Smoothness and derivatives for (cubic) curves

crates/bevy_core_pipeline/src/auto_exposure/compensation_curve.rs

@@ -1,6 +1,9 @@
 use bevy_asset::prelude::*;
 use bevy_ecs::system::{lifetimeless::SRes, SystemParamItem};
-use bevy_math::{cubic_splines::CubicGenerator, FloatExt, Vec2};
+use bevy_math::{
+    cubic_splines::{CubicGenerator, Smoothness},
+    FloatExt, Vec2,
+};
 use bevy_reflect::prelude::*;
 use bevy_render::{
     render_asset::{RenderAsset, RenderAssetUsages},
@@ -94,9 +97,10 @@ impl AutoExposureCompensationCurve {
     ///     .unwrap()
     /// );
     /// ```
-    pub fn from_curve<T>(curve: T) -> Result<Self, AutoExposureCompensationCurveError>
+    pub fn from_curve<T, S>(curve: T) -> Result<Self, AutoExposureCompensationCurveError>
     where
-        T: CubicGenerator<Vec2>,
+        T: CubicGenerator<Vec2, S>,
+        S: Smoothness,
     {
         let curve = curve.to_curve();
 

crates/bevy_math/src/common_traits.rs

@@ -305,3 +305,38 @@ impl StableInterpolate for Dir3A {
         self.slerp(*other, t)
     }
 }
+
+/// A type that has tangents.
+pub trait HasTangent {
+    /// The tangent type.
+    type Tangent;
+}
+
+/// A point with a tangent.
+pub struct WithDerivative<T>
+where
+    T: HasTangent,
+{
+    /// The underlying point.
+    pub point: T,
+    /// The derivative at `point`.
+    pub derivative: T::Tangent,
+}
+
+/// A point with a tangent and a second derivative.
+pub struct WithTwoDerivatives<T>
+where
+    T: HasTangent,
+    T::Tangent: HasTangent,
+{
+    /// The underlying point.
+    pub point: T,
+    /// The derivative at `point`.
+    pub derivative: T::Tangent,
+    /// The second derivative at `point`.
+    pub second_derivative: <T::Tangent as HasTangent>::Tangent,
+}
+
+impl<V: VectorSpace> HasTangent for V {
+    type Tangent = V;
+}