# 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>
# Objective
- Fixes#12570
## Solution
Previously, cardinal splines constructed by `CubicCardinalSpline` would
leave out their endpoints when constructing the cubic curve segments
connecting their points. (See the linked issue for details.)
Now, cardinal splines include the endpoints. For instance, the provided
usage example
```rust
let points = [
vec2(-1.0, -20.0),
vec2(3.0, 2.0),
vec2(5.0, 3.0),
vec2(9.0, 8.0),
];
let cardinal = CubicCardinalSpline::new(0.3, points).to_curve();
let positions: Vec<_> = cardinal.iter_positions(100).collect();
```
will actually produce a spline that connects all four of these points
instead of just the middle two "interior" points.
Internally, this is achieved by duplicating the endpoints of the vector
of control points before performing the construction of the associated
`CubicCurve`. This amounts to specifying that the tangents at the
endpoints `P_0` and `P_n` (say) should be parallel to `P_1 - P_0` and
`P_n - P_{n-1}`.
---
## Migration Guide
Any users relying on the old behavior of `CubicCardinalSpline` will have
to truncate any parametrizations they used in order to access a curve
identical to the one they had previously. This would be done by chopping
off a unit-distance segment from each end of the parametrizing interval.
For instance, if a user's existing code looks as follows
```rust
fn interpolate(t: f32) -> Vec2 {
let points = [
vec2(-1.0, -20.0),
vec2(3.0, 2.0),
vec2(5.0, 3.0),
vec2(9.0, 8.0),
];
let my_curve = CubicCardinalSpline::new(0.3, points).to_curve();
my_curve.position(t)
}
```
then in order to obtain similar behavior, `t` will need to be shifted up
by 1, since the output of `CubicCardinalSpline::to_curve` has introduced
a new segment in the interval [0,1], displacing the old segment from
[0,1] to [1,2]:
```rust
fn interpolate(t: f32) -> Vec2 {
let points = [
vec2(-1.0, -20.0),
vec2(3.0, 2.0),
vec2(5.0, 3.0),
vec2(9.0, 8.0),
];
let my_curve = CubicCardinalSpline::new(0.3, points).to_curve();
my_curve.position(t+1)
}
```
(Note that this does not provide identical output for values of `t`
outside of the interval [0,1].)
On the other hand, any user who was specifying additional endpoint
tangents simply to get the curve to pass through the right points (i.e.
not requiring exactly the same output) can simply omit the endpoints
that were being supplied only for control purposes.
---
## Discussion
### Design considerations
This is one of the two approaches outlined in #12570 — in this PR, we
are basically declaring that the docs are right and the implementation
was flawed.
One semi-interesting question is how the endpoint tangents actually
ought to be defined when we include them, and another option considered
was mirroring the control points adjacent to the endpoints instead of
duplicating them, which would have had the advantage that the expected
length of the corresponding difference should be more similar to that of
the other difference-tangents, provided that the points are equally
spaced.
In this PR, the duplication method (which produces smaller tangents) was
chosen for a couple reasons:
- It seems to be more standard
- It is exceptionally simple to implement
- I was a little concerned that the aforementioned alternative would
result in some over-extrapolation
### An annoyance
If you look at the code, you'll see I was unable to find a satisfactory
way of doing this without allocating a new vector. This doesn't seem
like a big problem given the context, but it does bother me. In
particular, if there is some easy parallel to `slice::windows` for
iterators that doesn't pull in an external dependency, I would love to
know about it.
# Objective
Improve the `bevy::math::cubic_splines` module by making it more
flexible and adding new curve types.
Closes#10220
## Solution
Added new spline types and improved existing
---
## Changelog
### Added
- `CubicNurbs` rational cubic curve generator, allows setting the knot
vector and weights associated with every point
- `LinearSpline` curve generator, allows generating a linearly
interpolated curve segment
- Ability to push additional cubic segments to `CubicCurve`
- `IntoIterator` and `Extend` implementations for `CubicCurve`
### Changed
- `Point` trait has been implemented for more types: `Quat` and `Vec4`.
