Dispatch normalization routines correctly (#87)

Addresses issue #86 by correctly dispatching the routine used to normalize spheres during nudging. Adds a test that would have detected the issue.

Since the tests aren't built for WebAssembly, we have to replace `console::log` with `console_log!` in all of the functions used by `assembly::curvature_drift_test`. We'll eventually want to do this replacement everywhere.

Co-authored-by: Aaron Fenyes <aaron.fenyes@fareycircles.ooo>
Reviewed-on: #87
Co-authored-by: Vectornaut <vectornaut@nobody@nowhere.net>
Co-committed-by: Vectornaut <vectornaut@nobody@nowhere.net>

app-proto/src/engine.rs

@@ -1,5 +1,6 @@
 use lazy_static::lazy_static;
 use nalgebra::{Const, DMatrix, DVector, DVectorView, Dyn, SymmetricEigen};
+use std::fmt::{Display, Error, Formatter};
 use web_sys::{console, wasm_bindgen::JsValue}; /* DEBUG */
 
 // --- elements ---
@@ -34,6 +35,21 @@ pub fn sphere_with_offset(dir_x: f64, dir_y: f64, dir_z: f64, off: f64, curv: f6
     ])
 }
 
+// project a sphere's representation vector to the normalization variety by
+// contracting toward the last coordinate axis
+pub fn project_sphere_to_normalized(rep: &mut DVector<f64>) {
+    let q_sp = rep.fixed_rows::<3>(0).norm_squared();
+    let half_q_lt = -2.0 * rep[3] * rep[4];
+    let half_q_lt_sq = half_q_lt * half_q_lt;
+    let scaling = half_q_lt + (q_sp + half_q_lt_sq).sqrt();
+    rep.fixed_rows_mut::<4>(0).scale_mut(1.0 / scaling);
+}
+
+// normalize a point's representation vector by scaling
+pub fn project_point_to_normalized(rep: &mut DVector<f64>) {
+    rep.scale_mut(0.5 / rep[3]);
+}
+
 // 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
@@ -94,15 +110,6 @@ impl PartialMatrix {
         }
     }
     
-    /* DEBUG */
-    pub fn log_to_console(&self) {
-        for &MatrixEntry { index: (row, col), value } in self {
-            console::log_1(&JsValue::from(
-                format!("  {} {} {}", row, col, value)
-            ));
-        }
-    }
-    
     fn freeze(&self, a: &DMatrix<f64>) -> DMatrix<f64> {
         let mut result = a.clone();
         for &MatrixEntry { index, value } in self {
@@ -128,6 +135,15 @@ impl PartialMatrix {
     }
 }
 
+impl Display for PartialMatrix {
+    fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error> {
+        for &MatrixEntry { index: (row, col), value } in self {
+            writeln!(f, "  {row} {col} {value}")?;
+        }
+        Ok(())
+    }
+}
+
 impl IntoIterator for PartialMatrix {
     type Item = MatrixEntry;
     type IntoIter = std::vec::IntoIter<Self::Item>;