dyna3/app-proto/src/components/test_assembly_chooser.rs

use itertools::izip;
use std::{f64::consts::{FRAC_1_SQRT_2, PI}, rc::Rc};
use nalgebra::Vector3;
use sycamore::prelude::*;
use web_sys::{console, wasm_bindgen::JsValue};

use crate::{
    AppState,
    assembly::{
        Assembly,
        Element,
        ElementColor,
        InversiveDistanceRegulator,
        Point,
        Sphere,
    },
    engine,
    engine::DescentHistory,
    specified::SpecifiedValue,
};

// --- loaders ---

/* DEBUG */
// each of these functions loads an example assembly for testing. once we've
// done more work on saving and loading assemblies, we should come back to this
// code to see if it can be simplified

fn load_general(assembly: &Assembly) {
    let _ = assembly.try_insert_element(
        Sphere::new(
            String::from("gemini_a"),
            String::from("Castor"),
            [1.00_f32, 0.25_f32, 0.00_f32],
            engine::sphere(0.5, 0.5, 0.0, 1.0),
        )
    );
    let _ = assembly.try_insert_element(
        Sphere::new(
            String::from("gemini_b"),
            String::from("Pollux"),
            [0.00_f32, 0.25_f32, 1.00_f32],
            engine::sphere(-0.5, -0.5, 0.0, 1.0),
        )
    );
    let _ = assembly.try_insert_element(
        Sphere::new(
            String::from("ursa_major"),
            String::from("Ursa major"),
            [0.25_f32, 0.00_f32, 1.00_f32],
            engine::sphere(-0.5, 0.5, 0.0, 0.75),
        )
    );
    let _ = assembly.try_insert_element(
        Sphere::new(
            String::from("ursa_minor"),
            String::from("Ursa minor"),
            [0.25_f32, 1.00_f32, 0.00_f32],
            engine::sphere(0.5, -0.5, 0.0, 0.5),
        )
    );
    let _ = assembly.try_insert_element(
        Sphere::new(
            String::from("moon_deimos"),
            String::from("Deimos"),
            [0.75_f32, 0.75_f32, 0.00_f32],
            engine::sphere(0.0, 0.15, 1.0, 0.25),
        )
    );
    let _ = assembly.try_insert_element(
        Sphere::new(
            String::from("moon_phobos"),
            String::from("Phobos"),
            [0.00_f32, 0.75_f32, 0.50_f32],
            engine::sphere(0.0, -0.15, -1.0, 0.25),
        )
    );
}

fn load_low_curvature(assembly: &Assembly) {
    // create the spheres
    let a = 0.75_f64.sqrt();
    let _ = assembly.try_insert_element(
        Sphere::new(
            "central".to_string(),
            "Central".to_string(),
            [0.75_f32, 0.75_f32, 0.75_f32],
            engine::sphere(0.0, 0.0, 0.0, 1.0),
        )
    );
    let _ = assembly.try_insert_element(
        Sphere::new(
            "assemb_plane".to_string(),
            "Assembly plane".to_string(),
            [0.75_f32, 0.75_f32, 0.75_f32],
            engine::sphere_with_offset(0.0, 0.0, 1.0, 0.0, 0.0),
        )
    );
    let _ = assembly.try_insert_element(
        Sphere::new(
            "side1".to_string(),
            "Side 1".to_string(),
            [1.00_f32, 0.00_f32, 0.25_f32],
            engine::sphere_with_offset(1.0, 0.0, 0.0, 1.0, 0.0),
        )
    );
    let _ = assembly.try_insert_element(
        Sphere::new(
            "side2".to_string(),
            "Side 2".to_string(),
            [0.25_f32, 1.00_f32, 0.00_f32],
            engine::sphere_with_offset(-0.5, a, 0.0, 1.0, 0.0),
        )
    );
    let _ = assembly.try_insert_element(
        Sphere::new(
            "side3".to_string(),
            "Side 3".to_string(),
            [0.00_f32, 0.25_f32, 1.00_f32],
            engine::sphere_with_offset(-0.5, -a, 0.0, 1.0, 0.0),
        )
    );
    let _ = assembly.try_insert_element(
        Sphere::new(
            "corner1".to_string(),
            "Corner 1".to_string(),
            [0.75_f32, 0.75_f32, 0.75_f32],
            engine::sphere(-4.0/3.0, 0.0, 0.0, 1.0/3.0),
        )
    );
    let _ = assembly.try_insert_element(
        Sphere::new(
            "corner2".to_string(),
            "Corner 2".to_string(),
            [0.75_f32, 0.75_f32, 0.75_f32],
            engine::sphere(2.0/3.0, -4.0/3.0 * a, 0.0, 1.0/3.0),
        )
    );
    let _ = assembly.try_insert_element(
        Sphere::new(
            String::from("corner3"),
            String::from("Corner 3"),
            [0.75_f32, 0.75_f32, 0.75_f32],
            engine::sphere(2.0/3.0, 4.0/3.0 * a, 0.0, 1.0/3.0),
        )
    );
    
