Merge branch 'main' into schema-types-metadata

benches/benches/bevy_math/bezier.rs

@@ -32,7 +32,7 @@ fn segment_ease(c: &mut Criterion) {
 
 fn curve_position(c: &mut Criterion) {
     /// A helper function that benchmarks calling [`CubicCurve::position()`] over a generic [`VectorSpace`].
-    fn bench_curve<M: Measurement, P: VectorSpace>(
+    fn bench_curve<M: Measurement, P: VectorSpace<Scalar = f32>>(
         group: &mut BenchmarkGroup<M>,
         name: &str,
         curve: CubicCurve<P>,

crates/bevy_animation/src/gltf_curves.rs

@@ -55,7 +55,7 @@ pub struct CubicKeyframeCurve<T> {
 
 impl<V> Curve<V> for CubicKeyframeCurve<V>
 where
-    V: VectorSpace,
+    V: VectorSpace<Scalar = f32>,
 {
     #[inline]
     fn domain(&self) -> Interval {
@@ -179,7 +179,7 @@ pub struct WideLinearKeyframeCurve<T> {
 
 impl<T> IterableCurve<T> for WideLinearKeyframeCurve<T>
 where
-    T: VectorSpace,
+    T: VectorSpace<Scalar = f32>,
 {
     #[inline]
     fn domain(&self) -> Interval {
@@ -289,7 +289,7 @@ pub struct WideCubicKeyframeCurve<T> {
 
 impl<T> IterableCurve<T> for WideCubicKeyframeCurve<T>
 where
-    T: VectorSpace,
+    T: VectorSpace<Scalar = f32>,
 {
     #[inline]
     fn domain(&self) -> Interval {
@@ -406,7 +406,7 @@ fn cubic_spline_interpolation<T>(
     step_duration: f32,
 ) -> T
 where
-    T: VectorSpace,
+    T: VectorSpace<Scalar = f32>,
 {
     let coeffs = (vec4(2.0, 1.0, -2.0, 1.0) * lerp + vec4(-3.0, -2.0, 3.0, -1.0)) * lerp;
     value_start * (coeffs.x * lerp + 1.0)
@@ -415,7 +415,7 @@ where
         + tangent_in_end * step_duration * lerp * coeffs.w
 }
 
-fn cubic_spline_interpolate_slices<'a, T: VectorSpace>(
+fn cubic_spline_interpolate_slices<'a, T: VectorSpace<Scalar = f32>>(
     width: usize,
     first: &'a [T],
     second: &'a [T],

crates/bevy_color/src/lib.rs

@@ -262,6 +262,7 @@ macro_rules! impl_componentwise_vector_space {
         }
 
         impl bevy_math::VectorSpace for $ty {
+            type Scalar = f32;
             const ZERO: Self = Self {
                 $($element: 0.0,)+
             };

crates/bevy_ecs/src/entity/map_entities.rs

@@ -358,7 +358,10 @@ mod tests {
         // Next allocated entity should be a further generation on the same index
         let entity = world.spawn_empty().id();
         assert_eq!(entity.index(), dead_ref.index());
-        assert!(entity.generation() > dead_ref.generation());
+        assert!(entity
+            .generation()
+            .cmp_approx(&dead_ref.generation())
+            .is_gt());
     }
 
     #[test]
@@ -373,7 +376,10 @@ mod tests {
         // Next allocated entity should be a further generation on the same index
         let entity = world.spawn_empty().id();
         assert_eq!(entity.index(), dead_ref.index());
-        assert!(entity.generation() > dead_ref.generation());
+        assert!(entity
+            .generation()
+            .cmp_approx(&dead_ref.generation())
+            .is_gt());
     }
 
     #[test]

crates/bevy_ecs/src/entity/mod.rs

@@ -185,29 +185,6 @@ impl SparseSetIndex for EntityRow {
 ///
 /// This should be treated as a opaque identifier, and its internal representation may be subject to change.
 ///
-/// # Ordering
-///
-/// [`EntityGeneration`] implements [`Ord`].
-/// Generations that are later will be [`Greater`](core::cmp::Ordering::Greater) than earlier ones.
-///
-/// ```
-/// # use bevy_ecs::entity::EntityGeneration;
-/// assert!(EntityGeneration::FIRST < EntityGeneration::FIRST.after_versions(400));
-/// let (aliased, did_alias) = EntityGeneration::FIRST.after_versions(400).after_versions_and_could_alias(u32::MAX);
-/// assert!(did_alias);
-/// assert!(EntityGeneration::FIRST < aliased);
-/// ```
-///
-/// Ordering will be incorrect for distant generations:
-///
-/// ```
-/// # use bevy_ecs::entity::EntityGeneration;
-/// // This ordering is wrong!
-/// assert!(EntityGeneration::FIRST > EntityGeneration::FIRST.after_versions(400 + (1u32 << 31)));
-/// ```
-///
-/// This strange behavior needed to account for aliasing.
-///
 /// # Aliasing
 ///
 /// Internally [`EntityGeneration`] wraps a `u32`, so it can't represent *every* possible generation.
@@ -235,6 +212,9 @@ impl EntityGeneration {
     /// Represents the first generation of an [`EntityRow`].
     pub const FIRST: Self = Self(0);
 
+    /// Non-wrapping difference between two generations after which a signed interpretation becomes negative.
+    const DIFF_MAX: u32 = 1u32 << 31;
+
     /// Gets some bits that represent this value.
     /// The bits are opaque and should not be regarded as meaningful.
     #[inline(always)]
@@ -266,18 +246,48 @@ impl EntityGeneration {
         let raw = self.0.overflowing_add(versions);
         (Self(raw.0), raw.1)
     }
-}
 
