untracked(
             |elts_by_id| elts_by_id[&format!("a{j}")].clone()
         );
-        let incidence_a = InversiveDistanceRegulator::new([face.clone(), vertex_a.clone()]);
+        let incidence_a = InversiveDistanceRegulator::new(
-        incidence_a.set_point.set(SpecifiedValue::try_from("0".to_string()).unwrap());
+            [face.clone(), vertex_a.clone()]);
+        incidence_a.set_point.set(
+            SpecifiedValue::try_from("0".to_string()).unwrap());
         assembly.insert_regulator(Rc::new(incidence_a));
 
         // regulate the B-C vertex distances
@@ -380,13 +398,16 @@ fn load_tridiminished_icosahedron(assembly: &Assembly) {
                 let vertex = assembly.elements_by_id.with_untracked(
                     |elts_by_id| elts_by_id[&format!("{series}{k}")].clone()
                 );
-                let incidence = InversiveDistanceRegulator::new([face.clone(), vertex.clone()]);
+                let incidence = InversiveDistanceRegulator::new(
-                incidence.set_point.set(SpecifiedValue::try_from("0".to_string()).unwrap());
+                    [face.clone(), vertex.clone()]);
+                incidence.set_point.set(
+                    SpecifiedValue::try_from("0".to_string()).unwrap());
                 assembly.insert_regulator(Rc::new(incidence));
 
                 // regulate the A-B and A-C vertex distances
                 assembly.insert_regulator(
-                    Rc::new(InversiveDistanceRegulator::new([vertex_a.clone(), vertex]))
+                    Rc::new(InversiveDistanceRegulator::new(
+                       [vertex_a.clone(), vertex]))
                 );
             }
         }
@@ -434,7 +455,8 @@ fn load_dodecahedral_packing(assembly: &Assembly) {
     const COLOR_A: ElementColor = [1.00_f32, 0.25_f32, 0.00_f32];
     const COLOR_B: ElementColor = [1.00_f32, 0.00_f32, 0.25_f32];
     const COLOR_C: ElementColor = [0.25_f32, 0.00_f32, 1.00_f32];
-    let phi = 0.5 + 1.25_f64.sqrt(); /* TO DO */ // replace with std::f64::consts::PHI when that gets stabilized
+    /* TO DO */ // replace with std::f64::consts::PHI when that gets stabilized
+    let phi = 0.5 + 1.25_f64.sqrt();
     let phi_inv = 1.0 / phi;
     let coord_scale = (phi + 2.0).sqrt();
     let face_scales = [phi_inv, (13.0 / 12.0) / coord_scale];
@@ -501,13 +523,16 @@ fn load_dodecahedral_packing(assembly: &Assembly) {
 
     // make each face sphere perpendicular to the substrate
     for face in faces {
-        let right_angle = InversiveDistanceRegulator::new([face, substrate.clone()]);
+        let right_angle = InversiveDistanceRegulator::new(
-        right_angle.set_point.set(SpecifiedValue::try_from("0".to_string()).unwrap());
+            [face, substrate.clone()]);
+        right_angle.set_point.set(
+            SpecifiedValue::try_from("0".to_string()).unwrap());
         assembly.insert_regulator(Rc::new(right_angle));
     }
 
     // set up the tangencies that define the packing
-    for [long_edge_plane, short_edge_plane] in [["a", "b"], ["b", "c"], ["c", "a"]] {
+    for [long_edge_plane, short_edge_plane]
+            in [["a", "b"], ["b", "c"], ["c", "a"]] {
         for k in 0..2 {
             let long_edge_ids = [
                 format!("{long_edge_plane}{k}0"),
@@ -526,9 +551,11 @@ fn load_dodecahedral_packing(assembly: &Assembly) {
             );
 
             // set up the short-edge tangency
-            let short_tangency = InversiveDistanceRegulator::new(short_edge.clone());
+            let short_tangency = InversiveDistanceRegulator::new(
+                short_edge.clone());
             if k == 0 {
-                short_tangency.set_point.set(SpecifiedValue::try_from("-1".to_string()).unwrap());
+                short_tangency.set_point.set(
+                    SpecifiedValue::try_from("-1".to_string()).unwrap());
             }
             assembly.insert_regulator(Rc::new(short_tangency));
 
