Refactor the Interpolate trait and add the Interpolator trait.
This commit represents 99% of the rework. From now on, implementing the API requires to provide the various interpolation implementations. This is actually a good thing, because people will now be able to either use the `impl_Interpolate!` macro, which implements the interpolation in a very “math” way (using std::ops::* traits and float literals), or by providing their own.
This commit is contained in:
Dimitri Sabadie
parent
3d43e4c644
commit
0ccc3c0956
@ -42,277 +42,126 @@ use core::ops::{Add, Mul, Sub};
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use std::f32;
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#[cfg(feature = "std")]
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use std::f64;
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#[cfg(feature = "std")]
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use std::ops::{Add, Mul, Sub};
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/// Keys that can be interpolated in between. Implementing this trait is required to perform
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/// sampling on splines.
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/// Types that can be used as interpolator in splines.
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///
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/// `T` is the variable used to sample with. Typical implementations use [`f32`] or [`f64`], but
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/// you’re free to use the ones you like. Feel free to have a look at [`Spline::sample`] for
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/// instance to know which trait your type must implement to be usable.
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/// An interpolator value is like the fabric on which control keys (and sampled values) live on.
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pub trait Interpolator: Sized + Copy + PartialOrd {
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/// Normalize the interpolator.
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fn normalize(self, start: Self, end: Self) -> Self;
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}
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macro_rules! impl_Interpolator {
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($t:ty) => {
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impl Interpolator for $t {
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fn normalize(self, start: Self, end: Self) -> Self {
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(self - start) / (end - start)
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}
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}
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};
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}
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impl_Interpolator!(f32);
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impl_Interpolator!(f64);
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/// Values that can be interpolated. Implementing this trait is required to perform sampling on splines.
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///
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/// [`Spline::sample`]: crate::spline::Spline::sample
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pub trait Interpolate<T>: Sized + Copy + Linear<T> {
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/// `T` is the interpolator used to sample with. Typical implementations use [`f32`] or [`f64`], but
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/// you’re free to use the ones you like.
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pub trait Interpolate<T>: Sized + Copy {
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/// Step interpolation.
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fn step(t: T, threshold: T, a: Self, b: Self) -> Self;
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/// Linear interpolation.
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fn lerp(a: Self, b: Self, t: T) -> Self;
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fn lerp(t: T, a: Self, b: Self) -> Self;
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/// Cosine interpolation.
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fn cosine(t: T, a: Self, b: Self) -> Self;
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/// Cubic hermite interpolation.
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///
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/// Default to [`lerp`].
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///
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/// [`lerp`]: Interpolate::lerp
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fn cubic_hermite(_: (Self, T), a: (Self, T), b: (Self, T), _: (Self, T), t: T) -> Self {
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Self::lerp(a.0, b.0, t)
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}
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fn cubic_hermite(t: T, x: (T, Self), a: (T, Self), b: (T, Self), y: (T, Self)) -> Self;
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/// Quadratic Bézier interpolation.
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fn quadratic_bezier(a: Self, u: Self, b: Self, t: T) -> Self;
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///
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/// `a` is the first point; `b` is the second point and `u` is the tangent of `a` to the curve.
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fn quadratic_bezier(t: T, a: Self, u: Self, b: Self) -> Self;
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/// Cubic Bézier interpolation.
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fn cubic_bezier(a: Self, u: Self, v: Self, b: Self, t: T) -> Self;
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}
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/// Set of types that support additions and subtraction.
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///
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/// The [`Copy`] trait is also a supertrait as it’s likely to be used everywhere.
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pub trait Additive: Copy + Add<Self, Output = Self> + Sub<Self, Output = Self> {}
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/// `a` is the first point; `b` is the second point; `u` is the output tangent of `a` to the curve and `v` is the
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/// input tangent of `b` to the curve.
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fn cubic_bezier(t: T, a: Self, u: Self, v: Self, b: Self) -> Self;
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impl<T> Additive for T where T: Copy + Add<Self, Output = Self> + Sub<Self, Output = Self> {}
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/// Set of additive types that support outer multiplication and division, making them linear.
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pub trait Linear<T>: Additive {
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/// Apply an outer multiplication law.
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fn outer_mul(self, t: T) -> Self;
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/// Apply an outer division law.
