Quelle vector.rs
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// Copyright 2013 The Servo Project Developers. See the COPYRIGHT
// file at the top-level directory of this distribution.
//
// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
// option. This file may not be copied, modified, or distributed
// except according to those terms.
use super::UnknownUnit;
use crate::approxeq::ApproxEq;
use crate::approxord::{max, min};
use crate::length::Length;
use crate::num::*;
use crate::point::{point2, point3, Point2D, Point3D};
use crate::scale::Scale;
use crate::size::{size2, size3, Size2D, Size3D};
use crate::transform2d::Transform2D;
use crate::transform3d::Transform3D;
use crate::trig::Trig;
use crate::Angle;
use core::cmp::{Eq, PartialEq};
use core::fmt;
use core::hash::Hash;
use core::iter::Sum;
use core::marker::PhantomData;
use core::ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, Sub, SubAssign};
#[cfg(feature = "mint")]
use mint;
use num_traits::real::Real;
use num_traits::{Float, NumCast, Signed};
#[cfg(feature = "serde")]
use serde;
#[cfg(feature = "bytemuck")]
use bytemuck::{Pod, Zeroable};
/// A 2d Vector tagged with a unit.
#[repr(C)]
pub struct Vector2D<T, U> {
/// The `x` (traditionally, horizontal) coordinate.
pub x: T,
/// The `y` (traditionally, vertical) coordinate.
pub y: T,
#[doc(hidden)]
pub _unit: PhantomData<U>,
}
mint_vec!(Vector2D[x, y] = Vector2);
impl<T: Copy, U> Copy for Vector2D<T, U> {}
impl<T: Clone, U> Clone for Vector2D<T, U> {
fn clone(&self) -> Self {
Vector2D {
x: self.x.clone(),
y: self.y.clone(),
_unit: PhantomData,
}
}
}
#[cfg(feature = "serde")]
impl<'de, T, U> serde::Deserialize<'de> for Vector2D<T, U>
where
T: serde::Deserialize<'de>,
{
fn deserialize<D>(deserializer: D) -> Result<Self, D::Error>
where
D: serde::Deserializer<'de>,
{
let (x, y) = serde::Deserialize::deserialize(deserializer)?;
Ok(Vector2D {
x,
y,
_unit: PhantomData,
})
}
}
#[cfg(feature = "serde")]
impl<T, U> serde::Serialize for Vector2D<T, U>
where
T: serde::Serialize,
{
fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error>
where
S: serde::Serializer,
{
(&self.x, &self.y).serialize(serializer)
}
}
#[cfg(feature = "arbitrary")]
impl<'a, T, U> arbitrary::Arbitrary<'a> for Vector2D<T, U>
where
T: arbitrary::Arbitrary<'a>,
{
fn arbitrary(u: &mut arbitrary::Unstructured<'a>) -> arbitrary::Result<Self> {
let (x, y) = arbitrary::Arbitrary::arbitrary(u)?;
Ok(Vector2D {
x,
y,
_unit: PhantomData,
})
}
}
#[cfg(feature = "bytemuck")]
unsafe impl<T: Zeroable, U> Zeroable for Vector2D<T, U> {}
#[cfg(feature = "bytemuck")]
unsafe impl<T: Pod, U: 'static> Pod for Vector2D<T, U> {}
impl<T: Eq, U> Eq for Vector2D<T, U> {}
impl<T: PartialEq, U> PartialEq for Vector2D<T, U> {
fn eq(&self, other: &Self) -> bool {
self.x == other.x && self.y == other.y
}
}
impl<T: Hash, U> Hash for Vector2D<T, U> {
fn hash<H: core::hash::Hasher>(&self, h: &mut H) {
self.x.hash(h);
self.y.hash(h);
}
}
impl<T: Zero, U> Zero for Vector2D<T, U> {
/// Constructor, setting all components to zero.
#[inline]
fn zero() -> Self {
Vector2D::new(Zero::zero(), Zero::zero())
}
}
impl<T: fmt::Debug, U> fmt::Debug for Vector2D<T, U> {
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
f.debug_tuple("").field(&self.x).field(&self.y).finish()
}
}
impl<T: Default, U> Default for Vector2D<T, U> {
fn default() -> Self {
Vector2D::new(Default::default(), Default::default())
}
}
impl<T, U> Vector2D<T, U> {
/// Constructor, setting all components to zero.
#[inline]
pub fn zero() -> Self
where
T: Zero,
{
Vector2D::new(Zero::zero(), Zero::zero())
}
/// Constructor, setting all components to one.
#[inline]
pub fn one() -> Self
where
T: One,
{
Vector2D::new(One::one(), One::one())
}
/// Constructor taking scalar values directly.
#[inline]
pub const fn new(x: T, y: T) -> Self {
Vector2D {
x,
y,
_unit: PhantomData,
}
}
/// Constructor setting all components to the same value.
#[inline]
pub fn splat(v: T) -> Self
where
T: Clone,
{
Vector2D {
x: v.clone(),
y: v,
_unit: PhantomData,
}
}
/// Constructor taking angle and length
pub fn from_angle_and_length(angle: Angle<T>, length: T) -> Self
where
T: Trig + Mul<Output = T> + Copy,
{
vec2(length * angle.radians.cos(), length * angle.radians.sin())
}
/// Constructor taking properly Lengths instead of scalar values.
#[inline]
pub fn from_lengths(x: Length<T, U>, y: Length<T, U>) -> Self {
vec2(x.0, y.0)
}
/// Tag a unit-less value with units.
#[inline]
pub fn from_untyped(p: Vector2D<T, UnknownUnit>) -> Self {
vec2(p.x, p.y)
}
/// Apply the function `f` to each component of this vector.
///
/// # Example
///
/// This may be used to perform unusual arithmetic which is not already offered as methods.
///
/// ```
/// use euclid::default::Vector2D;
///
/// let p = Vector2D::<u32>::new(5, 11);
/// assert_eq!(p.map(|coord| coord.saturating_sub(10)), Vector2D::new(0, 1));
/// ```
#[inline]
pub fn map<V, F: FnMut(T) -> V>(self, mut f: F) -> Vector2D<V, U> {
vec2(f(self.x), f(self.y))
}
/// Apply the function `f` to each pair of components of this point and `rhs`.
///
/// # Example
///
/// This may be used to perform unusual arithmetic which is not already offered as methods.
///
/// ```
/// use euclid::default::Vector2D;
///
/// let a: Vector2D<u8> = Vector2D::new(50, 200);
/// let b: Vector2D<u8> = Vector2D::new(100, 100);
/// assert_eq!(a.zip(b, u8::saturating_add), Vector2D::new(150, 255));
/// ```
#[inline]
pub fn zip<V, F: FnMut(T, T) -> V>(self, rhs: Self, mut f: F) -> Vector2D<V, U> {
vec2(f(self.x, rhs.x), f(self.y, rhs.y))
}
/// Computes the vector with absolute values of each component.
///
/// # Example
///
/// ```rust
/// # use std::{i32, f32};
/// # use euclid::vec2;
/// enum U {}
///
/// assert_eq!(vec2::<_, U>(-1, 2).abs(), vec2(1, 2));
///
/// let vec = vec2::<_, U>(f32::NAN, -f32::MAX).abs();
/// assert!(vec.x.is_nan());
/// assert_eq!(vec.y, f32::MAX);
/// ```
///
/// # Panics
///
/// The behavior for each component follows the scalar type's implementation of
/// `num_traits::Signed::abs`.
pub fn abs(self) -> Self
where
T: Signed,
{
vec2(self.x.abs(), self.y.abs())
}
/// Dot product.
#[inline]
pub fn dot(self, other: Self) -> T
where
T: Add<Output = T> + Mul<Output = T>,
{
self.x * other.x + self.y * other.y
}
/// Returns the norm of the cross product [self.x, self.y, 0] x [other.x, other.y, 0].
#[inline]
pub fn cross(self, other: Self) -> T
where
T: Sub<Output = T> + Mul<Output = T>,
{
self.x * other.y - self.y * other.x
}
/// Returns the component-wise multiplication of the two vectors.
#[inline]
pub fn component_mul(self, other: Self) -> Self
where
T: Mul<Output = T>,
{
vec2(self.x * other.x, self.y * other.y)
}
/// Returns the component-wise division of the two vectors.
#[inline]
pub fn component_div(self, other: Self) -> Self
where
T: Div<Output = T>,
{
vec2(self.x / other.x, self.y / other.y)
}
}
impl<T: Copy, U> Vector2D<T, U> {
/// Create a 3d vector from this one, using the specified z value.
#[inline]
pub fn extend(self, z: T) -> Vector3D<T, U> {
vec3(self.x, self.y, z)
}
/// Cast this vector into a point.
///
/// Equivalent to adding this vector to the origin.