@@ -539,7 +566,9 @@ fn load_dodecahedral_packing(assembly: &Assembly) {
                         [long_edge[i].clone(), short_edge[j].clone()]
                     );
                     if i == 0 && k == 0 {
-                        side_tangency.set_point.set(SpecifiedValue::try_from("-1".to_string()).unwrap());
+                        side_tangency.set_point.set(
+                            SpecifiedValue::try_from("-1".to_string()).unwrap()
+                        );
                     }
                     assembly.insert_regulator(Rc::new(side_tangency));
                 }
@@ -604,7 +633,8 @@ fn load_balanced(assembly: &Assembly) {
     // initial configuration deliberately violates these constraints
     for inner in [a, b] {
         let tangency = InversiveDistanceRegulator::new([outer.clone(), inner]);
-        tangency.set_point.set(SpecifiedValue::try_from("1".to_string()).unwrap());
+        tangency.set_point.set(
+            SpecifiedValue::try_from("1".to_string()).unwrap());
         assembly.insert_regulator(Rc::new(tangency));
     }
 }
@@ -712,10 +742,14 @@ fn load_radius_ratio(assembly: &Assembly) {
             [0.25_f32, 0.00_f32, 1.00_f32],
         ].into_iter(),
         [
-            engine::sphere_with_offset(base_dir[0], base_dir[1], base_dir[2], offset, 0.0),
+            engine::sphere_with_offset(
-            engine::sphere_with_offset(base_dir[0], -base_dir[1], -base_dir[2], offset, 0.0),
+                base_dir[0], base_dir[1], base_dir[2], offset, 0.0),
-            engine::sphere_with_offset(-base_dir[0], base_dir[1], -base_dir[2], offset, 0.0),
+            engine::sphere_with_offset(
-            engine::sphere_with_offset(-base_dir[0], -base_dir[1], base_dir[2], offset, 0.0),
+                base_dir[0], -base_dir[1], -base_dir[2], offset, 0.0),
+            engine::sphere_with_offset(
+                -base_dir[0], base_dir[1], -base_dir[2], offset, 0.0),
+            engine::sphere_with_offset(
+                -base_dir[0], -base_dir[1], base_dir[2], offset, 0.0),
         ].into_iter()
     ).map(
         |(k, color, representation)| {
@@ -765,8 +799,10 @@ fn load_radius_ratio(assembly: &Assembly) {
             }
 
             // put the vertices on the faces
-            let incidence_regulator = InversiveDistanceRegulator::new([face_j.clone(), vertex_k.clone()]);
+            let incidence_regulator = InversiveDistanceRegulator::new(
-            incidence_regulator.set_point.set(SpecifiedValue::try_from("0".to_string()).unwrap());
+                [face_j.clone(), vertex_k.clone()]);
+            incidence_regulator.set_point.set(
+                SpecifiedValue::try_from("0".to_string()).unwrap());
             assembly.insert_regulator(Rc::new(incidence_regulator));
         }
     }
@@ -860,25 +896,33 @@ fn load_irisawa_hexlet(assembly: &Assembly) {
             |elts_by_id| elts_by_id[&format!("chain{k}")].clone()
         )
     );
-    for (chain_sphere, chain_sphere_next) in chain.clone().zip(chain.cycle().skip(1)) {
+    for (chain_sphere, chain_sphere_next)
+            in chain.clone().zip(chain.cycle().skip(1)) {
         for (other_sphere, inversive_distance) in [
             (outer.clone(), "1"),
             (sun.clone(), "-1"),
             (moon.clone(), "-1"),
             (chain_sphere_next.clone(), "-1"),
         ] {
-            let tangency = InversiveDistanceRegulator::new([chain_sphere.clone(), other_sphere]);
+            let tangency = InversiveDistanceRegulator::new(
-            tangency.set_point.set(SpecifiedValue::try_from(inversive_distance.to_string()).unwrap());
+                [chain_sphere.clone(), other_sphere]);
+            tangency.set_point.set(
+                SpecifiedValue::try_from(
+                    inversive_distance.to_string()).unwrap());
             assembly.insert_regulator(Rc::new(tangency));
         }
     }
 
-    let outer_sun_tangency = InversiveDistanceRegulator::new([outer.clone(), sun]);
+    let outer_sun_tangency = InversiveDistanceRegulator::new(
-    outer_sun_tangency.set_point.set(SpecifiedValue::try_from("1".to_string()).unwrap());
+        [outer.clone(), sun]);
+    outer_sun_tangency.set_point.set(
+        SpecifiedValue::try_from("1".to_string()).unwrap());
     assembly.insert_regulator(Rc::new(outer_sun_tangency));
 