- `CubicCurve::coefficients` was moved to `CubicSegment::coefficients`
because the function returns `CubicSegment`, so it seems logical to be
associated with `CubicSegment` instead. The method is still not public.
### Fixed
- `CubicBSpline::new` was referencing Cardinal spline instead of
B-Spline
---------
Co-authored-by: Alice Cecile <alice.i.cecile@gmail.com>
Co-authored-by: IQuick 143 <IQuick143cz@gmail.com>
Co-authored-by: Miles Silberling-Cook <nth.tensor@gmail.com>
Co-authored-by: Joona Aalto <jondolf.dev@gmail.com>
# Objective
- Implementing `Default` for
[`CubicCurve`](https://docs.rs/bevy/latest/bevy/math/cubic_splines/struct.CubicCurve.html)
does not make sense because it cannot be mutated after creation.
- Closes#11209.
- Alternative to #11211.
## Solution
- Remove `Default` from `CubicCurve`'s derive statement.
Based off of @mockersf comment
(https://github.com/bevyengine/bevy/pull/11211#issuecomment-1880088036):
> CubicCurve can't be updated once created... I would prefer to remove
the Default impl as it doesn't make sense
---
## Changelog
- Removed the `Default` implementation for `CubicCurve`.
## Migration Guide
- Remove `CubicCurve` from any structs that implement `Default`.
- Wrap `CubicCurve` in a new type and provide your own default.
```rust
#[derive(Deref)]
struct MyCubicCurve<P: Point>(pub CubicCurve<P>);
impl Default for MyCubicCurve<Vec2> {
fn default() -> Self {
let points = [[
vec2(-1.0, -20.0),
vec2(3.0, 2.0),
vec2(5.0, 3.0),
vec2(9.0, 8.0),
]];
Self(CubicBezier::new(points).to_curve())
}
}
```
# 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
[Rust 1.72.0](https://blog.rust-lang.org/2023/08/24/Rust-1.72.0.html) is
now stable.
# Notes
- `let-else` formatting has arrived!
- I chose to allow `explicit_iter_loop` due to
https://github.com/rust-lang/rust-clippy/issues/11074.
We didn't hit any of the false positives that prevent compilation, but
fixing this did produce a lot of the "symbol soup" mentioned, e.g. `for
image in &mut *image_events {`.
Happy to undo this if there's consensus the other way.
---------
Co-authored-by: François <mockersf@gmail.com>
## Objective
- Provide a way to use `CubicCurve` non-iter methods
- Accept a `FnMut` over a `fn` pointer on `iter_samples`
- Improve `build_*_cubic_100_points` benchmark by -45% (this means they
are twice as fast)
### Solution
Previously, the only way to iterate over an evenly spaced set of points
on a `CubicCurve` was to use one of the `iter_*` methods.
The return value of those methods were bound by `&self` lifetime, making
them unusable in certain contexts.
Furthermore, other `CubicCurve` methods (`position`, `velocity`,
`acceleration`) required normalizing `t` over the `CubicCurve`'s
internal segment count.
There were no way to access this segment count, making those methods
pretty much unusable.
The newly added `segment_count` allows accessing the segment count.
`iter_samples` used to accept a `fn`, a function pointer. This is
surprising and contrary to the rust stdlib APIs, which accept `Fn`
traits for `Iterator` combinators.
`iter_samples` now accepts a `FnMut`.
I don't trust a bit the bevy benchmark suit, but according to it, this
doubles (-45%) the performance on the `build_pos_cubic_100_points` and
`build_accel_cubic_100_points` benchmarks.
---
## Changelog
- Added the `CubicCurve::segments` method to access the underlying
segments of a cubic curve
- Allow closures as `CubicCurve::iter_samples` `sample_function`
argument.
# Objective
Fix `CubicCurve::iter_samples` iteration count.
## Solution
If I understand the function and the docs correctly, this should iterate
over `0..=subdivisions` instead of `0..subdivisions`.
For example: Now the iteration returns 3 points at `subdivisions = 2`,
as indicated in the documentation.
# 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.