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fn outer_div(self, t: T) -> Self;
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}
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macro_rules! impl_linear_simple {
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($t:ty) => {
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impl Linear<$t> for $t {
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fn outer_mul(self, t: $t) -> Self {
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self * t
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}
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/// Apply an outer division law.
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fn outer_div(self, t: $t) -> Self {
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self / t
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}
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}
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};
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}
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impl_linear_simple!(f32);
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impl_linear_simple!(f64);
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macro_rules! impl_linear_cast {
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($t:ty, $q:ty) => {
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impl Linear<$t> for $q {
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fn outer_mul(self, t: $t) -> Self {
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self * t as $q
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}
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/// Apply an outer division law.
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fn outer_div(self, t: $t) -> Self {
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self / t as $q
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}
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}
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};
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}
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impl_linear_cast!(f32, f64);
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impl_linear_cast!(f64, f32);
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/// Types with a neutral element for multiplication.
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pub trait One {
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/// The neutral element for the multiplicative monoid — typically called `1`.
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fn one() -> Self;
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}
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macro_rules! impl_one_float {
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($t:ty) => {
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impl One for $t {
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#[inline(always)]
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fn one() -> Self {
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1.
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}
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}
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};
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}
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impl_one_float!(f32);
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impl_one_float!(f64);
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/// Types with a sane definition of π and cosine.
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pub trait Trigo {
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/// π.
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fn pi() -> Self;
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/// Cosine of the argument.
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fn cos(self) -> Self;
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}
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impl Trigo for f32 {
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#[inline(always)]
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fn pi() -> Self {
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f32::consts::PI
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}
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#[inline(always)]
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fn cos(self) -> Self {
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#[cfg(feature = "std")]
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{
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self.cos()
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}
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#[cfg(not(feature = "std"))]
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{
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unsafe { cosf32(self) }
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}
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}
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}
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impl Trigo for f64 {
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#[inline(always)]
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fn pi() -> Self {
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f64::consts::PI
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}
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#[inline(always)]
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fn cos(self) -> Self {
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#[cfg(feature = "std")]
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{
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self.cos()
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}
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#[cfg(not(feature = "std"))]
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{
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unsafe { cosf64(self) }
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}
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}
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}
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/// Default implementation of [`Interpolate::cubic_hermite`].
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/// Cubic Bézier interpolation – special case for non-explicit second tangent.
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///
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/// `V` is the value being interpolated. `T` is the sampling value (also sometimes called time).
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pub fn cubic_hermite_def<V, T>(x: (V, T), a: (V, T), b: (V, T), y: (V, T), t: T) -> V
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where
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V: Linear<T>,
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T: Additive + Mul<T, Output = T> + One,
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{
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// some stupid generic constants, because Rust doesn’t have polymorphic literals…
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let one_t = T::one();
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let two_t = one_t + one_t; // lolololol
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let three_t = two_t + one_t; // megalol
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/// This version does the same computation as [`Interpolate::cubic_bezier`] but computes the second tangent by
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/// inversing it (typical when the next point uses a Bézier interpolation, where input and output tangents are
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/// mirrored for the same key).
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fn cubic_bezier_mirrored(t: T, a: Self, u: Self, v: Self, b: Self) -> Self;
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}
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#[macro_export]
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macro_rules! impl_Interpolate {
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($t:ty, $v:ty, $pi:expr) => {
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impl $crate::interpolate::Interpolate<$t> for $v {
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fn step(t: $t, threshold: $t, a: Self, b: Self) -> Self {
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if t < threshold {
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a
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} else {
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b
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}
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}
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fn cosine(t: $t, a: Self, b: Self) -> Self {
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let cos_nt = (1. - (t * $pi).cos()) * 0.5;
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<Self as $crate::interpolate::Interpolate<$t>>::lerp(cos_nt, a, b)
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}
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fn lerp(t: $t, a: Self, b: Self) -> Self {
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a * (1. - t) + b * t
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}
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fn cubic_hermite(t: $t, x: ($t, Self), a: ($t, Self), b: ($t, Self), y: ($t, Self)) -> Self {
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// sampler stuff
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let two_t = t * 2.;
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let three_t = t * 3.;
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let t2 = t * t;
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let t3 = t2 * t;
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let two_t3 = t3 * two_t;
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let three_t2 = t2 * three_t;
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// tangents
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let m0 = (b.0 - x.0).outer_div(b.1 - x.1);
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let m1 = (y.0 - a.0).outer_div(y.1 - a.1);
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let m0 = (b.1 - x.1) / (b.0 - x.0);
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let m1 = (y.1 - a.1) / (y.0 - a.0);
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a.0.outer_mul(two_t3 - three_t2 + one_t)
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+ m0.outer_mul(t3 - t2 * two_t + t)
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+ b.0.outer_mul(three_t2 - two_t3)
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+ m1.outer_mul(t3 - t2)
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a.1 * (two_t3 - three_t2 + 1.)