    // impose the desired tangencies and make the sides planar
    let index_range = 1..=3;
    let [central, assemb_plane] = ["central", "assemb_plane"].map(
        |id| assembly.elements_by_id.with_untracked(
            |elts_by_id| elts_by_id[id].clone()
        )
    );
    let sides = index_range.clone().map(
        |k| assembly.elements_by_id.with_untracked(
            |elts_by_id| elts_by_id[&format!("side{k}")].clone()
        )
    );
    let corners = index_range.map(
        |k| assembly.elements_by_id.with_untracked(
            |elts_by_id| elts_by_id[&format!("corner{k}")].clone()
        )
    );
    for plane in [assemb_plane.clone()].into_iter().chain(sides.clone()) {
        // fix the curvature of each plane
        let curvature = plane.regulators().with_untracked(
            |regs| regs.first().unwrap().clone()
        );
        curvature.set_point().set(SpecifiedValue::try_from("0".to_string()).unwrap());
    }
    let all_perpendicular = [central.clone()].into_iter()
        .chain(sides.clone())
        .chain(corners.clone());
    for sphere in all_perpendicular {
        // make each side and packed sphere perpendicular to the assembly plane
        let right_angle = InversiveDistanceRegulator::new([sphere, assemb_plane.clone()]);
        right_angle.set_point.set(SpecifiedValue::try_from("0".to_string()).unwrap());
        assembly.insert_regulator(Rc::new(right_angle));
    }
    for sphere in sides.clone().chain(corners.clone()) {
        // make each side and corner sphere tangent to the central sphere
        let tangency = InversiveDistanceRegulator::new([sphere.clone(), central.clone()]);
        tangency.set_point.set(SpecifiedValue::try_from("-1".to_string()).unwrap());
        assembly.insert_regulator(Rc::new(tangency));
    }
    for (side_index, side) in sides.enumerate() {
        // make each side tangent to the two adjacent corner spheres
        for (corner_index, corner) in corners.clone().enumerate() {
            if side_index != corner_index {
                let tangency = InversiveDistanceRegulator::new([side.clone(), corner]);
                tangency.set_point.set(SpecifiedValue::try_from("-1".to_string()).unwrap());
                assembly.insert_regulator(Rc::new(tangency));
            }
        }
    }
}

fn load_pointed(assembly: &Assembly) {
    let _ = assembly.try_insert_element(
        Point::new(
            format!("point_front"),
            format!("Front point"),
            [0.75_f32, 0.75_f32, 0.75_f32],
            engine::point(0.0, 0.0, FRAC_1_SQRT_2),
        )
    );
    let _ = assembly.try_insert_element(
        Point::new(
            format!("point_back"),
            format!("Back point"),
            [0.75_f32, 0.75_f32, 0.75_f32],
            engine::point(0.0, 0.0, -FRAC_1_SQRT_2),
        )
    );
    for index_x in 0..=1 {
        for index_y in 0..=1 {
            let x = index_x as f64 - 0.5;
            let y = index_y as f64 - 0.5;
            
            let _ = assembly.try_insert_element(
                Sphere::new(
                    format!("sphere{index_x}{index_y}"),
                    format!("Sphere {index_x}{index_y}"),
                    [0.5*(1.0 + x) as f32, 0.5*(1.0 + y) as f32, 0.5*(1.0 - x*y) as f32],
                    engine::sphere(x, y, 0.0, 1.0),
                )
            );
            
            let _ = assembly.try_insert_element(
                Point::new(
                    format!("point{index_x}{index_y}"),
                    format!("Point {index_x}{index_y}"),
                    [0.5*(1.0 + x) as f32, 0.5*(1.0 + y) as f32, 0.5*(1.0 - x*y) as f32],
                    engine::point(x, y, 0.0),
                )
            );
        }
    }
}

