fix(city): correct vehicle yaw calculation and expose orientation API

- Extracts yawFromDelta helper to standardize rotation math
- Removes incorrect PI/2 offset causing reverse-facing vehicles
- Accounts for direction sign in shuttle vehicle rotation
- Adds vehicleOrientations() for test validation

public/js/city/app.js

@@ -980,6 +980,15 @@ function probeAhead(pts, s, L) {
     return { distToCorner: 999, axis: 'x', corner: pts[0] };
 }
 
+/**
+ * Yaw so a mesh whose nose is local +X faces the world direction (dx, dz).
+ *
+ * Three.js: local +X after rotation.y=θ becomes (cos θ, 0, -sin θ).
+ */
+function yawFromDelta(dx, dz) {
+    return Math.atan2(-dz, dx);
+}
+
 function updateLoopVehicle(v, dt) {
     const probe = probeAhead(v.pts, v.s, v.L);
     const distToCorner = probe.distToCorner;
@@ -1008,7 +1017,7 @@ function updateLoopVehicle(v, dt) {
     posOnPath(v.pts, v.s + 0.6, v.L, tmp);
     v.mesh.position.copy(pos);
     if (tmp.distanceToSquared(pos) > 0.0001) {
-        v.mesh.rotation.y = Math.atan2(tmp.x - pos.x, tmp.z - pos.z) + Math.PI / 2;
+        v.mesh.rotation.y = yawFromDelta(tmp.x - pos.x, tmp.z - pos.z);
     }
     const wheelSpin = v.speed * dt * 3;
     for (const w of v.mesh.userData.wheels || []) w.rotation.z += wheelSpin;
@@ -1049,7 +1058,7 @@ function updateShuttleVehicle(v, dt) {
     v.mesh.position.copy(pos);
     const look = new THREE.Vector3().lerpVectors(v.a, v.b, Math.max(0, Math.min(1, v.t + v.dir * 0.05)));
     if (look.distanceToSquared(pos) > 0.0001) {
-        v.mesh.rotation.y = Math.atan2(look.x - pos.x, look.z - pos.z) + Math.PI / 2;
+        v.mesh.rotation.y = yawFromDelta(look.x - pos.x, look.z - pos.z);
     }
     for (const w of v.mesh.userData.wheels || []) w.rotation.z += v.speed * dt * 3;
 }
@@ -2632,10 +2641,11 @@ function vehicleBoxes() {
             posOnPath(v.pts, v.s, v.L, p);
             const ahead = new THREE.Vector3();
             posOnPath(v.pts, v.s + 0.6, v.L, ahead);
-            rot = Math.atan2(ahead.x - p.x, ahead.z - p.z);
+            rot = yawFromDelta(ahead.x - p.x, ahead.z - p.z);
         } else {
             p.lerpVectors(v.a, v.b, v.t);
-            rot = Math.atan2(v.b.x - v.a.x, v.b.z - v.a.z) + Math.PI / 2;
+            const dirSign = v.dir >= 0 ? 1 : -1;
+            rot = yawFromDelta((v.b.x - v.a.x) * dirSign, (v.b.z - v.a.z) * dirSign);
         }
         const halfL = v.mesh?.userData?.halfL ?? (v.pts ? 2.1 : 2.0);
         const halfW = v.mesh?.userData?.halfW ?? 1.0;
@@ -3459,6 +3469,40 @@ window.__city10 = {
         };
     },
     vehiclePositions() { return vehicleSystem ? vehicleSystem.positions() : []; },
+    /** Sample vehicle heading vs velocity so tests can detect reverse-facing models. */
+    vehicleOrientations() {
+        if (!vehicleSystem) return [];
+        const out = [];
+        for (const v of vehicleSystem.vehicles) {
+            const p = new THREE.Vector3();
+            const ahead = new THREE.Vector3();
+            if (v.pts) {
+                posOnPath(v.pts, v.s, v.L, p);
+                posOnPath(v.pts, v.s + 0.8, v.L, ahead);
+            } else {
+                p.lerpVectors(v.a, v.b, v.t);
+                const lookT = Math.max(0, Math.min(1, v.t + v.dir * 0.05));
+                ahead.lerpVectors(v.a, v.b, lookT);
+            }
+            const dx = ahead.x - p.x;
+            const dz = ahead.z - p.z;
+            const len = Math.hypot(dx, dz) || 1;
+            const vx = dx / len;
+            const vz = dz / len;
+            // Mesh nose is local +X → world forward = (cos yaw, -sin yaw).
+            const yaw = v.mesh.rotation.y;
+            const fx = Math.cos(yaw);
+            const fz = -Math.sin(yaw);
+            const dot = fx * vx + fz * vz;
+            out.push({
+                kind: v.mesh?.userData?.kind || 'car',
+                speed: +(v.speed || 0).toFixed(2),
+                dot: +dot.toFixed(3),
+                aligned: dot > 0.5,
+            });
+        }
+        return out;
+    },
     pedestrianPositions() { return pedestrianSystem ? pedestrianSystem.positions() : []; },
     get me() { return meCharacter; },
     refreshMe: async function () {