-impl PartialOrd for EntityGeneration {
+    /// Compares two generations.
-    fn partial_cmp(&self, other: &Self) -> Option<core::cmp::Ordering> {
+    ///
-        Some(self.cmp(other))
+    /// Generations that are later will be [`Greater`](core::cmp::Ordering::Greater) than earlier ones.
-    }
+    ///
-}
+    /// ```
-
+    /// # use bevy_ecs::entity::EntityGeneration;
-impl Ord for EntityGeneration {
+    /// # use core::cmp::Ordering;
-    fn cmp(&self, other: &Self) -> core::cmp::Ordering {
+    /// let later_generation = EntityGeneration::FIRST.after_versions(400);
-        let diff = self.0.wrapping_sub(other.0);
+    /// assert_eq!(EntityGeneration::FIRST.cmp_approx(&later_generation), Ordering::Less);
-        (1u32 << 31).cmp(&diff)
+    ///
+    /// let (aliased, did_alias) = EntityGeneration::FIRST.after_versions(400).after_versions_and_could_alias(u32::MAX);
+    /// assert!(did_alias);
+    /// assert_eq!(EntityGeneration::FIRST.cmp_approx(&aliased), Ordering::Less);
+    /// ```
+    ///
+    /// Ordering will be incorrect and [non-transitive](https://en.wikipedia.org/wiki/Transitive_relation)
+    /// for distant generations:
+    ///
+    /// ```should_panic
+    /// # use bevy_ecs::entity::EntityGeneration;
+    /// # use core::cmp::Ordering;
+    /// let later_generation = EntityGeneration::FIRST.after_versions(3u32 << 31);
+    /// let much_later_generation = later_generation.after_versions(3u32 << 31);
+    ///
+    /// // while these orderings are correct and pass assertions...
+    /// assert_eq!(EntityGeneration::FIRST.cmp_approx(&later_generation), Ordering::Less);
+    /// assert_eq!(later_generation.cmp_approx(&much_later_generation), Ordering::Less);
+    ///
+    /// // ... this ordering is not and the assertion fails!
+    /// assert_eq!(EntityGeneration::FIRST.cmp_approx(&much_later_generation), Ordering::Less);
+    /// ```
+    ///
+    /// Because of this, `EntityGeneration` does not implement `Ord`/`PartialOrd`.
+    #[inline]
+    pub const fn cmp_approx(&self, other: &Self) -> core::cmp::Ordering {
+        use core::cmp::Ordering;
+        match self.0.wrapping_sub(other.0) {
+            0 => Ordering::Equal,
+            1..Self::DIFF_MAX => Ordering::Greater,
+            _ => Ordering::Less,
+        }
     }
 }
 
@@ -1422,7 +1432,10 @@ mod tests {
         // The very next entity allocated should be a further generation on the same index
         let next_entity = entities.alloc();
         assert_eq!(next_entity.index(), entity.index());
-        assert!(next_entity.generation() > entity.generation().after_versions(GENERATIONS));
+        assert!(next_entity
+            .generation()
+            .cmp_approx(&entity.generation().after_versions(GENERATIONS))
+            .is_gt());
     }
 
     #[test]
@@ -1609,6 +1622,24 @@ mod tests {
         }
     }
 
+    #[test]
+    fn entity_generation_is_approximately_ordered() {
+        use core::cmp::Ordering;
+
+        let old = EntityGeneration::FIRST;
+        let middle = old.after_versions(1);
+        let younger_before_ord_wrap = middle.after_versions(EntityGeneration::DIFF_MAX);
+        let younger_after_ord_wrap = younger_before_ord_wrap.after_versions(1);
+
+        assert_eq!(middle.cmp_approx(&old), Ordering::Greater);
+        assert_eq!(middle.cmp_approx(&middle), Ordering::Equal);
+        assert_eq!(middle.cmp_approx(&younger_before_ord_wrap), Ordering::Less);
+        assert_eq!(
+            middle.cmp_approx(&younger_after_ord_wrap),
+            Ordering::Greater
+        );
+    }
+
     #[test]
     fn entity_debug() {
         let entity = Entity::from_raw(EntityRow::new(NonMaxU32::new(42).unwrap()));

crates/bevy_math/src/common_traits.rs

@@ -1,6 +1,6 @@
 //! This module contains abstract mathematical traits shared by types used in `bevy_math`.
 
-use crate::{ops, Dir2, Dir3, Dir3A, Quat, Rot2, Vec2, Vec3, Vec3A, Vec4};
+use crate::{ops, DVec2, DVec3, DVec4, Dir2, Dir3, Dir3A, Quat, Rot2, Vec2, Vec3, Vec3A, Vec4};
 use core::{
     fmt::Debug,
     ops::{Add, Div, Mul, Neg, Sub},
@@ -9,7 +9,7 @@ use variadics_please::all_tuples_enumerated;
 
 /// 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`
+/// - Scalar multiplication and division on the right by elements of `Self::Scalar`
 /// - Negation
 /// - Addition and subtraction
 /// - Zero
@@ -19,16 +19,16 @@ use variadics_please::all_tuples_enumerated;
 /// - (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`.
+/// - (Compatibility of multiplication) For all `a, b: Self::Scalar`, `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 vector addition) For all `a: Self::Scalar`, `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`.
+/// - (Distributivity for scalar addition) For all `a, b: Self::Scalar`, `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>
+    Mul<Self::Scalar, Output = Self>
-    + Div<f32, Output = Self>
+    + Div<Self::Scalar, Output = Self>
     + Add<Self, Output = Self>
     + Sub<Self, Output = Self>
     + Neg<Output = Self>
@@ -37,6 +37,9 @@ pub trait VectorSpace:
     + Clone
     + Copy
 {
+    /// The scalar type of this vector space.
+    type Scalar: ScalarField;
+
     /// The zero vector, which is the identity of addition for the vector space type.
     const ZERO: Self;
 