-    let outer_moon_tangency = InversiveDistanceRegulator::new([outer.clone(), moon]);
+    let outer_moon_tangency = InversiveDistanceRegulator::new(
-    outer_moon_tangency.set_point.set(SpecifiedValue::try_from("1".to_string()).unwrap());
+        [outer.clone(), moon]);
+    outer_moon_tangency.set_point.set(
+        SpecifiedValue::try_from("1".to_string()).unwrap());
     assembly.insert_regulator(Rc::new(outer_moon_tangency));
 }
 
@@ -912,7 +956,8 @@ pub fn TestAssemblyChooser() -> View {
                 "general" => load_general(assembly),
                 "low-curvature" => load_low_curvature(assembly),
                 "pointed" => load_pointed(assembly),
-                "tridiminished-icosahedron" => load_tridiminished_icosahedron(assembly),
+                "tridiminished-icosahedron" =>
+                    load_tridiminished_icosahedron(assembly),
                 "dodecahedral-packing" => load_dodecahedral_packing(assembly),
                 "balanced" => load_balanced(assembly),
                 "off-center" => load_off_center(assembly),
@@ -929,7 +974,9 @@ pub fn TestAssemblyChooser() -> View {
             option(value = "general") { "General" }
             option(value = "low-curvature") { "Low-curvature" }
             option(value = "pointed") { "Pointed" }
-            option(value = "tridiminished-icosahedron") { "Tridiminished icosahedron" }
+            option(value = "tridiminished-icosahedron") {
+                "Tridiminished icosahedron"
+            }
             option(value = "dodecahedral-packing") { "Dodecahedral packing" }
             option(value = "balanced") { "Balanced" }
             option(value = "off-center") { "Off-center" }

app-proto/src/engine.rs

@@ -9,8 +9,11 @@ pub fn point(x: f64, y: f64, z: f64) -> DVector<f64> {
 }
 
 // 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> {
+pub fn sphere(center_x: f64, center_y: f64, center_z: f64, radius: f64)
-    let center_norm_sq = center_x * center_x + center_y * center_y + center_z * center_z;
+    -> DVector<f64>
+{
+    let center_norm_sq =
+        center_x * center_x + center_y * center_y + center_z * center_z;
     DVector::from_column_slice(&[
         center_x / radius,
         center_y / radius,
@@ -23,7 +26,9 @@ pub fn sphere(center_x: f64, center_y: f64, center_z: f64, radius: f64) -> DVect
 // the sphere of curvature `curv` whose closest point to the origin has position
 // `off * dir` and normal `dir`, where `dir` is a unit vector. setting the
 // curvature to zero gives a plane
-pub fn sphere_with_offset(dir_x: f64, dir_y: f64, dir_z: f64, off: f64, curv: f64) -> DVector<f64> {
+pub fn sphere_with_offset(
+    dir_x: f64, dir_y: f64, dir_z: f64, off: f64, curv: f64) -> DVector<f64>
+{
     let norm_sp = 1.0 + off * curv;
     DVector::from_column_slice(&[
         norm_sp * dir_x,
@@ -200,7 +205,9 @@ impl ConfigSubspace {
     // with the given column index has velocity `v`. the velocity is given in
     // projection coordinates, and the projection is done with respect to the
     // projection inner product
-    pub fn proj(&self, v: &DVectorView<f64>, column_index: usize) -> DMatrix<f64> {
+    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)
@@ -291,7 +298,9 @@ impl SearchState {
     }
 }
 
-fn basis_matrix(index: (usize, usize), nrows: usize, ncols: usize) -> DMatrix<f64> {
+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
@@ -414,7 +423,8 @@ pub fn realize_gram(
     for _ in 0..max_descent_steps {
         // 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>);
+        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
@@ -431,7 +441,8 @@ pub fn realize_gram(
                     -&basis_mat * &state.err_proj
                     + &state.config * &neg_d_err_proj
                 );
-                hess_cols.push(deriv_grad.reshape_generic(Dyn(total_dim), Const::<1>));
+                hess_cols.push(
+                    deriv_grad.reshape_generic(Dyn(total_dim), Const::<1>));
             }
         }
         hess = DMatrix::from_columns(hess_cols.as_slice());
@@ -440,7 +451,8 @@ pub fn realize_gram(
         let hess_eigvals = hess.symmetric_eigenvalues();
         let min_eigval = hess_eigvals.min();
         if min_eigval <= 0.0 {
-            hess -= reg_scale * min_eigval * DMatrix::identity(total_dim, total_dim);
+            hess -= reg_scale * min_eigval
+                * DMatrix::identity(total_dim, total_dim);
         }
         history.hess_eigvals.push(hess_eigvals);
 