#[inline]
pub fn to_point(self) -> Point2D<T, U> {
Point2D {
x: self.x,
y: self.y,
_unit: PhantomData,
}
}
/// Swap x and y.
#[inline]
pub fn yx(self) -> Self {
vec2(self.y, self.x)
}
/// Cast this vector into a size.
#[inline]
pub fn to_size(self) -> Size2D<T, U> {
size2(self.x, self.y)
}
/// Drop the units, preserving only the numeric value.
#[inline]
pub fn to_untyped(self) -> Vector2D<T, UnknownUnit> {
vec2(self.x, self.y)
}
/// Cast the unit.
#[inline]
pub fn cast_unit<V>(self) -> Vector2D<T, V> {
vec2(self.x, self.y)
}
/// Cast into an array with x and y.
#[inline]
pub fn to_array(self) -> [T; 2] {
[self.x, self.y]
}
/// Cast into a tuple with x and y.
#[inline]
pub fn to_tuple(self) -> (T, T) {
(self.x, self.y)
}
/// Convert into a 3d vector with `z` coordinate equals to `T::zero()`.
#[inline]
pub fn to_3d(self) -> Vector3D<T, U>
where
T: Zero,
{
vec3(self.x, self.y, Zero::zero())
}
/// Rounds each component to the nearest integer value.
///
/// This behavior is preserved for negative values (unlike the basic cast).
///
/// ```rust
/// # use euclid::vec2;
/// enum Mm {}
///
/// assert_eq!(vec2::<_, Mm>(-0.1, -0.8).round(), vec2::<_, Mm>(0.0, -1.0))
/// ```
#[inline]
#[must_use]
pub fn round(self) -> Self
where
T: Round,
{
vec2(self.x.round(), self.y.round())
}
/// Rounds each component to the smallest integer equal or greater than the original value.
///
/// This behavior is preserved for negative values (unlike the basic cast).
///
/// ```rust
/// # use euclid::vec2;
/// enum Mm {}
///
/// assert_eq!(vec2::<_, Mm>(-0.1, -0.8).ceil(), vec2::<_, Mm>(0.0, 0.0))
/// ```
#[inline]
#[must_use]
pub fn ceil(self) -> Self
where
T: Ceil,
{
vec2(self.x.ceil(), self.y.ceil())
}
/// Rounds each component to the biggest integer equal or lower than the original value.
///
/// This behavior is preserved for negative values (unlike the basic cast).
///
/// ```rust
/// # use euclid::vec2;
/// enum Mm {}
///
/// assert_eq!(vec2::<_, Mm>(-0.1, -0.8).floor(), vec2::<_, Mm>(-1.0, -1.0))
/// ```
#[inline]
#[must_use]
pub fn floor(self) -> Self
where
T: Floor,
{
vec2(self.x.floor(), self.y.floor())
}
/// Returns the signed angle between this vector and the x axis.
/// Positive values counted counterclockwise, where 0 is `+x` axis, `PI/2`
/// is `+y` axis.
///
/// The returned angle is between -PI and PI.
pub fn angle_from_x_axis(self) -> Angle<T>
where
T: Trig,
{
Angle::radians(Trig::fast_atan2(self.y, self.x))
}
/// Creates translation by this vector in vector units.
#[inline]
pub fn to_transform(self) -> Transform2D<T, U, U>
where
T: Zero + One,
{
Transform2D::translation(self.x, self.y)
}
}
impl<T, U> Vector2D<T, U>
where
T: Copy + Mul<T, Output = T> + Add<T, Output = T>,
{
/// Returns the vector's length squared.
#[inline]
pub fn square_length(self) -> T {
self.x * self.x + self.y * self.y
}
/// Returns this vector projected onto another one.
///
/// Projecting onto a nil vector will cause a division by zero.
#[inline]
pub fn project_onto_vector(self, onto: Self) -> Self
where
T: Sub<T, Output = T> + Div<T, Output = T>,
{
onto * (self.dot(onto) / onto.square_length())
}
/// Returns the signed angle between this vector and another vector.
///
/// The returned angle is between -PI and PI.
pub fn angle_to(self, other: Self) -> Angle<T>
where
T: Sub<Output = T> + Trig,
{
Angle::radians(Trig::fast_atan2(self.cross(other), self.dot(other)))
}
}
impl<T: Float, U> Vector2D<T, U> {
/// Return the normalized vector even if the length is larger than the max value of Float.
#[inline]
#[must_use]
pub fn robust_normalize(self) -> Self {
let length = self.length();
if length.is_infinite() {
let scaled = self / T::max_value();
scaled / scaled.length()
} else {
self / length
}
}
/// Returns true if all members are finite.
#[inline]
pub fn is_finite(self) -> bool {
self.x.is_finite() && self.y.is_finite()
}
}
impl<T: Real, U> Vector2D<T, U> {
/// Returns the vector length.
#[inline]
pub fn length(self) -> T {
self.square_length().sqrt()
}
/// Returns the vector with length of one unit.
#[inline]
#[must_use]
pub fn normalize(self) -> Self {
self / self.length()
}
/// Returns the vector with length of one unit.
///
/// Unlike [`Vector2D::normalize`](#method.normalize), this returns None in the case that the
/// length of the vector is zero.
#[inline]
#[must_use]
pub fn try_normalize(self) -> Option<Self> {
let len = self.length();
if len == T::zero() {
None
} else {
Some(self / len)
}
}
/// Return this vector scaled to fit the provided length.
#[inline]
pub fn with_length(self, length: T) -> Self {
self.normalize() * length
}
/// Return this vector capped to a maximum length.
#[inline]
pub fn with_max_length(self, max_length: T) -> Self {
let square_length = self.square_length();
if square_length > max_length * max_length {
return self * (max_length / square_length.sqrt());
}
self
}
/// Return this vector with a minimum length applied.
#[inline]
pub fn with_min_length(self, min_length: T) -> Self {
let square_length = self.square_length();
if square_length < min_length * min_length {
return self * (min_length / square_length.sqrt());
}
self
}
/// Return this vector with minimum and maximum lengths applied.
#[inline]
pub fn clamp_length(self, min: T, max: T) -> Self {
debug_assert!(min <= max);
self.with_min_length(min).with_max_length(max)
}
}
impl<T, U> Vector2D<T, U>
where
T: Copy + One + Add<Output = T> + Sub<Output = T> + Mul<Output = T>,
{
/// Linearly interpolate each component between this vector and another vector.
///
/// # Example
///
/// ```rust
/// use euclid::vec2;
/// use euclid::default::Vector2D;
///
/// let from: Vector2D<_> = vec2(0.0, 10.0);
/// let to: Vector2D<_> = vec2(8.0, -4.0);
///
/// assert_eq!(from.lerp(to, -1.0), vec2(-8.0, 24.0));
/// assert_eq!(from.lerp(to, 0.0), vec2( 0.0, 10.0));
/// assert_eq!(from.lerp(to, 0.5), vec2( 4.0, 3.0));
/// assert_eq!(from.lerp(to, 1.0), vec2( 8.0, -4.0));
/// assert_eq!(from.lerp(to, 2.0), vec2(16.0, -18.0));
/// ```
#[inline]
pub fn lerp(self, other: Self, t: T) -> Self {
let one_t = T::one() - t;
self * one_t + other * t
}
/// Returns a reflection vector using an incident ray and a surface normal.
#[inline]
pub fn reflect(self, normal: Self) -> Self {
let two = T::one() + T::one();
self - normal * two * self.dot(normal)
}
}
impl<T: PartialOrd, U> Vector2D<T, U> {
/// Returns the vector each component of which are minimum of this vector and another.
#[inline]
pub fn min(self, other: Self) -> Self {
vec2(min(self.x, other.x), min(self.y, other.y))
}
/// Returns the vector each component of which are maximum of this vector and another.
#[inline]
pub fn max(self, other: Self) -> Self {
vec2(max(self.x, other.x), max(self.y, other.y))
}
/// Returns the vector each component of which is clamped by corresponding
/// components of `start` and `end`.
///
/// Shortcut for `self.max(start).min(end)`.
#[inline]
pub fn clamp(self, start: Self, end: Self) -> Self
where
T: Copy,
{
self.max(start).min(end)
}
/// Returns vector with results of "greater than" operation on each component.
#[inline]
pub fn greater_than(self, other: Self) -> BoolVector2D {
BoolVector2D {
x: self.x > other.x,
y: self.y > other.y,
}
}
/// Returns vector with results of "lower than" operation on each component.
#[inline]
pub fn lower_than(self, other: Self) -> BoolVector2D {
BoolVector2D {
x: self.x < other.x,
y: self.y < other.y,
}
}
}
impl<T: PartialEq, U> Vector2D<T, U> {
/// Returns vector with results of "equal" operation on each component.