@@ -47,29 +50,99 @@ pub trait VectorSpace:
     /// Note that the value of `t` is not clamped by this function, so extrapolating outside
     /// of the interval `[0,1]` is allowed.
     #[inline]
-    fn lerp(self, rhs: Self, t: f32) -> Self {
+    fn lerp(self, rhs: Self, t: Self::Scalar) -> Self {
-        self * (1. - t) + rhs * t
+        self * (Self::Scalar::ONE - t) + rhs * t
     }
 }
 
 impl VectorSpace for Vec4 {
+    type Scalar = f32;
     const ZERO: Self = Vec4::ZERO;
 }
 
 impl VectorSpace for Vec3 {
+    type Scalar = f32;
     const ZERO: Self = Vec3::ZERO;
 }
 
 impl VectorSpace for Vec3A {
+    type Scalar = f32;
     const ZERO: Self = Vec3A::ZERO;
 }
 
 impl VectorSpace for Vec2 {
+    type Scalar = f32;
     const ZERO: Self = Vec2::ZERO;
 }
 
-impl VectorSpace for f32 {
+impl VectorSpace for DVec4 {
+    type Scalar = f64;
+    const ZERO: Self = DVec4::ZERO;
+}
+
+impl VectorSpace for DVec3 {
+    type Scalar = f64;
+    const ZERO: Self = DVec3::ZERO;
+}
+
+impl VectorSpace for DVec2 {
+    type Scalar = f64;
+    const ZERO: Self = DVec2::ZERO;
+}
+
+// Every scalar field is a 1-dimensional vector space over itself.
+impl<T: ScalarField> VectorSpace for T {
+    type Scalar = Self;
+    const ZERO: Self = Self::ZERO;
+}
+
+/// A type that supports the operations of a scalar field. An implementation should support:
+/// - Addition and subtraction
+/// - Multiplication and division
+/// - Negation
+/// - Zero (additive identity)
+/// - One (multiplicative identity)
+///
+/// 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`.
+/// - (Associativity of multiplication) For all `u, v, w: Self`, `(u * v) * w == u * (v * w)`.
+/// - (Commutativity of multiplication) For all `u, v: Self`, `u * v == v * u`.
+/// - (Multiplicative identity) For all `v: Self`, `v * Self::ONE == v`.
+/// - (Multiplicative inverse) For all `v: Self`, `v / v == v * v.inverse() == Self::ONE`.
+/// - (Distributivity over addition) For all `a, b: Self`, `u, v: Self`, `(u + v) * a == u * a + v * a`.
+pub trait ScalarField:
+    Mul<Self, Output = Self>
+    + Div<Self, Output = Self>
+    + Add<Self, Output = Self>
+    + Sub<Self, Output = Self>
+    + Neg<Output = Self>
+    + Default
+    + Debug
+    + Clone
+    + Copy
+{
+    /// The additive identity.
+    const ZERO: Self;
+    /// The multiplicative identity.
+    const ONE: Self;
+
+    /// The multiplicative inverse of this element. This is equivalent to `1.0 / self`.
+    fn recip(self) -> Self {
+        Self::ONE / self
+    }
+}
+
+impl ScalarField for f32 {
     const ZERO: Self = 0.0;
+    const ONE: Self = 1.0;
+}
+
+impl ScalarField for f64 {
+    const ZERO: Self = 0.0;
+    const ONE: Self = 1.0;
 }
 
 /// A type consisting of formal sums of elements from `V` and `W`. That is,
@@ -84,24 +157,24 @@ impl VectorSpace for f32 {
 #[cfg_attr(feature = "bevy_reflect", derive(bevy_reflect::Reflect))]
 pub struct Sum<V, W>(pub V, pub W);
 
-impl<V, W> Mul<f32> for Sum<V, W>
+impl<F: ScalarField, V, W> Mul<F> for Sum<V, W>
 where
-    V: VectorSpace,
+    V: VectorSpace<Scalar = F>,
-    W: VectorSpace,
+    W: VectorSpace<Scalar = F>,
 {
     type Output = Self;
-    fn mul(self, rhs: f32) -> Self::Output {
+    fn mul(self, rhs: F) -> Self::Output {
         Sum(self.0 * rhs, self.1 * rhs)
     }
 }
 
-impl<V, W> Div<f32> for Sum<V, W>
+impl<F: ScalarField, V, W> Div<F> for Sum<V, W>
 where
-    V: VectorSpace,
+    V: VectorSpace<Scalar = F>,
-    W: VectorSpace,
+    W: VectorSpace<Scalar = F>,
 {
     type Output = Self;
-    fn div(self, rhs: f32) -> Self::Output {
+    fn div(self, rhs: F) -> Self::Output {
         Sum(self.0 / rhs, self.1 / rhs)
     }
 }
@@ -149,11 +222,12 @@ where
     }
 }
 
-impl<V, W> VectorSpace for Sum<V, W>
+impl<F: ScalarField, V, W> VectorSpace for Sum<V, W>
 where
-    V: VectorSpace,
+    V: VectorSpace<Scalar = F>,
-    W: VectorSpace,
+    W: VectorSpace<Scalar = F>,
 {
+    type Scalar = F;
     const ZERO: Self = Sum(V::ZERO, W::ZERO);
 }
 
@@ -162,32 +236,32 @@ where
 /// 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()`.
+/// - (Absolute homogeneity) For all `c: Self::Scalar`, `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;
+    fn norm(self) -> Self::Scalar;
 
     /// The squared norm of this element. Computing this is often faster than computing
     /// [`NormedVectorSpace::norm`].
     #[inline]
-    fn norm_squared(self) -> f32 {
+    fn norm_squared(self) -> Self::Scalar {
         self.norm() * self.norm()
     }
 
     /// The distance between this element and another, as determined by the norm.
     #[inline]
-    fn distance(self, rhs: Self) -> f32 {
+    fn distance(self, rhs: Self) -> Self::Scalar {
         (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 {
+    fn distance_squared(self, rhs: Self) -> Self::Scalar {
         (rhs - self).norm_squared()
     }
 }
@@ -245,10 +319,55 @@ impl NormedVectorSpace for f32 {
     fn norm(self) -> f32 {
         ops::abs(self)
     }
+}
+
+impl NormedVectorSpace for DVec4 {
+    #[inline]
+    fn norm(self) -> f64 {
+        self.length()
+    }
 
