0294fa89db
16 Commits
| Author | SHA1 | Message | Date | |
|---|---|---|---|---|
JoshValjosh
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ddee5cca85
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Improve Bevy's double-precision story for third-party crates (#19194)
# Objective Certain classes of games, usually those with enormous worlds, require some amount of support for double-precision. Libraries like `big_space` exist to allow for large worlds while integrating cleanly with Bevy's primarily single-precision ecosystem, but even then, games will often still work directly in double-precision throughout the part of the pipeline that feeds into the Bevy interface. Currently, working with double-precision types in Bevy is a pain. `glam` provides types like `DVec3`, but Bevy doesn't provide double-precision analogs for `glam` wrappers like `Dir3`. This is mostly because doing so involves one of: - code duplication - generics - templates (like `glam` uses) - macros Each of these has issues that are enough to be deal-breakers as far as maintainability, usability or readability. To work around this, I'm putting together `bevy_dmath`, a crate that duplicates `bevy_math` types and functionality to allow downstream users to enjoy the ergonomics and power of `bevy_math` in double-precision. For the most part, it's a smooth process, but in order to fully integrate, there are some necessary changes that can only be made in `bevy_math`. ## Solution This PR addresses the first and easiest issue with downstream double-precision math support: `VectorSpace` currently can only represent vector spaces over `f32`. This automatically closes the door to double-precision curves, among other things. This restriction can be easily lifted by allowing vector spaces to specify the underlying scalar field. This PR adds a new trait `ScalarField` that satisfies the properties of a scalar field (the ones that can be upheld statically) and adds a new associated type `type Scalar: ScalarField` to `VectorSpace`. It's mostly an unintrusive change. The biggest annoyances are: - it touches a lot of curve code - `bevy_math::ops` doesn't support `f64`, so there are some annoying workarounds As far as curves code, I wanted to make this change unintrusive and bite-sized, so I'm trying to touch as little code as possible. To prove to myself it can be done, I went ahead and (*not* in this PR) migrated most of the curves API to support different `ScalarField`s and it went really smoothly! The ugliest thing was adding `P::Scalar: From<usize>` in several places. There's an argument to be made here that we should be using `num-traits`, but that's not immediately relevant. The point is that for now, the smallest change I could make was to go into every curve impl and make them generic over `VectorSpace<Scalar = f32>`. Curves work exactly like before and don't change the user API at all. # Follow-up - **Extend `bevy_math::ops` to work with `f64`.** `bevy_math::ops` is used all over, and if curves are ever going to support different `ScalarField` types, we'll need to be able to use the correct `std` or `libm` ops for `f64` types as well. Adding an `ops64` mod turned out to be really ugly, but I'll point out the maintenance burden is low because we're not going to be adding new floating-point ops anytime soon. Another solution is to build a floating-point trait that calls the right op variant and impl it for `f32` and `f64`. This reduces maintenance burden because on the off chance we ever *do* want to go modify it, it's all tied together: you can't change the interface on one without changing the trait, which forces you to update the other. A third option is to use `num-traits`, which is basically option 2 but someone else did the work for us. They already support `no_std` using `libm`, so it would be more or less a drop-in replacement. They're missing a couple floating-point ops like `floor` and `ceil`, but we could make our own floating-point traits for those (there's even the potential for upstreaming them into `num-traits`). - **Tweak curves to accept vector spaces over any `ScalarField`.** Curves are ready to support custom scalar types as soon as the bullet above is addressed. I will admit that the code is not as fun to look at: `P::Scalar` instead of `f32` everywhere. We could consider an alternate design where we use `f32` even to interpolate something like a `DVec3`, but personally I think that's a worse solution than parameterizing curves over the vector space's scalar type. At the end of the day, it's not really bad to deal with in my opinion... `ScalarType` supports enough operations that working with them is almost like working with raw float types, and it unlocks a whole ecosystem for games that want to use double-precision. |
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Matty Weatherley
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47f46b5bdf
|
Expose the output curve type in with_derivative (#18826)
# Objective
I was wrong about how RPITIT works when I wrote this stuff initially,
and in order to actually give people access to all the traits
implemented by the output (e.g. Debug and so on) it's important to
expose the real output type, even if it makes the trait uglier and less
comprehensible. (☹️)
## Solution
Expose the curve output type of the `CurveWithDerivative` trait and its
double-derivative companion. I also added a bunch of trait derives to
`WithDerivative<T>`, since I think that was just an oversight.
