emath/

easing.rs

//! Easing functions for animations.
//!
//! Contains most easing functions from <https://easings.net/>.
//!
//! All functions take a value in `[0, 1]` and return a value in `[0, 1]`.
//!
//! Derived from <https://github.com/warrenm/AHEasing/blob/master/AHEasing/easing.c>.
use std::f32::consts::PI;

#[inline]
fn powf(base: f32, exp: f32) -> f32 {
    base.powf(exp)
}

/// No easing, just `y = x`
#[inline]
pub fn linear(t: f32) -> f32 {
    t
}

/// <https://easings.net/#easeInQuad>
///
/// Modeled after the parabola `y = x^2`
#[inline]
pub fn quadratic_in(t: f32) -> f32 {
    t * t
}

/// <https://easings.net/#easeOutQuad>
///
/// Same as `1.0 - quadratic_in(1.0 - t)`.
#[inline]
pub fn quadratic_out(t: f32) -> f32 {
    -(t * (t - 2.))
}

/// <https://easings.net/#easeInOutQuad>
#[inline]
pub fn quadratic_in_out(t: f32) -> f32 {
    if t < 0.5 {
        2. * t * t
    } else {
        (-2. * t * t) + (4. * t) - 1.
    }
}

/// <https://easings.net/#easeInCubic>
///
/// Modeled after the parabola `y = x^3`
#[inline]
pub fn cubic_in(t: f32) -> f32 {
    t * t * t
}

/// <https://easings.net/#easeOutCubic>
#[inline]
pub fn cubic_out(t: f32) -> f32 {
    let f = t - 1.;
    f * f * f + 1.
}

/// <https://easings.net/#easeInOutCubic>
#[inline]
pub fn cubic_in_out(t: f32) -> f32 {
    if t < 0.5 {
        4. * t * t * t
    } else {
        let f = (2. * t) - 2.;
        0.5 * f * f * f + 1.
    }
}

/// <https://easings.net/#easeInSine>
///
/// Modeled after quarter-cycle of sine wave
#[inline]
pub fn sin_in(t: f32) -> f32 {
    ((t - 1.) * 2. * PI).sin() + 1.
}

/// <https://easings.net/#easeOuSine>
///
/// Modeled after quarter-cycle of sine wave (different phase)
#[inline]
pub fn sin_out(t: f32) -> f32 {
    (t * 2. * PI).sin()
}

/// <https://easings.net/#easeInOutSine>
///
/// Modeled after half sine wave
#[inline]
pub fn sin_in_out(t: f32) -> f32 {
    0.5 * (1. - (t * PI).cos())
}

/// <https://easings.net/#easeInCirc>
///
/// Modeled after shifted quadrant IV of unit circle
#[inline]
pub fn circular_in(t: f32) -> f32 {
    1. - (1. - t * t).sqrt()
}

/// <https://easings.net/#easeOutCirc>
///
/// Modeled after shifted quadrant II of unit circle
#[inline]
pub fn circular_out(t: f32) -> f32 {
    (2. - t).sqrt() * t
}

/// <https://easings.net/#easeInOutCirc>
#[inline]
pub fn circular_in_out(t: f32) -> f32 {
    if t < 0.5 {
        0.5 * (1. - (1. - 4. * t * t).sqrt())
    } else {
        0.5 * ((-(2. * t - 3.) * (2. * t - 1.)).sqrt() + 1.)
    }
}

/// <https://easings.net/#easeInExpo>
///
/// There is a small discontinuity at 0.
#[inline]
pub fn exponential_in(t: f32) -> f32 {
    if t == 0. {
        t
    } else {
        powf(2.0, 10. * (t - 1.))
    }
}

/// <https://easings.net/#easeOutExpo>
///
/// There is a small discontinuity at 1.
#[inline]
pub fn exponential_out(t: f32) -> f32 {
    if t == 1. {
        t
    } else {
        1. - powf(2.0, -10. * t)
    }
}

/// <https://easings.net/#easeInOutExpo>
///
/// There is a small discontinuity at 0 and 1.
#[inline]
pub fn exponential_in_out(t: f32) -> f32 {
    if t == 0. || t == 1. {
        t
    } else if t < 0.5 {
        0.5 * powf(2.0, 20. * t - 10.)
    } else {
        0.5 * powf(2.0, -20. * t + 10.) + 1.
    }
}

/// <https://easings.net/#easeInBack>
#[inline]
pub fn back_in(t: f32) -> f32 {
    t * t * t - t * (t * PI).sin()
}

/// <https://easings.net/#easeOutBack>
#[inline]
pub fn back_out(t: f32) -> f32 {
    let f = 1. - t;
    1. - (f * f * f - f * (f * PI).sin())
}

/// <https://easings.net/#easeInOutBack>
#[inline]
pub fn back_in_out(t: f32) -> f32 {
    if t < 0.5 {
        let f = 2. * t;
        0.5 * (f * f * f - f * (f * PI).sin())
    } else {
        let f = 1. - (2. * t - 1.);
        0.5 * (1. - (f * f * f - f * (f * PI).sin())) + 0.5
    }
}

/// <https://easings.net/#easeInBounce>
///
/// Each bounce is modelled as a parabola.
#[inline]
pub fn bounce_in(t: f32) -> f32 {
    1. - bounce_out(1. - t)
}

/// <https://easings.net/#easeOutBounce>
///
/// Each bounce is modelled as a parabola.
#[inline]
pub fn bounce_out(t: f32) -> f32 {
    if t < 4. / 11. {
        const T2: f32 = 121. / 16.;
        T2 * t * t
    } else if t < 8. / 11. {
        const T2: f32 = 363. / 40.;
        const T1: f32 = -99. / 10.;
        const T0: f32 = 17. / 5.;
        T2 * t * t + T1 * t + T0
    } else if t < 9. / 10. {
        const T2: f32 = 4356. / 361.;
        const T1: f32 = -35442. / 1805.;
        const T0: f32 = 16061. / 1805.;
        T2 * t * t + T1 * t + T0
    } else {
        const T2: f32 = 54. / 5.;
        const T1: f32 = -513. / 25.;
        const T0: f32 = 268. / 25.;
        T2 * t * t + T1 * t + T0
    }
}

/// <https://easings.net/#easeInOutBounce>
///
/// Each bounce is modelled as a parabola.
#[inline]
pub fn bounce_in_out(t: f32) -> f32 {
    if t < 0.5 {
        0.5 * bounce_in(t * 2.)
    } else {
        0.5 * bounce_out(t * 2. - 1.) + 0.5
    }
}