diff --git a/app-proto/full-interface/src/engine.rs b/app-proto/full-interface/src/engine.rs
new file mode 100644
index 0000000..79668bb
--- /dev/null
+++ b/app-proto/full-interface/src/engine.rs
@@ -0,0 +1,27 @@
+use nalgebra::DVector;
+
+// 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> {
+    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,
+        center_z / radius,
+        0.5 / radius,
+        0.5 * (center_norm_sq / radius - radius)
+    ])
+}
+
+// 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> {
+    let norm_sp = 1.0 + off * curv;
+    DVector::from_column_slice(&[
+        norm_sp * dir_x,
+        norm_sp * dir_y,
+        norm_sp * dir_z,
+        0.5 * curv,
+        off * (1.0 + 0.5 * off * curv)
+    ])
+}
\ No newline at end of file
diff --git a/app-proto/full-interface/src/main.rs b/app-proto/full-interface/src/main.rs
index 5ed9d30..0ca2209 100644
--- a/app-proto/full-interface/src/main.rs
+++ b/app-proto/full-interface/src/main.rs
@@ -1,6 +1,7 @@
 mod add_remove;
 mod assembly;
 mod display;
+mod engine;
 mod outline;
 
 use nalgebra::DVector;
@@ -34,36 +35,63 @@ fn main() {
         let assemb = &state.assembly;
         let _ = assemb.try_insert_element(
             Element {
-                id: String::from("wing_a"),
-                label: String::from("Wing A"),
+                id: String::from("gemini_a"),
+                label: String::from("Castor"),
                 color: [1.00_f32, 0.25_f32, 0.00_f32],
-                rep: DVector::<f64>::from_column_slice(&[0.5, 0.5, 0.0, 0.5, -0.25]),
+                rep: engine::sphere(0.5, 0.5, 0.0, 1.0),
                 constraints: BTreeSet::default()
             }
         );
         let _ = assemb.try_insert_element(
             Element {
-                id: String::from("wing_b"),
-                label: String::from("Wing B"),
+                id: String::from("gemini_b"),
+                label: String::from("Pollux"),
                 color: [0.00_f32, 0.25_f32, 1.00_f32],
-                rep: DVector::<f64>::from_column_slice(&[-0.5, -0.5, 0.0, 0.5, -0.25]),
+                rep: engine::sphere(-0.5, -0.5, 0.0, 1.0),
                 constraints: BTreeSet::default()
             }
         );
         let _ = assemb.try_insert_element(
             Element {
-                id: String::from("central"),
-                label: String::from("Central"),
-                color: [0.75_f32, 0.75_f32, 0.75_f32],
-                rep: DVector::<f64>::from_column_slice(&[0.0, 0.0, 0.0, 0.4, -0.625]),
+                id: String::from("ursa_major"),
+                label: String::from("Ursa major"),
+                color: [0.25_f32, 0.00_f32, 1.00_f32],
+                rep: engine::sphere(-0.5, 0.5, 0.0, 0.75),
+                constraints: BTreeSet::default()
+            }
+        );
+        let _ = assemb.try_insert_element(
+            Element {
+                id: String::from("ursa_minor"),
+                label: String::from("Ursa minor"),
+                color: [0.25_f32, 1.00_f32, 0.00_f32],
+                rep: engine::sphere(0.5, -0.5, 0.0, 0.5),
+                constraints: BTreeSet::default()
+            }
+        );
+        let _ = assemb.try_insert_element(
+            Element {
+                id: String::from("moon_deimos"),
+                label: String::from("Deimos"),
+                color: [0.75_f32, 0.75_f32, 0.00_f32],
+                rep: engine::sphere(0.0, 0.15, 1.0, 0.25),
+                constraints: BTreeSet::default()
+            }
+        );
+        let _ = assemb.try_insert_element(
+            Element {
+                id: String::from("moon_phobos"),
+                label: String::from("Phobos"),
+                color: [0.00_f32, 0.75_f32, 0.50_f32],
+                rep: engine::sphere(0.0, -0.15, -1.0, 0.25),
                 constraints: BTreeSet::default()
             }
         );
         assemb.insert_constraint(
             Constraint {
                 args: (
-                    assemb.elements_by_id.with(|elts_by_id| elts_by_id["wing_a"]),
-                    assemb.elements_by_id.with(|elts_by_id| elts_by_id["wing_b"])
+                    assemb.elements_by_id.with(|elts_by_id| elts_by_id["gemini_a"]),
+                    assemb.elements_by_id.with(|elts_by_id| elts_by_id["gemini_b"])
                 ),
                 rep: 0.5
             }