#[inline]
pub fn equal(self, other: Self) -> BoolVector2D {
BoolVector2D {
x: self.x == other.x,
y: self.y == other.y,
}
}
/// Returns vector with results of "not equal" operation on each component.
#[inline]
pub fn not_equal(self, other: Self) -> BoolVector2D {
BoolVector2D {
x: self.x != other.x,
y: self.y != other.y,
}
}
}
impl<T: NumCast + Copy, U> Vector2D<T, U> {
/// Cast from one numeric representation to another, preserving the units.
///
/// When casting from floating vector to integer coordinates, the decimals are truncated
/// as one would expect from a simple cast, but this behavior does not always make sense
/// geometrically. Consider using `round()`, `ceil()` or `floor()` before casting.
#[inline]
pub fn cast<NewT: NumCast>(self) -> Vector2D<NewT, U> {
self.try_cast().unwrap()
}
/// Fallible cast from one numeric representation to another, preserving the units.
///
/// When casting from floating vector to integer coordinates, the decimals are truncated
/// as one would expect from a simple cast, but this behavior does not always make sense
/// geometrically. Consider using `round()`, `ceil()` or `floor()` before casting.
pub fn try_cast<NewT: NumCast>(self) -> Option<Vector2D<NewT, U>> {
match (NumCast::from(self.x), NumCast::from(self.y)) {
(Some(x), Some(y)) => Some(Vector2D::new(x, y)),
_ => None,
}
}
// Convenience functions for common casts.
/// Cast into an `f32` vector.
#[inline]
pub fn to_f32(self) -> Vector2D<f32, U> {
self.cast()
}
/// Cast into an `f64` vector.
#[inline]
pub fn to_f64(self) -> Vector2D<f64, U> {
self.cast()
}
/// Cast into an `usize` vector, truncating decimals if any.
///
/// When casting from floating vector vectors, it is worth considering whether
/// to `round()`, `ceil()` or `floor()` before the cast in order to obtain
/// the desired conversion behavior.
#[inline]
pub fn to_usize(self) -> Vector2D<usize, U> {
self.cast()
}
/// Cast into an `u32` vector, truncating decimals if any.
///
/// When casting from floating vector vectors, it is worth considering whether
/// to `round()`, `ceil()` or `floor()` before the cast in order to obtain
/// the desired conversion behavior.
#[inline]
pub fn to_u32(self) -> Vector2D<u32, U> {
self.cast()
}
/// Cast into an i32 vector, truncating decimals if any.
///
/// When casting from floating vector vectors, it is worth considering whether
/// to `round()`, `ceil()` or `floor()` before the cast in order to obtain
/// the desired conversion behavior.
#[inline]
pub fn to_i32(self) -> Vector2D<i32, U> {
self.cast()
}
/// Cast into an i64 vector, truncating decimals if any.
///
/// When casting from floating vector vectors, it is worth considering whether
/// to `round()`, `ceil()` or `floor()` before the cast in order to obtain
/// the desired conversion behavior.
#[inline]
pub fn to_i64(self) -> Vector2D<i64, U> {
self.cast()
}
}
impl<T: Neg, U> Neg for Vector2D<T, U> {
type Output = Vector2D<T::Output, U>;
#[inline]
fn neg(self) -> Self::Output {
vec2(-self.x, -self.y)
}
}
impl<T: Add, U> Add for Vector2D<T, U> {
type Output = Vector2D<T::Output, U>;
#[inline]
fn add(self, other: Self) -> Self::Output {
Vector2D::new(self.x + other.x, self.y + other.y)
}
}
impl<T: Add + Copy, U> Add<&Self> for Vector2D<T, U> {
type Output = Vector2D<T::Output, U>;
#[inline]
fn add(self, other: &Self) -> Self::Output {
Vector2D::new(self.x + other.x, self.y + other.y)
}
}
impl<T: Add<Output = T> + Zero, U> Sum for Vector2D<T, U> {
fn sum<I: Iterator<Item = Self>>(iter: I) -> Self {
iter.fold(Self::zero(), Add::add)
}
}
impl<'a, T: 'a + Add<Output = T> + Copy + Zero, U: 'a> Sum<&'a Self> for Vector2D<T, U> {
fn sum<I: Iterator<Item = &'a Self>>(iter: I) -> Self {
iter.fold(Self::zero(), Add::add)
}
}
impl<T: Copy + Add<T, Output = T>, U> AddAssign for Vector2D<T, U> {
#[inline]
fn add_assign(&mut self, other: Self) {
*self = *self + other
}
}
impl<T: Sub, U> Sub for Vector2D<T, U> {
type Output = Vector2D<T::Output, U>;
#[inline]
fn sub(self, other: Self) -> Self::Output {
vec2(self.x - other.x, self.y - other.y)
}
}
impl<T: Copy + Sub<T, Output = T>, U> SubAssign<Vector2D<T, U>> for Vector2D<T, U> {
#[inline]
fn sub_assign(&mut self, other: Self) {
*self = *self - other
}
}
impl<T: Copy + Mul, U> Mul<T> for Vector2D<T, U> {
type Output = Vector2D<T::Output, U>;
#[inline]
fn mul(self, scale: T) -> Self::Output {
vec2(self.x * scale, self.y * scale)
}
}
impl<T: Copy + Mul<T, Output = T>, U> MulAssign<T> for Vector2D<T, U> {
#[inline]
fn mul_assign(&mut self, scale: T) {
*self = *self * scale
}
}
impl<T: Copy + Mul, U1, U2> Mul<Scale<T, U1, U2>> for Vector2D<T, U1> {
type Output = Vector2D<T::Output, U2>;
#[inline]
fn mul(self, scale: Scale<T, U1, U2>) -> Self::Output {
vec2(self.x * scale.0, self.y * scale.0)
}
}
impl<T: Copy + MulAssign, U> MulAssign<Scale<T, U, U>> for Vector2D<T, U> {
#[inline]
fn mul_assign(&mut self, scale: Scale<T, U, U>) {
self.x *= scale.0;
self.y *= scale.0;
}
}
impl<T: Copy + Div, U> Div<T> for Vector2D<T, U> {
type Output = Vector2D<T::Output, U>;
#[inline]
fn div(self, scale: T) -> Self::Output {
vec2(self.x / scale, self.y / scale)
}
}
impl<T: Copy + Div<T, Output = T>, U> DivAssign<T> for Vector2D<T, U> {
#[inline]
fn div_assign(&mut self, scale: T) {
*self = *self / scale
}
}
impl<T: Copy + Div, U1, U2> Div<Scale<T, U1, U2>> for Vector2D<T, U2> {
type Output = Vector2D<T::Output, U1>;
#[inline]
fn div(self, scale: Scale<T, U1, U2>) -> Self::Output {
vec2(self.x / scale.0, self.y / scale.0)
}
}
impl<T: Copy + DivAssign, U> DivAssign<Scale<T, U, U>> for Vector2D<T, U> {
#[inline]
fn div_assign(&mut self, scale: Scale<T, U, U>) {
self.x /= scale.0;
self.y /= scale.0;
}
}
impl<T: Round, U> Round for Vector2D<T, U> {
/// See [`Vector2D::round()`](#method.round)
#[inline]
fn round(self) -> Self {
self.round()
}
}
impl<T: Ceil, U> Ceil for Vector2D<T, U> {
/// See [`Vector2D::ceil()`](#method.ceil)
#[inline]
fn ceil(self) -> Self {
self.ceil()
}
}
impl<T: Floor, U> Floor for Vector2D<T, U> {
/// See [`Vector2D::floor()`](#method.floor)
#[inline]
fn floor(self) -> Self {
self.floor()
}
}
impl<T: ApproxEq<T>, U> ApproxEq<Vector2D<T, U>> for Vector2D<T, U> {
#[inline]
fn approx_epsilon() -> Self {
vec2(T::approx_epsilon(), T::approx_epsilon())
}
#[inline]
fn approx_eq_eps(&self, other: &Self, eps: &Self) -> bool {
self.x.approx_eq_eps(&other.x, &eps.x) && self.y.approx_eq_eps(&other.y, &eps.y)
}
}
impl<T, U> From<Vector2D<T, U>> for [T; 2] {
fn from(v: Vector2D<T, U>) -> Self {
[v.x, v.y]
}
}
impl<T, U> From<[T; 2]> for Vector2D<T, U> {
fn from([x, y]: [T; 2]) -> Self {
vec2(x, y)
}
}
impl<T, U> From<Vector2D<T, U>> for (T, T) {
fn from(v: Vector2D<T, U>) -> Self {
(v.x, v.y)
}
}
impl<T, U> From<(T, T)> for Vector2D<T, U> {
fn from(tuple: (T, T)) -> Self {
vec2(tuple.0, tuple.1)
}
}
impl<T, U> From<Size2D<T, U>> for Vector2D<T, U> {
fn from(s: Size2D<T, U>) -> Self {
vec2(s.width, s.height)
}
}
/// A 3d Vector tagged with a unit.
