Refactoring, reorganization and cleanup (#7)

### New `math` module
 * Traits for error-tolerant floating-point comparisons
 * Traits for interpolation and easing
 * Bevy plugin to manage 3D interpolations with ECS components

### `skybox` module refactor
 * ECS resource to enable external skybox selection/updates
 * System run conditions for more idiomatic/ECS-friendly control flow

### Camera controller refactor
 * Renamed from `orbit_cam` to `camera_controller`
 * Now delegates to the new interpolation plugin for WASD motion smoothing
 * Simple API for attaching the `CameraController` component to the camera from
   another module -- this resolves an awkward separation-of-concerns situation
	where we had to configure a bunch of render-quality settings in the camera
	controller module

### Scene module refactor
 * Renamed from `test_scene` to `scene`
 * This module is now responsible for configuring the skybox
 * This module is now responsible for spawning the camera and configuring the
   render settings

studio/src/math/interp/ecs.rs

@@ -0,0 +1,129 @@
+use bevy::prelude::*;
+
+use crate::math::{NearlyEq, NearlyZero};
+
+use super::{CurveSin, Easing, Lerp};
+
+pub struct InterpolationPlugin;
+
+#[derive(SystemSet, Clone, Copy, PartialEq, Eq, Hash, Debug)]
+pub struct InterpolationSystem;
+
+impl Plugin for InterpolationPlugin {
+    fn build(&self, app: &mut App) {
+        app.add_systems(
+            Update,
+            (interp_velocity, interp_position).in_set(InterpolationSystem),
+        )
+        .add_systems(PostUpdate, cleanup_finished_interps);
+    }
+}
+
+/// A `newtype` component for a `t` interpolation parameter.
+#[derive(Component, Deref, DerefMut, Debug, Clone, Copy)]
+pub struct Interp(pub f32);
+
+pub struct Interpolation<T>
+where
+    f32: Lerp<T>,
+{
+    pub initial: T,
+    pub target: T,
+    pub t: f32,
+    pub easing: Easing,
+}
+
+impl<T> Interpolation<T>
+where
+    f32: Lerp<T>,
+    T: Copy,
+{
+    fn tick(&mut self, dt: f32) -> T {
+        self.t = (self.t + dt).clamp(0., 1.);
+        self.current()
+    }
+
+    pub fn current(&self) -> T {
+        if self.t.nearly_zero() {
+            self.initial
+        } else if self.t.nearly_eq(1.) {
+            self.target
+        } else {
+            let t = match self.easing {
+                Easing::Linear => self.t,
+                Easing::Sine => self.t.curve_sin(),
+            };
+
+            t.lerp(self.initial, self.target)
+        }
+    }
+}
+
+impl<T> Default for Interpolation<T>
+where
+    f32: Lerp<T>,
+    T: Default,
+{
+    fn default() -> Self {
+        Self {
+            initial: default(),
+            target: default(),
+            t: 0.,
+            easing: Easing::Linear,
+        }
+    }
+}
+
+#[derive(Component, Deref, DerefMut)]
+pub struct InterpVelocity {
+    #[deref]
+    pub inner: Interpolation<Vec3>,
+    pub accel_zero2max: f32,
+}
+
+// TODO: Does this belong here?
+#[derive(Component, Deref, DerefMut)]
+pub struct Velocity(pub Vec3);
+
+#[derive(Component, Deref, DerefMut)]
+pub struct InterpPosition {
+    #[deref]
+    pub inner: Interpolation<Vec3>,
+    pub duration: f32,
+}
+
+fn interp_velocity(time: Res<Time>, mut q_interp: Query<(&mut Velocity, &mut InterpVelocity)>) {
+    let delta_seconds = time.delta_seconds();
+
+    for (mut velocity, mut interp) in q_interp.iter_mut() {
+        let dt = delta_seconds / interp.accel_zero2max;
+        **velocity = interp.tick(dt);
+    }
+}
+
+fn interp_position(time: Res<Time>, mut q_interp: Query<&mut InterpPosition>) {
+    let delta_seconds = time.delta_seconds();
+
+    for mut interp in q_interp.iter_mut() {
+        let dt = delta_seconds / interp.duration;
+        interp.tick(dt);
+    }
+}
+
+fn cleanup_finished_interps(
+    mut cmd: Commands,
+    q_interp_velocity: Query<(Entity, &InterpVelocity)>,
+    q_interp_position: Query<(Entity, &InterpPosition)>,
+) {
+    for (ent, interp) in q_interp_velocity.iter() {
+        if interp.t.nearly_eq(1.) {
+            cmd.entity(ent).remove::<InterpVelocity>();
+        }
+    }
+
+    for (ent, interp) in q_interp_position.iter() {
+        if interp.t.nearly_eq(1.) {
+            cmd.entity(ent).remove::<InterpPosition>();
+        }
+    }
+}

studio/src/math/interp/mod.rs

@@ -0,0 +1,19 @@
+//! Helpers for interpolating between values.
+
+pub use ecs::*;
+pub use traits::*;
+
+mod ecs;
+mod traits;
+
+#[derive(Clone, Copy, Debug)]
+pub enum Easing {
+    Linear,
+    Sine,
+}
+
+impl Default for Easing {
+    fn default() -> Self {
+        Self::Linear
+    }
+}