// to finish describing the tridiminished icosahedron, set the inversive
// distance regulators as follows:
//   A-A   -0.25
//   A-B     "
//   B-C     "
//   C-C     "
//   A-C   -0.25 * φ^2 = -0.6545084971874737
fn load_tridiminished_icosahedron(assembly: &Assembly) {
    // create the vertices
    const COLOR_A: ElementColor = [1.00_f32, 0.25_f32, 0.25_f32];
    const COLOR_B: ElementColor = [0.75_f32, 0.75_f32, 0.75_f32];
    const COLOR_C: ElementColor = [0.25_f32, 0.50_f32, 1.00_f32];
    let vertices = [
        Point::new(
            "a1".to_string(),
            "A₁".to_string(),
            COLOR_A,
            engine::point(0.25, 0.75, 0.75),
        ),
        Point::new(
            "a2".to_string(),
            "A₂".to_string(),
            COLOR_A,
            engine::point(0.75, 0.25, 0.75),
        ),
        Point::new(
            "a3".to_string(),
            "A₃".to_string(),
            COLOR_A,
            engine::point(0.75, 0.75, 0.25),
        ),
        Point::new(
            "b1".to_string(),
            "B₁".to_string(),
            COLOR_B,
            engine::point(0.75, -0.25, -0.25),
        ),
        Point::new(
            "b2".to_string(),
            "B₂".to_string(),
            COLOR_B,
            engine::point(-0.25, 0.75, -0.25),
        ),
        Point::new(
            "b3".to_string(),
            "B₃".to_string(),
            COLOR_B,
            engine::point(-0.25, -0.25, 0.75),
        ),
        Point::new(
            "c1".to_string(),
            "C₁".to_string(),
            COLOR_C,
            engine::point(0.0, -1.0, -1.0),
        ),
        Point::new(
            "c2".to_string(),
            "C₂".to_string(),
            COLOR_C,
            engine::point(-1.0, 0.0, -1.0),
        ),
        Point::new(
            "c3".to_string(),
            "C₃".to_string(),
            COLOR_C,
            engine::point(-1.0, -1.0, 0.0),
        ),
    ];
    for vertex in vertices {
        let _ = assembly.try_insert_element(vertex);
    }
    
    // create the faces
    const COLOR_FACE: ElementColor = [0.75_f32, 0.75_f32, 0.75_f32];
    let frac_1_sqrt_6 = 1.0 / 6.0_f64.sqrt();
    let frac_2_sqrt_6 = 2.0 * frac_1_sqrt_6;
    let faces = [
        Sphere::new(
            "face1".to_string(),
            "Face 1".to_string(),
            COLOR_FACE,
            engine::sphere_with_offset(frac_2_sqrt_6, -frac_1_sqrt_6, -frac_1_sqrt_6, -frac_1_sqrt_6, 0.0),
        ),
        Sphere::new(
            "face2".to_string(),
            "Face 2".to_string(),
            COLOR_FACE,
            engine::sphere_with_offset(-frac_1_sqrt_6, frac_2_sqrt_6, -frac_1_sqrt_6, -frac_1_sqrt_6, 0.0),
        ),
        Sphere::new(
            "face3".to_string(),
            "Face 3".to_string(),
            COLOR_FACE,
            engine::sphere_with_offset(-frac_1_sqrt_6, -frac_1_sqrt_6, frac_2_sqrt_6, -frac_1_sqrt_6, 0.0),
        ),
    ];
    for face in faces {
        face.ghost().set(true);
        let _ = assembly.try_insert_element(face);
    }
    
    let index_range = 1..=3;
    for j in index_range.clone() {
        // make each face planar
        let face = assembly.elements_by_id.with_untracked(
            |elts_by_id| elts_by_id[&format!("face{j}")].clone()
        );
        let curvature_regulator = face.regulators().with_untracked(
            |regs| regs.first().unwrap().clone()
        );
        curvature_regulator.set_point().set(
            SpecifiedValue::try_from("0".to_string()).unwrap()
        );
        
        // put each A vertex on the face it belongs to
        let vertex_a = assembly.elements_by_id.with_untracked(
            |elts_by_id| elts_by_id[&format!("a{j}")].clone()
        );
        let incidence_a = InversiveDistanceRegulator::new([face.clone(), vertex_a.clone()]);
        incidence_a.set_point.set(SpecifiedValue::try_from("0".to_string()).unwrap());
        assembly.insert_regulator(Rc::new(incidence_a));
        