#[repr(C)]
pub struct Vector3D<T, U> {
/// The `x` (traditionally, horizontal) coordinate.
pub x: T,
/// The `y` (traditionally, vertical) coordinate.
pub y: T,
/// The `z` (traditionally, depth) coordinate.
pub z: T,
#[doc(hidden)]
pub _unit: PhantomData<U>,
}
mint_vec!(Vector3D[x, y, z] = Vector3);
impl<T: Copy, U> Copy for Vector3D<T, U> {}
impl<T: Clone, U> Clone for Vector3D<T, U> {
fn clone(&self) -> Self {
Vector3D {
x: self.x.clone(),
y: self.y.clone(),
z: self.z.clone(),
_unit: PhantomData,
}
}
}
#[cfg(feature = "serde")]
impl<'de, T, U> serde::Deserialize<'de> for Vector3D<T, U>
where
T: serde::Deserialize<'de>,
{
fn deserialize<D>(deserializer: D) -> Result<Self, D::Error>
where
D: serde::Deserializer<'de>,
{
let (x, y, z) = serde::Deserialize::deserialize(deserializer)?;
Ok(Vector3D {
x,
y,
z,
_unit: PhantomData,
})
}
}
#[cfg(feature = "serde")]
impl<T, U> serde::Serialize for Vector3D<T, U>
where
T: serde::Serialize,
{
fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error>
where
S: serde::Serializer,
{
(&self.x, &self.y, &self.z).serialize(serializer)
}
}
#[cfg(feature = "bytemuck")]
unsafe impl<T: Zeroable, U> Zeroable for Vector3D<T, U> {}
#[cfg(feature = "bytemuck")]
unsafe impl<T: Pod, U: 'static> Pod for Vector3D<T, U> {}
impl<T: Eq, U> Eq for Vector3D<T, U> {}
impl<T: PartialEq, U> PartialEq for Vector3D<T, U> {
fn eq(&self, other: &Self) -> bool {
self.x == other.x && self.y == other.y && self.z == other.z
}
}
impl<T: Hash, U> Hash for Vector3D<T, U> {
fn hash<H: core::hash::Hasher>(&self, h: &mut H) {
self.x.hash(h);
self.y.hash(h);
self.z.hash(h);
}
}
impl<T: Zero, U> Zero for Vector3D<T, U> {
/// Constructor, setting all components to zero.
#[inline]
fn zero() -> Self {
vec3(Zero::zero(), Zero::zero(), Zero::zero())
}
}
impl<T: fmt::Debug, U> fmt::Debug for Vector3D<T, U> {
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
f.debug_tuple("")
.field(&self.x)
.field(&self.y)
.field(&self.z)
.finish()
}
}
impl<T: Default, U> Default for Vector3D<T, U> {
fn default() -> Self {
Vector3D::new(Default::default(), Default::default(), Default::default())
}
}
impl<T, U> Vector3D<T, U> {
/// Constructor, setting all components to zero.
#[inline]
pub fn zero() -> Self
where
T: Zero,
{
vec3(Zero::zero(), Zero::zero(), Zero::zero())
}
/// Constructor, setting all components to one.
#[inline]
pub fn one() -> Self
where
T: One,
{
vec3(One::one(), One::one(), One::one())
}
/// Constructor taking scalar values directly.
#[inline]
pub const fn new(x: T, y: T, z: T) -> Self {
Vector3D {
x,
y,
z,
_unit: PhantomData,
}
}
/// Constructor setting all components to the same value.
#[inline]
pub fn splat(v: T) -> Self
where
T: Clone,
{
Vector3D {
x: v.clone(),
y: v.clone(),
z: v,
_unit: PhantomData,
}
}
/// Constructor taking properly Lengths instead of scalar values.
#[inline]
pub fn from_lengths(x: Length<T, U>, y: Length<T, U>, z: Length<T, U>) -> Vector3D<T, U> {
vec3(x.0, y.0, z.0)
}
/// Tag a unitless value with units.
#[inline]
pub fn from_untyped(p: Vector3D<T, UnknownUnit>) -> Self {
vec3(p.x, p.y, p.z)
}
/// Apply the function `f` to each component of this vector.
///
/// # Example
///
/// This may be used to perform unusual arithmetic which is not already offered as methods.
///
/// ```
/// use euclid::default::Vector3D;
///
/// let p = Vector3D::<u32>::new(5, 11, 15);
/// assert_eq!(p.map(|coord| coord.saturating_sub(10)), Vector3D::new(0, 1, 5));
/// ```
#[inline]
pub fn map<V, F: FnMut(T) -> V>(self, mut f: F) -> Vector3D<V, U> {
vec3(f(self.x), f(self.y), f(self.z))
}
/// Apply the function `f` to each pair of components of this point and `rhs`.
///
/// # Example
///
/// This may be used to perform unusual arithmetic which is not already offered as methods.
///
/// ```
/// use euclid::default::Vector3D;
///
/// let a: Vector3D<u8> = Vector3D::new(50, 200, 10);
/// let b: Vector3D<u8> = Vector3D::new(100, 100, 0);
/// assert_eq!(a.zip(b, u8::saturating_add), Vector3D::new(150, 255, 10));
/// ```
#[inline]
pub fn zip<V, F: FnMut(T, T) -> V>(self, rhs: Self, mut f: F) -> Vector3D<V, U> {
vec3(f(self.x, rhs.x), f(self.y, rhs.y), f(self.z, rhs.z))
}
/// Computes the vector with absolute values of each component.
///
/// # Example
///
/// ```rust
/// # use std::{i32, f32};
/// # use euclid::vec3;
/// enum U {}
///
/// assert_eq!(vec3::<_, U>(-1, 0, 2).abs(), vec3(1, 0, 2));
///
/// let vec = vec3::<_, U>(f32::NAN, 0.0, -f32::MAX).abs();
/// assert!(vec.x.is_nan());
/// assert_eq!(vec.y, 0.0);
/// assert_eq!(vec.z, f32::MAX);
/// ```
///
/// # Panics
///
/// The behavior for each component follows the scalar type's implementation of
/// `num_traits::Signed::abs`.
pub fn abs(self) -> Self
where
T: Signed,
{
vec3(self.x.abs(), self.y.abs(), self.z.abs())
}
/// Dot product.
#[inline]
pub fn dot(self, other: Self) -> T
where
T: Add<Output = T> + Mul<Output = T>,
{
self.x * other.x + self.y * other.y + self.z * other.z
}
}
impl<T: Copy, U> Vector3D<T, U> {
/// Cross product.
#[inline]
pub fn cross(self, other: Self) -> Self
where
T: Sub<Output = T> + Mul<Output = T>,
{
vec3(
self.y * other.z - self.z * other.y,
self.z * other.x - self.x * other.z,
self.x * other.y - self.y * other.x,
)
}
/// Returns the component-wise multiplication of the two vectors.
#[inline]
pub fn component_mul(self, other: Self) -> Self
where
T: Mul<Output = T>,
{
vec3(self.x * other.x, self.y * other.y, self.z * other.z)
}
/// Returns the component-wise division of the two vectors.
#[inline]
pub fn component_div(self, other: Self) -> Self
where
T: Div<Output = T>,
{
vec3(self.x / other.x, self.y / other.y, self.z / other.z)
}
/// Cast this vector into a point.
///
/// Equivalent to adding this vector to the origin.
#[inline]
pub fn to_point(self) -> Point3D<T, U> {
point3(self.x, self.y, self.z)
}
/// Returns a 2d vector using this vector's x and y coordinates
#[inline]
pub fn xy(self) -> Vector2D<T, U> {
vec2(self.x, self.y)
}
/// Returns a 2d vector using this vector's x and z coordinates
#[inline]
pub fn xz(self) -> Vector2D<T, U> {
vec2(self.x, self.z)
}
/// Returns a 2d vector using this vector's x and z coordinates
#[inline]
pub fn yz(self) -> Vector2D<T, U> {
vec2(self.y, self.z)
}
/// Cast into an array with x, y and z.
#[inline]
pub fn to_array(self) -> [T; 3] {
[self.x, self.y, self.z]
}
/// Cast into an array with x, y, z and 0.
#[inline]
pub fn to_array_4d(self) -> [T; 4]
where
T: Zero,
{
[self.x, self.y, self.z, Zero::zero()]
}
/// Cast into a tuple with x, y and z.
#[inline]
pub fn to_tuple(self) -> (T, T, T) {
(self.x, self.y, self.z)
}
/// Cast into a tuple with x, y, z and 0.
