euclid/

vector.rs

// 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 = "malloc_size_of")]
use malloc_size_of::{MallocSizeOf, MallocSizeOfOps};
#[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 = "malloc_size_of")]
impl<T: MallocSizeOf, U> MallocSizeOf for Vector2D<T, U> {
    fn size_of(&self, ops: &mut MallocSizeOfOps) -> usize {
        self.x.size_of(ops) + self.y.size_of(ops)
    }
}

#[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`], 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 `isize` 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_isize(self) -> Vector2D<isize, 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`].
    #[inline]
    fn round(self) -> Self {
        self.round()
    }
}

impl<T: Ceil, U> Ceil for Vector2D<T, U> {
    /// See [`Vector2D::ceil`].
    #[inline]
    fn ceil(self) -> Self {
        self.ceil()
    }
}

impl<T: Floor, U> Floor for Vector2D<T, U> {
    /// See [`Vector2D::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 = "arbitrary")]
impl<'a, T, U> arbitrary::Arbitrary<'a> for Vector3D<T, U>
where
    T: arbitrary::Arbitrary<'a>,
{
    fn arbitrary(u: &mut arbitrary::Unstructured<'a>) -> arbitrary::Result<Self> {
        let (x, y, z) = arbitrary::Arbitrary::arbitrary(u)?;
        Ok(Vector3D {
            x,
            y,
            z,
            _unit: PhantomData,
        })
    }
}

#[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> {}

#[cfg(feature = "malloc_size_of")]
impl<T: MallocSizeOf, U> MallocSizeOf for Vector3D<T, U> {
    fn size_of(&self, ops: &mut MallocSizeOfOps) -> usize {
        self.x.size_of(ops) + self.y.size_of(ops) + self.z.size_of(ops)
    }
}

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`], 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 `isize` 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_isize(self) -> Vector3D<isize, 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`].
    #[inline]
    fn round(self) -> Self {
        self.round()
    }
}

impl<T: Ceil, U> Ceil for Vector3D<T, U> {
    /// See [`Vector3D::ceil`].
    #[inline]
    fn ceil(self) -> Self {
        self.ceil()
    }
}

impl<T: Floor, U> Floor for Vector3D<T, U> {
    /// See [`Vector3D::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,
        }
    }
}

#[cfg(feature = "arbitrary")]
impl<'a> arbitrary::Arbitrary<'a> for BoolVector2D {
    fn arbitrary(u: &mut arbitrary::Unstructured<'a>) -> arbitrary::Result<Self> {
        Ok(BoolVector2D {
            x: arbitrary::Arbitrary::arbitrary(u)?,
            y: arbitrary::Arbitrary::arbitrary(u)?,
        })
    }
}

#[cfg(feature = "arbitrary")]
impl<'a> arbitrary::Arbitrary<'a> for BoolVector3D {
    fn arbitrary(u: &mut arbitrary::Unstructured<'a>) -> arbitrary::Result<Self> {
        Ok(BoolVector3D {
            x: arbitrary::Arbitrary::arbitrary(u)?,
            y: arbitrary::Arbitrary::arbitrary(u)?,
            z: arbitrary::Arbitrary::arbitrary(u)?,
        })
    }
}

/// 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());
        let p5: Vec3 = Vec3::new(f32::MIN_POSITIVE, f32::MIN_POSITIVE, f32::MIN_POSITIVE);
        assert!(p5.try_normalize().is_none());

        let p6: Vec3 = vec3(4.0, 0.0, 3.0);
        let p7: Vec3 = vec3(3.0, -4.0, 0.0);
        assert_eq!(p6.try_normalize().unwrap(), vec3(0.8, 0.0, 0.6));
        assert_eq!(p7.try_normalize().unwrap(), vec3(0.6, -0.8, 0.0));
    }

