bevy/examples/movement/smooth_follow.rs

143 lines
4.4 KiB
Rust
Raw Normal View History

Stable interpolation and smooth following (#13741) # Objective Partially address #13408 Rework of #13613 Unify the very nice forms of interpolation specifically present in `bevy_math` under a shared trait upon which further behavior can be based. The ideas in this PR were prompted by [Lerp smoothing is broken by Freya Holmer](https://www.youtube.com/watch?v=LSNQuFEDOyQ). ## Solution There is a new trait `StableInterpolate` in `bevy_math::common_traits` which enshrines a quite-specific notion of interpolation with a lot of guarantees: ```rust /// A type with a natural interpolation that provides strong subdivision guarantees. /// /// Although the only required method is `interpolate_stable`, many things are expected of it: /// /// 1. The notion of interpolation should follow naturally from the semantics of the type, so /// that inferring the interpolation mode from the type alone is sensible. /// /// 2. The interpolation recovers something equivalent to the starting value at `t = 0.0` /// and likewise with the ending value at `t = 1.0`. /// /// 3. Importantly, the interpolation must be *subdivision-stable*: for any interpolation curve /// between two (unnamed) values and any parameter-value pairs `(t0, p)` and `(t1, q)`, the /// interpolation curve between `p` and `q` must be the *linear* reparametrization of the original /// interpolation curve restricted to the interval `[t0, t1]`. /// /// The last of these conditions is very strong and indicates something like constant speed. It /// is called "subdivision stability" because it guarantees that breaking up the interpolation /// into segments and joining them back together has no effect. /// /// Here is a diagram depicting it: /// ```text /// top curve = u.interpolate_stable(v, t) /// /// t0 => p t1 => q /// |-------------|---------|-------------| /// 0 => u / \ 1 => v /// / \ /// / \ /// / linear \ /// / reparametrization \ /// / t = t0 * (1 - s) + t1 * s \ /// / \ /// |-------------------------------------| /// 0 => p 1 => q /// /// bottom curve = p.interpolate_stable(q, s) /// ``` /// /// Note that some common forms of interpolation do not satisfy this criterion. For example, /// [`Quat::lerp`] and [`Rot2::nlerp`] are not subdivision-stable. /// /// Furthermore, this is not to be used as a general trait for abstract interpolation. /// Consumers rely on the strong guarantees in order for behavior based on this trait to be /// well-behaved. /// /// [`Quat::lerp`]: crate::Quat::lerp /// [`Rot2::nlerp`]: crate::Rot2::nlerp pub trait StableInterpolate: Clone { /// Interpolate between this value and the `other` given value using the parameter `t`. /// Note that the parameter `t` is not necessarily clamped to lie between `0` and `1`. /// When `t = 0.0`, `self` is recovered, while `other` is recovered at `t = 1.0`, /// with intermediate values lying between the two. fn interpolate_stable(&self, other: &Self, t: f32) -> Self; } ``` This trait has a blanket implementation over `NormedVectorSpace`, where `lerp` is used, along with implementations for `Rot2`, `Quat`, and the direction types using variants of `slerp`. Other areas may choose to implement this trait in order to hook into its functionality, but the stringent requirements must actually be met. This trait bears no direct relationship with `bevy_animation`'s `Animatable` trait, although they may choose to use `interpolate_stable` in their trait implementations if they wish, as both traits involve type-inferred interpolations of the same kind. `StableInterpolate` is not a supertrait of `Animatable` for a couple reasons: 1. Notions of interpolation in animation are generally going to be much more general than those allowed under these constraints. 2. Laying out these generalized interpolation notions is the domain of `bevy_animation` rather than of `bevy_math`. (Consider also that inferring interpolation from types is not universally desirable.) Similarly, this is not implemented on `bevy_color`'s color types, although their current mixing behavior does meet the conditions of the trait. As an aside, the subdivision-stability condition is of interest specifically for the [Curve RFC](https://github.com/bevyengine/rfcs/pull/80), where it also ensures a kind of stability for subsampling. Importantly, this trait ensures that the "smooth following" behavior defined in this PR behaves predictably: ```rust /// Smoothly nudge this value towards the `target` at a given decay rate. The `decay_rate` /// parameter controls how fast the distance between `self` and `target` decays relative to /// the units of `delta`; the intended usage is for `decay_rate` to generally remain fixed, /// while `delta` is something like `delta_time` from an updating system. This produces a /// smooth following of the target that is independent of framerate. /// /// More specifically, when this is called repeatedly, the result is that the distance between /// `self` and a fixed `target` attenuates exponentially, with the rate of this exponential /// decay given by `decay_rate`. /// /// For example, at `decay_rate = 0.0`, this has no effect. /// At `decay_rate = f32::INFINITY`, `self` immediately snaps to `target`. /// In general, higher rates mean that `self` moves more quickly towards `target`. /// /// # Example /// ``` /// # use bevy_math::{Vec3, StableInterpolate}; /// # let delta_time: f32 = 1.0 / 60.0; /// let mut object_position: Vec3 = Vec3::ZERO; /// let target_position: Vec3 = Vec3::new(2.0, 3.0, 5.0); /// // Decay rate of ln(10) => after 1 second, remaining distance is 1/10th /// let decay_rate = f32::ln(10.0); /// // Calling this repeatedly will move `object_position` towards `target_position`: /// object_position.smooth_nudge(&target_position, decay_rate, delta_time); /// ``` fn smooth_nudge(&mut self, target: &Self, decay_rate: f32, delta: f32) { self.interpolate_stable_assign(target, 1.0 - f32::exp(-decay_rate * delta)); } ``` As the documentation indicates, the intention is for this to be called in game update systems, and `delta` would be something like `Time::delta_seconds` in Bevy, allowing positions, orientations, and so on to smoothly follow a target. A new example, `smooth_follow`, demonstrates a basic implementation of this, with a sphere smoothly following a sharply moving target: https://github.com/bevyengine/bevy/assets/2975848/7124b28b-6361-47e3-acf7-d1578ebd0347 ## Testing Tested by running the example with various parameters.