        // regulate the B-C vertex distances
        let vertices_bc = ["b", "c"].map(
            |series| assembly.elements_by_id.with_untracked(
                |elts_by_id| elts_by_id[&format!("{series}{j}")].clone()
            )
        );
        assembly.insert_regulator(
            Rc::new(InversiveDistanceRegulator::new(vertices_bc))
        );
        
        // get the pair of indices adjacent to `j`
        let adjacent_indices = [j % 3 + 1, (j + 1) % 3 + 1];
        
        for k in adjacent_indices.clone() {
            for series in ["b", "c"] {
                // put each B and C vertex on the faces it belongs to
                let vertex = assembly.elements_by_id.with_untracked(
                    |elts_by_id| elts_by_id[&format!("{series}{k}")].clone()
                );
                let incidence = InversiveDistanceRegulator::new([face.clone(), vertex.clone()]);
                incidence.set_point.set(SpecifiedValue::try_from("0".to_string()).unwrap());
                assembly.insert_regulator(Rc::new(incidence));
                
                // regulate the A-B and A-C vertex distances
                assembly.insert_regulator(
                    Rc::new(InversiveDistanceRegulator::new([vertex_a.clone(), vertex]))
                );
            }
        }
        
        // regulate the A-A and C-C vertex distances
        let adjacent_pairs = ["a", "c"].map(
            |series| adjacent_indices.map(
                |index| assembly.elements_by_id.with_untracked(
                    |elts_by_id| elts_by_id[&format!("{series}{index}")].clone()
                )
            )
        );
        for pair in adjacent_pairs {
            assembly.insert_regulator(
                Rc::new(InversiveDistanceRegulator::new(pair))
            );
        }
    }
}

// to finish describing the dodecahedral circle packing, set the inversive
// distance regulators to -1. some of the regulators have already been set
fn load_dodecahedral_packing(assembly: &Assembly) {
    // add the substrate
    let _ = assembly.try_insert_element(
        Sphere::new(
            "substrate".to_string(),
            "Substrate".to_string(),
            [0.75_f32, 0.75_f32, 0.75_f32],
            engine::sphere(0.0, 0.0, 0.0, 1.0),
        )
    );
    let substrate = assembly.elements_by_id.with_untracked(
        |elts_by_id| elts_by_id["substrate"].clone()
    );
    
    // fix the substrate's curvature
    substrate.regulators().with_untracked(
        |regs| regs.first().unwrap().clone()
    ).set_point().set(
        SpecifiedValue::try_from("0.5".to_string()).unwrap()
    );
    
    // add the circles to be packed
    const COLOR_A: ElementColor = [1.00_f32, 0.25_f32, 0.00_f32];
    const COLOR_B: ElementColor = [1.00_f32, 0.00_f32, 0.25_f32];
    const COLOR_C: ElementColor = [0.25_f32, 0.00_f32, 1.00_f32];
    let phi = 0.5 + 1.25_f64.sqrt(); /* TO DO */ // replace with std::f64::consts::PHI when that gets stabilized
    let phi_inv = 1.0 / phi;
    let coord_scale = (phi + 2.0).sqrt();
    let face_scales = [phi_inv, (13.0 / 12.0) / coord_scale];
    let face_radii = [phi_inv, 5.0 / 12.0];
    let mut faces = Vec::<Rc<dyn Element>>::new();
    let subscripts = ["₀", "₁"];
    for j in 0..2 {
        for k in 0..2 {
            let small_coord = face_scales[k] * (2.0*(j as f64) - 1.0);
            let big_coord = face_scales[k] * (2.0*(k as f64) - 1.0) * phi;
            
            let id_num = format!("{j}{k}");
            let label_sub = format!("{}{}", subscripts[j], subscripts[k]);
            
            // add the A face
            let id_a = format!("a{id_num}");
            let _ = assembly.try_insert_element(
                Sphere::new(
                    id_a.clone(),
                    format!("A{label_sub}"),
                    COLOR_A,
                    engine::sphere(0.0, small_coord, big_coord, face_radii[k]),
                )
            );
            faces.push(
                assembly.elements_by_id.with_untracked(
                    |elts_by_id| elts_by_id[&id_a].clone()
                )
            );
            