|
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Matty Weatherley
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ee9bea1ba9
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Use variadics_please to implement StableInterpolate on tuples. (#16931)
# Objective Now that `variadics_please` has a 1.1 release, we can re-implement the original solution. ## Solution Copy-paste the code from the [original PR](https://github.com/bevyengine/bevy/pull/15931) branch :) |
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Matty Weatherley
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c60dcea231
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Derivative access patterns for curves (#16503)
# Objective
- For curves that also include derivatives, make accessing derivative
information via the `Curve` API ergonomic: that is, provide access to a
curve that also samples derivative information.
- Implement this functionality for cubic spline curves provided by
`bevy_math`.
Ultimately, this is to serve the purpose of doing more geometric
operations on curves, like reparametrization by arclength and the
construction of moving frames.
## Solution
This has several parts, some of which may seem redundant. However, care
has been put into this to satisfy the following constraints:
- Accessing a `Curve` that samples derivative information should be not
just possible but easy and non-error-prone. For example, given a
differentiable `Curve<Vec2>`, one should be able to access something
like a `Curve<(Vec2, Vec2)>` ergonomically, and not just sample the
derivatives piecemeal from point to point.
- Derivative access should not step on the toes of ordinary curve usage.
In particular, in the above scenario, we want to avoid simply making the
same curve both a `Curve<Vec2>` and a `Curve<(Vec2, Vec2)>` because this
requires manual disambiguation when the API is used.
- Derivative access must work gracefully in both owned and borrowed
contexts.
### `HasTangent`
We introduce a trait `HasTangent` that provides an associated `Tangent`
type for types that have tangent spaces:
```rust
pub trait HasTangent {
/// The tangent type.
type Tangent: VectorSpace;
}
```
(Mathematically speaking, it would be more precise to say that these are
types that represent spaces which are canonically
[parallelized](https://en.wikipedia.org/wiki/Parallelizable_manifold). )
The idea here is that a point moving through a `HasTangent` type may
have a derivative valued in the associated `Tangent` type at each time
in its journey. We reify this with a `WithDerivative<T>` type that uses
`HasTangent` to include derivative information:
```rust
pub struct WithDerivative<T>
where
T: HasTangent,
{
/// The underlying value.
pub value: T,
/// The derivative at `value`.
pub derivative: T::Tangent,
}
```
And we can play the same game with second derivatives as well, since
every `VectorSpace` type is `HasTangent` where `Tangent` is itself (we
may want to be more restrictive with this in practice, but this holds
mathematically).
```rust
pub struct WithTwoDerivatives<T>
where
T: HasTangent,
{
/// The underlying value.
pub value: T,
/// The derivative at `value`.
pub derivative: T::Tangent,
/// The second derivative at `value`.
pub second_derivative: <T::Tangent as HasTangent>::Tangent,
}
```
In this PR, `HasTangent` is only implemented for `VectorSpace` types,
but it would be valuable to have this implementation for types like
`Rot2` and `Quat` as well. We could also do it for the isometry types
and, potentially, transforms as well. (This is in decreasing order of
value in my opinion.)
### `CurveWithDerivative`
This is a trait for a `Curve<T>` which allows the construction of a
`Curve<WithDerivative<T>>` when derivative information is known
intrinsically. It looks like this:
```rust
/// Trait for curves that have a well-defined notion of derivative, allowing for
/// derivatives to be extracted along with values.
pub trait CurveWithDerivative<T>
where
T: HasTangent,
{
/// This curve, but with its first derivative included in sampling.
fn with_derivative(self) -> impl Curve<WithDerivative<T>>;
}
```
The idea here is to provide patterns like this:
```rust
let value_and_derivative = my_curve.with_derivative().sample_clamped(t);
```
One of the main points here is that `Curve<WithDerivative<T>>` is useful
as an output because it can be used durably. For example, in a dynamic
context, something that needs curves with derivatives can store
something like a `Box<dyn Curve<WithDerivative<T>>>`. Note that
`CurveWithDerivative` is not dyn-compatible.
