emath/lib.rs
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//! Opinionated 2D math library for building GUIs.
//!
//! Includes vectors, positions, rectangles etc.
//!
//! Conventions (unless otherwise specified):
//!
//! * All angles are in radians
//! * X+ is right and Y+ is down.
//! * (0,0) is left top.
//! * Dimension order is always `x y`
//!
//! ## Integrating with other math libraries.
//! `emath` does not strive to become a general purpose or all-powerful math library.
//!
//! For that, use something else ([`glam`](https://docs.rs/glam), [`nalgebra`](https://docs.rs/nalgebra), …)
//! and enable the `mint` feature flag in `emath` to enable implicit conversion to/from `emath`.
//!
//! ## Feature flags
#![cfg_attr(feature = "document-features", doc = document_features::document_features!())]
//!
#![allow(clippy::float_cmp)]
use std::ops::{Add, Div, Mul, RangeInclusive, Sub};
// ----------------------------------------------------------------------------
pub mod align;
pub mod easing;
mod history;
mod numeric;
mod ordered_float;
mod pos2;
mod range;
mod rect;
mod rect_transform;
mod rot2;
pub mod smart_aim;
mod ts_transform;
mod vec2;
mod vec2b;
pub use self::{
align::{Align, Align2},
history::History,
numeric::*,
ordered_float::*,
pos2::*,
range::Rangef,
rect::*,
rect_transform::*,
rot2::*,
ts_transform::*,
vec2::*,
vec2b::*,
};
// ----------------------------------------------------------------------------
/// Helper trait to implement [`lerp`] and [`remap`].
pub trait One {
const ONE: Self;
}
impl One for f32 {
const ONE: Self = 1.0;
}
impl One for f64 {
const ONE: Self = 1.0;
}
/// Helper trait to implement [`lerp`] and [`remap`].
pub trait Real:
Copy
+ PartialEq
+ PartialOrd
+ One
+ Add<Self, Output = Self>
+ Sub<Self, Output = Self>
+ Mul<Self, Output = Self>
+ Div<Self, Output = Self>
{
}
impl Real for f32 {}
impl Real for f64 {}
// ----------------------------------------------------------------------------
/// Linear interpolation.
///
/// ```
/// # use emath::lerp;
/// assert_eq!(lerp(1.0..=5.0, 0.0), 1.0);
/// assert_eq!(lerp(1.0..=5.0, 0.5), 3.0);
/// assert_eq!(lerp(1.0..=5.0, 1.0), 5.0);
/// assert_eq!(lerp(1.0..=5.0, 2.0), 9.0);
/// ```
#[inline(always)]
pub fn lerp<R, T>(range: impl Into<RangeInclusive<R>>, t: T) -> R
where
T: Real + Mul<R, Output = R>,
R: Copy + Add<R, Output = R>,
{
let range = range.into();
(T::ONE - t) * *range.start() + t * *range.end()
}
/// Where in the range is this value? Returns 0-1 if within the range.
///
/// Returns <0 if before and >1 if after.
///
/// Returns `None` if the input range is zero-width.
///
/// ```
/// # use emath::inverse_lerp;
/// assert_eq!(inverse_lerp(1.0..=5.0, 1.0), Some(0.0));
/// assert_eq!(inverse_lerp(1.0..=5.0, 3.0), Some(0.5));
/// assert_eq!(inverse_lerp(1.0..=5.0, 5.0), Some(1.0));
/// assert_eq!(inverse_lerp(1.0..=5.0, 9.0), Some(2.0));
/// assert_eq!(inverse_lerp(1.0..=1.0, 3.0), None);
/// ```
#[inline]
pub fn inverse_lerp<R>(range: RangeInclusive<R>, value: R) -> Option<R>
where
R: Copy + PartialEq + Sub<R, Output = R> + Div<R, Output = R>,
{
let min = *range.start();
let max = *range.end();
if min == max {
None
} else {
Some((value - min) / (max - min))
}
}
/// Linearly remap a value from one range to another,
/// so that when `x == from.start()` returns `to.start()`
/// and when `x == from.end()` returns `to.end()`.
pub fn remap<T>(x: T, from: impl Into<RangeInclusive<T>>, to: impl Into<RangeInclusive<T>>) -> T
where
T: Real,
{
let from = from.into();
let to = to.into();
debug_assert!(from.start() != from.end());
let t = (x - *from.start()) / (*from.end() - *from.start());
lerp(to, t)
}
/// Like [`remap`], but also clamps the value so that the returned value is always in the `to` range.