            // add the B face
            let id_b = format!("b{id_num}");
            let _ = assembly.try_insert_element(
                Sphere::new(
                    id_b.clone(),
                    format!("B{label_sub}"),
                    COLOR_B,
                    engine::sphere(small_coord, big_coord, 0.0, face_radii[k]),
                )
            );
            faces.push(
                assembly.elements_by_id.with_untracked(
                    |elts_by_id| elts_by_id[&id_b].clone()
                )
            );
            
            // add the C face
            let id_c = format!("c{id_num}");
            let _ = assembly.try_insert_element(
                Sphere::new(
                    id_c.clone(),
                    format!("C{label_sub}"),
                    COLOR_C,
                    engine::sphere(big_coord, 0.0, small_coord, face_radii[k]),
                )
            );
            faces.push(
                assembly.elements_by_id.with_untracked(
                    |elts_by_id| elts_by_id[&id_c].clone()
                )
            );
        }
    }
    
    // make each face sphere perpendicular to the substrate
    for face in faces {
        let right_angle = InversiveDistanceRegulator::new([face, substrate.clone()]);
        right_angle.set_point.set(SpecifiedValue::try_from("0".to_string()).unwrap());
        assembly.insert_regulator(Rc::new(right_angle));
    }
    
    // set up the tangencies that define the packing
    for [long_edge_plane, short_edge_plane] in [["a", "b"], ["b", "c"], ["c", "a"]] {
        for k in 0..2 {
            let long_edge_ids = [
                format!("{long_edge_plane}{k}0"),
                format!("{long_edge_plane}{k}1")
            ];
            let short_edge_ids = [
                format!("{short_edge_plane}0{k}"),
                format!("{short_edge_plane}1{k}")
            ];
            let [long_edge, short_edge] = [long_edge_ids, short_edge_ids].map(
                |edge_ids| edge_ids.map(
                    |id| assembly.elements_by_id.with_untracked(
                        |elts_by_id| elts_by_id[&id].clone()
                    )
                )
            );
            
            // set up the short-edge tangency
            let short_tangency = InversiveDistanceRegulator::new(short_edge.clone());
            if k == 0 {
                short_tangency.set_point.set(SpecifiedValue::try_from("-1".to_string()).unwrap());
            }
            assembly.insert_regulator(Rc::new(short_tangency));
            
            // set up the side tangencies
            for i in 0..2 {
                for j in 0..2 {
                    let side_tangency = InversiveDistanceRegulator::new(
                        [long_edge[i].clone(), short_edge[j].clone()]
                    );
                    if i == 0 && k == 0 {
                        side_tangency.set_point.set(SpecifiedValue::try_from("-1".to_string()).unwrap());
                    }
                    assembly.insert_regulator(Rc::new(side_tangency));
                }
            }
        }
    }
}

// the initial configuration of this test assembly deliberately violates the
// constraints, so loading the assembly will trigger a non-trivial realization
fn load_balanced(assembly: &Assembly) {
    // create the spheres
    const R_OUTER: f64 = 10.0;
    const R_INNER: f64 = 4.0;
    let spheres = [
        Sphere::new(
            "outer".to_string(),
            "Outer".to_string(),
            [0.75_f32, 0.75_f32, 0.75_f32],
            engine::sphere(0.0, 0.0, 0.0, R_OUTER),
        ),
        Sphere::new(
            "a".to_string(),
            "A".to_string(),
            [1.00_f32, 0.00_f32, 0.25_f32],
            engine::sphere(0.0, 4.0, 0.0, R_INNER),
        ),
        Sphere::new(
            "b".to_string(),
            "B".to_string(),
            [0.00_f32, 0.25_f32, 1.00_f32],
            engine::sphere(0.0, -4.0, 0.0, R_INNER),
        ),
    ];
    for sphere in spheres {
        let _ = assembly.try_insert_element(sphere);
    }
    
    // get references to the spheres
    let [outer, a, b] = ["outer", "a", "b"].map(
        |id| assembly.elements_by_id.with_untracked(
            |elts_by_id| elts_by_id[id].clone()
        )
    );
    
    // fix the diameters of the outer, sun, and moon spheres
    for (sphere, radius) in [
        (outer.clone(), R_OUTER),
        (a.clone(), R_INNER),
        (b.clone(), R_INNER),
    ] {
        let curvature_regulator = sphere.regulators().with_untracked(
            |regs| regs.first().unwrap().clone()
        );
        let curvature = 0.5 / radius;
        curvature_regulator.set_point().set(
            SpecifiedValue::try_from(curvature.to_string()).unwrap()
        );
    }
    