#[inline]
pub fn to_tuple_4d(self) -> (T, T, T, T)
where
T: Zero,
{
(self.x, self.y, self.z, Zero::zero())
}
/// Drop the units, preserving only the numeric value.
#[inline]
pub fn to_untyped(self) -> Vector3D<T, UnknownUnit> {
vec3(self.x, self.y, self.z)
}
/// Cast the unit.
#[inline]
pub fn cast_unit<V>(self) -> Vector3D<T, V> {
vec3(self.x, self.y, self.z)
}
/// Convert into a 2d vector.
#[inline]
pub fn to_2d(self) -> Vector2D<T, U> {
self.xy()
}
/// Rounds each component to the nearest integer value.
///
/// This behavior is preserved for negative values (unlike the basic cast).
///
/// ```rust
/// # use euclid::vec3;
/// enum Mm {}
///
/// assert_eq!(vec3::<_, Mm>(-0.1, -0.8, 0.4).round(), vec3::<_, Mm>(0.0, -1.0, 0.0))
/// ```
#[inline]
#[must_use]
pub fn round(self) -> Self
where
T: Round,
{
vec3(self.x.round(), self.y.round(), self.z.round())
}
/// Rounds each component to the smallest integer equal or greater than the original value.
///
/// This behavior is preserved for negative values (unlike the basic cast).
///
/// ```rust
/// # use euclid::vec3;
/// enum Mm {}
///
/// assert_eq!(vec3::<_, Mm>(-0.1, -0.8, 0.4).ceil(), vec3::<_, Mm>(0.0, 0.0, 1.0))
/// ```
#[inline]
#[must_use]
pub fn ceil(self) -> Self
where
T: Ceil,
{
vec3(self.x.ceil(), self.y.ceil(), self.z.ceil())
}
/// Rounds each component to the biggest integer equal or lower than the original value.
///
/// This behavior is preserved for negative values (unlike the basic cast).
///
/// ```rust
/// # use euclid::vec3;
/// enum Mm {}
///
/// assert_eq!(vec3::<_, Mm>(-0.1, -0.8, 0.4).floor(), vec3::<_, Mm>(-1.0, -1.0, 0.0))
/// ```
#[inline]
#[must_use]
pub fn floor(self) -> Self
where
T: Floor,
{
vec3(self.x.floor(), self.y.floor(), self.z.floor())
}
/// Creates translation by this vector in vector units
#[inline]
pub fn to_transform(self) -> Transform3D<T, U, U>
where
T: Zero + One,
{
Transform3D::translation(self.x, self.y, self.z)
}
}
impl<T, U> Vector3D<T, U>
where
T: Copy + Mul<T, Output = T> + Add<T, Output = T>,
{
/// Returns the vector's length squared.
#[inline]
pub fn square_length(self) -> T {
self.x * self.x + self.y * self.y + self.z * self.z
}
/// Returns this vector projected onto another one.
///
/// Projecting onto a nil vector will cause a division by zero.
#[inline]
pub fn project_onto_vector(self, onto: Self) -> Self
where
T: Sub<T, Output = T> + Div<T, Output = T>,
{
onto * (self.dot(onto) / onto.square_length())
}
}
impl<T: Float, U> Vector3D<T, U> {
/// Return the normalized vector even if the length is larger than the max value of Float.
#[inline]
#[must_use]
pub fn robust_normalize(self) -> Self {
let length = self.length();
if length.is_infinite() {
let scaled = self / T::max_value();
scaled / scaled.length()
} else {
self / length
}
}
/// Returns true if all members are finite.
#[inline]
pub fn is_finite(self) -> bool {
self.x.is_finite() && self.y.is_finite() && self.z.is_finite()
}
}
impl<T: Real, U> Vector3D<T, U> {
/// Returns the positive angle between this vector and another vector.
///
/// The returned angle is between 0 and PI.
pub fn angle_to(self, other: Self) -> Angle<T>
where
T: Trig,
{
Angle::radians(Trig::fast_atan2(
self.cross(other).length(),
self.dot(other),
))
}
/// Returns the vector length.
#[inline]
pub fn length(self) -> T {
self.square_length().sqrt()
}
/// Returns the vector with length of one unit
#[inline]
#[must_use]
pub fn normalize(self) -> Self {
self / self.length()
}
/// Returns the vector with length of one unit.
///
/// Unlike [`Vector2D::normalize`](#method.normalize), this returns None in the case that the
/// length of the vector is zero.
#[inline]
#[must_use]
pub fn try_normalize(self) -> Option<Self> {
let len = self.length();
if len == T::zero() {
None
} else {
Some(self / len)
}
}
/// Return this vector capped to a maximum length.
#[inline]
pub fn with_max_length(self, max_length: T) -> Self {
let square_length = self.square_length();
if square_length > max_length * max_length {
return self * (max_length / square_length.sqrt());
}
self
}
/// Return this vector with a minimum length applied.
#[inline]
pub fn with_min_length(self, min_length: T) -> Self {
let square_length = self.square_length();
if square_length < min_length * min_length {
return self * (min_length / square_length.sqrt());
}
self
}
/// Return this vector with minimum and maximum lengths applied.
#[inline]
pub fn clamp_length(self, min: T, max: T) -> Self {
debug_assert!(min <= max);
self.with_min_length(min).with_max_length(max)
}
}
impl<T, U> Vector3D<T, U>
where
T: Copy + One + Add<Output = T> + Sub<Output = T> + Mul<Output = T>,
{
/// Linearly interpolate each component between this vector and another vector.
///
/// # Example
///
/// ```rust
/// use euclid::vec3;
/// use euclid::default::Vector3D;
///
/// let from: Vector3D<_> = vec3(0.0, 10.0, -1.0);
/// let to: Vector3D<_> = vec3(8.0, -4.0, 0.0);
///
/// assert_eq!(from.lerp(to, -1.0), vec3(-8.0, 24.0, -2.0));
/// assert_eq!(from.lerp(to, 0.0), vec3( 0.0, 10.0, -1.0));
/// assert_eq!(from.lerp(to, 0.5), vec3( 4.0, 3.0, -0.5));
/// assert_eq!(from.lerp(to, 1.0), vec3( 8.0, -4.0, 0.0));
/// assert_eq!(from.lerp(to, 2.0), vec3(16.0, -18.0, 1.0));
/// ```
#[inline]
pub fn lerp(self, other: Self, t: T) -> Self {
let one_t = T::one() - t;
self * one_t + other * t
}
/// Returns a reflection vector using an incident ray and a surface normal.
#[inline]
pub fn reflect(self, normal: Self) -> Self {
let two = T::one() + T::one();
self - normal * two * self.dot(normal)
}
}
impl<T: PartialOrd, U> Vector3D<T, U> {
/// Returns the vector each component of which are minimum of this vector and another.
#[inline]
pub fn min(self, other: Self) -> Self {
vec3(
min(self.x, other.x),
min(self.y, other.y),
min(self.z, other.z),
)
}
/// Returns the vector each component of which are maximum of this vector and another.
#[inline]
pub fn max(self, other: Self) -> Self {
vec3(
max(self.x, other.x),
max(self.y, other.y),
max(self.z, other.z),
)
}
/// Returns the vector each component of which is clamped by corresponding
/// components of `start` and `end`.
///
/// Shortcut for `self.max(start).min(end)`.
#[inline]
pub fn clamp(self, start: Self, end: Self) -> Self
where
T: Copy,
{
self.max(start).min(end)
}
/// Returns vector with results of "greater than" operation on each component.
#[inline]
pub fn greater_than(self, other: Self) -> BoolVector3D {
BoolVector3D {
x: self.x > other.x,
y: self.y > other.y,
z: self.z > other.z,
}
}
/// Returns vector with results of "lower than" operation on each component.
#[inline]
pub fn lower_than(self, other: Self) -> BoolVector3D {
BoolVector3D {
x: self.x < other.x,
y: self.y < other.y,
z: self.z < other.z,
}
}
}
impl<T: PartialEq, U> Vector3D<T, U> {
/// Returns vector with results of "equal" operation on each component.
#[inline]
pub fn equal(self, other: Self) -> BoolVector3D {
BoolVector3D {
x: self.x == other.x,
y: self.y == other.y,
z: self.z == other.z,
}
}
/// Returns vector with results of "not equal" operation on each component.
#[inline]
pub fn not_equal(self, other: Self) -> BoolVector3D {
BoolVector3D {
x: self.x != other.x,
y: self.y != other.y,
z: self.z != other.z,
}
}
}
impl<T: NumCast + Copy, U> Vector3D<T, U> {
/// Cast from one numeric representation to another, preserving the units.
///
/// When casting from floating vector to integer coordinates, the decimals are truncated
/// as one would expect from a simple cast, but this behavior does not always make sense
/// geometrically. Consider using `round()`, `ceil()` or `floor()` before casting.