    #[test]
    pub fn test_min() {
        let p1: Vec3 = vec3(1.0, 3.0, 5.0);
        let p2: Vec3 = vec3(2.0, 2.0, -1.0);

        let result = p1.min(p2);

        assert_eq!(result, vec3(1.0, 2.0, -1.0));
    }

    #[test]
    pub fn test_max() {
        let p1: Vec3 = vec3(1.0, 3.0, 5.0);
        let p2: Vec3 = vec3(2.0, 2.0, -1.0);

        let result = p1.max(p2);

        assert_eq!(result, vec3(2.0, 3.0, 5.0));
    }

    #[test]
    pub fn test_clamp() {
        let p1: Vec3 = vec3(1.0, -1.0, 5.0);
        let p2: Vec3 = vec3(2.0, 5.0, 10.0);
        let p3: Vec3 = vec3(-1.0, 2.0, 20.0);

        let result = p3.clamp(p1, p2);

        assert_eq!(result, vec3(1.0, 2.0, 10.0));
    }

    #[test]
    pub fn test_typed_scalar_mul() {
        enum Mm {}
        enum Cm {}

        let p1 = super::Vector3D::<f32, Mm>::new(1.0, 2.0, 3.0);
        let cm_per_mm = Scale::<f32, Mm, Cm>::new(0.1);

        let result: super::Vector3D<f32, Cm> = p1 * cm_per_mm;

        assert_eq!(result, vec3(0.1, 0.2, 0.3));
    }

    #[test]
    pub fn test_swizzling() {
        let p: Vec3 = vec3(1.0, 2.0, 3.0);
        assert_eq!(p.xy(), vec2(1.0, 2.0));
        assert_eq!(p.xz(), vec2(1.0, 3.0));
        assert_eq!(p.yz(), vec2(2.0, 3.0));
    }

    #[cfg(feature = "mint")]
    #[test]
    pub fn test_mint() {
        let v1 = Vec3::new(1.0, 3.0, 5.0);
        let vm: mint::Vector3<_> = v1.into();
        let v2 = Vec3::from(vm);

        assert_eq!(v1, v2);
    }

    #[test]
    pub fn test_reflect() {
        use crate::approxeq::ApproxEq;
        let a: Vec3 = vec3(1.0, 3.0, 2.0);
        let n1: Vec3 = vec3(0.0, -1.0, 0.0);
        let n2: Vec3 = vec3(0.0, 1.0, 1.0).normalize();

        assert!(a.reflect(n1).approx_eq(&vec3(1.0, -3.0, 2.0)));
        assert!(a.reflect(n2).approx_eq(&vec3(1.0, -2.0, -3.0)));
    }

    #[test]
    pub fn test_angle_to() {
        use crate::approxeq::ApproxEq;
        use core::f32::consts::FRAC_PI_2;

        let right: Vec3 = vec3(10.0, 0.0, 0.0);
        let right2: Vec3 = vec3(1.0, 0.0, 0.0);
        let up: Vec3 = vec3(0.0, -1.0, 0.0);
        let up_left: Vec3 = vec3(-1.0, -1.0, 0.0);

        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: Vec3 = vec3(0.5, 0.5, 0.0);
        let v2: Vec3 = vec3(1.0, 0.0, 0.0);
        let v3: Vec3 = vec3(0.1, 0.2, 0.3);
        let v4: Vec3 = vec3(2.0, -2.0, 2.0);
        let v5: Vec3 = vec3(1.0, 2.0, -3.0);
        let v6: Vec3 = vec3(-1.0, 3.0, 2.0);

        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: Vec3 = vec3(1.0, 2.0, 3.0);
        let x: Vec3 = vec3(1.0, 0.0, 0.0);
        let y: Vec3 = vec3(0.0, 1.0, 0.0);
        let z: Vec3 = vec3(0.0, 0.0, 1.0);

        assert!(v1.project_onto_vector(x).approx_eq(&vec3(1.0, 0.0, 0.0)));
        assert!(v1.project_onto_vector(y).approx_eq(&vec3(0.0, 2.0, 0.0)));
        assert!(v1.project_onto_vector(z).approx_eq(&vec3(0.0, 0.0, 3.0)));
        assert!(v1.project_onto_vector(-x).approx_eq(&vec3(1.0, 0.0, 0.0)));
        assert!(v1
            .project_onto_vector(x * 10.0)
            .approx_eq(&vec3(1.0, 0.0, 0.0)));
        assert!(v1.project_onto_vector(v1 * 2.0).approx_eq(&v1));
        assert!(v1.project_onto_vector(-v1).approx_eq(&v1));
    }
}