    // set the inversive distances between the spheres. as described above, the
    // initial configuration deliberately violates these constraints
    for inner in [a, b] {
        let tangency = InversiveDistanceRegulator::new([outer.clone(), inner]);
        tangency.set_point.set(SpecifiedValue::try_from("1".to_string()).unwrap());
        assembly.insert_regulator(Rc::new(tangency));
    }
}

// the initial configuration of this test assembly deliberately violates the
// constraints, so loading the assembly will trigger a non-trivial realization
fn load_off_center(assembly: &Assembly) {
    // create a point almost at the origin and a sphere centered on the origin
    let _ = assembly.try_insert_element(
        Point::new(
            "point".to_string(),
            "Point".to_string(),
            [0.75_f32, 0.75_f32, 0.75_f32],
            engine::point(1e-9, 0.0, 0.0),
        ),
    );
    let _ = assembly.try_insert_element(
        Sphere::new(
            "sphere".to_string(),
            "Sphere".to_string(),
            [0.75_f32, 0.75_f32, 0.75_f32],
            engine::sphere(0.0, 0.0, 0.0, 1.0),
        ),
    );
    
    // get references to the elements
    let point_and_sphere = ["point", "sphere"].map(
        |id| assembly.elements_by_id.with_untracked(
            |elts_by_id| elts_by_id[id].clone()
        )
    );
    
    // put the point on the sphere
    let incidence = InversiveDistanceRegulator::new(point_and_sphere);
    incidence.set_point.set(SpecifiedValue::try_from("0".to_string()).unwrap());
    assembly.insert_regulator(Rc::new(incidence));
}

// setting the inversive distances between the vertices to -2 gives a regular
// tetrahedron with side length 1, whose insphere and circumsphere have radii
// sqrt(1/6) and sqrt(3/2), respectively. to measure those radii, set an
// inversive distance of -1 between the insphere and each face, and then set an
// inversive distance of 0 between the circumsphere and each vertex
fn load_radius_ratio(assembly: &Assembly) {
    let index_range = 1..=4;
    
    // create the spheres
    const GRAY: ElementColor = [0.75_f32, 0.75_f32, 0.75_f32];
    let spheres = [
        Sphere::new(
            "sphere_faces".to_string(),
            "Insphere".to_string(),
            GRAY,
            engine::sphere(0.0, 0.0, 0.0, 0.5),
        ),
        Sphere::new(
            "sphere_vertices".to_string(),
            "Circumsphere".to_string(),
            GRAY,
            engine::sphere(0.0, 0.0, 0.0, 0.25),
        ),
    ];
    for sphere in spheres {
        let _ = assembly.try_insert_element(sphere);
    }
    
    // create the vertices
    let vertices = izip!(
        index_range.clone(),
        [
            [1.00_f32, 0.50_f32, 0.75_f32],
            [1.00_f32, 0.75_f32, 0.50_f32],
            [1.00_f32, 1.00_f32, 0.50_f32],
            [0.75_f32, 0.50_f32, 1.00_f32],
        ].into_iter(),
        [
            engine::point(-0.6, -0.8, -0.6),
            engine::point(-0.6, 0.8, 0.6),
            engine::point(0.6, -0.8, 0.6),
            engine::point(0.6, 0.8, -0.6),
        ].into_iter()
    ).map(
        |(k, color, representation)| {
            Point::new(
                format!("v{k}"),
                format!("Vertex {k}"),
                color,
                representation,
            )
        }
    );
    for vertex in vertices {
        let _ = assembly.try_insert_element(vertex);
    }
    
    // create the faces
    let base_dir = Vector3::new(1.0, 0.75, 1.0).normalize();
    let offset = base_dir.dot(&Vector3::new(-0.6, 0.8, 0.6));
    let faces = izip!(
        index_range.clone(),
        [
            [1.00_f32, 0.00_f32, 0.25_f32],
            [1.00_f32, 0.25_f32, 0.00_f32],
            [0.75_f32, 0.75_f32, 0.00_f32],
            [0.25_f32, 0.00_f32, 1.00_f32],
        ].into_iter(),
        [
            engine::sphere_with_offset(base_dir[0], base_dir[1], base_dir[2], offset, 0.0),
            engine::sphere_with_offset(base_dir[0], -base_dir[1], -base_dir[2], offset, 0.0),
            engine::sphere_with_offset(-base_dir[0], base_dir[1], -base_dir[2], offset, 0.0),
            engine::sphere_with_offset(-base_dir[0], -base_dir[1], base_dir[2], offset, 0.0),
        ].into_iter()
    ).map(
        |(k, color, representation)| {
            Sphere::new(
                format!("f{k}"),
                format!("Face {k}"),
                color,
                representation,
            )
        }
    );
    for face in faces {
        face.ghost().set(true);
        let _ = assembly.try_insert_element(face);
    }
    