#[inline]
pub fn cast<NewT: NumCast>(self) -> Vector3D<NewT, U> {
self.try_cast().unwrap()
}
/// Fallible cast from one numeric representation to another, preserving the units.
///
/// When casting from floating vector to integer coordinates, the decimals are truncated
/// as one would expect from a simple cast, but this behavior does not always make sense
/// geometrically. Consider using `round()`, `ceil()` or `floor()` before casting.
pub fn try_cast<NewT: NumCast>(self) -> Option<Vector3D<NewT, U>> {
match (
NumCast::from(self.x),
NumCast::from(self.y),
NumCast::from(self.z),
) {
(Some(x), Some(y), Some(z)) => Some(vec3(x, y, z)),
_ => None,
}
}
// Convenience functions for common casts.
/// Cast into an `f32` vector.
#[inline]
pub fn to_f32(self) -> Vector3D<f32, U> {
self.cast()
}
/// Cast into an `f64` vector.
#[inline]
pub fn to_f64(self) -> Vector3D<f64, U> {
self.cast()
}
/// Cast into an `usize` vector, truncating decimals if any.
///
/// When casting from floating vector vectors, it is worth considering whether
/// to `round()`, `ceil()` or `floor()` before the cast in order to obtain
/// the desired conversion behavior.
#[inline]
pub fn to_usize(self) -> Vector3D<usize, U> {
self.cast()
}
/// Cast into an `u32` vector, truncating decimals if any.
///
/// When casting from floating vector vectors, it is worth considering whether
/// to `round()`, `ceil()` or `floor()` before the cast in order to obtain
/// the desired conversion behavior.
#[inline]
pub fn to_u32(self) -> Vector3D<u32, U> {
self.cast()
}
/// Cast into an `i32` vector, truncating decimals if any.
///
/// When casting from floating vector vectors, it is worth considering whether
/// to `round()`, `ceil()` or `floor()` before the cast in order to obtain
/// the desired conversion behavior.
#[inline]
pub fn to_i32(self) -> Vector3D<i32, U> {
self.cast()
}
/// Cast into an `i64` vector, truncating decimals if any.
///
/// When casting from floating vector vectors, it is worth considering whether
/// to `round()`, `ceil()` or `floor()` before the cast in order to obtain
/// the desired conversion behavior.
#[inline]
pub fn to_i64(self) -> Vector3D<i64, U> {
self.cast()
}
}
impl<T: Neg, U> Neg for Vector3D<T, U> {
type Output = Vector3D<T::Output, U>;
#[inline]
fn neg(self) -> Self::Output {
vec3(-self.x, -self.y, -self.z)
}
}
impl<T: Add, U> Add for Vector3D<T, U> {
type Output = Vector3D<T::Output, U>;
#[inline]
fn add(self, other: Self) -> Self::Output {
vec3(self.x + other.x, self.y + other.y, self.z + other.z)
}
}
impl<'a, T: 'a + Add + Copy, U: 'a> Add<&Self> for Vector3D<T, U> {
type Output = Vector3D<T::Output, U>;
#[inline]
fn add(self, other: &Self) -> Self::Output {
vec3(self.x + other.x, self.y + other.y, self.z + other.z)
}
}
impl<T: Add<Output = T> + Zero, U> Sum for Vector3D<T, U> {
fn sum<I: Iterator<Item = Self>>(iter: I) -> Self {
iter.fold(Self::zero(), Add::add)
}
}
impl<'a, T: 'a + Add<Output = T> + Copy + Zero, U: 'a> Sum<&'a Self> for Vector3D<T, U> {
fn sum<I: Iterator<Item = &'a Self>>(iter: I) -> Self {
iter.fold(Self::zero(), Add::add)
}
}
impl<T: Copy + Add<T, Output = T>, U> AddAssign for Vector3D<T, U> {
#[inline]
fn add_assign(&mut self, other: Self) {
*self = *self + other
}
}
impl<T: Sub, U> Sub for Vector3D<T, U> {
type Output = Vector3D<T::Output, U>;
#[inline]
fn sub(self, other: Self) -> Self::Output {
vec3(self.x - other.x, self.y - other.y, self.z - other.z)
}
}
impl<T: Copy + Sub<T, Output = T>, U> SubAssign<Vector3D<T, U>> for Vector3D<T, U> {
#[inline]
fn sub_assign(&mut self, other: Self) {
*self = *self - other
}
}
impl<T: Copy + Mul, U> Mul<T> for Vector3D<T, U> {
type Output = Vector3D<T::Output, U>;
#[inline]
fn mul(self, scale: T) -> Self::Output {
vec3(self.x * scale, self.y * scale, self.z * scale)
}
}
impl<T: Copy + Mul<T, Output = T>, U> MulAssign<T> for Vector3D<T, U> {
#[inline]
fn mul_assign(&mut self, scale: T) {
*self = *self * scale
}
}
impl<T: Copy + Mul, U1, U2> Mul<Scale<T, U1, U2>> for Vector3D<T, U1> {
type Output = Vector3D<T::Output, U2>;
#[inline]
fn mul(self, scale: Scale<T, U1, U2>) -> Self::Output {
vec3(self.x * scale.0, self.y * scale.0, self.z * scale.0)
}
}
impl<T: Copy + MulAssign, U> MulAssign<Scale<T, U, U>> for Vector3D<T, U> {
#[inline]
fn mul_assign(&mut self, scale: Scale<T, U, U>) {
self.x *= scale.0;
self.y *= scale.0;
self.z *= scale.0;
}
}
impl<T: Copy + Div, U> Div<T> for Vector3D<T, U> {
type Output = Vector3D<T::Output, U>;
#[inline]
fn div(self, scale: T) -> Self::Output {
vec3(self.x / scale, self.y / scale, self.z / scale)
}
}
impl<T: Copy + Div<T, Output = T>, U> DivAssign<T> for Vector3D<T, U> {
#[inline]
fn div_assign(&mut self, scale: T) {
*self = *self / scale
}
}
impl<T: Copy + Div, U1, U2> Div<Scale<T, U1, U2>> for Vector3D<T, U2> {
type Output = Vector3D<T::Output, U1>;
#[inline]
fn div(self, scale: Scale<T, U1, U2>) -> Self::Output {
vec3(self.x / scale.0, self.y / scale.0, self.z / scale.0)
}
}
impl<T: Copy + DivAssign, U> DivAssign<Scale<T, U, U>> for Vector3D<T, U> {
#[inline]
fn div_assign(&mut self, scale: Scale<T, U, U>) {
self.x /= scale.0;
self.y /= scale.0;
self.z /= scale.0;
}
}
impl<T: Round, U> Round for Vector3D<T, U> {
/// See [`Vector3D::round()`](#method.round)
#[inline]
fn round(self) -> Self {
self.round()
}
}
impl<T: Ceil, U> Ceil for Vector3D<T, U> {
/// See [`Vector3D::ceil()`](#method.ceil)
#[inline]
fn ceil(self) -> Self {
self.ceil()
}
}
impl<T: Floor, U> Floor for Vector3D<T, U> {
/// See [`Vector3D::floor()`](#method.floor)
#[inline]
fn floor(self) -> Self {
self.floor()
}
}
impl<T: ApproxEq<T>, U> ApproxEq<Vector3D<T, U>> for Vector3D<T, U> {
#[inline]
fn approx_epsilon() -> Self {
vec3(
T::approx_epsilon(),
T::approx_epsilon(),
T::approx_epsilon(),
)
}
#[inline]
fn approx_eq_eps(&self, other: &Self, eps: &Self) -> bool {
self.x.approx_eq_eps(&other.x, &eps.x)
&& self.y.approx_eq_eps(&other.y, &eps.y)
&& self.z.approx_eq_eps(&other.z, &eps.z)
}
}
impl<T, U> From<Vector3D<T, U>> for [T; 3] {
fn from(v: Vector3D<T, U>) -> Self {
[v.x, v.y, v.z]
}
}
impl<T, U> From<[T; 3]> for Vector3D<T, U> {
fn from([x, y, z]: [T; 3]) -> Self {
vec3(x, y, z)
}
}
impl<T, U> From<Vector3D<T, U>> for (T, T, T) {
fn from(v: Vector3D<T, U>) -> Self {
(v.x, v.y, v.z)
}
}
impl<T, U> From<(T, T, T)> for Vector3D<T, U> {
fn from(tuple: (T, T, T)) -> Self {
vec3(tuple.0, tuple.1, tuple.2)
}
}
/// A 2d vector of booleans, useful for component-wise logic operations.
#[derive(Copy, Clone, Debug, PartialEq, Eq, Hash)]
pub struct BoolVector2D {
pub x: bool,
pub y: bool,
}
/// A 3d vector of booleans, useful for component-wise logic operations.
