Use quaternionic smooth_nudge in the align example (#14858)

# Objective

This example previously had kind of a needlessly complex state machine
that tracked moves between its previous orientation and the new one that
was randomly generated. Using `smooth_nudge` simplifies the example in
addition to making good use of the new API.

## Solution

Use `smooth_nudge` to transition between the current transform and the
new one. This does away with the need to keep track of the move's
starting position and progress. It also just sort of looks nicer.

## Testing

Run the `align` example:
`cargo run --example align`

Author: mweatherley

examples/transforms/align.rs

@@ -2,6 +2,7 @@
 
 use bevy::color::palettes::basic::{GRAY, RED, WHITE};
 use bevy::input::mouse::{AccumulatedMouseMotion, MouseButtonInput};
+use bevy::math::StableInterpolate;
 use bevy::prelude::*;
 use rand::{Rng, SeedableRng};
 use rand_chacha::ChaCha8Rng;
@@ -18,15 +19,9 @@ fn main() {
 /// This struct stores metadata for a single rotational move of the ship
 #[derive(Component, Default)]
 struct Ship {
-    /// The initial transform of the ship move, the starting point of interpolation
-    initial_transform: Transform,
-
     /// The target transform of the ship move, the endpoint of interpolation
     target_transform: Transform,
 
-    /// The progress of the ship move in percentage points
-    progress: u16,
-
     /// Whether the ship is currently in motion; allows motion to be paused
     in_motion: bool,
 }
@@ -92,7 +87,6 @@ fn setup(
             ..default()
         },
         Ship {
-            initial_transform: Transform::IDENTITY,
             target_transform: random_axes_target_alignment(&RandomAxes(first, second)),
             ..default()
         },
@@ -147,37 +141,33 @@ fn draw_random_axes(mut gizmos: Gizmos, query: Query<&RandomAxes>) {
 }
 
 // Actually update the ship's transform according to its initial source and target
-fn rotate_ship(mut ship: Query<(&mut Ship, &mut Transform)>) {
+fn rotate_ship(mut ship: Query<(&mut Ship, &mut Transform)>, time: Res<Time>) {
     let (mut ship, mut ship_transform) = ship.single_mut();
 
     if !ship.in_motion {
         return;
     }
 
-    let start = ship.initial_transform.rotation;
-    let end = ship.target_transform.rotation;
-
-    let p: f32 = ship.progress.into();
-    let t = p / 100.;
+    let target_rotation = ship.target_transform.rotation;
 
-    *ship_transform = Transform::from_rotation(start.slerp(end, t));
+    ship_transform
+        .rotation
+        .smooth_nudge(&target_rotation, 3.0, time.delta_seconds());
 
-    if ship.progress == 100 {
+    if ship_transform.rotation.angle_between(target_rotation) <= f32::EPSILON {
         ship.in_motion = false;
-    } else {
-        ship.progress += 1;
     }
 }
 
 // Handle user inputs from the keyboard for dynamically altering the scenario
 fn handle_keypress(
-    mut ship: Query<(&mut Ship, &Transform)>,
+    mut ship: Query<&mut Ship>,
     mut random_axes: Query<&mut RandomAxes>,
     mut instructions: Query<&mut Visibility, With<Instructions>>,
     keyboard: Res<ButtonInput<KeyCode>>,
     mut seeded_rng: ResMut<SeededRng>,
 ) {
-    let (mut ship, ship_transform) = ship.single_mut();
+    let mut ship = ship.single_mut();
     let mut random_axes = random_axes.single_mut();
 
     if keyboard.just_pressed(KeyCode::KeyR) {
@@ -188,9 +178,7 @@ fn handle_keypress(
 
         // Stop the ship and set it up to transform from its present orientation to the new one
         ship.in_motion = false;
-        ship.initial_transform = *ship_transform;
         ship.target_transform = random_axes_target_alignment(&random_axes);
-        ship.progress = 0;
     }
 
     if keyboard.just_pressed(KeyCode::KeyT) {