Quickly animate scroll when calling ui.scroll_to_cursor etc (#4119)

Uses ease-in-ease-out interpolation, with a time between 0.1s and 0.3s,
depending on the distance needed to scroll.


![smooth-scroll-to-target](https://github.com/emilk/egui/assets/1148717/c5c8556d-476b-4597-842b-aa0e5927fbb9)

crates/emath/src/lib.rs

@@ -383,6 +383,52 @@ pub fn exponential_smooth_factor(
     1.0 - (1.0 - reach_this_fraction).powf(dt / in_this_many_seconds)
 }
 
+/// If you have a value animating over time,
+/// how much towards its target do you need to move it this frame?
+///
+/// You only need to store the start time and target value in order to animate using this function.
+///
+/// ``` rs
+/// struct Animation {
+///     current_value: f32,
+///
+///     animation_time_span: (f64, f64),
+///     target_value: f32,
+/// }
+///
+/// impl Animation {
+///     fn update(&mut self, now: f64, dt: f32) {
+///         let t = interpolation_factor(self.animation_time_span, now, dt, ease_in_ease_out);
+///         self.current_value = emath::lerp(self.current_value..=self.target_value, t);
+///     }
+/// }
+/// ```
+pub fn interpolation_factor(
+    (start_time, end_time): (f64, f64),
+    current_time: f64,
+    dt: f32,
+    easing: impl Fn(f32) -> f32,
+) -> f32 {
+    let animation_duration = (end_time - start_time) as f32;
+    let prev_time = current_time - dt as f64;
+    let prev_t = easing((prev_time - start_time) as f32 / animation_duration);
+    let end_t = easing((current_time - start_time) as f32 / animation_duration);
+    if end_t < 1.0 {
+        (end_t - prev_t) / (1.0 - prev_t)
+    } else {
+        1.0
+    }
+}
+
+/// Ease in, ease out.
+///
+/// `f(0) = 0, f'(0) = 0, f(1) = 1, f'(1) = 0`.
+#[inline]
+pub fn ease_in_ease_out(t: f32) -> f32 {
+    let t = t.clamp(0.0, 1.0);
+    (3.0 * t * t - 2.0 * t * t * t).clamp(0.0, 1.0)
+}
+
 // ----------------------------------------------------------------------------
 
 /// An assert that is only active when `emath` is compiled with the `extra_asserts` feature