     #[inline]
-    fn norm_squared(self) -> f32 {
+    fn norm_squared(self) -> f64 {
-        self * self
+        self.length_squared()
+    }
+}
+
+impl NormedVectorSpace for DVec3 {
+    #[inline]
+    fn norm(self) -> f64 {
+        self.length()
+    }
+
+    #[inline]
+    fn norm_squared(self) -> f64 {
+        self.length_squared()
+    }
+}
+
+impl NormedVectorSpace for DVec2 {
+    #[inline]
+    fn norm(self) -> f64 {
+        self.length()
+    }
+
+    #[inline]
+    fn norm_squared(self) -> f64 {
+        self.length_squared()
+    }
+}
+
+impl NormedVectorSpace for f64 {
+    #[inline]
+    #[cfg(feature = "std")]
+    fn norm(self) -> f64 {
+        f64::abs(self)
+    }
+
+    #[inline]
+    #[cfg(all(any(feature = "libm", feature = "nostd-libm"), not(feature = "std")))]
+    fn norm(self) -> f64 {
+        libm::fabs(self)
     }
 }
 
@@ -353,7 +472,7 @@ pub trait StableInterpolate: Clone {
 // VectorSpace type, but the "natural from the semantics" part is less clear in general.
 impl<V> StableInterpolate for V
 where
-    V: NormedVectorSpace,
+    V: NormedVectorSpace<Scalar = f32>,
 {
     #[inline]
     fn interpolate_stable(&self, other: &Self, t: f32) -> Self {
@@ -462,10 +581,13 @@ impl<V: VectorSpace> HasTangent for V {
     type Tangent = V;
 }
 
-impl<M, N> HasTangent for (M, N)
+impl<F, U, V, M, N> HasTangent for (M, N)
 where
-    M: HasTangent,
+    F: ScalarField,
-    N: HasTangent,
+    U: VectorSpace<Scalar = F>,
+    V: VectorSpace<Scalar = F>,
+    M: HasTangent<Tangent = U>,
+    N: HasTangent<Tangent = V>,
 {
     type Tangent = Sum<M::Tangent, N::Tangent>;
 }

crates/bevy_math/src/cubic_splines/curve_impls.rs

@@ -10,7 +10,7 @@ use super::{CubicCurve, RationalCurve};
 
 // -- CubicSegment
 
-impl<P: VectorSpace> Curve<P> for CubicSegment<P> {
+impl<P: VectorSpace<Scalar = f32>> Curve<P> for CubicSegment<P> {
     #[inline]
     fn domain(&self) -> Interval {
         Interval::UNIT
@@ -22,7 +22,7 @@ impl<P: VectorSpace> Curve<P> for CubicSegment<P> {
     }
 }
 
-impl<P: VectorSpace> SampleDerivative<P> for CubicSegment<P> {
+impl<P: VectorSpace<Scalar = f32>> SampleDerivative<P> for CubicSegment<P> {
     #[inline]
     fn sample_with_derivative_unchecked(&self, t: f32) -> WithDerivative<P> {
         WithDerivative {
@@ -32,7 +32,7 @@ impl<P: VectorSpace> SampleDerivative<P> for CubicSegment<P> {
     }
 }
 
-impl<P: VectorSpace> SampleTwoDerivatives<P> for CubicSegment<P> {
+impl<P: VectorSpace<Scalar = f32>> SampleTwoDerivatives<P> for CubicSegment<P> {
     #[inline]
     fn sample_with_two_derivatives_unchecked(&self, t: f32) -> WithTwoDerivatives<P> {
         WithTwoDerivatives {
@@ -46,7 +46,7 @@ impl<P: VectorSpace> SampleTwoDerivatives<P> for CubicSegment<P> {
 // -- CubicCurve
 
 #[cfg(feature = "alloc")]
-impl<P: VectorSpace> Curve<P> for CubicCurve<P> {
+impl<P: VectorSpace<Scalar = f32>> Curve<P> for CubicCurve<P> {
     #[inline]
     fn domain(&self) -> Interval {
         // The non-emptiness invariant guarantees that this succeeds.
@@ -61,7 +61,7 @@ impl<P: VectorSpace> Curve<P> for CubicCurve<P> {
 }
 
 #[cfg(feature = "alloc")]
-impl<P: VectorSpace> SampleDerivative<P> for CubicCurve<P> {
+impl<P: VectorSpace<Scalar = f32>> SampleDerivative<P> for CubicCurve<P> {
     #[inline]
     fn sample_with_derivative_unchecked(&self, t: f32) -> WithDerivative<P> {
         WithDerivative {
@@ -72,7 +72,7 @@ impl<P: VectorSpace> SampleDerivative<P> for CubicCurve<P> {
 }
 
 #[cfg(feature = "alloc")]
-impl<P: VectorSpace> SampleTwoDerivatives<P> for CubicCurve<P> {
+impl<P: VectorSpace<Scalar = f32>> SampleTwoDerivatives<P> for CubicCurve<P> {
     #[inline]
     fn sample_with_two_derivatives_unchecked(&self, t: f32) -> WithTwoDerivatives<P> {
         WithTwoDerivatives {
@@ -85,7 +85,7 @@ impl<P: VectorSpace> SampleTwoDerivatives<P> for CubicCurve<P> {
 
 // -- RationalSegment
 
-impl<P: VectorSpace> Curve<P> for RationalSegment<P> {
+impl<P: VectorSpace<Scalar = f32>> Curve<P> for RationalSegment<P> {
     #[inline]
     fn domain(&self) -> Interval {
         Interval::UNIT
@@ -97,7 +97,7 @@ impl<P: VectorSpace> Curve<P> for RationalSegment<P> {
     }
 }
 