@@ -477,7 +489,8 @@ pub fn realize_gram(
             },
         };
         let base_step_stacked = hess_cholesky.solve(&neg_grad_stacked);
-        let base_step = base_step_stacked.reshape_generic(Dyn(element_dim), Dyn(assembly_dim));
+        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
@@ -507,9 +520,12 @@ pub fn realize_gram(
         }
 
         // find the kernel of the Hessian. give it the uniform inner product
-        let tangent = ConfigSubspace::symmetric_kernel(hess, unif_to_std, assembly_dim);
+        let tangent =
+            ConfigSubspace::symmetric_kernel(hess, unif_to_std, assembly_dim);
 
-        Ok(ConfigNeighborhood { #[cfg(feature = "dev")] config: state.config, nbhd: tangent })
+        Ok(ConfigNeighborhood {
+            #[cfg(feature = "dev")] config: state.config, nbhd: tangent
+        })
     } else {
         Err("Failed to reach target accuracy".to_string())
     };
@@ -608,7 +624,8 @@ pub mod examples {
             for j in 0..2 {
                 // diagonal and hinge edges
                 for k in j..2 {
-                    problem.gram.push_sym(block + j, block + k, if j == k { 0.0 } else { -0.5 });
+                    problem.gram.push_sym(
+                        block + j, block + k, if j == k { 0.0 } else { -0.5 });
                 }
 
                 // non-hinge edges
@@ -702,7 +719,8 @@ mod tests {
         ]);
         for j in 0..2 {
             for k in j..2 {
-                problem.gram.push_sym(j, k, if (j, k) == (1, 1) { 1.0 } else { 0.0 });
+                problem.gram.push_sym(
+                    j, k, if (j, k) == (1, 1) { 1.0 } else { 0.0 });
             }
         }
         problem.frozen.push(3, 0, problem.guess[(3, 0)]);
@@ -729,7 +747,8 @@ mod tests {
 
         // check against Irisawa's solution
         let entry_tol = SCALED_TOL.sqrt();
-        let solution_diams = [30.0, 10.0, 6.0, 5.0, 15.0, 10.0, 3.75, 2.5, 2.0 + 8.0/11.0];
+        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);
         }
@@ -794,22 +813,29 @@ mod tests {
         // 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 tol_sq = ((element_dim * assembly_dim) as f64) * SCALED_TOL * SCALED_TOL;
+        let tol_sq = ((element_dim * assembly_dim) as f64)
-        for (motion_unif, motion_std) in tangent_motions_unif.into_iter().zip(tangent_motions_std) {
+            * SCALED_TOL * SCALED_TOL;
-            let motion_proj: DMatrix<_> = motion_unif.column_iter().enumerate().map(
+        for (motion_unif, motion_std)
-                |(k, v)| tangent.proj(&v, k)
+                in tangent_motions_unif.into_iter().zip(tangent_motions_std) {
-            ).sum();
+            let motion_proj: DMatrix<_> =
+                motion_unif.column_iter().enumerate().map(
+                    |(k, v)| tangent.proj(&v, k)
+                ).sum();
             assert!((motion_std - motion_proj).norm_squared() < tol_sq);
         }
     }
 
-    fn translation_motion_unif(vel: &Vector3<f64>, assembly_dim: usize) -> Vec<DVector<f64>> {
+    fn translation_motion_unif(vel: &Vector3<f64>, assembly_dim: usize)
+        -> Vec<DVector<f64>>
+    {
         let mut elt_motion = DVector::zeros(4);
         elt_motion.fixed_rows_mut::<3>(0).copy_from(vel);
         iter::repeat(elt_motion).take(assembly_dim).collect()
     }
 
