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# 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. |
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What is Bevy?
Bevy is a refreshingly simple data-driven game engine built in Rust. It is free and open-source forever!
WARNING
Bevy is still in the early stages of development. Important features are missing. Documentation is sparse. A new version of Bevy containing breaking changes to the API is released approximately once every 3 months. We provide migration guides, but we can't guarantee migrations will always be easy. Use only if you are willing to work in this environment.
MSRV: Bevy relies heavily on improvements in the Rust language and compiler. As a result, the Minimum Supported Rust Version (MSRV) is generally close to "the latest stable release" of Rust.
Design Goals
- Capable: Offer a complete 2D and 3D feature set
- Simple: Easy for newbies to pick up, but infinitely flexible for power users
- Data Focused: Data-oriented architecture using the Entity Component System paradigm
- Modular: Use only what you need. Replace what you don't like
- Fast: App logic should run quickly, and when possible, in parallel
- Productive: Changes should compile quickly ... waiting isn't fun
About
- Features: A quick overview of Bevy's features.
- News: A development blog that covers our progress, plans and shiny new features.
Docs
- Quick Start Guide: Bevy's official Quick Start Guide. The best place to start learning Bevy.
- Bevy Rust API Docs: Bevy's Rust API docs, which are automatically generated from the doc comments in this repo.
- Official Examples: Bevy's dedicated, runnable examples, which are great for digging into specific concepts.
- Community-Made Learning Resources: More tutorials, documentation, and examples made by the Bevy community.
Community
Before contributing or participating in discussions with the community, you should familiarize yourself with our Code of Conduct.
- Discord: Bevy's official discord server.
- Reddit: Bevy's official subreddit.
- GitHub Discussions: The best place for questions about Bevy, answered right here!
- Bevy Assets: A collection of awesome Bevy projects, tools, plugins and learning materials.
Contributing
If you'd like to help build Bevy, check out the Contributor's Guide. For simple problems, feel free to open an issue or PR and tackle it yourself!
For more complex architecture decisions and experimental mad science, please open an RFC (Request For Comments) so we can brainstorm together effectively!
Getting Started
We recommend checking out the Quick Start Guide for a brief introduction.
Follow the Setup guide to ensure your development environment is set up correctly. Once set up, you can quickly try out the examples by cloning this repo and running the following commands:
# Switch to the correct version (latest release, default is main development branch)
git checkout latest
# Runs the "breakout" example
cargo run --example breakout
To draw a window with standard functionality enabled, use:
use bevy::prelude::*;
fn main(){
App::new()
.add_plugins(DefaultPlugins)
.run();
}
Fast Compiles
Bevy can be built just fine using default configuration on stable Rust. However for really fast iterative compiles, you should enable the "fast compiles" setup by following the instructions here.
Bevy Cargo Features
This list outlines the different cargo features supported by Bevy. These allow you to customize the Bevy feature set for your use-case.
Thanks
Bevy is the result of the hard work of many people. A huge thanks to all Bevy contributors, the many open source projects that have come before us, the Rust gamedev ecosystem, and the many libraries we build on.
A huge thanks to Bevy's generous sponsors. Bevy will always be free and open source, but it isn't free to make. Please consider sponsoring our work if you like what we're building.
This project is tested with BrowserStack.
License
Bevy is free, open source and permissively licensed! Except where noted (below and/or in individual files), all code in this repository is dual-licensed under either:
- MIT License (LICENSE-MIT or http://opensource.org/licenses/MIT)
- Apache License, Version 2.0 (LICENSE-APACHE or http://www.apache.org/licenses/LICENSE-2.0)
at your option. This means you can select the license you prefer! This dual-licensing approach is the de-facto standard in the Rust ecosystem and there are very good reasons to include both.
Some of the engine's code carries additional copyright notices and license terms due to their external origins.
These are generally BSD-like, but exact details vary by crate:
If the README of a crate contains a 'License' header (or similar), the additional copyright notices and license terms applicable to that crate will be listed.
The above licensing requirement still applies to contributions to those crates, and sections of those crates will carry those license terms.
The license field of each crate will also reflect this.
For example, bevy_mikktspace has code under the Zlib license (as well as a copyright notice when choosing the MIT license).
The assets included in this repository (for our examples) typically fall under different open licenses. These will not be included in your game (unless copied in by you), and they are not distributed in the published bevy crates. See CREDITS.md for the details of the licenses of those files.
Your contributions
Unless you explicitly state otherwise, any contribution intentionally submitted for inclusion in the work by you, as defined in the Apache-2.0 license, shall be dual licensed as above, without any additional terms or conditions.