pub fn remap_clamp<T>(
x: T,
from: impl Into<RangeInclusive<T>>,
to: impl Into<RangeInclusive<T>>,
) -> T
where
T: Real,
{
let from = from.into();
let to = to.into();
if from.end() < from.start() {
return remap_clamp(x, *from.end()..=*from.start(), *to.end()..=*to.start());
}
if x <= *from.start() {
*to.start()
} else if *from.end() <= x {
*to.end()
} else {
debug_assert!(from.start() != from.end());
let t = (x - *from.start()) / (*from.end() - *from.start());
// Ensure no numerical inaccuracies sneak in:
if T::ONE <= t {
*to.end()
} else {
lerp(to, t)
}
}
}
/// Round a value to the given number of decimal places.
pub fn round_to_decimals(value: f64, decimal_places: usize) -> f64 {
// This is a stupid way of doing this, but stupid works.
format!("{value:.decimal_places$}").parse().unwrap_or(value)
}
pub fn format_with_minimum_decimals(value: f64, decimals: usize) -> String {
format_with_decimals_in_range(value, decimals..=6)
}
/// Use as few decimals as possible to show the value accurately, but within the given range.
///
/// Decimals are counted after the decimal point.
pub fn format_with_decimals_in_range(value: f64, decimal_range: RangeInclusive<usize>) -> String {
let min_decimals = *decimal_range.start();
let max_decimals = *decimal_range.end();
debug_assert!(min_decimals <= max_decimals);
debug_assert!(max_decimals < 100);
let max_decimals = max_decimals.min(16);
let min_decimals = min_decimals.min(max_decimals);
if min_decimals < max_decimals {
// Ugly/slow way of doing this. TODO(emilk): clean up precision.
for decimals in min_decimals..max_decimals {
let text = format!("{value:.decimals$}");
let epsilon = 16.0 * f32::EPSILON; // margin large enough to handle most peoples round-tripping needs
if almost_equal(text.parse::<f32>().unwrap(), value as f32, epsilon) {
// Enough precision to show the value accurately - good!
return text;
}
}
// The value has more precision than we expected.
// Probably the value was set not by the slider, but from outside.
// In any case: show the full value
}
format!("{value:.max_decimals$}")
}
/// Return true when arguments are the same within some rounding error.
///
/// For instance `almost_equal(x, x.to_degrees().to_radians(), f32::EPSILON)` should hold true for all x.
/// The `epsilon` can be `f32::EPSILON` to handle simple transforms (like degrees -> radians)
/// but should be higher to handle more complex transformations.
pub fn almost_equal(a: f32, b: f32, epsilon: f32) -> bool {
if a == b {
true // handle infinites
} else {
let abs_max = a.abs().max(b.abs());
abs_max <= epsilon || ((a - b).abs() / abs_max) <= epsilon
}
}
#[allow(clippy::approx_constant)]
#[test]
fn test_format() {
assert_eq!(format_with_minimum_decimals(1_234_567.0, 0), "1234567");
assert_eq!(format_with_minimum_decimals(1_234_567.0, 1), "1234567.0");
assert_eq!(format_with_minimum_decimals(3.14, 2), "3.14");
assert_eq!(format_with_minimum_decimals(3.14, 3), "3.140");
assert_eq!(
format_with_minimum_decimals(std::f64::consts::PI, 2),
"3.14159"
);
}
#[test]
fn test_almost_equal() {
for &x in &[
0.0_f32,
f32::MIN_POSITIVE,
1e-20,
1e-10,
f32::EPSILON,
0.1,
0.99,
1.0,
1.001,
1e10,
f32::MAX / 100.0,
// f32::MAX, // overflows in rad<->deg test
f32::INFINITY,
] {
for &x in &[-x, x] {
for roundtrip in &[
|x: f32| x.to_degrees().to_radians(),
|x: f32| x.to_radians().to_degrees(),
] {
let epsilon = f32::EPSILON;
assert!(
almost_equal(x, roundtrip(x), epsilon),
"{} vs {}",
x,
roundtrip(x)
);
}
}
}
}
#[test]
fn test_remap() {
assert_eq!(remap_clamp(1.0, 0.0..=1.0, 0.0..=16.0), 16.0);
assert_eq!(remap_clamp(1.0, 1.0..=0.0, 16.0..=0.0), 16.0);
assert_eq!(remap_clamp(0.5, 1.0..=0.0, 16.0..=0.0), 8.0);
}
// ----------------------------------------------------------------------------
/// Extends `f32`, [`Vec2`] etc with `at_least` and `at_most` as aliases for `max` and `min`.