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+ m0 * (t3 - t2 * two_t + t)
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+ b.1 * (three_t2 - two_t3)
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+ m1 * (t3 - t2)
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}
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/// Default implementation of [`Interpolate::quadratic_bezier`].
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///
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/// `V` is the value being interpolated. `T` is the sampling value (also sometimes called time).
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pub fn quadratic_bezier_def<V, T>(a: V, u: V, b: V, t: T) -> V
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where
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V: Linear<T>,
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T: Additive + Mul<T, Output = T> + One,
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{
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let one_t = T::one() - t;
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let one_t_2 = one_t * one_t;
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u + (a - u).outer_mul(one_t_2) + (b - u).outer_mul(t * t)
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fn quadratic_bezier(t: $t, a: Self, u: Self, b: Self) -> Self {
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let one_t = 1. - t;
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let one_t2 = one_t * one_t;
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u + (a - u) * one_t2 + (b - u) * t * t
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}
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/// Default implementation of [`Interpolate::cubic_bezier`].
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///
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/// `V` is the value being interpolated. `T` is the sampling value (also sometimes called time).
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pub fn cubic_bezier_def<V, T>(a: V, u: V, v: V, b: V, t: T) -> V
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where
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V: Linear<T>,
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T: Additive + Mul<T, Output = T> + One,
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{
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let one_t = T::one() - t;
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let one_t_2 = one_t * one_t;
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let one_t_3 = one_t_2 * one_t;
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let three = T::one() + T::one() + T::one();
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fn cubic_bezier(t: $t, a: Self, u: Self, v: Self, b: Self) -> Self {
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let one_t = 1. - t;
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let one_t2 = one_t * one_t;
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let one_t3 = one_t2 * one_t;
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let t2 = t * t;
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a.outer_mul(one_t_3)
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+ u.outer_mul(three * one_t_2 * t)
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+ v.outer_mul(three * one_t * t * t)
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+ b.outer_mul(t * t * t)
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a * one_t3 + (u * one_t2 * t + v * one_t * t2) * 3. + b * t2 * t
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}
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macro_rules! impl_interpolate_simple {
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($t:ty) => {
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impl Interpolate<$t> for $t {
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fn lerp(a: Self, b: Self, t: $t) -> Self {
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a * (1. - t) + b * t
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}
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fn cubic_hermite(x: (Self, $t), a: (Self, $t), b: (Self, $t), y: (Self, $t), t: $t) -> Self {
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cubic_hermite_def(x, a, b, y, t)
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}
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fn quadratic_bezier(a: Self, u: Self, b: Self, t: $t) -> Self {
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quadratic_bezier_def(a, u, b, t)
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}
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fn cubic_bezier(a: Self, u: Self, v: Self, b: Self, t: $t) -> Self {
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cubic_bezier_def(a, u, v, b, t)
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fn cubic_bezier_mirrored(t: $t, a: Self, u: Self, v: Self, b: Self) -> Self {
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<Self as $crate::interpolate::Interpolate<$t>>::cubic_bezier(t, a, u, b + b - v, b)
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}
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}
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};
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}
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impl_interpolate_simple!(f32);
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impl_interpolate_simple!(f64);
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macro_rules! impl_interpolate_via {
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($t:ty, $v:ty) => {
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impl Interpolate<$t> for $v {
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fn lerp(a: Self, b: Self, t: $t) -> Self {
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a * (1. - t as $v) + b * t as $v
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}
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fn cubic_hermite(
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(x, xt): (Self, $t),
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(a, at): (Self, $t),
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(b, bt): (Self, $t),
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(y, yt): (Self, $t),
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t: $t,
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) -> Self {
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cubic_hermite_def(
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(x, xt as $v),
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(a, at as $v),
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(b, bt as $v),
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(y, yt as $v),
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t as $v,
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)
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}
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fn quadratic_bezier(a: Self, u: Self, b: Self, t: $t) -> Self {
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quadratic_bezier_def(a, u, b, t as $v)
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}
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fn cubic_bezier(a: Self, u: Self, v: Self, b: Self, t: $t) -> Self {
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cubic_bezier_def(a, u, v, b, t as $v)
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}
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}
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};
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}
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impl_interpolate_via!(f32, f64);
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impl_interpolate_via!(f64, f32);
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impl_Interpolate!(f32, f32, std::f32::consts::PI);
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impl_Interpolate!(f64, f64, std::f64::consts::PI);
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@ -1,5 +1,9 @@
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//! Spline curves and operations.
