Add a tetrahedron radius ratio test assembly

This partial setup of the tetrahedron radius ratio problem is from the
summer 2025 tech demo.

app-proto/src/add_remove.rs

@@ -1,4 +1,6 @@
+use itertools::izip;
 use std::{f64::consts::FRAC_1_SQRT_2, rc::Rc};
+use nalgebra::Vector3;
 use sycamore::prelude::*;
 use web_sys::{console, wasm_bindgen::JsValue};
 
@@ -6,7 +8,14 @@ use crate::{
     AppState,
     engine,
     engine::DescentHistory,
-    assembly::{Assembly, InversiveDistanceRegulator, Point, Sphere},
+    assembly::{
+        Assembly,
+        Element,
+        ElementColor,
+        InversiveDistanceRegulator,
+        Point,
+        Sphere
+    },
     specified::SpecifiedValue
 };
 
@@ -229,6 +238,135 @@ fn load_pointed_assemb(assembly: &Assembly) {
     }
 }
 
+// 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_assemb(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));
+        }
+    }
+}
+
 #[component]
 pub fn AddRemove() -> View {
     /* DEBUG */
@@ -259,6 +397,7 @@ pub fn AddRemove() -> View {
                 "general" => load_gen_assemb(assembly),
                 "low-curv" => load_low_curv_assemb(assembly),
                 "pointed" => load_pointed_assemb(assembly),
+                "radius-ratio" => load_radius_ratio_assemb(assembly),
                 _ => ()
             };
             
@@ -310,6 +449,7 @@ pub fn AddRemove() -> View {
                 option(value="general") { "General" }
                 option(value="low-curv") { "Low-curvature" }
                 option(value="pointed") { "Pointed" }
+                option(value="radius-ratio") { "Radius ratio" }
                 option(value="empty") { "Empty" }
             }
         }