#[derive(Copy, Clone, Debug, PartialEq, Eq, Hash)]
pub struct BoolVector3D {
pub x: bool,
pub y: bool,
pub z: bool,
}
impl BoolVector2D {
/// Returns `true` if all components are `true` and `false` otherwise.
#[inline]
pub fn all(self) -> bool {
self.x && self.y
}
/// Returns `true` if any component are `true` and `false` otherwise.
#[inline]
pub fn any(self) -> bool {
self.x || self.y
}
/// Returns `true` if all components are `false` and `false` otherwise. Negation of `any()`.
#[inline]
pub fn none(self) -> bool {
!self.any()
}
/// Returns new vector with by-component AND operation applied.
#[inline]
pub fn and(self, other: Self) -> Self {
BoolVector2D {
x: self.x && other.x,
y: self.y && other.y,
}
}
/// Returns new vector with by-component OR operation applied.
#[inline]
pub fn or(self, other: Self) -> Self {
BoolVector2D {
x: self.x || other.x,
y: self.y || other.y,
}
}
/// Returns new vector with results of negation operation on each component.
#[inline]
pub fn not(self) -> Self {
BoolVector2D {
x: !self.x,
y: !self.y,
}
}
/// Returns point, each component of which or from `a`, or from `b` depending on truly value
/// of corresponding vector component. `true` selects value from `a` and `false` from `b`.
#[inline]
pub fn select_point<T, U>(self, a: Point2D<T, U>, b: Point2D<T, U>) -> Point2D<T, U> {
point2(
if self.x { a.x } else { b.x },
if self.y { a.y } else { b.y },
)
}
/// Returns vector, each component of which or from `a`, or from `b` depending on truly value
/// of corresponding vector component. `true` selects value from `a` and `false` from `b`.
#[inline]
pub fn select_vector<T, U>(self, a: Vector2D<T, U>, b: Vector2D<T, U>) -> Vector2D<T, U> {
vec2(
if self.x { a.x } else { b.x },
if self.y { a.y } else { b.y },
)
}
/// Returns size, each component of which or from `a`, or from `b` depending on truly value
/// of corresponding vector component. `true` selects value from `a` and `false` from `b`.
#[inline]
pub fn select_size<T, U>(self, a: Size2D<T, U>, b: Size2D<T, U>) -> Size2D<T, U> {
size2(
if self.x { a.width } else { b.width },
if self.y { a.height } else { b.height },
)
}
}
impl BoolVector3D {
/// Returns `true` if all components are `true` and `false` otherwise.
#[inline]
pub fn all(self) -> bool {
self.x && self.y && self.z
}
/// Returns `true` if any component are `true` and `false` otherwise.
#[inline]
pub fn any(self) -> bool {
self.x || self.y || self.z
}
/// Returns `true` if all components are `false` and `false` otherwise. Negation of `any()`.
#[inline]
pub fn none(self) -> bool {
!self.any()
}
/// Returns new vector with by-component AND operation applied.
#[inline]
pub fn and(self, other: Self) -> Self {
BoolVector3D {
x: self.x && other.x,
y: self.y && other.y,
z: self.z && other.z,
}
}
/// Returns new vector with by-component OR operation applied.
#[inline]
pub fn or(self, other: Self) -> Self {
BoolVector3D {
x: self.x || other.x,
y: self.y || other.y,
z: self.z || other.z,
}
}
/// Returns new vector with results of negation operation on each component.
#[inline]
pub fn not(self) -> Self {
BoolVector3D {
x: !self.x,
y: !self.y,
z: !self.z,
}
}
/// Returns point, each component of which or from `a`, or from `b` depending on truly value
/// of corresponding vector component. `true` selects value from `a` and `false` from `b`.
#[inline]
pub fn select_point<T, U>(self, a: Point3D<T, U>, b: Point3D<T, U>) -> Point3D<T, U> {
point3(
if self.x { a.x } else { b.x },
if self.y { a.y } else { b.y },
if self.z { a.z } else { b.z },
)
}
/// Returns vector, each component of which or from `a`, or from `b` depending on truly value
/// of corresponding vector component. `true` selects value from `a` and `false` from `b`.
#[inline]
pub fn select_vector<T, U>(self, a: Vector3D<T, U>, b: Vector3D<T, U>) -> Vector3D<T, U> {
vec3(
if self.x { a.x } else { b.x },
if self.y { a.y } else { b.y },
if self.z { a.z } else { b.z },
)
}
/// Returns size, each component of which or from `a`, or from `b` depending on truly value
/// of corresponding vector component. `true` selects value from `a` and `false` from `b`.
#[inline]
#[must_use]
pub fn select_size<T, U>(self, a: Size3D<T, U>, b: Size3D<T, U>) -> Size3D<T, U> {
size3(
if self.x { a.width } else { b.width },
if self.y { a.height } else { b.height },
if self.z { a.depth } else { b.depth },
)
}
/// Returns a 2d vector using this vector's x and y coordinates.
#[inline]
pub fn xy(self) -> BoolVector2D {
BoolVector2D {
x: self.x,
y: self.y,
}
}
/// Returns a 2d vector using this vector's x and z coordinates.
#[inline]
pub fn xz(self) -> BoolVector2D {
BoolVector2D {
x: self.x,
y: self.z,
}
}
/// Returns a 2d vector using this vector's y and z coordinates.
#[inline]
pub fn yz(self) -> BoolVector2D {
BoolVector2D {
x: self.y,
y: self.z,
}
}
}
/// Convenience constructor.
#[inline]
pub const fn vec2<T, U>(x: T, y: T) -> Vector2D<T, U> {
Vector2D {
x,
y,
_unit: PhantomData,
}
}
/// Convenience constructor.
#[inline]
pub const fn vec3<T, U>(x: T, y: T, z: T) -> Vector3D<T, U> {
Vector3D {
x,
y,
z,
_unit: PhantomData,
}
}
/// Shorthand for `BoolVector2D { x, y }`.
#[inline]
pub const fn bvec2(x: bool, y: bool) -> BoolVector2D {
BoolVector2D { x, y }
}
/// Shorthand for `BoolVector3D { x, y, z }`.
#[inline]
pub const fn bvec3(x: bool, y: bool, z: bool) -> BoolVector3D {
BoolVector3D { x, y, z }
}
#[cfg(test)]
mod vector2d {
use crate::scale::Scale;
use crate::{default, vec2};
#[cfg(feature = "mint")]
use mint;
type Vec2 = default::Vector2D<f32>;
#[test]
pub fn test_scalar_mul() {
let p1: Vec2 = vec2(3.0, 5.0);
let result = p1 * 5.0;
assert_eq!(result, Vec2::new(15.0, 25.0));
}
#[test]
pub fn test_dot() {
let p1: Vec2 = vec2(2.0, 7.0);
let p2: Vec2 = vec2(13.0, 11.0);
assert_eq!(p1.dot(p2), 103.0);
}
#[test]
pub fn test_cross() {
let p1: Vec2 = vec2(4.0, 7.0);
let p2: Vec2 = vec2(13.0, 8.0);
let r = p1.cross(p2);
assert_eq!(r, -59.0);
}
#[test]
pub fn test_normalize() {
use std::f32;
let p0: Vec2 = Vec2::zero();
let p1: Vec2 = vec2(4.0, 0.0);
let p2: Vec2 = vec2(3.0, -4.0);
assert!(p0.normalize().x.is_nan() && p0.normalize().y.is_nan());
assert_eq!(p1.normalize(), vec2(1.0, 0.0));
assert_eq!(p2.normalize(), vec2(0.6, -0.8));
let p3: Vec2 = vec2(::std::f32::MAX, ::std::f32::MAX);
assert_ne!(
p3.normalize(),