-impl<P: VectorSpace> SampleDerivative<P> for RationalSegment<P> {
+impl<P: VectorSpace<Scalar = f32>> SampleDerivative<P> for RationalSegment<P> {
     #[inline]
     fn sample_with_derivative_unchecked(&self, t: f32) -> WithDerivative<P> {
         WithDerivative {
@@ -107,7 +107,7 @@ impl<P: VectorSpace> SampleDerivative<P> for RationalSegment<P> {
     }
 }
 
-impl<P: VectorSpace> SampleTwoDerivatives<P> for RationalSegment<P> {
+impl<P: VectorSpace<Scalar = f32>> SampleTwoDerivatives<P> for RationalSegment<P> {
     #[inline]
     fn sample_with_two_derivatives_unchecked(&self, t: f32) -> WithTwoDerivatives<P> {
         WithTwoDerivatives {
@@ -121,7 +121,7 @@ impl<P: VectorSpace> SampleTwoDerivatives<P> for RationalSegment<P> {
 // -- RationalCurve
 
 #[cfg(feature = "alloc")]
-impl<P: VectorSpace> Curve<P> for RationalCurve<P> {
+impl<P: VectorSpace<Scalar = f32>> Curve<P> for RationalCurve<P> {
     #[inline]
     fn domain(&self) -> Interval {
         // The non-emptiness invariant guarantees the success of this.
@@ -136,7 +136,7 @@ impl<P: VectorSpace> Curve<P> for RationalCurve<P> {
 }
 
 #[cfg(feature = "alloc")]
-impl<P: VectorSpace> SampleDerivative<P> for RationalCurve<P> {
+impl<P: VectorSpace<Scalar = f32>> SampleDerivative<P> for RationalCurve<P> {
     #[inline]
     fn sample_with_derivative_unchecked(&self, t: f32) -> WithDerivative<P> {
         WithDerivative {
@@ -147,7 +147,7 @@ impl<P: VectorSpace> SampleDerivative<P> for RationalCurve<P> {
 }
 
 #[cfg(feature = "alloc")]
-impl<P: VectorSpace> SampleTwoDerivatives<P> for RationalCurve<P> {
+impl<P: VectorSpace<Scalar = f32>> SampleTwoDerivatives<P> for RationalCurve<P> {
     #[inline]
     fn sample_with_two_derivatives_unchecked(&self, t: f32) -> WithTwoDerivatives<P> {
         WithTwoDerivatives {

crates/bevy_math/src/cubic_splines/mod.rs

@@ -68,7 +68,7 @@ impl<P: VectorSpace> CubicBezier<P> {
 }
 
 #[cfg(feature = "alloc")]
-impl<P: VectorSpace> CubicGenerator<P> for CubicBezier<P> {
+impl<P: VectorSpace<Scalar = f32>> CubicGenerator<P> for CubicBezier<P> {
     type Error = CubicBezierError;
 
     #[inline]
@@ -176,7 +176,7 @@ impl<P: VectorSpace> CubicHermite<P> {
 }
 
 #[cfg(feature = "alloc")]
-impl<P: VectorSpace> CubicGenerator<P> for CubicHermite<P> {
+impl<P: VectorSpace<Scalar = f32>> CubicGenerator<P> for CubicHermite<P> {
     type Error = InsufficientDataError;
 
     #[inline]
@@ -202,7 +202,7 @@ impl<P: VectorSpace> CubicGenerator<P> for CubicHermite<P> {
 }
 
 #[cfg(feature = "alloc")]
-impl<P: VectorSpace> CyclicCubicGenerator<P> for CubicHermite<P> {
+impl<P: VectorSpace<Scalar = f32>> CyclicCubicGenerator<P> for CubicHermite<P> {
     type Error = InsufficientDataError;
 
     #[inline]
@@ -313,7 +313,7 @@ impl<P: VectorSpace> CubicCardinalSpline<P> {
 }
 
 #[cfg(feature = "alloc")]
-impl<P: VectorSpace> CubicGenerator<P> for CubicCardinalSpline<P> {
+impl<P: VectorSpace<Scalar = f32>> CubicGenerator<P> for CubicCardinalSpline<P> {
     type Error = InsufficientDataError;
 
     #[inline]
@@ -351,7 +351,7 @@ impl<P: VectorSpace> CubicGenerator<P> for CubicCardinalSpline<P> {
 }
 
 #[cfg(feature = "alloc")]
-impl<P: VectorSpace> CyclicCubicGenerator<P> for CubicCardinalSpline<P> {
+impl<P: VectorSpace<Scalar = f32>> CyclicCubicGenerator<P> for CubicCardinalSpline<P> {
     type Error = InsufficientDataError;
 
     #[inline]
@@ -471,7 +471,7 @@ impl<P: VectorSpace> CubicBSpline<P> {
 }
 
 #[cfg(feature = "alloc")]
-impl<P: VectorSpace> CubicGenerator<P> for CubicBSpline<P> {
+impl<P: VectorSpace<Scalar = f32>> CubicGenerator<P> for CubicBSpline<P> {
     type Error = InsufficientDataError;
 
     #[inline]
@@ -494,7 +494,7 @@ impl<P: VectorSpace> CubicGenerator<P> for CubicBSpline<P> {
 }
 
 #[cfg(feature = "alloc")]
-impl<P: VectorSpace> CyclicCubicGenerator<P> for CubicBSpline<P> {
+impl<P: VectorSpace<Scalar = f32>> CyclicCubicGenerator<P> for CubicBSpline<P> {
     type Error = InsufficientDataError;
 
     #[inline]
@@ -620,7 +620,7 @@ pub struct CubicNurbs<P: VectorSpace> {
 }
 
 #[cfg(feature = "alloc")]
-impl<P: VectorSpace> CubicNurbs<P> {
+impl<P: VectorSpace<Scalar = f32>> CubicNurbs<P> {
     /// Build a Non-Uniform Rational B-Spline.
     ///
     /// If provided, weights must be the same length as the control points. Defaults to equal weights.
@@ -781,7 +781,7 @@ impl<P: VectorSpace> CubicNurbs<P> {
 }
 