-    fn rotation_motion_unif(ang_vel: &Vector3<f64>, points: Vec<DVectorView<f64>>) -> Vec<DVector<f64>> {
+    fn rotation_motion_unif(
+        ang_vel: &Vector3<f64>, points: Vec<DVectorView<f64>>
+    ) -> Vec<DVector<f64>> {
         points.into_iter().map(
             |pt| {
                 let vel = ang_vel.cross(&pt.fixed_rows::<3>(0));
@@ -840,9 +866,12 @@ mod tests {
             translation_motion_unif(&Vector3::new(0.0, 0.0, 1.0), assembly_dim),
 
             // the rotations about the coordinate axes
-            rotation_motion_unif(&Vector3::new(1.0, 0.0, 0.0), config.column_iter().collect()),
+            rotation_motion_unif(
-            rotation_motion_unif(&Vector3::new(0.0, 1.0, 0.0), config.column_iter().collect()),
+                &Vector3::new(1.0, 0.0, 0.0), config.column_iter().collect()),
-            rotation_motion_unif(&Vector3::new(0.0, 0.0, 1.0), config.column_iter().collect()),
+            rotation_motion_unif(
+                &Vector3::new(0.0, 1.0, 0.0), config.column_iter().collect()),
+            rotation_motion_unif(
+                &Vector3::new(0.0, 0.0, 1.0), config.column_iter().collect()),
 
             // the twist motion. more precisely: a motion that keeps the center
             // of mass stationary and preserves the distances between the
@@ -859,8 +888,10 @@ mod tests {
                     [
                         DVector::from_column_slice(&[0.0, 0.0, 5.0, 0.0]),
                         DVector::from_column_slice(&[0.0, 0.0, 1.0, 0.0]),
-                        DVector::from_column_slice(&[-vel_vert_x, -vel_vert_y, -3.0, 0.0]),
+                        DVector::from_column_slice(
-                        DVector::from_column_slice(&[vel_vert_x, vel_vert_y, -3.0, 0.0]),
+                            &[-vel_vert_x, -vel_vert_y, -3.0, 0.0]),
+                        DVector::from_column_slice(
+                            &[vel_vert_x, vel_vert_y, -3.0, 0.0]),
                     ]
                 }
             ).collect::<Vec<_>>(),
@@ -880,11 +911,14 @@ mod tests {
         // 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 tol_sq = ((element_dim * assembly_dim) as f64) * SCALED_TOL * SCALED_TOL;
+        let tol_sq = ((element_dim * assembly_dim) as f64)
-        for (motion_unif, motion_std) in tangent_motions_unif.into_iter().zip(tangent_motions_std) {
+            * SCALED_TOL * SCALED_TOL;
-            let motion_proj: DMatrix<_> = motion_unif.into_iter().enumerate().map(
+        for (motion_unif, motion_std)
-                |(k, v)| tangent.proj(&v.as_view(), k)
+                in tangent_motions_unif.into_iter().zip(tangent_motions_std) {
-            ).sum();
+            let motion_proj: DMatrix<_> =
+                motion_unif.into_iter().enumerate().map(
+                    |(k, v)| tangent.proj(&v.as_view(), k)
+                ).sum();
             assert!((motion_std - motion_proj).norm_squared() < tol_sq);
         }
     }
@@ -913,10 +947,10 @@ mod tests {
         problem_orig.gram.push_sym(0, 0, 1.0);
         problem_orig.gram.push_sym(1, 1, 1.0);
         problem_orig.gram.push_sym(0, 1, 0.5);
-        let Realization { result: result_orig, history: history_orig } = realize_gram(
+        let Realization { result: result_orig, history: history_orig } =
-            &problem_orig, SCALED_TOL, 0.5, 0.9, 1.1, 200, 110
+            realize_gram(&problem_orig, SCALED_TOL, 0.5, 0.9, 1.1, 200, 110);
-        );
+        let ConfigNeighborhood { config: config_orig, nbhd: tangent_orig } =
-        let ConfigNeighborhood { config: config_orig, nbhd: tangent_orig } = result_orig.unwrap();
+            result_orig.unwrap();
         assert_eq!(config_orig, problem_orig.guess);
         assert_eq!(history_orig.scaled_loss.len(), 1);
 