### `SampleDerivative`
Many curves "know" how to sample their derivatives instrinsically, but
implementing `CurveWithDerivative` as given would be onerous or require
an annoying amount of boilerplate. There are also hurdles to overcome
that involve references to curves: for the `Curve` API, the expectation
is that curve transformations like `with_derivative` take things by
value, with the contract that they can still be used by reference
through deref-magic by including `by_ref` in a method chain.
These problems are solved simultaneously by a trait `SampleDerivative`
which, when implemented, automatically derives `CurveWithDerivative` for
a type and all types that dereference to it. It just looks like this:
```rust
pub trait SampleDerivative<T>: Curve<T>
where
T: HasTangent,
{
fn sample_with_derivative_unchecked(&self, t: f32) -> WithDerivative<T>;
// ... other sampling variants as default methods
}
```
The point is that the output of `with_derivative` is a
`Curve<WithDerivative<T>>` that uses the `SampleDerivative`
implementation. On a `SampleDerivative` type, you can also just call
`my_curve.sample_with_derivative(t)` instead of something like
`my_curve.by_ref().with_derivative().sample(t)`, which is more verbose
and less accessible.
In practice, `CurveWithDerivative<T>` is actually a "sealed" extension
trait of `SampleDerivative<T>`.
## Adaptors
`SampleDerivative` has automatic implementations on all curve adaptors
except for `FunctionCurve`, `MapCurve`, and `ReparamCurve` (because we
do not have a notion of differentiable Rust functions).
For example, `CurveReparamCurve` (the reparametrization of a curve by
another curve) can compute derivatives using the chain rule in the case
both its constituents have them.
## Testing
Tests for derivatives on the curve adaptors are included.
---
## Showcase
This development allows derivative information to be included with and
extracted from curves using the `Curve` API.
```rust
let points = [
vec2(-1.0, -20.0),
vec2(3.0, 2.0),
vec2(5.0, 3.0),
vec2(9.0, 8.0),
];
// A cubic spline curve that goes through `points`.
let curve = CubicCardinalSpline::new(0.3, points).to_curve().unwrap();
// Calling `with_derivative` causes derivative output to be included in the output of the curve API.
let curve_with_derivative = curve.with_derivative();
// A `Curve<f32>` that outputs the speed of the original.
let speed_curve = curve_with_derivative.map(|x| x.derivative.norm());
```
---
## Questions
- ~~Maybe we should seal `WithDerivative` or make it require
`SampleDerivative` (i.e. make it unimplementable except through
`SampleDerivative`).~~ I decided this is a good idea.
- ~~Unclear whether `VectorSpace: HasTangent` blanket implementation is
really appropriate. For colors, for example, I'm not sure that the
derivative values can really be interpreted as a color. In any case, it
should still remain the case that `VectorSpace` types are `HasTangent`
and that `HasTangent::Tangent: HasTangent`.~~ I think this is fine.
- Infinity bikeshed on names of traits and things.
## Future
- Faster implementations of `SampleDerivative` for cubic spline curves.
- Improve ergonomics for accessing only derivatives (and other kinds of
transformations on derivative curves).
- Implement `HasTangent` for:
- `Rot2`/`Quat`
- `Isometry` types
- `Transform`, maybe
- Implement derivatives for easing curves.
- Marker traits for continuous/differentiable curves. (It's actually
unclear to me how much value this has in practice, but we have discussed
it in the past.)