 #[cfg(feature = "alloc")]
-impl<P: VectorSpace> RationalGenerator<P> for CubicNurbs<P> {
+impl<P: VectorSpace<Scalar = f32>> RationalGenerator<P> for CubicNurbs<P> {
     type Error = InsufficientDataError;
 
     #[inline]
@@ -962,7 +962,7 @@ pub struct CubicSegment<P: VectorSpace> {
     pub coeff: [P; 4],
 }
 
-impl<P: VectorSpace> CubicSegment<P> {
+impl<P: VectorSpace<Scalar = f32>> CubicSegment<P> {
     /// Instantaneous position of a point at parametric value `t`.
     #[inline]
     pub fn position(&self, t: f32) -> P {
@@ -1184,7 +1184,7 @@ pub struct CubicCurve<P: VectorSpace> {
 }
 
 #[cfg(feature = "alloc")]
-impl<P: VectorSpace> CubicCurve<P> {
+impl<P: VectorSpace<Scalar = f32>> CubicCurve<P> {
     /// Create a new curve from a collection of segments. If the collection of segments is empty,
     /// a curve cannot be built and `None` will be returned instead.
     pub fn from_segments(segments: impl IntoIterator<Item = CubicSegment<P>>) -> Option<Self> {
@@ -1347,7 +1347,7 @@ pub struct RationalSegment<P: VectorSpace> {
     /// The width of the domain of this segment.
     pub knot_span: f32,
 }
-impl<P: VectorSpace> RationalSegment<P> {
+impl<P: VectorSpace<Scalar = f32>> RationalSegment<P> {
     /// Instantaneous position of a point at parametric value `t` in `[0, 1]`.
     #[inline]
     pub fn position(&self, t: f32) -> P {
@@ -1484,7 +1484,7 @@ pub struct RationalCurve<P: VectorSpace> {
 }
 
 #[cfg(feature = "alloc")]
-impl<P: VectorSpace> RationalCurve<P> {
+impl<P: VectorSpace<Scalar = f32>> RationalCurve<P> {
     /// Create a new curve from a collection of segments. If the collection of segments is empty,
     /// a curve cannot be built and `None` will be returned instead.
     pub fn from_segments(segments: impl IntoIterator<Item = RationalSegment<P>>) -> Option<Self> {

crates/bevy_math/src/curve/derivatives/adaptor_impls.rs

@@ -208,10 +208,12 @@ where
 
 // -- ZipCurve
 
-impl<S, T, C, D> SampleDerivative<(S, T)> for ZipCurve<S, T, C, D>
+impl<U, V, S, T, C, D> SampleDerivative<(S, T)> for ZipCurve<S, T, C, D>
 where
-    S: HasTangent,
+    U: VectorSpace<Scalar = f32>,
-    T: HasTangent,
+    V: VectorSpace<Scalar = f32>,
+    S: HasTangent<Tangent = U>,
+    T: HasTangent<Tangent = V>,
     C: SampleDerivative<S>,
     D: SampleDerivative<T>,
 {
@@ -225,10 +227,12 @@ where
     }
 }
 
-impl<S, T, C, D> SampleTwoDerivatives<(S, T)> for ZipCurve<S, T, C, D>
+impl<U, V, S, T, C, D> SampleTwoDerivatives<(S, T)> for ZipCurve<S, T, C, D>
 where
-    S: HasTangent,
+    U: VectorSpace<Scalar = f32>,
-    T: HasTangent,
+    V: VectorSpace<Scalar = f32>,
+    S: HasTangent<Tangent = U>,
+    T: HasTangent<Tangent = V>,
     C: SampleTwoDerivatives<S>,
     D: SampleTwoDerivatives<T>,
 {
@@ -248,9 +252,10 @@ where
 
 // -- GraphCurve
 
-impl<T, C> SampleDerivative<(f32, T)> for GraphCurve<T, C>
+impl<V, T, C> SampleDerivative<(f32, T)> for GraphCurve<T, C>
 where
-    T: HasTangent,
+    V: VectorSpace<Scalar = f32>,
+    T: HasTangent<Tangent = V>,
     C: SampleDerivative<T>,
 {
     fn sample_with_derivative_unchecked(&self, t: f32) -> WithDerivative<(f32, T)> {
@@ -262,9 +267,10 @@ where
     }
 }
 
-impl<T, C> SampleTwoDerivatives<(f32, T)> for GraphCurve<T, C>
+impl<V, T, C> SampleTwoDerivatives<(f32, T)> for GraphCurve<T, C>
 where
-    T: HasTangent,
+    V: VectorSpace<Scalar = f32>,
+    T: HasTangent<Tangent = V>,
     C: SampleTwoDerivatives<T>,
 {
     fn sample_with_two_derivatives_unchecked(&self, t: f32) -> WithTwoDerivatives<(f32, T)> {
@@ -321,9 +327,10 @@ where
 
 // -- CurveReparamCurve
 
-impl<T, C, D> SampleDerivative<T> for CurveReparamCurve<T, C, D>
+impl<V, T, C, D> SampleDerivative<T> for CurveReparamCurve<T, C, D>
 where
-    T: HasTangent,
+    V: VectorSpace<Scalar = f32>,
+    T: HasTangent<Tangent = V>,
     C: SampleDerivative<T>,
     D: SampleDerivative<f32>,
 {
@@ -349,9 +356,10 @@ where
     }
 }
 
-impl<T, C, D> SampleTwoDerivatives<T> for CurveReparamCurve<T, C, D>
+impl<V, T, C, D> SampleTwoDerivatives<T> for CurveReparamCurve<T, C, D>
 where
-    T: HasTangent,
+    V: VectorSpace<Scalar = f32>,
+    T: HasTangent<Tangent = V>,
     C: SampleTwoDerivatives<T>,
     D: SampleTwoDerivatives<f32>,
 {
@@ -386,9 +394,10 @@ where
 
