Aevyrie 2a598d3e5a Add Beziers to bevy_math (#7653) ... # 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.		2023-02-20 18:34:52 +00:00
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benches	Add Beziers to bevy_math (#7653)	2023-02-20 18:34:52 +00:00
Cargo.toml	Add Beziers to bevy_math (#7653)	2023-02-20 18:34:52 +00:00