---------
Co-authored-by: Alice Cecile <alice.i.cecile@gmail.com>
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Zachary Harrold
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a8b9c945c7
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Add no_std Support to bevy_math (#15810)
# Objective - Contributes to #15460 ## Solution - Added two new features, `std` (default) and `alloc`, gating `std` and `alloc` behind them respectively. - Added missing `f32` functions to `std_ops` as required. These `f32` methods have been added to the `clippy.toml` deny list to aid in `no_std` development. ## Testing - CI - `cargo clippy -p bevy_math --no-default-features --features libm --target "x86_64-unknown-none"` - `cargo test -p bevy_math --no-default-features --features libm` - `cargo test -p bevy_math --no-default-features --features "libm, alloc"` - `cargo test -p bevy_math --no-default-features --features "libm, alloc, std"` - `cargo test -p bevy_math --no-default-features --features "std"` ## Notes The following items require the `alloc` feature to be enabled: - `CubicBSpline` - `CubicBezier` - `CubicCardinalSpline` - `CubicCurve` - `CubicGenerator` - `CubicHermite` - `CubicNurbs` - `CyclicCubicGenerator` - `RationalCurve` - `RationalGenerator` - `BoxedPolygon` - `BoxedPolyline2d` - `BoxedPolyline3d` - `SampleCurve` - `SampleAutoCurve` - `UnevenSampleCurve` - `UnevenSampleAutoCurve` - `EvenCore` - `UnevenCore` - `ChunkedUnevenCore` This requirement could be relaxed in certain cases, but I had erred on the side of gating rather than modifying. Since `no_std` is a new set of platforms we are adding support to, and the `alloc` feature is enabled by default, this is not a breaking change. --------- Co-authored-by: Benjamin Brienen <benjamin.brienen@outlook.com> Co-authored-by: Matty <2975848+mweatherley@users.noreply.github.com> Co-authored-by: Joona Aalto <jondolf.dev@gmail.com> |
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Martín Maita
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a44b668b90
|
Bump crate-ci/typos from 1.26.8 to 1.27.0 (#16236)
# Objective - Closes #16224 ## Solution - Bumps `crate-ci/typos@v1.26.8` to `crate-ci/typos@v1.27.0`. ## Testing - CI checks should pass. --------- Signed-off-by: dependabot[bot] <support@github.com> Co-authored-by: dependabot[bot] <49699333+dependabot[bot]@users.noreply.github.com> |
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Tau Gärtli
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ed351294ec
|
Use #[doc(fake_variadic)] on StableInterpolate (#15933)
This is a follow-up to #15931 that adds `#[doc(fake_variadic)]` for improved docs output :) |
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Matty
|
a09104b62c
|
Infer StableInterpolate on tuples (#15931)
# Objective
Make `StableInterpolate` "just work" on tuples whose parts are each
`StableInterpolate` types. These types arise notably through
`Curve::zip` (or just through explicit mapping of a similar form). It
would otherwise be kind of frustrating to stumble upon such a thing and
then realize that, e.g., automatic resampling just doesn't work, even
though there is a very "obvious" way to do it.
## Solution
Infer `StableInterpolate` on tuples of up to size 11. I can make that
number bigger, if desired. Unfortunately, I don't think that our
standard "fake variadics" tools actually work for this; the anonymous
field accessors of tuples are `:tt` for purposes of macro expansion,
which means that you can't simplify away the identifiers by doing
something clever like using recursion (which would work if they were
`:expr`). Maybe someone who knows some incredibly dark magic could chime
in with a better solution.
The expanded impls look like this:
```rust
impl<
T0: StableInterpolate,
T1: StableInterpolate,
T2: StableInterpolate,
T3: StableInterpolate,
T4: StableInterpolate,
> StableInterpolate for (T0, T1, T2, T3, T4)
{
fn interpolate_stable(&self, other: &Self, t: f32) -> Self {
(
<T0 as StableInterpolate>::interpolate_stable(&self.0, &other.0, t),
<T1 as StableInterpolate>::interpolate_stable(&self.1, &other.1, t),
<T2 as StableInterpolate>::interpolate_stable(&self.2, &other.2, t),
<T3 as StableInterpolate>::interpolate_stable(&self.3, &other.3, t),
<T4 as StableInterpolate>::interpolate_stable(&self.4, &other.4, t),
)
}
}
```
## Testing
Expanded macros; it compiles.
## Future
Make a version of the fake variadics workflow that supports this kind of
thing.
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Matty
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e563f86a1d
|
Simplified easing curves (#15711)
# Objective
Simplify the API surrounding easing curves. Broaden the base of types
that support easing.
