[Merged by Bors] - Add generic cubic splines to `bevy_math` #7683

aevyrie · 2023-02-15T10:36:46Z

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

2023-02-27.22-10-31.mp4

2023-02-27.22-11-29.mp4

2023-02-27.22-24-01.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 CubicCurves, 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, CubicCurves are simply a list of CubicSegments, 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 CubicSegments.
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.

crates/bevy_math/src/catmull_rom.rs

aevyrie · 2023-02-15T20:41:41Z

@alice-i-cecile based on the work in #7653, I'm wondering if the sampling, position, velocity, and acceleration should be part of a spline trait? Also means to_positions and friends could be implemented for all splines automatically, to remove the boilerplate.

alice-i-cecile · 2023-02-15T21:47:00Z

@alice-i-cecile based on the work in #7653, I'm wondering if the sampling, position, velocity, and acceleration should be part of a spline trait? Also means to_positions and friends could be implemented for all splines automatically, to remove the boilerplate.

Yes, this is my preference. There seems to be a general class of objects here that it would be very nice to work generically over.

maniwani

I like the generalization to CubicCurve and CubicSegment. My only suggestion is to consider linking to an explanation of continuity wherever you mention it in the docs, maybe this one. Not everyone will know what C_k means.

maniwani · 2023-03-03T20:34:11Z

crates/bevy_math/src/cubic_splines.rs

+        let [a, b, c, d] = self.coeff;
+        a + b * t + c * t.powi(2) + d * t.powi(3)


Suggested change

let [a, b, c, d] = self.coeff;

a + b * t + c * t.powi(2) + d * t.powi(3)

let [a, b, c, d] = self.coeff;

a + t * (b + t * (c + t * d))

You may be able to save a tiny bit more time by doing it like this. https://rust.godbolt.org/z/TvEMqY8Ps

Thanks for these suggestions. I'll investigate this optimization and link to wikipedia in the docs.

alice-i-cecile

I like the generalization too. This is well-made and documented, and Blazing Fast.

alice-i-cecile · 2023-03-03T22:06:25Z

bors r+

# 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.mp4 https://user-images.githubusercontent.com/2632925/221780524-2b154016-699f-404f-9c18-02092f589b04.mp4 https://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.

bors · 2023-03-03T22:22:06Z

Pull request successfully merged into main.

Build succeeded:

# 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.mp4 https://user-images.githubusercontent.com/2632925/221780524-2b154016-699f-404f-9c18-02092f589b04.mp4 https://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.

alice-i-cecile reviewed Feb 15, 2023

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alice-i-cecile reviewed Feb 15, 2023

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alice-i-cecile reviewed Feb 15, 2023

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alice-i-cecile added C-Enhancement A new feature A-Math Fundamental domain-agnostic mathematical operations labels Feb 15, 2023

initial catmull-rom implementation

520cd52

aevyrie force-pushed the catmull-rom branch from fdb7874 to 520cd52 Compare February 21, 2023 07:53

general purpose cubic curves

18aa56f

aevyrie changed the title ~~Add Catmull-Rom splines to bevy_math~~ Add generic cubic splines to bevy_math Feb 25, 2023

aevyrie requested a review from james7132 February 25, 2023 11:39

fix ci errors

20d31ac

aevyrie force-pushed the catmull-rom branch from 06a3e4e to 20d31ac Compare February 27, 2023 06:27

alice-i-cecile added this to the 0.11 milestone Feb 27, 2023

aevyrie added 3 commits February 27, 2023 21:42

Improve docs

22a3303

Fix impl bugs

d8acb4d

Add missing benchmark import

44887ff

maniwani approved these changes Mar 3, 2023

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Fix doc typos

f140a69

alice-i-cecile approved these changes Mar 3, 2023

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alice-i-cecile added the S-Ready-For-Final-Review This PR has been approved by the community. It's ready for a maintainer to consider merging it label Mar 3, 2023

bors bot changed the title ~~Add generic cubic splines to bevy_math~~ [Merged by Bors] - Add generic cubic splines to bevy_math Mar 3, 2023

bors bot closed this Mar 3, 2023

james7132 modified the milestones: 0.11, 0.10 Mar 4, 2023

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[Merged by Bors] - Add generic cubic splines to `bevy_math` #7683

[Merged by Bors] - Add generic cubic splines to `bevy_math` #7683

aevyrie commented Feb 15, 2023 •

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bors bot commented Mar 3, 2023

		let [a, b, c, d] = self.coeff;
		a + b * t + c * t.powi(2) + d * t.powi(3)

[Merged by Bors] - Add generic cubic splines to bevy_math #7683

[Merged by Bors] - Add generic cubic splines to bevy_math #7683

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aevyrie commented Feb 15, 2023 • edited Loading

Objective

Solution

Performance

Changelog

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[Merged by Bors] - Add generic cubic splines to `bevy_math` #7683

[Merged by Bors] - Add generic cubic splines to `bevy_math` #7683

aevyrie commented Feb 15, 2023 •

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