@@ -934,10 +968,10 @@ mod tests {
             frozen: problem_orig.frozen,
             guess: guess_tfm,
         };
-        let Realization { result: result_tfm, history: history_tfm } = realize_gram(
+        let Realization { result: result_tfm, history: history_tfm } =
-            &problem_tfm, SCALED_TOL, 0.5, 0.9, 1.1, 200, 110
+            realize_gram(&problem_tfm, SCALED_TOL, 0.5, 0.9, 1.1, 200, 110);
-        );
+        let ConfigNeighborhood { config: config_tfm, nbhd: tangent_tfm } =
-        let ConfigNeighborhood { config: config_tfm, nbhd: tangent_tfm } = result_tfm.unwrap();
+            result_tfm.unwrap();
         assert_eq!(config_tfm, problem_tfm.guess);
         assert_eq!(history_tfm.scaled_loss.len(), 1);
 
@@ -948,7 +982,8 @@ mod tests {
 
         // project the equivalent nudge to the tangent space of the solution
         // variety at the transformed solution
-        let motion_tfm = DVector::from_column_slice(&[FRAC_1_SQRT_2, 0.0, FRAC_1_SQRT_2, 0.0]);
+        let motion_tfm = DVector::from_column_slice(
+            &[FRAC_1_SQRT_2, 0.0, FRAC_1_SQRT_2, 0.0]);
         let motion_tfm_proj = tangent_tfm.proj(&motion_tfm.as_view(), 0);
 
         // take the transformation that sends the original solution to the
@@ -969,7 +1004,9 @@ mod tests {
         // the comparison tolerance because the transformation seems to
         // introduce some numerical error
         const SCALED_TOL_TFM: f64 = 1.0e-9;
-        let tol_sq = ((problem_orig.guess.nrows() * problem_orig.guess.ncols()) as f64) * SCALED_TOL_TFM * SCALED_TOL_TFM;
+        let tol_sq = ((problem_orig.guess.nrows()
+            * problem_orig.guess.ncols()) as f64)
+            * SCALED_TOL_TFM * SCALED_TOL_TFM;
         assert!((motion_proj_tfm - motion_tfm_proj).norm_squared() < tol_sq);
     }
 }

notes/inversive.md

@@ -33,7 +33,7 @@ The unification of spheres/planes is indeed attractive for a project like Dyna3.
 Discussed coordinates with Alex Kontorovich. He was suggesting "inversive coordinates" -- for a sphere, that's 1/coradius, 1/radius, center/radius (where coradius is radius of sphere inverted in the unit sphere.) The advantage is tangent to and perpendicular to are linear in these coordinates (in the sense that if one is known, the condition of being tangent to or perpendicular to that one are linear). Planes have 1/radius = 0, and in fact, you can take the coordinates to be (2s, 0, x, y, z) where s is the distance to the origin and x,y,z are the normal direction. (Note the normal direction is only determined up to a scalar multiple. So could always scale so that the first non-zero coordinate is 1, or if you like only allow x, y to vary and let z be determined as sqrt(1-x^2^-y^2^). ) Points can be given by (r^2,1,x,y,z) where x,y,z are the coordinates and r is the distance to the origin. Quadratic form that tells you if something is a sphere/plane, or in the boundary, or up in the hyperbolic plane above. There are some details, but not quite explicit for modeling R^3, at http://sites.math.rutgers.edu/~alexk/files/LetterToDuke.pdf -- all this emphasize need to be agnostic with respect to geometric model so that we can experiment. Not really sure exactly how this relates or not to conformal geometric algebra, and whether it can be combined with geometric algebra. As formulated, there are clear-ish reps for planes/spheres and for points, but not as clear for lines. Have to see how to compute distance and/or specify a given distance. To combine inversive coordinates and geometric algebra, maybe think dually; there should be a lift from a normal vector and distance from origin to the five-vector; bivectors would rep circles/lines; trivectors would rep point pairs/points. What is the signature of this algebra, i.e. how many coordinates square to +1, -1, or 0? But it doesn't seem worth it for three dimensions, because there is a natural representation of points, as follows:
 