## Solution
There is now a single library function, `easing_curve`, which constructs
a unit-parametrized easing curve between two values based on an
`EaseFunction`:
```rust
/// Given a `start` and `end` value, create a curve parametrized over [the unit interval]
/// that connects them, using the given [ease function] to determine the form of the
/// curve in between.
///
/// [the unit interval]: Interval::UNIT
/// [ease function]: EaseFunction
pub fn easing_curve<T: Ease>(start: T, end: T, ease_fn: EaseFunction) -> EasingCurve<T> { //... }
```
As this shows, the type of the output curve is generic only in `T`. In
particular, as long as `T` is `Reflect` (and `FromReflect` etc. — i.e.,
a standard "well-behaved" reflectable type), `EasingCurve<T>` is also
`Reflect`, and there is no special field handling nonsense. Therefore,
`EasingCurve` is the kind of thing that would be able to be easily
changed in an editor. This is made possible by storing the actual
`EaseFunction` on `EasingCurve<T>` instead of indirecting through some
kind of function type (which generally leads to issues with reflection).
The types that can be eased are those that implement a trait `Ease`:
```rust
/// A type whose values can be eased between.
///
/// This requires the construction of an interpolation curve that actually extends
/// beyond the curve segment that connects two values, because an easing curve may
/// extrapolate before the starting value and after the ending value. This is
/// especially common in easing functions that mimic elastic or springlike behavior.
pub trait Ease: Sized {
/// Given `start` and `end` values, produce a curve with [unlimited domain]
/// that:
/// - takes a value equivalent to `start` at `t = 0`
/// - takes a value equivalent to `end` at `t = 1`
/// - has constant speed everywhere, including outside of `[0, 1]`
///
/// [unlimited domain]: Interval::EVERYWHERE
fn interpolating_curve_unbounded(start: &Self, end: &Self) -> impl Curve<Self>;
}
```
(I know, I know, yet *another* interpolation trait. See 'Future
direction'.)
The other existing easing functions from the previous version of this
module have also become new members of `EaseFunction`: `Linear`,
`Steps`, and `Elastic` (which maybe needs a different name). The latter
two are parametrized.
## Testing
Tested using the `easing_functions` example. I also axed the
`cubic_curve` example which was of questionable value and replaced it
with `eased_motion`, which uses this API in the context of animation:
https://github.com/user-attachments/assets/3c802992-6b9b-4b56-aeb1-a47501c29ce2
---
## Future direction
Morally speaking, `Ease` is incredibly similar to `StableInterpolate`.
Probably, we should just merge `StableInterpolate` into `Ease`, and then
make `SmoothNudge` an automatic extension trait of `Ease`. The reason I
didn't do that is that `StableInterpolate` is not implemented for
`VectorSpace` because of concerns about the `Color` types, and I wanted
to avoid controversy. I think that may be a good idea though.
As Alice mentioned before, we should also probably get rid of the
`interpolation` dependency.
The parametrized `Elastic` variant probably also needs some additional
work (e.g. renaming, in/out/in-out variants, etc.) if we want to keep
it.
