# Objective
Apparently #14382 broke this, but it's not a part of CI, so it wasn't
found until earlier today.
## Solution
Update the benchmark like we updated the examples.
## Testing
Running `cargo bench` actually works now.
# Objective
A Bezier curve is a curve defined by two or more control points. In the
simplest form, it's just a line. The (arguably) most common type of
Bezier curve is a cubic Bezier, defined by four control points. These
are often used in animation, etc. Bevy has a Bezier curve struct called
`Bezier`. However, this is technically a misnomer as it only represents
cubic Bezier curves.
## Solution
This PR changes the struct name to `CubicBezier` to more accurately
reflect the struct's usage. Since it's exposed in Bevy's prelude, it can
potentially collide with other `Bezier` implementations. While that
might instead be an argument for removing it from the prelude, there's
also something to be said for adding a more general `Bezier` into Bevy,
in which case we'd likely want to use the name `Bezier`. As a final
motivator, not only is the struct located in `cubic_spines.rs`, there
are also several other spline-related structs which follow the
`CubicXxx` naming convention where applicable. For example,
`CubicSegment` represents a cubic Bezier curve (with coefficients
pre-baked).
---
## Migration Guide
- Change all `Bezier` references to `CubicBezier`
# Objective
- Make cubic splines more flexible and more performant
- Remove the existing spline implementation that is generic over many degrees
- This is a potential performance footgun and adds type complexity for negligible gain.
- Add implementations of:
- Bezier splines
- Cardinal splines (inc. Catmull-Rom)
- B-Splines
- Hermite splines
https://user-images.githubusercontent.com/2632925/221780519-495d1b20-ab46-45b4-92a3-32c46da66034.mp4https://user-images.githubusercontent.com/2632925/221780524-2b154016-699f-404f-9c18-02092f589b04.mp4https://user-images.githubusercontent.com/2632925/221780525-f934f99d-9ad4-4999-bae2-75d675f5644f.mp4
## Solution
- Implements the concept that splines are curve generators (e.g. https://youtu.be/jvPPXbo87ds?t=3488) via the `CubicGenerator` trait.
- Common splines are bespoke data types that implement this trait. This gives us flexibility to add custom spline-specific methods on these types, while ultimately all generating a `CubicCurve`.
- All splines generate `CubicCurve`s, which are a chain of precomputed polynomial coefficients. This means that all splines have the same evaluation cost, as the calculations for determining position, velocity, and acceleration are all identical. In addition, `CubicCurve`s are simply a list of `CubicSegment`s, which are evaluated from t=0 to t=1. This also means cubic splines of different type can be chained together, as ultimately they all are simply a collection of `CubicSegment`s.
- Because easing is an operation on a singe segment of a Bezier curve, we can simply implement easing on `Beziers` that use the `Vec2` type for points. Higher level crates such as `bevy_ui` can wrap this in a more ergonomic interface as needed.
### Performance
Measured on a desktop i5 8600K (6-year-old CPU):
- easing: 2.7x faster (19ns)
- cubic vec2 position sample: 1.5x faster (1.8ns)
- cubic vec3 position sample: 1.5x faster (2.6ns)
- cubic vec3a position sample: 1.9x faster (1.4ns)
On a laptop i7 11800H:
- easing: 16ns
- cubic vec2 position sample: 1.6ns
- cubic vec3 position sample: 2.3ns
- cubic vec3a position sample: 1.2ns
---
## Changelog
- Added a generic cubic curve trait, and implementation for Cardinal splines (including Catmull-Rom), B-Splines, Beziers, and Hermite Splines. 2D cubic curve segments also implement easing functionality for animation.
# Objective
- Adds foundational math for Bezier curves, useful for UI/2D/3D animation and smooth paths.
https://user-images.githubusercontent.com/2632925/218883143-e138f994-1795-40da-8c59-21d779666991.mp4
## Solution
- Adds the generic `Bezier` type, and a `Point` trait. The `Point` trait allows us to use control points of any dimension, as long as they support vector math. I've implemented it for `f32`(1D), `Vec2`(2D), and `Vec3`/`Vec3A`(3D).
- Adds `CubicBezierEasing` on top of `Bezier` with the addition of an implementation of cubic Bezier easing, which is a foundational tool for UI animation.
- This involves solving for $t$ in the parametric Bezier function $B(t)$ using the Newton-Raphson method to find a value with error $\leq$ 1e-7, capped at 8 iterations.
- Added type aliases for common Bezier curves: `CubicBezier2d`, `CubicBezier3d`, `QuadraticBezier2d`, and `QuadraticBezier3d`. These types use `Vec3A` to represent control points, as this was found to have an 80-90% speedup over using `Vec3`.
- Benchmarking shows quadratic/cubic Bezier evaluations $B(t)$ take \~1.8/2.4ns respectively. Easing, which requires an iterative solve takes \~50ns for cubic Beziers.
---
## Changelog
- Added `CubicBezier2d`, `CubicBezier3d`, `QuadraticBezier2d`, and `QuadraticBezier3d` types with methods for sampling position, velocity, and acceleration. The generic `Bezier` type is also available, and generic over any degree of Bezier curve.
- Added `CubicBezierEasing`, with additional methods to allow for smooth easing animations.