    // impose the constraints
    for j in index_range.clone() {
        let [face_j, vertex_j] = [
            format!("f{j}"),
            format!("v{j}"),
        ].map(
            |id| assembly.elements_by_id.with_untracked(
                |elts_by_id| elts_by_id[&id].clone()
            )
        );
        
        // make the faces planar
        let curvature_regulator = face_j.regulators().with_untracked(
            |regs| regs.first().unwrap().clone()
        );
        curvature_regulator.set_point().set(
            SpecifiedValue::try_from("0".to_string()).unwrap()
        );
        
        for k in index_range.clone().filter(|&index| index != j) {
            let vertex_k = assembly.elements_by_id.with_untracked(
                |elts_by_id| elts_by_id[&format!("v{k}")].clone()
            );
            
            // fix the distances between the vertices
            if j < k {
                let distance_regulator = InversiveDistanceRegulator::new(
                    [vertex_j.clone(), vertex_k.clone()]
                );
                assembly.insert_regulator(Rc::new(distance_regulator));
            }
            
            // put the vertices on the faces
            let incidence_regulator = InversiveDistanceRegulator::new([face_j.clone(), vertex_k.clone()]);
            incidence_regulator.set_point.set(SpecifiedValue::try_from("0".to_string()).unwrap());
            assembly.insert_regulator(Rc::new(incidence_regulator));
        }
    }
}

// to finish setting up the problem, fix the following curvatures:
//   sun      1
//   moon     5/3 = 1.666666666666666...
//   chain1   2
// a tiny `x` or `z` nudge of the outer sphere reliably prevents realization
// failures before they happen, or resolves them after they happen. the result
// depends sensitively on the translation direction, suggesting that realization
// is failing because the engine is having trouble breaking a symmetry
// /* TO DO */
// the engine's performance on this problem is scale-dependent! with the current
// initial conditions, realization fails for any order of imposing the remaining
// curvature constraints. scaling everything up by a factor of ten, as done in
// the original problem, makes realization succeed reliably. one potentially
// relevant difference is that a lot of the numbers in the current initial
// conditions are exactly representable as floats, unlike the analogous numbers
// in the scaled-up problem. the inexact representations might break the
// symmetry that's getting the engine stuck
fn load_irisawa_hexlet(assembly: &Assembly) {
    let index_range = 1..=6;
    let colors = [
        [1.00_f32, 0.00_f32, 0.25_f32],
        [1.00_f32, 0.25_f32, 0.00_f32],
        [0.75_f32, 0.75_f32, 0.00_f32],
        [0.25_f32, 1.00_f32, 0.00_f32],
        [0.00_f32, 0.25_f32, 1.00_f32],
        [0.25_f32, 0.00_f32, 1.00_f32],
    ].into_iter();
    
    // create the spheres
    let spheres = [
        Sphere::new(
            "outer".to_string(),
            "Outer".to_string(),
            [0.5_f32, 0.5_f32, 0.5_f32],
            engine::sphere(0.0, 0.0, 0.0, 1.5),
        ),
        Sphere::new(
            "sun".to_string(),
            "Sun".to_string(),
            [0.75_f32, 0.75_f32, 0.75_f32],
            engine::sphere(0.0, -0.75, 0.0, 0.75),
        ),
        Sphere::new(
            "moon".to_string(),
            "Moon".to_string(),
            [0.25_f32, 0.25_f32, 0.25_f32],
            engine::sphere(0.0, 0.75, 0.0, 0.75),
        ),
    ].into_iter().chain(
        index_range.clone().zip(colors).map(
            |(k, color)| {
                let ang = (k as f64) * PI/3.0;
                Sphere::new(
                    format!("chain{k}"),
                    format!("Chain {k}"),
                    color,
                    engine::sphere(1.0 * ang.sin(), 0.0, 1.0 * ang.cos(), 0.5),
                )
            }
        )
    );
    for sphere in spheres {
        let _ = assembly.try_insert_element(sphere);
    }
    