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Zachary Harrold
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d70595b667
|
Add core and alloc over std Lints (#15281)
# Objective - Fixes #6370 - Closes #6581 ## Solution - Added the following lints to the workspace: - `std_instead_of_core` - `std_instead_of_alloc` - `alloc_instead_of_core` - Used `cargo +nightly fmt` with [item level use formatting](https://rust-lang.github.io/rustfmt/?version=v1.6.0&search=#Item%5C%3A) to split all `use` statements into single items. - Used `cargo clippy --workspace --all-targets --all-features --fix --allow-dirty` to _attempt_ to resolve the new linting issues, and intervened where the lint was unable to resolve the issue automatically (usually due to needing an `extern crate alloc;` statement in a crate root). - Manually removed certain uses of `std` where negative feature gating prevented `--all-features` from finding the offending uses. - Used `cargo +nightly fmt` with [crate level use formatting](https://rust-lang.github.io/rustfmt/?version=v1.6.0&search=#Crate%5C%3A) to re-merge all `use` statements matching Bevy's previous styling. - Manually fixed cases where the `fmt` tool could not re-merge `use` statements due to conditional compilation attributes. ## Testing - Ran CI locally ## Migration Guide The MSRV is now 1.81. Please update to this version or higher. ## Notes - This is a _massive_ change to try and push through, which is why I've outlined the semi-automatic steps I used to create this PR, in case this fails and someone else tries again in the future. - Making this change has no impact on user code, but does mean Bevy contributors will be warned to use `core` and `alloc` instead of `std` where possible. - This lint is a critical first step towards investigating `no_std` options for Bevy. --------- Co-authored-by: François Mockers <francois.mockers@vleue.com> |
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Clar Fon
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efda7f3f9c
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Simpler lint fixes: makes ci lints work but disables a lint for now (#15376)
Takes the first two commits from #15375 and adds suggestions from this comment: https://github.com/bevyengine/bevy/pull/15375#issuecomment-2366968300 See #15375 for more reasoning/motivation. ## Rebasing (rerunning) ```rust git switch simpler-lint-fixes git reset --hard main cargo fmt --all -- --unstable-features --config normalize_comments=true,imports_granularity=Crate cargo fmt --all git add --update git commit --message "rustfmt" cargo clippy --workspace --all-targets --all-features --fix cargo fmt --all -- --unstable-features --config normalize_comments=true,imports_granularity=Crate cargo fmt --all git add --update git commit --message "clippy" git cherry-pick e6c0b94f6795222310fb812fa5c4512661fc7887 ``` |
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Matty
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61a1530c56
|
Make bevy_math's libm feature use libm for all f32methods with unspecified precision (#14693)
# Objective Closes #14474 Previously, the `libm` feature of bevy_math would just pass the same feature flag down to glam. However, bevy_math itself had many uses of floating-point arithmetic with unspecified precision. For example, `f32::sin_cos` and `f32::powi` have unspecified precision, which means that the exact details of their output are not guaranteed to be stable across different systems and/or versions of Rust. This means that users of bevy_math could observe slightly different behavior on different systems if these methods were used. The goal of this PR is to make it so that the `libm` feature flag actually guarantees some degree of determinacy within bevy_math itself by switching to the libm versions of these functions when the `libm` feature is enabled. ## Solution bevy_math now has an internal module `bevy_math::ops`, which re-exports either the standard versions of the operations or the libm versions depending on whether the `libm` feature is enabled. For example, `ops::sin` compiles to `f32::sin` without the `libm` feature and to `libm::sinf` with it. This approach has a small shortfall, which is that `f32::powi` (integer powers of floating point numbers) does not have an equivalent in `libm`. On the other hand, this method is only used for squaring and cubing numbers in bevy_math. Accordingly, this deficit is covered by the introduction of a trait `ops::FloatPow`: ```rust pub(crate) trait FloatPow { fn squared(self) -> Self; fn cubed(self) -> Self; } ``` Next, each current usage of the unspecified-precision methods has been replaced by its equivalent in `ops`, so that when `libm` is enabled, the libm version is used instead. The exception, of course, is that `.powi(2)`/`.powi(3)` have been replaced with `.squared()`/`.cubed()`. Finally, the usage of the plain `f32` methods with unspecified precision is now linted out of bevy_math (and hence disallowed in CI). For example, using `f32::sin` within bevy_math produces a warning that tells the user to use the `ops::sin` version instead. ## Testing Ran existing tests. It would be nice to check some benchmarks on NURBS things once #14677 merges. I'm happy to wait until then if the rest of this PR is fine. --- ## Discussion In the future, it might make sense to actually expose `bevy_math::ops` as public if any downstream Bevy crates want to provide similar determinacy guarantees. For now, it's all just `pub(crate)`. This PR also only covers `f32`. If we find ourselves using `f64` internally in parts of bevy_math for better robustness, we could extend the module and lints to cover the `f64` versions easily enough. I don't know how feasible it is, but it would also be nice if we could standardize the bevy_math tests with the `libm` feature in CI, since their success is currently platform-dependent (e.g. 8 of them fail on my machine when run locally). --------- Co-authored-by: IQuick 143 <IQuick143cz@gmail.com> |
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Matty
|
9af2ef740b
|
Make bevy_math::common_traits public (#14245)
# Objective Fixes #14243 ## Solution `bevy_math::common_traits` is now a public module. |
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Matty
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a569b35c18
|
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. |
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Verte
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97f0555cb0
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Remove VectorSpace impl on Quat (#12796)
- Fixes #[12762](https://github.com/bevyengine/bevy/issues/12762). ## Migration Guide - `Quat` no longer implements `VectorSpace` as unit quaternions don't actually form proper vector spaces. If you're absolutely certain that what you're doing is correct, convert the `Quat` into a `Vec4` and perform the operations before converting back. |
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Matty
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f924b4d9ef
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Move Point out of cubic splines module and expand it (#12747)
# Objective
Previously, the `Point` trait, which abstracts all of the operations of
a real vector space, was sitting in the submodule of `bevy_math` for
cubic splines. However, the trait has broader applications than merely
cubic splines, and we should use it when possible to avoid code
duplication when performing vector operations.
