diff --git a/app-proto/src/assembly.rs b/app-proto/src/assembly.rs
index 387b567..161859d 100644
--- a/app-proto/src/assembly.rs
+++ b/app-proto/src/assembly.rs
@@ -8,6 +8,7 @@ use web_sys::{console, wasm_bindgen::JsValue}; /* DEBUG */
 use crate::{
     engine::{
         Q,
+        change_half_curvature,
         local_unif_to_std,
         realize_gram,
         sphere,
@@ -401,37 +402,9 @@ impl Assembly {
                 let representation = self_for_effect.elements.with_untracked(
                     |elts| elts[subject].representation
                 );
-                representation.update(|rep| {
-                    // set the sphere's half-curvature to the desired value
-                    rep[3] = half_curv;
-                    
-                    // restore normalization by contracting toward the curvature
-                    // axis
-                    const SIZE_THRESHOLD: f64 = 1e-9;
-                    let half_q_lt = -2.0 * half_curv * rep[4];
-                    let half_q_lt_sq = half_q_lt * half_q_lt;
-                    let mut spatial = rep.fixed_rows_mut::<3>(0);
-                    let q_sp = spatial.norm_squared();
-                    if q_sp < SIZE_THRESHOLD && half_q_lt_sq < SIZE_THRESHOLD {
-                        spatial.copy_from_slice(
-                            &[0.0, 0.0, (1.0 - 2.0 * half_q_lt).sqrt()]
-                        );
-                    } else {
-                        let scaling = half_q_lt + (q_sp + half_q_lt_sq).sqrt();
-                        spatial.scale_mut(1.0 / scaling);
-                        rep[4] /= scaling;
-                    }
-                    
-                    /* DEBUG */
-                    // verify normalization
-                    let rep_for_debug = rep.clone();
-                    console::log_1(&JsValue::from(
-                        format!(
-                            "Sphere self-product after curvature change: {}",
-                            rep_for_debug.dot(&(&*Q * &rep_for_debug))
-                        )
-                    ));
-                });
+                representation.update(
+                    |rep| change_half_curvature(rep, half_curv)
+                );
                 self_for_effect.realize();
             }
         });
diff --git a/app-proto/src/engine.rs b/app-proto/src/engine.rs
index 44f44e0..869a7de 100644
--- a/app-proto/src/engine.rs
+++ b/app-proto/src/engine.rs
@@ -35,6 +35,40 @@ pub fn sphere_with_offset(dir_x: f64, dir_y: f64, dir_z: f64, off: f64, curv: f6
     ])
 }
 
+// given a sphere's representation vector, change the sphere's half-curvature to
+// `half-curv` and then restore normalization by contracting the representation
+// vector toward the curvature axis
+pub fn change_half_curvature(rep: &mut DVector<f64>, half_curv: f64) {
+    // set the sphere's half-curvature to the desired value
+    rep[3] = half_curv;
+    
+    // restore normalization by contracting toward the curvature axis
+    const SIZE_THRESHOLD: f64 = 1e-9;
+    let half_q_lt = -2.0 * half_curv * rep[4];
+    let half_q_lt_sq = half_q_lt * half_q_lt;
+    let mut spatial = rep.fixed_rows_mut::<3>(0);
+    let q_sp = spatial.norm_squared();
+    if q_sp < SIZE_THRESHOLD && half_q_lt_sq < SIZE_THRESHOLD {
+        spatial.copy_from_slice(
+            &[0.0, 0.0, (1.0 - 2.0 * half_q_lt).sqrt()]
+        );
+    } else {
+        let scaling = half_q_lt + (q_sp + half_q_lt_sq).sqrt();
+        spatial.scale_mut(1.0 / scaling);
+        rep[4] /= scaling;
+    }
+    
+    /* DEBUG */
+    // verify normalization
+    let rep_for_debug = rep.clone();
+    console::log_1(&JsValue::from(
+        format!(
+            "Sphere self-product after curvature change: {}",
+            rep_for_debug.dot(&(&*Q * &rep_for_debug))
+        )
+    ));
+}
+
 // --- partial matrices ---
 
 pub struct MatrixEntry {