#[cfg(test)]
mod bool_vector {
    use super::*;
    use crate::default;
    type Vec2 = default::Vector2D<f32>;
    type Vec3 = default::Vector3D<f32>;

    #[test]
    fn test_bvec2() {
        assert_eq!(
            Vec2::new(1.0, 2.0).greater_than(Vec2::new(2.0, 1.0)),
            bvec2(false, true),
        );

        assert_eq!(
            Vec2::new(1.0, 2.0).lower_than(Vec2::new(2.0, 1.0)),
            bvec2(true, false),
        );

        assert_eq!(
            Vec2::new(1.0, 2.0).equal(Vec2::new(1.0, 3.0)),
            bvec2(true, false),
        );

        assert_eq!(
            Vec2::new(1.0, 2.0).not_equal(Vec2::new(1.0, 3.0)),
            bvec2(false, true),
        );

        assert!(bvec2(true, true).any());
        assert!(bvec2(false, true).any());
        assert!(bvec2(true, false).any());
        assert!(!bvec2(false, false).any());
        assert!(bvec2(false, false).none());
        assert!(bvec2(true, true).all());
        assert!(!bvec2(false, true).all());
        assert!(!bvec2(true, false).all());
        assert!(!bvec2(false, false).all());

        assert_eq!(bvec2(true, false).not(), bvec2(false, true));
        assert_eq!(
            bvec2(true, false).and(bvec2(true, true)),
            bvec2(true, false)
        );
        assert_eq!(bvec2(true, false).or(bvec2(true, true)), bvec2(true, true));

        assert_eq!(
            bvec2(true, false).select_vector(Vec2::new(1.0, 2.0), Vec2::new(3.0, 4.0)),
            Vec2::new(1.0, 4.0),
        );
    }

    #[test]
    fn test_bvec3() {
        assert_eq!(
            Vec3::new(1.0, 2.0, 3.0).greater_than(Vec3::new(3.0, 2.0, 1.0)),
            bvec3(false, false, true),
        );

        assert_eq!(
            Vec3::new(1.0, 2.0, 3.0).lower_than(Vec3::new(3.0, 2.0, 1.0)),
            bvec3(true, false, false),
        );

        assert_eq!(
            Vec3::new(1.0, 2.0, 3.0).equal(Vec3::new(3.0, 2.0, 1.0)),
            bvec3(false, true, false),
        );

        assert_eq!(
            Vec3::new(1.0, 2.0, 3.0).not_equal(Vec3::new(3.0, 2.0, 1.0)),
            bvec3(true, false, true),
        );

        assert!(bvec3(true, true, false).any());
        assert!(bvec3(false, true, false).any());
        assert!(bvec3(true, false, false).any());
        assert!(!bvec3(false, false, false).any());
        assert!(bvec3(false, false, false).none());
        assert!(bvec3(true, true, true).all());
        assert!(!bvec3(false, true, false).all());
        assert!(!bvec3(true, false, false).all());
        assert!(!bvec3(false, false, false).all());

        assert_eq!(bvec3(true, false, true).not(), bvec3(false, true, false));
        assert_eq!(
            bvec3(true, false, true).and(bvec3(true, true, false)),
            bvec3(true, false, false)
        );
        assert_eq!(
            bvec3(true, false, false).or(bvec3(true, true, false)),
            bvec3(true, true, false)
        );

        assert_eq!(
            bvec3(true, false, true)
                .select_vector(Vec3::new(1.0, 2.0, 3.0), Vec3::new(4.0, 5.0, 6.0)),
            Vec3::new(1.0, 5.0, 3.0),
        );
    }
}