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#[cfg(feature = "std")]
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use crate::interpolate::{Interpolate, Interpolator};
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use crate::interpolation::Interpolation;
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use crate::key::Key;
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#[cfg(not(feature = "std"))]
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use alloc::vec::Vec;
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#[cfg(not(feature = "std"))]
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@ -10,12 +14,6 @@ use core::ops::{Div, Mul};
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use serde_derive::{Deserialize, Serialize};
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#[cfg(feature = "std")]
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use std::cmp::Ordering;
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#[cfg(feature = "std")]
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use std::ops::{Div, Mul};
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use crate::interpolate::{Additive, Interpolate, One, Trigo};
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use crate::interpolation::Interpolation;
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use crate::key::Key;
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/// Spline curve used to provide interpolation between control points (keys).
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///
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@ -104,8 +102,8 @@ impl<T, V> Spline<T, V> {
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/// the sampling.
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pub fn sample_with_key(&self, t: T) -> Option<SampledWithKey<V>>
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where
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T: Additive + One + Trigo + Mul<T, Output = T> + Div<T, Output = T> + PartialOrd,
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V: Additive + Interpolate<T>,
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T: Interpolator,
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V: Interpolate<T>,
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{
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let keys = &self.0;
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let i = search_lower_cp(keys, t)?;
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@ -114,26 +112,24 @@ impl<T, V> Spline<T, V> {
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let value = match cp0.interpolation {
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Interpolation::Step(threshold) => {
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let cp1 = &keys[i + 1];
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let nt = normalize_time(t, cp0, cp1);
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let value = if nt < threshold { cp0.value } else { cp1.value };
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let nt = t.normalize(cp0.t, cp1.t);
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let value = V::step(nt, threshold, cp0.value, cp1.value);
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Some(value)
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}
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Interpolation::Linear => {
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let cp1 = &keys[i + 1];
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let nt = normalize_time(t, cp0, cp1);
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let value = Interpolate::lerp(cp0.value, cp1.value, nt);
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let nt = t.normalize(cp0.t, cp1.t);
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let value = V::lerp(nt, cp0.value, cp1.value);
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Some(value)
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}
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Interpolation::Cosine => {
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let two_t = T::one() + T::one();
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let cp1 = &keys[i + 1];
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let nt = normalize_time(t, cp0, cp1);
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let cos_nt = (T::one() - (nt * T::pi()).cos()) / two_t;
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let value = Interpolate::lerp(cp0.value, cp1.value, cos_nt);
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let nt = t.normalize(cp0.t, cp1.t);
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let value = V::cosine(nt, cp0.value, cp1.value);
|
||||
|
||||
Some(value)
|
||||
}
|
||||
@ -147,13 +143,13 @@ impl<T, V> Spline<T, V> {
|
||||
let cp1 = &keys[i + 1];
|
||||
let cpm0 = &keys[i - 1];
|
||||
let cpm1 = &keys[i + 2];
|
||||
let nt = normalize_time(t, cp0, cp1);
|
||||
let value = Interpolate::cubic_hermite(
|
||||
(cpm0.value, cpm0.t),
|
||||
(cp0.value, cp0.t),
|
||||
(cp1.value, cp1.t),
|
||||
(cpm1.value, cpm1.t),
|
||||
let nt = t.normalize(cp0.t, cp1.t);
|
||||
let value = V::cubic_hermite(
|
||||
nt,
|
||||
(cpm0.t, cpm0.value),
|
||||
(cp0.t, cp0.value),
|
||||
(cp1.t, cp1.value),
|
||||
(cpm1.t, cpm1.value),
|
||||
);
|
||||
|
||||
Some(value)
|
||||
@ -163,18 +159,14 @@ impl<T, V> Spline<T, V> {
|
||||
Interpolation::Bezier(u) | Interpolation::StrokeBezier(_, u) => {
|
||||
// We need to check the next control point to see whether we want quadratic or cubic Bezier.