studio/src/math/interp/traits.rs

@@ -0,0 +1,152 @@
+use std::ops;
+
+use bevy::prelude::Vec3;
+
+use crate::math::{
+    internal::{Clamp, One, Zero},
+    NearlyZero,
+};
+
+pub trait Lerp<Operand> {
+    /// Interpolate linearly between `a` and `b`, using `self` as the `t` parameter.
+    fn lerp(self, a: Operand, b: Operand) -> Operand;
+}
+
+pub trait InvLerp<T: Sized> {
+    /// Derive a `t` interpolation parameter for `self`, where `a` is the
+    /// "origin" and `b` is the "destination".
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// use math::NearlyEq;
+    ///
+    /// let t = 48_f32.inv_lerp(32., 64.);
+    /// // The expected result is 0.5, because 48 is halfway between 32 and 64.
+    /// assert!(t.nearly_eq(0.5));
+    /// ```
+    fn inv_lerp(self, a: Self, b: Self) -> T;
+}
+
+pub trait Remap<T: Sized>
+where
+    Self: Sized,
+{
+    /// Re-map a value from its interpolated position in the range `from`, to
+    /// the equivalent position in the range `to`.
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// use math::NearlyEq;
+    ///
+    /// let x = 48_f32.remap((32., 64.), (32., 128.));
+    /// // The expected result is 80, because 48 is halfway between 32 and 64,
+    /// // and 80 is halfway between 32 and 128.
+    /// assert!(x.nearly_eq_within(80., 1e-3));
+    /// ```
+    fn remap(self, from: (Self, Self), to: (Self, Self)) -> Self;
+}
+
+pub trait CurveSin {
+    /// Fit a `t` interpolation parameter to a sine curve. Mostly useful for
+    /// "easing" between steps in an animation.
+    ///
+    /// https://www.desmos.com/calculator/k9x4c4cr5y
+    ///
+    /// # Example
+    ///
+    /// ```
+    /// // This is fine, but it will feel "jerky" because the velocity is
+    /// // constant from start to end.
+    /// fn update_position(dt: f32, start: Vec3, end: Vec3, t: f32) -> Vec3 {
+    ///     (t + dt).clamp(0., 1.).lerp(start, end)
+    /// }
+    ///
+    /// // This will smoothly accelerate from a standstill at t=0, and
+    /// // smoothly decelerate back to a stop at t=1.
+    /// fn update_position_eased(dt: f32, start: Vec3, end: Vec3, t: f32) -> Vec3 {
+    ///     (t + dt)
+    ///         .clamp(0., 1.)
+    ///         .curve_sin()
+    ///         .lerp(start, end)
+    /// }
+    /// ```
+    fn curve_sin(self) -> Self;
+}
+
+impl<T, Operand> Lerp<Operand> for T
+where
+    T: Copy,
+    T: One,
+    T: ops::Sub<Output = T>,
+    Operand: ops::Mul<T, Output = Operand>,
+    Operand: ops::Add<Output = Operand>,
+{
+    #[inline]
+    fn lerp(self, a: Operand, b: Operand) -> Operand {
+        a * (Self::one() - self) + b * self
+    }
+}
+
+impl<T> InvLerp<T> for T
+where
+    T: One + Zero,
+    T: Clamp,
+    T: NearlyZero,
+    T: Copy,
+    T: ops::Sub<Output = T>,
+    T: ops::Div<Output = T>,
+{
+    #[inline]
+    fn inv_lerp(self, a: T, b: T) -> T {
+        let dividend = b - a;
+        if !dividend.nearly_zero() {
+            ((self - a) / dividend).clamp(T::zero(), T::one())
+        } else {
+            T::one()
+        }
+    }
+}
+
+// Vector inverse lerp requires a special implementation, yoinked from here:
+// https://discussions.unity.com/t/inverselerp-for-vector3/177038
+impl InvLerp<f32> for Vec3 {
+    #[inline]
+    fn inv_lerp(self, a: Vec3, b: Vec3) -> f32 {
+        let ab = b - a;
+        let av = self - a;
+        if !ab.nearly_zero() {
+            av.dot(ab) / ab.length_squared()
+        } else {
+            1.
+        }
+    }
+}
+
+impl<T, Operand> Remap<T> for Operand
+where
+    Operand: InvLerp<T>,
+    T: Lerp<Operand>,
+{
+    #[inline]
+    fn remap(self, from: (Self, Self), to: (Self, Self)) -> Self {
+        self.inv_lerp(from.0, from.1).lerp(to.0, to.1)
+    }
+}
+
+impl CurveSin for f32 {
+    fn curve_sin(self) -> Self {
+        use std::f32::consts::PI;
+
+        -1. * ((self * PI).cos() / 2.) + 0.5
+    }
+}
+
+impl CurveSin for f64 {
+    fn curve_sin(self) -> Self {
+        use std::f64::consts::PI;
+
+        -1. * ((self * PI).cos() / 2.) + 0.5
+    }
+}