 // -- LinearReparamCurve
 
-impl<T, C> SampleDerivative<T> for LinearReparamCurve<T, C>
+impl<V, T, C> SampleDerivative<T> for LinearReparamCurve<T, C>
 where
-    T: HasTangent,
+    V: VectorSpace<Scalar = f32>,
+    T: HasTangent<Tangent = V>,
     C: SampleDerivative<T>,
 {
     fn sample_with_derivative_unchecked(&self, t: f32) -> WithDerivative<T> {
@@ -413,9 +422,10 @@ where
     }
 }
 
-impl<T, C> SampleTwoDerivatives<T> for LinearReparamCurve<T, C>
+impl<V, T, C> SampleTwoDerivatives<T> for LinearReparamCurve<T, C>
 where
-    T: HasTangent,
+    V: VectorSpace<Scalar = f32>,
+    T: HasTangent<Tangent = V>,
     C: SampleTwoDerivatives<T>,
 {
     fn sample_with_two_derivatives_unchecked(&self, t: f32) -> WithTwoDerivatives<T> {

crates/bevy_math/src/curve/easing.rs

@@ -32,7 +32,7 @@ pub trait Ease: Sized {
     fn interpolating_curve_unbounded(start: Self, end: Self) -> impl Curve<Self>;
 }
 
-impl<V: VectorSpace> Ease for V {
+impl<V: VectorSpace<Scalar = f32>> Ease for V {
     fn interpolating_curve_unbounded(start: Self, end: Self) -> impl Curve<Self> {
         FunctionCurve::new(Interval::EVERYWHERE, move |t| V::lerp(start, end, t))
     }

crates/bevy_math/src/sampling/shape_sampling.rs

@@ -40,11 +40,12 @@
 
 use core::f32::consts::{PI, TAU};
 
-use crate::{ops, primitives::*, NormedVectorSpace, Vec2, Vec3};
+use crate::{ops, primitives::*, NormedVectorSpace, ScalarField, Vec2, Vec3};
 use rand::{
     distributions::{Distribution, WeightedIndex},
     Rng,
 };
+use rand_distr::uniform::SampleUniform;
 
 /// Exposes methods to uniformly sample a variety of primitive shapes.
 pub trait ShapeSample {
@@ -281,22 +282,24 @@ impl ShapeSample for Cuboid {
 }
 
 /// Interior sampling for triangles which doesn't depend on the ambient dimension.
-fn sample_triangle_interior<P: NormedVectorSpace, R: Rng + ?Sized>(
+fn sample_triangle_interior<P, R>(vertices: [P; 3], rng: &mut R) -> P
-    vertices: [P; 3],
+where
-    rng: &mut R,
+    P: NormedVectorSpace,
-) -> P {
+    P::Scalar: SampleUniform + PartialOrd,
+    R: Rng + ?Sized,
+{
     let [a, b, c] = vertices;
     let ab = b - a;
     let ac = c - a;
 
     // Generate random points on a parallelepiped and reflect so that
     // we can use the points that lie outside the triangle
-    let u = rng.gen_range(0.0..=1.0);
+    let u = rng.gen_range(P::Scalar::ZERO..=P::Scalar::ONE);
-    let v = rng.gen_range(0.0..=1.0);
+    let v = rng.gen_range(P::Scalar::ZERO..=P::Scalar::ONE);
 
-    if u + v > 1. {
+    if u + v > P::Scalar::ONE {
-        let u1 = 1. - v;
+        let u1 = P::Scalar::ONE - v;
-        let v1 = 1. - u;
+        let v1 = P::Scalar::ONE - u;
         a + (ab * u1 + ac * v1)
     } else {
         a + (ab * u + ac * v)
@@ -304,16 +307,18 @@ fn sample_triangle_interior<P: NormedVectorSpace, R: Rng + ?Sized>(
 }
 
 /// Boundary sampling for triangles which doesn't depend on the ambient dimension.
-fn sample_triangle_boundary<P: NormedVectorSpace, R: Rng + ?Sized>(
+fn sample_triangle_boundary<P, R>(vertices: [P; 3], rng: &mut R) -> P
-    vertices: [P; 3],
+where
-    rng: &mut R,
+    P: NormedVectorSpace,
-) -> P {
+    P::Scalar: SampleUniform + PartialOrd + for<'a> ::core::ops::AddAssign<&'a P::Scalar>,
+    R: Rng + ?Sized,
+{
     let [a, b, c] = vertices;
     let ab = b - a;
     let ac = c - a;
     let bc = c - b;
 
-    let t = rng.gen_range(0.0..=1.0);
+    let t = rng.gen_range(P::Scalar::ZERO..=P::Scalar::ONE);
 
     if let Ok(dist) = WeightedIndex::new([ab.norm(), ac.norm(), bc.norm()]) {
         match dist.sample(rng) {

docs/linux_dependencies.md

@@ -91,7 +91,7 @@ Set the `PKG_CONFIG_PATH` env var to `/usr/lib/<target>/pkgconfig/`. For example
 export PKG_CONFIG_PATH="/usr/lib/x86_64-linux-gnu/pkgconfig/"
 ```
 
-## Arch / Manjaro
+## [Arch](https://archlinux.org/) / [Manjaro](https://manjaro.org/)
 
 ```bash
 sudo pacman -S libx11 pkgconf alsa-lib libxcursor libxrandr libxi
@@ -102,7 +102,7 @@ Install `pipewire-alsa` or `pulseaudio-alsa` depending on the sound server you a
 Depending on your graphics card, you may have to install one of the following:
 `vulkan-radeon`, `vulkan-intel`, or `mesa-vulkan-drivers`
 