## Solution
`Point` has been moved into a new submodule in `bevy_math` named
`common_traits`. Furthermore, it has been renamed to `VectorSpace`,
which is more descriptive, and an additional trait `NormedVectorSpace`
has been introduced to expand the API to cover situations involving
geometry in addition to algebra. Additionally, `VectorSpace` itself now
requires a `ZERO` constant and `Neg`. It also supports a `lerp` function
as an automatic trait method.
Here is what that looks like:
```rust
/// A type that supports the mathematical operations of a real vector space, irrespective of dimension.
/// In particular, this means that the implementing type supports:
/// - Scalar multiplication and division on the right by elements of `f32`
/// - Negation
/// - Addition and subtraction
/// - Zero
///
/// Within the limitations of floating point arithmetic, all the following are required to hold:
/// - (Associativity of addition) For all `u, v, w: Self`, `(u + v) + w == u + (v + w)`.
/// - (Commutativity of addition) For all `u, v: Self`, `u + v == v + u`.
/// - (Additive identity) For all `v: Self`, `v + Self::ZERO == v`.
/// - (Additive inverse) For all `v: Self`, `v - v == v + (-v) == Self::ZERO`.
/// - (Compatibility of multiplication) For all `a, b: f32`, `v: Self`, `v * (a * b) == (v * a) * b`.
/// - (Multiplicative identity) For all `v: Self`, `v * 1.0 == v`.
/// - (Distributivity for vector addition) For all `a: f32`, `u, v: Self`, `(u + v) * a == u * a + v * a`.
/// - (Distributivity for scalar addition) For all `a, b: f32`, `v: Self`, `v * (a + b) == v * a + v * b`.
///
/// Note that, because implementing types use floating point arithmetic, they are not required to actually
/// implement `PartialEq` or `Eq`.
pub trait VectorSpace:
Mul<f32, Output = Self>
+ Div<f32, Output = Self>
+ Add<Self, Output = Self>
+ Sub<Self, Output = Self>
+ Neg
+ Default
+ Debug
+ Clone
+ Copy
{
/// The zero vector, which is the identity of addition for the vector space type.
const ZERO: Self;
/// Perform vector space linear interpolation between this element and another, based
/// on the parameter `t`. When `t` is `0`, `self` is recovered. When `t` is `1`, `rhs`
/// is recovered.
///
/// Note that the value of `t` is not clamped by this function, so interpolating outside
/// of the interval `[0,1]` is allowed.
#[inline]
fn lerp(&self, rhs: Self, t: f32) -> Self {
*self * (1. - t) + rhs * t
}
}
```
```rust
/// A type that supports the operations of a normed vector space; i.e. a norm operation in addition
/// to those of [`VectorSpace`]. Specifically, the implementor must guarantee that the following
/// relationships hold, within the limitations of floating point arithmetic:
/// - (Nonnegativity) For all `v: Self`, `v.norm() >= 0.0`.
/// - (Positive definiteness) For all `v: Self`, `v.norm() == 0.0` implies `v == Self::ZERO`.