 The signature of Q will be (1,4), and in fact Q(I1,I2) = 1/2(ab+ba) - E1\dot E2, where a is the "first" or "coradius" coordinate, "b" is the "second" or "radius" coordinate, and E is the Euclidean part (x,y,z). Then the inversive coordinates of a sphere with center (x,y,z) and radius r will be I = (1/\hat{r},1/r,x/r,y/r,z/r) where \hat{r} = r/(|E|^2 -r^2). These coordinates satisfy Q(I,I) = -1. For this to make sense, of course r > 0, but we get planes by letting the radius of a tangent sphere to the plane go to infinity, and we get I = (2s, 0, x0, y0, z0) where (x0,y0,z0) is the unit normal to the plane and s is the perpendicular distance from the plane to the origin. Still Q(I,I) = -1.
-Since r>0, we can't represent individual points this way. Instead we will use some coordinates J for which Q(J,J) = 0. In particular, if you take for the Euclidean point E = (u,v,w) the coordinates J = (`|E|`^2,1,u,v,w) then Q(J,J) = 0 and moreover it comes out that Q(I,J) = 0 
+Since r>0, we can't represent individual points this way. Instead we will use some coordinates J for which Q(J,J) = 0. In particular, if you take for the Euclidean point E = (u,v,w) the coordinates J = (`|E|`^2,1,u,v,w) then Q(J,J) = 0 and moreover it comes out that Q(I,J) = 0
 whenever E lies on the sphere or plane described by some I with Q(I,I) = -1.
 The condition that two spheres I1 and I2 are tangent seems to be that Q(I1,I2) = 1. So given a fixed sphere, the condition that another sphere be tangent to it is linear in the coordinates of that other sphere.
 This system does seem promising for encoding points, spheres, and planes, and doing basic computations with them. I guess I would just encode a circle as the intersection of the concentric sphere and the containing plane, and a line as either a pair of points or a pair of planes (modulo some equivalence relation, since I can't see any canonical choice of either two planes or two points). Or actually as described below, there is a more canonical choice.
@@ -62,4 +62,4 @@ In the engine's coordinate conventions, a sphere with radius $r > 0$ centered on
 $$I'_s = \left(\frac{P_x}{r}, \frac{P_y}{r}, \frac{P_z}{r}, \frac1{2r}, \frac{\|P\|^2 - r^2}{2r}\right),$$
 which has the normalization $Q'(I'_s, I'_s) = 1$. The point $P$ is represented by the vector
 $$I'_P = \left(P_x, P_y, P_z, \frac{1}{2}, \frac{\|P\|^2}{2}\right).$$
-In the `engine` module, these formulas are encoded in the `sphere` and `point` functions.
+In the `engine` module, these formulas are encoded in the `sphere` and `point` functions.

notes/theory.md

@@ -22,9 +22,10 @@ Jürgen also emphasized the need for an intuitive user interface. Notes on that
 His final mathematical advice was reasonably encouraging, however:
 
 "But still I would consider it all more or less doable. One should very precisely think about a doable scope.
-I think three things are essential for the math no matter what you exactly plan.
+I think three things are essential for the math no matter what you exactly
+plan.
 
-1. Think projectively, 
+1. Think projectively.
    Use Projective Geometry, Homogeneous Coordinates (or to a certain extent Quaternions, and Clifford Algebras, which are more or less an elegant way to merge Complex numbers with projective concepts.)
 2. Consider ambient complex spaces.
    The true nature of the objects can only be understood if embedded into a complex ambient space.
@@ -37,10 +38,8 @@ I think three things are essential for the math no matter what you exactly plan.
 
 It would be nice to see how Jürgen handled some of these issues in a 2D system that he designed. Unfortunately, Cinderella was and remains closed-source; it was distributed for profit for some stretch of time. However, (a part of?) it was reimplemented in JavaScript as CindyJS, which is open source. I took a relatively quick look at that source code at one point, and these were my observations:
 
-CindyJS uses very concrete basic objects: 2D points are represented via projective geometry as a list of three floating-point numbers, and everything is done numerically.  There are no symbolic representations or exact algebraic numbers. (Not sure how a point on a circle or line is handled, that would take further investigation.) 
+CindyJS uses very concrete basic objects: 2D points are represented via projective geometry as a list of three floating-point numbers, and everything is done numerically.  There are no symbolic representations or exact algebraic numbers. (Not sure how a point on a circle or line is handled, that would take further investigation.)
 
 Lines are given by explicit coordinates as well (not sure of the internal details/exact coordinatization, or of how a "LineThrough" is represented).
 
 Was unclear to me how the complex parametrization for preserving continuity was handled in the code, even though Jürgen harps on complex ambient spaces; where are the complex numbers? Perhaps that part of Cinderella was never re-implemented?
-
-

src/index.html

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