2024-06-10 12:50:59 +00:00
//! This example demonstrates how to use interpolation to make one entity smoothly follow another.
use bevy::math::{prelude::*, vec3, NormedVectorSpace};
use bevy::prelude::*;
use rand::SeedableRng;
use rand_chacha::ChaCha8Rng;
fn main() {
App::new()
.add_plugins(DefaultPlugins)
.add_systems(Startup, setup)
.add_systems(Update, (move_target, move_follower).chain())
.run();
}
// The sphere that the following sphere targets at all times:
#[derive(Component)]
struct TargetSphere;
// The speed of the target sphere moving to its next location:
#[derive(Resource)]
struct TargetSphereSpeed(f32);
// The position that the target sphere always moves linearly toward:
#[derive(Resource)]
struct TargetPosition(Vec3);
// The decay rate used by the smooth following:
#[derive(Resource)]
struct DecayRate(f32);
// The sphere that follows the target sphere by moving towards it with nudging:
#[derive(Component)]
struct FollowingSphere;
/// The source of randomness used by this example.
#[derive(Resource)]
struct RandomSource(ChaCha8Rng);
fn setup(
mut commands: Commands,
mut meshes: ResMut<Assets<Mesh>>,
mut materials: ResMut<Assets<StandardMaterial>>,
) {
// A plane:
commands.spawn(PbrBundle {
mesh: meshes.add(Plane3d::default().mesh().size(12.0, 12.0)),
material: materials.add(Color::srgb(0.3, 0.15, 0.3)),
transform: Transform::from_xyz(0.0, -2.5, 0.0),
..default()
});
// The target sphere:
commands.spawn((
PbrBundle {
mesh: meshes.add(Sphere::new(0.3)),
material: materials.add(Color::srgb(0.3, 0.15, 0.9)),
..default()
},
TargetSphere,
));
// The sphere that follows it:
commands.spawn((
PbrBundle {
mesh: meshes.add(Sphere::new(0.3)),
material: materials.add(Color::srgb(0.9, 0.3, 0.3)),
transform: Transform::from_translation(vec3(0.0, -2.0, 0.0)),
..default()
},
FollowingSphere,
));
// A light:
commands.spawn(PointLightBundle {
point_light: PointLight {
intensity: 15_000_000.0,
shadows_enabled: true,
..default()
},
transform: Transform::from_xyz(4.0, 8.0, 4.0),
..default()
});
// A camera:
commands.spawn(Camera3dBundle {
transform: Transform::from_xyz(-2.0, 3.0, 5.0).looking_at(Vec3::ZERO, Vec3::Y),
..default()
});
// Set starting values for resources used by the systems:
commands.insert_resource(TargetSphereSpeed(5.0));
commands.insert_resource(DecayRate(2.0));
commands.insert_resource(TargetPosition(Vec3::ZERO));
commands.insert_resource(RandomSource(ChaCha8Rng::seed_from_u64(68941654987813521)));
}
fn move_target(
mut target: Query<&mut Transform, With<TargetSphere>>,
target_speed: Res<TargetSphereSpeed>,
mut target_pos: ResMut<TargetPosition>,
time: Res<Time>,
mut rng: ResMut<RandomSource>,
) {
let mut target = target.single_mut();
match Dir3::new(target_pos.0 - target.translation) {
// The target and the present position of the target sphere are far enough to have a well-
// defined direction between them, so let's move closer:
Ok(dir) => {
let delta_time = time.delta_seconds();
let abs_delta = (target_pos.0 - target.translation).norm();
// Avoid overshooting in case of high values of `delta_time`:
let magnitude = f32::min(abs_delta, delta_time * target_speed.0);
target.translation += dir * magnitude;
}
// The two are really close, so let's generate a new target position:
Err(_) => {
let legal_region = Cuboid::from_size(Vec3::splat(4.0));
*target_pos = TargetPosition(legal_region.sample_interior(&mut rng.0));
}
}
}
fn move_follower(
mut following: Query<&mut Transform, With<FollowingSphere>>,
target: Query<&Transform, (With<TargetSphere>, Without<FollowingSphere>)>,
decay_rate: Res<DecayRate>,
time: Res<Time>,
) {
let target = target.single();
let mut following = following.single_mut();
let decay_rate = decay_rate.0;
let delta_time = time.delta_seconds();
// Calling `smooth_nudge` is what moves the following sphere smoothly toward the target.
following
.translation
.smooth_nudge(&target.translation, decay_rate, delta_time);
}