|
||||
let cp1 = &keys[i + 1];
|
||||
let nt = normalize_time(t, cp0, cp1);
|
||||
let nt = t.normalize(cp0.t, cp1.t);
|
||||
|
||||
let value = match cp1.interpolation {
|
||||
Interpolation::Bezier(v) => {
|
||||
Interpolate::cubic_bezier(cp0.value, u, cp1.value + cp1.value - v, cp1.value, nt)
|
||||
}
|
||||
Interpolation::Bezier(v) => V::cubic_bezier_mirrored(nt, cp0.value, u, v, cp1.value),
|
||||
|
||||
Interpolation::StrokeBezier(v, _) => {
|
||||
Interpolate::cubic_bezier(cp0.value, u, v, cp1.value, nt)
|
||||
}
|
||||
Interpolation::StrokeBezier(v, _) => V::cubic_bezier(nt, cp0.value, u, v, cp1.value),
|
||||
|
||||
_ => Interpolate::quadratic_bezier(cp0.value, u, cp1.value, nt),
|
||||
_ => V::quadratic_bezier(nt, cp0.value, u, cp1.value),
|
||||
};
|
||||
|
||||
Some(value)
|
||||
@ -188,8 +180,8 @@ impl<T, V> Spline<T, V> {
|
||||
///
|
||||
pub fn sample(&self, t: T) -> Option<V>
|
||||
where
|
||||
T: Additive + One + Trigo + Mul<T, Output = T> + Div<T, Output = T> + PartialOrd,
|
||||
V: Additive + Interpolate<T>,
|
||||
T: Interpolator,
|
||||
V: Interpolate<T>,
|
||||
{
|
||||
self.sample_with_key(t).map(|sampled| sampled.value)
|
||||
}
|
||||
@ -207,8 +199,8 @@ impl<T, V> Spline<T, V> {
|
||||
/// This function returns [`None`] if you have no key.
|
||||
pub fn clamped_sample_with_key(&self, t: T) -> Option<SampledWithKey<V>>
|
||||
where
|
||||
T: Additive + One + Trigo + Mul<T, Output = T> + Div<T, Output = T> + PartialOrd,
|
||||
V: Additive + Interpolate<T>,
|
||||
T: Interpolator,
|
||||
V: Interpolate<T>,
|
||||
{
|
||||
if self.0.is_empty() {
|
||||
return None;
|
||||
@ -242,8 +234,8 @@ impl<T, V> Spline<T, V> {
|
||||
/// Sample a spline at a given time with clamping.
|
||||
pub fn clamped_sample(&self, t: T) -> Option<V>
|
||||
where
|
||||
T: Additive + One + Trigo + Mul<T, Output = T> + Div<T, Output = T> + PartialOrd,
|
||||
V: Additive + Interpolate<T>,
|
||||
T: Interpolator,
|
||||
V: Interpolate<T>,
|
||||
{
|
||||
self.clamped_sample_with_key(t).map(|sampled| sampled.value)
|
||||
}
|
||||
@ -322,16 +314,6 @@ pub struct KeyMut<'a, T, V> {
|
||||
pub interpolation: &'a mut Interpolation<T, V>,
|
||||
}
|
||||
|
||||
// Normalize a time ([0;1]) given two control points.
|
||||
#[inline(always)]
|
||||
pub(crate) fn normalize_time<T, V>(t: T, cp: &Key<T, V>, cp1: &Key<T, V>) -> T
|
||||
where
|
||||
T: Additive + Div<T, Output = T> + PartialEq,
|
||||
{
|
||||
assert!(cp1.t != cp.t, "overlapping keys");
|
||||
(t - cp.t) / (cp1.t - cp.t)
|
||||
}
|
||||
|
||||
// Find the lower control point corresponding to a given time.
|
||||
fn search_lower_cp<T, V>(cps: &[Key<T, V>], t: T) -> Option<usize>
|
||||
where
|
||||
|
||||
Loading…
Reference in New Issue
Block a user