-## Void
+## [Void](https://voidlinux.org/)
 
 ```bash
 sudo xbps-install -S pkgconf alsa-lib-devel libX11-devel eudev-libudev-devel
@@ -110,6 +110,80 @@ sudo xbps-install -S pkgconf alsa-lib-devel libX11-devel eudev-libudev-devel
 
 ## [Nix](https://nixos.org)
 
+### flake.nix
+
+Add a `flake.nix` file to the root of your GitHub repository containing:
+
+```nix
+{
+  description = "bevy flake";
+
+  inputs = {
+    nixpkgs.url = "github:NixOS/nixpkgs/nixos-unstable";
+    rust-overlay.url = "github:oxalica/rust-overlay";
+    flake-utils.url = "github:numtide/flake-utils";
+  };
+
+  outputs =
+    {
+      nixpkgs,
+      rust-overlay,
+      flake-utils,
+      ...
+    }:
+    flake-utils.lib.eachDefaultSystem (
+      system:
+      let
+        overlays = [ (import rust-overlay) ];
+        pkgs = import nixpkgs {
+          inherit system overlays;
+        };
+      in
+      {
+        devShells.default =
+          with pkgs;
+          mkShell {
+            buildInputs =
+              [
+                # Rust dependencies
+                (rust-bin.stable.latest.default.override { extensions = [ "rust-src" ]; })
+                pkg-config
+              ]
+              ++ lib.optionals (lib.strings.hasInfix "linux" system) [
+                # for Linux
+                # Audio (Linux only)
+                alsa-lib
+                # Cross Platform 3D Graphics API
+                vulkan-loader
+                # For debugging around vulkan
+                vulkan-tools
+                # Other dependencies
+                libudev-zero
+                xorg.libX11
+                xorg.libXcursor
+                xorg.libXi
+                xorg.libXrandr
+                libxkbcommon
+              ];
+            RUST_SRC_PATH = "${pkgs.rust.packages.stable.rustPlatform.rustLibSrc}";
+            LD_LIBRARY_PATH = lib.makeLibraryPath [
+              vulkan-loader
+              xorg.libX11
+              xorg.libXi
+              xorg.libXcursor
+              libxkbcommon
+            ];
+          };
+      }
+    );
+}
+```
+
+> [!TIP]
+> We have confirmed that this flake.nix can be used successfully on NixOS and MacOS with Rust's edition set to 2021.
+
+### shell.nix
+
 Add a `shell.nix` file to the root of the project containing:
 
 ```nix
@@ -138,8 +212,8 @@ If running nix on a non NixOS system (such as ubuntu, arch etc.), [NixGL](https:
 to link graphics drivers into the context of software installed by nix:
 
 1. Install a system specific nixGL wrapper ([docs](https://github.com/nix-community/nixGL)).
-   * If you're running a nvidia GPU choose `nixVulkanNvidia`.
+   - If you're running a nvidia GPU choose `nixVulkanNvidia`.
-   * Otherwise, choose another wrapper appropriate for your system.
+   - Otherwise, choose another wrapper appropriate for your system.
 2. Run `nixVulkanNvidia-xxx.xxx.xx cargo run` to compile a bevy program, where `xxx-xxx-xx` denotes the graphics driver version `nixVulkanNvidia` was compiled with.
 
 This is also possible with [Nix flakes](https://nixos.org/manual/nix/unstable/command-ref/new-cli/nix3-flake.html).
@@ -152,7 +226,7 @@ for more information about `devShells`.
 Note that this template does not add Rust to the environment because there are many ways to do it.
 For example, to use stable Rust from nixpkgs, you can add `cargo` and `rustc` to `nativeBuildInputs`.
 
-[Here]([https://github.com/NixOS/nixpkgs/blob/master/pkgs/by-name/ju/jumpy/package.nix](https://github.com/NixOS/nixpkgs/blob/0da3c44a9460a26d2025ec3ed2ec60a895eb1114/pkgs/games/jumpy/default.nix))
+[Here](https://github.com/NixOS/nixpkgs/blob/master/pkgs/by-name/ju/jumpy/package.nix)
 is an example of packaging a Bevy program in nix.
 
 ## [OpenSUSE](https://www.opensuse.org/)
@@ -161,7 +235,7 @@ is an example of packaging a Bevy program in nix.
    sudo zypper install libudev-devel gcc-c++ alsa-lib-devel
 ```
 
-## Gentoo
+## [Gentoo](https://www.gentoo.org/)
 
 ```bash
    sudo emerge --ask libX11 pkgconf alsa-lib

examples/animation/color_animation.rs

@@ -3,8 +3,8 @@
 use bevy::{math::VectorSpace, prelude::*};
 
 // We define this trait so we can reuse the same code for multiple color types that may be implemented using curves.
-trait CurveColor: VectorSpace + Into<Color> + Send + Sync + 'static {}
+trait CurveColor: VectorSpace<Scalar = f32> + Into<Color> + Send + Sync + 'static {}
-impl<T: VectorSpace + Into<Color> + Send + Sync + 'static> CurveColor for T {}
+impl<T: VectorSpace<Scalar = f32> + Into<Color> + Send + Sync + 'static> CurveColor for T {}
 
 // We define this trait so we can reuse the same code for multiple color types that may be implemented using mixing.
 trait MixedColor: Mix + Into<Color> + Send + Sync + 'static {}

release-content/migration-guides/scalar-field-on-vector-space.md

@@ -0,0 +1,8 @@
+---
+title: `VectorSpace` implementations
+pull_requests: [19194]
+---
+
+Previously, implementing `VectorSpace` for a type required your type to use or at least interface with `f32`. This made implementing `VectorSpace` for double-precision types (like `DVec3`) less meaningful and useful, requiring lots of casting. `VectorSpace` has a new required associated type `Scalar` that's bounded by a new trait `ScalarField`. `bevy_math` implements this trait for `f64` and `f32` out of the box, and `VectorSpace` is now implemented for `DVec[N]` types.
+
+If you manually implemented `VectorSpace` for any type, you'll need to implement `Scalar` for it. If you were working with single-precision floating-point types and you want the exact behavior from before, set it to `f32`.