App: use general test assembly from inversive-display

This moves us toward dropping the separate display prototype.

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)
+    ])
+}