/// - (Absolute homogeneity) For all `c: f32`, `v: Self`, `(v * c).norm() == v.norm() * c.abs()`.
/// - (Triangle inequality) For all `v, w: Self`, `(v + w).norm() <= v.norm() + w.norm()`.
///
/// Note that, because implementing types use floating point arithmetic, they are not required to actually
/// implement `PartialEq` or `Eq`.
pub trait NormedVectorSpace: VectorSpace {
/// The size of this element. The return value should always be nonnegative.
fn norm(self) -> f32;
/// The squared norm of this element. Computing this is often faster than computing
/// [`NormedVectorSpace::norm`].
#[inline]
fn norm_squared(self) -> f32 {
self.norm() * self.norm()
}
/// The distance between this element and another, as determined by the norm.
#[inline]
fn distance(self, rhs: Self) -> f32 {
(rhs - self).norm()
}
/// The squared distance between this element and another, as determined by the norm. Note that
/// this is often faster to compute in practice than [`NormedVectorSpace::distance`].
#[inline]
fn distance_squared(self, rhs: Self) -> f32 {
(rhs - self).norm_squared()
}
}
```
Furthermore, this PR also demonstrates the use of the
`NormedVectorSpace` combined API to implement `ShapeSample` for
`Triangle2d` and `Triangle3d` simultaneously. Such deduplication is one
of the drivers for developing these APIs.
---
## Changelog
- `Point` from `cubic_splines` becomes `VectorSpace`, exported as
`bevy::math::VectorSpace`.
- `VectorSpace` requires `Neg` and `VectorSpace::ZERO` in addition to
its existing prerequisites.
- Introduced public traits `bevy::math::NormedVectorSpace` for generic
geometry tasks involving vectors.
- Implemented `ShapeSample` for `Triangle2d` and `Triangle3d`.
## Migration Guide
Since `Point` no longer exists, any projects using it must switch to
`bevy::math::VectorSpace`. Additionally, third-party implementations of
this trait now require the `Neg` trait; the constant `VectorSpace::ZERO`
must be provided as well.
---
## Discussion
### Design considerations
Originally, the `NormedVectorSpace::norm` method was part of a separate
trait `Normed`. However, I think that was probably too broad and, more
importantly, the semantics of having it in `NormedVectorSpace` are much
clearer.
As it currently stands, the API exposed here is pretty minimal, and
there is definitely a lot more that we could do, but there are more
questions to answer along the way. As a silly example, we could
implement `NormedVectorSpace::length` as an alias for
`NormedVectorSpace::norm`, but this overlaps with methods in all of the
glam types, so we would want to make sure that the implementations are
effectively identical (for what it's worth, I think they are already).
### Future directions
One example of something that could belong in the `NormedVectorSpace`
API is normalization. Actually, such a thing previously existed on this
branch before I decided to shelve it because of concerns with namespace
collision. It looked like this:
```rust
/// This element, but normalized to norm 1 if possible. Returns an error when the reciprocal of
/// the element's norm is not finite.
#[inline]
#[must_use]
fn normalize(&self) -> Result<Self, NonNormalizableError> {
let reciprocal = 1.0 / self.norm();
if reciprocal.is_finite() {
Ok(*self * reciprocal)
} else {
Err(NonNormalizableError { reciprocal })
}
}
/// An error indicating that an element of a [`NormedVectorSpace`] was non-normalizable due to having
/// non-finite norm-reciprocal.
#[derive(Debug, Error)]
#[error("Element with norm reciprocal {reciprocal} cannot be normalized")]
pub struct NonNormalizableError {
reciprocal: f32
}
```
With this kind of thing in hand, it might be worth considering
eventually making the passage from vectors to directions fully generic
by employing a wrapper type. (Of course, for our concrete types, we
would leave the existing names in place as aliases.) That is, something
like:
```rust
pub struct NormOne<T>
where T: NormedVectorSpace { //... }
```
Utterly separately, the reason that I implemented `ShapeSample` for
`Triangle2d`/`Triangle3d` was to prototype uniform sampling of abstract
meshes, so that's also a future direction.
---------
Co-authored-by: Zachary Harrold <zac@harrold.com.au>
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