vec2(1.0 / 2.0f32.sqrt(), 1.0 / 2.0f32.sqrt())
);
assert_eq!(
p3.robust_normalize(),
vec2(1.0 / 2.0f32.sqrt(), 1.0 / 2.0f32.sqrt())
);
let p4: Vec2 = Vec2::zero();
assert!(p4.try_normalize().is_none());
let p5: Vec2 = Vec2::new(f32::MIN_POSITIVE, f32::MIN_POSITIVE);
assert!(p5.try_normalize().is_none());
let p6: Vec2 = vec2(4.0, 0.0);
let p7: Vec2 = vec2(3.0, -4.0);
assert_eq!(p6.try_normalize().unwrap(), vec2(1.0, 0.0));
assert_eq!(p7.try_normalize().unwrap(), vec2(0.6, -0.8));
}
#[test]
pub fn test_min() {
let p1: Vec2 = vec2(1.0, 3.0);
let p2: Vec2 = vec2(2.0, 2.0);
let result = p1.min(p2);
assert_eq!(result, vec2(1.0, 2.0));
}
#[test]
pub fn test_max() {
let p1: Vec2 = vec2(1.0, 3.0);
let p2: Vec2 = vec2(2.0, 2.0);
let result = p1.max(p2);
assert_eq!(result, vec2(2.0, 3.0));
}
#[test]
pub fn test_angle_from_x_axis() {
use crate::approxeq::ApproxEq;
use core::f32::consts::FRAC_PI_2;
let right: Vec2 = vec2(10.0, 0.0);
let down: Vec2 = vec2(0.0, 4.0);
let up: Vec2 = vec2(0.0, -1.0);
assert!(right.angle_from_x_axis().get().approx_eq(&0.0));
assert!(down.angle_from_x_axis().get().approx_eq(&FRAC_PI_2));
assert!(up.angle_from_x_axis().get().approx_eq(&-FRAC_PI_2));
}
#[test]
pub fn test_angle_to() {
use crate::approxeq::ApproxEq;
use core::f32::consts::FRAC_PI_2;
let right: Vec2 = vec2(10.0, 0.0);
let right2: Vec2 = vec2(1.0, 0.0);
let up: Vec2 = vec2(0.0, -1.0);
let up_left: Vec2 = vec2(-1.0, -1.0);
assert!(right.angle_to(right2).get().approx_eq(&0.0));
assert!(right.angle_to(up).get().approx_eq(&-FRAC_PI_2));
assert!(up.angle_to(right).get().approx_eq(&FRAC_PI_2));
assert!(up_left
.angle_to(up)
.get()
.approx_eq_eps(&(0.5 * FRAC_PI_2), &0.0005));
}
#[test]
pub fn test_with_max_length() {
use crate::approxeq::ApproxEq;
let v1: Vec2 = vec2(0.5, 0.5);
let v2: Vec2 = vec2(1.0, 0.0);
let v3: Vec2 = vec2(0.1, 0.2);
let v4: Vec2 = vec2(2.0, -2.0);
let v5: Vec2 = vec2(1.0, 2.0);
let v6: Vec2 = vec2(-1.0, 3.0);
assert_eq!(v1.with_max_length(1.0), v1);
assert_eq!(v2.with_max_length(1.0), v2);
assert_eq!(v3.with_max_length(1.0), v3);
assert_eq!(v4.with_max_length(10.0), v4);
assert_eq!(v5.with_max_length(10.0), v5);
assert_eq!(v6.with_max_length(10.0), v6);
let v4_clamped = v4.with_max_length(1.0);
assert!(v4_clamped.length().approx_eq(&1.0));
assert!(v4_clamped.normalize().approx_eq(&v4.normalize()));
let v5_clamped = v5.with_max_length(1.5);
assert!(v5_clamped.length().approx_eq(&1.5));
assert!(v5_clamped.normalize().approx_eq(&v5.normalize()));
let v6_clamped = v6.with_max_length(2.5);
assert!(v6_clamped.length().approx_eq(&2.5));
assert!(v6_clamped.normalize().approx_eq(&v6.normalize()));
}
#[test]
pub fn test_project_onto_vector() {
use crate::approxeq::ApproxEq;
let v1: Vec2 = vec2(1.0, 2.0);
let x: Vec2 = vec2(1.0, 0.0);
let y: Vec2 = vec2(0.0, 1.0);
assert!(v1.project_onto_vector(x).approx_eq(&vec2(1.0, 0.0)));
assert!(v1.project_onto_vector(y).approx_eq(&vec2(0.0, 2.0)));
assert!(v1.project_onto_vector(-x).approx_eq(&vec2(1.0, 0.0)));
assert!(v1.project_onto_vector(x * 10.0).approx_eq(&vec2(1.0, 0.0)));
assert!(v1.project_onto_vector(v1 * 2.0).approx_eq(&v1));
assert!(v1.project_onto_vector(-v1).approx_eq(&v1));
}
#[cfg(feature = "mint")]
#[test]
pub fn test_mint() {
let v1 = Vec2::new(1.0, 3.0);
let vm: mint::Vector2<_> = v1.into();
let v2 = Vec2::from(vm);
assert_eq!(v1, v2);
}
pub enum Mm {}
pub enum Cm {}
pub type Vector2DMm<T> = super::Vector2D<T, Mm>;
pub type Vector2DCm<T> = super::Vector2D<T, Cm>;
#[test]
pub fn test_add() {
let p1 = Vector2DMm::new(1.0, 2.0);
let p2 = Vector2DMm::new(3.0, 4.0);
assert_eq!(p1 + p2, vec2(4.0, 6.0));
assert_eq!(p1 + &p2, vec2(4.0, 6.0));
}
#[test]
pub fn test_sum() {
let vecs = [
Vector2DMm::new(1.0, 2.0),
Vector2DMm::new(3.0, 4.0),
Vector2DMm::new(5.0, 6.0),
];
let sum = Vector2DMm::new(9.0, 12.0);
assert_eq!(vecs.iter().sum::<Vector2DMm<_>>(), sum);
}
#[test]
pub fn test_add_assign() {
let mut p1 = Vector2DMm::new(1.0, 2.0);
p1 += vec2(3.0, 4.0);
assert_eq!(p1, vec2(4.0, 6.0));
}
#[test]
pub fn test_typed_scalar_mul() {
let p1 = Vector2DMm::new(1.0, 2.0);
let cm_per_mm = Scale::<f32, Mm, Cm>::new(0.1);
let result: Vector2DCm<f32> = p1 * cm_per_mm;
assert_eq!(result, vec2(0.1, 0.2));
}
#[test]
pub fn test_swizzling() {
let p: default::Vector2D<i32> = vec2(1, 2);
assert_eq!(p.yx(), vec2(2, 1));
}
#[test]
pub fn test_reflect() {
use crate::approxeq::ApproxEq;
let a: Vec2 = vec2(1.0, 3.0);
let n1: Vec2 = vec2(0.0, -1.0);
let n2: Vec2 = vec2(1.0, -1.0).normalize();
assert!(a.reflect(n1).approx_eq(&vec2(1.0, -3.0)));
assert!(a.reflect(n2).approx_eq(&vec2(3.0, 1.0)));
}
}
#[cfg(test)]
mod vector3d {
use crate::scale::Scale;
use crate::{default, vec2, vec3};
#[cfg(feature = "mint")]
use mint;
type Vec3 = default::Vector3D<f32>;
#[test]
pub fn test_add() {
let p1 = Vec3::new(1.0, 2.0, 3.0);
let p2 = Vec3::new(4.0, 5.0, 6.0);
assert_eq!(p1 + p2, vec3(5.0, 7.0, 9.0));
assert_eq!(p1 + &p2, vec3(5.0, 7.0, 9.0));
}
#[test]
pub fn test_sum() {
let vecs = [
Vec3::new(1.0, 2.0, 3.0),
Vec3::new(4.0, 5.0, 6.0),
Vec3::new(7.0, 8.0, 9.0),
];
let sum = Vec3::new(12.0, 15.0, 18.0);
assert_eq!(vecs.iter().sum::<Vec3>(), sum);
}
#[test]
pub fn test_dot() {
let p1: Vec3 = vec3(7.0, 21.0, 32.0);
let p2: Vec3 = vec3(43.0, 5.0, 16.0);
assert_eq!(p1.dot(p2), 918.0);
}
#[test]
pub fn test_cross() {
let p1: Vec3 = vec3(4.0, 7.0, 9.0);
let p2: Vec3 = vec3(13.0, 8.0, 3.0);
let p3 = p1.cross(p2);
assert_eq!(p3, vec3(-51.0, 105.0, -59.0));
}
#[test]
pub fn test_normalize() {
use std::f32;
let p0: Vec3 = Vec3::zero();
let p1: Vec3 = vec3(0.0, -6.0, 0.0);
let p2: Vec3 = vec3(1.0, 2.0, -2.0);
assert!(
p0.normalize().x.is_nan() && p0.normalize().y.is_nan() && p0.normalize().z.is_nan()
);
assert_eq!(p1.normalize(), vec3(0.0, -1.0, 0.0));
assert_eq!(p2.normalize(), vec3(1.0 / 3.0, 2.0 / 3.0, -2.0 / 3.0));
let p3: Vec3 = vec3(::std::f32::MAX, ::std::f32::MAX, 0.0);
assert_ne!(
p3.normalize(),
vec3(1.0 / 2.0f32.sqrt(), 1.0 / 2.0f32.sqrt(), 0.0)
);
assert_eq!(
p3.robust_normalize(),
vec3(1.0 / 2.0f32.sqrt(), 1.0 / 2.0f32.sqrt(), 0.0)
);
let p4: Vec3 = Vec3::zero();
assert!(p4.try_normalize().is_none());
--> --------------------
--> maximum size reached
--> --------------------
[ Dauer der Verarbeitung: 0.49 Sekunden
(vorverarbeitet)
]
|
2026-04-04
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