pub trait NumExt {
/// More readable version of `self.max(lower_limit)`
#[must_use]
fn at_least(self, lower_limit: Self) -> Self;
/// More readable version of `self.min(upper_limit)`
#[must_use]
fn at_most(self, upper_limit: Self) -> Self;
}
macro_rules! impl_num_ext {
($t: ty) => {
impl NumExt for $t {
#[inline(always)]
fn at_least(self, lower_limit: Self) -> Self {
self.max(lower_limit)
}
#[inline(always)]
fn at_most(self, upper_limit: Self) -> Self {
self.min(upper_limit)
}
}
};
}
impl_num_ext!(u8);
impl_num_ext!(u16);
impl_num_ext!(u32);
impl_num_ext!(u64);
impl_num_ext!(u128);
impl_num_ext!(usize);
impl_num_ext!(i8);
impl_num_ext!(i16);
impl_num_ext!(i32);
impl_num_ext!(i64);
impl_num_ext!(i128);
impl_num_ext!(isize);
impl_num_ext!(f32);
impl_num_ext!(f64);
impl_num_ext!(Vec2);
impl_num_ext!(Pos2);
// ----------------------------------------------------------------------------
/// Wrap angle to `[-PI, PI]` range.
pub fn normalized_angle(mut angle: f32) -> f32 {
use std::f32::consts::{PI, TAU};
angle %= TAU;
if angle > PI {
angle -= TAU;
} else if angle < -PI {
angle += TAU;
}
angle
}
#[test]
fn test_normalized_angle() {
macro_rules! almost_eq {
($left: expr, $right: expr) => {
let left = $left;
let right = $right;
assert!((left - right).abs() < 1e-6, "{} != {}", left, right);
};
}
use std::f32::consts::TAU;
almost_eq!(normalized_angle(-3.0 * TAU), 0.0);
almost_eq!(normalized_angle(-2.3 * TAU), -0.3 * TAU);
almost_eq!(normalized_angle(-TAU), 0.0);
almost_eq!(normalized_angle(0.0), 0.0);
almost_eq!(normalized_angle(TAU), 0.0);
almost_eq!(normalized_angle(2.7 * TAU), -0.3 * TAU);
}
// ----------------------------------------------------------------------------
/// Calculate a lerp-factor for exponential smoothing using a time step.
///
/// * `exponential_smooth_factor(0.90, 1.0, dt)`: reach 90% in 1.0 seconds
/// * `exponential_smooth_factor(0.50, 0.2, dt)`: reach 50% in 0.2 seconds
///
/// Example:
/// ```
/// # use emath::{lerp, exponential_smooth_factor};
/// # let (mut smoothed_value, target_value, dt) = (0.0_f32, 1.0_f32, 0.01_f32);
/// let t = exponential_smooth_factor(0.90, 0.2, dt); // reach 90% in 0.2 seconds
/// smoothed_value = lerp(smoothed_value..=target_value, t);
/// ```
pub fn exponential_smooth_factor(
reach_this_fraction: f32,
in_this_many_seconds: f32,
dt: f32,
) -> f32 {
1.0 - (1.0 - reach_this_fraction).powf(dt / in_this_many_seconds)
}
/// If you have a value animating over time,
/// how much towards its target do you need to move it this frame?
///
/// You only need to store the start time and target value in order to animate using this function.
///
/// ``` rs
/// struct Animation {
/// current_value: f32,
///
/// animation_time_span: (f64, f64),
/// target_value: f32,
/// }
///
/// impl Animation {
/// fn update(&mut self, now: f64, dt: f32) {
/// let t = interpolation_factor(self.animation_time_span, now, dt, ease_in_ease_out);
/// self.current_value = emath::lerp(self.current_value..=self.target_value, t);
/// }
/// }
/// ```
pub fn interpolation_factor(
(start_time, end_time): (f64, f64),
current_time: f64,
dt: f32,
easing: impl Fn(f32) -> f32,
) -> f32 {
let animation_duration = (end_time - start_time) as f32;
let prev_time = current_time - dt as f64;
let prev_t = easing((prev_time - start_time) as f32 / animation_duration);
let end_t = easing((current_time - start_time) as f32 / animation_duration);
if end_t < 1.0 {
(end_t - prev_t) / (1.0 - prev_t)
} else {
1.0
}
}
/// Ease in, ease out.
///
/// `f(0) = 0, f'(0) = 0, f(1) = 1, f'(1) = 0`.
#[inline]
pub fn ease_in_ease_out(t: f32) -> f32 {
let t = t.clamp(0.0, 1.0);
(3.0 * t * t - 2.0 * t * t * t).clamp(0.0, 1.0)
}