    // put the outer sphere in ghost mode and fix its curvature
    let outer = assembly.elements_by_id.with_untracked(
        |elts_by_id| elts_by_id["outer"].clone()
    );
    outer.ghost().set(true);
    let outer_curvature_regulator = outer.regulators().with_untracked(
        |regs| regs.first().unwrap().clone()
    );
    outer_curvature_regulator.set_point().set(
        SpecifiedValue::try_from((1.0 / 3.0).to_string()).unwrap()
    );
    
    // impose the desired tangencies
    let [outer, sun, moon] = ["outer", "sun", "moon"].map(
        |id| assembly.elements_by_id.with_untracked(
            |elts_by_id| elts_by_id[id].clone()
        )
    );
    let chain = index_range.map(
        |k| assembly.elements_by_id.with_untracked(
            |elts_by_id| elts_by_id[&format!("chain{k}")].clone()
        )
    );
    for (chain_sphere, chain_sphere_next) in chain.clone().zip(chain.cycle().skip(1)) {
        for (other_sphere, inversive_distance) in [
            (outer.clone(), "1"),
            (sun.clone(), "-1"),
            (moon.clone(), "-1"),
            (chain_sphere_next.clone(), "-1"),
        ] {
            let tangency = InversiveDistanceRegulator::new([chain_sphere.clone(), other_sphere]);
            tangency.set_point.set(SpecifiedValue::try_from(inversive_distance.to_string()).unwrap());
            assembly.insert_regulator(Rc::new(tangency));
        }
    }
    
    let outer_sun_tangency = InversiveDistanceRegulator::new([outer.clone(), sun]);
    outer_sun_tangency.set_point.set(SpecifiedValue::try_from("1".to_string()).unwrap());
    assembly.insert_regulator(Rc::new(outer_sun_tangency));
    
    let outer_moon_tangency = InversiveDistanceRegulator::new([outer.clone(), moon]);
    outer_moon_tangency.set_point.set(SpecifiedValue::try_from("1".to_string()).unwrap());
    assembly.insert_regulator(Rc::new(outer_moon_tangency));
}

// --- chooser ---

/* DEBUG */
#[component]
pub fn TestAssemblyChooser() -> View {
    // create an effect that loads the selected test assembly
    let assembly_name = create_signal("general".to_string());
    create_effect(move || {
        // get name of chosen assembly
        let name = assembly_name.get_clone();
        console::log_1(
            &JsValue::from(format!("Showing assembly \"{}\"", name.clone()))
        );
        
        batch(|| {
            let state = use_context::<AppState>();
            let assembly = &state.assembly;
            
            // clear state
            assembly.regulators.update(|regs| regs.clear());
            assembly.elements.update(|elts| elts.clear());
            assembly.elements_by_id.update(|elts_by_id| elts_by_id.clear());
            assembly.descent_history.set(DescentHistory::new());
            state.selection.update(|sel| sel.clear());
            
            // load assembly
            match name.as_str() {
                "general" => load_general(assembly),
                "low-curvature" => load_low_curvature(assembly),
                "pointed" => load_pointed(assembly),
                "tridiminished-icosahedron" => load_tridiminished_icosahedron(assembly),
                "dodecahedral-packing" => load_dodecahedral_packing(assembly),
                "balanced" => load_balanced(assembly),
                "off-center" => load_off_center(assembly),
                "radius-ratio" => load_radius_ratio(assembly),
                "irisawa-hexlet" => load_irisawa_hexlet(assembly),
                _ => (),
            };
        });
    });
    
    // build the chooser
    view! {
        select(bind:value = assembly_name) {
            option(value = "general") { "General" }
            option(value = "low-curvature") { "Low-curvature" }
            option(value = "pointed") { "Pointed" }
            option(value = "tridiminished-icosahedron") { "Tridiminished icosahedron" }
            option(value = "dodecahedral-packing") { "Dodecahedral packing" }
            option(value = "balanced") { "Balanced" }
            option(value = "off-center") { "Off-center" }
            option(value = "radius-ratio") { "Radius ratio" }
            option(value = "irisawa-hexlet") { "Irisawa hexlet" }
            option(value = "empty") { "Empty" }
        }
    }
}