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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::{Zeroable, Pod};
+
+/// 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)
+ }
+
+ /// 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> Into<[T; 2]> for Vector2D<T, U> {
+ fn into(self) -> [T; 2] {
+ [self.x, self.y]
+ }
+}
+
+impl<T, U> From<[T; 2]> for Vector2D<T, U> {
+ fn from([x, y]: [T; 2]) -> Self {
+ vec2(x, y)
+ }
+}
+
+impl<T, U> Into<(T, T)> for Vector2D<T, U> {
+ fn into(self) -> (T, T) {
+ (self.x, self.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(size: Size2D<T, U>) -> Self {
+ vec2(size.width, size.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)
+ }
+
+ /// 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> Into<[T; 3]> for Vector3D<T, U> {
+ fn into(self) -> [T; 3] {
+ [self.x, self.y, self.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> Into<(T, T, T)> for Vector3D<T, U> {
+ fn into(self) -> (T, T, T) {
+ (self.x, self.y, self.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_tpyed_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),
+ );
+ }
+}
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