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fuchsia / fuchsia / cafe43e483c36c5bfaa6e2decea566ed245832f8 / . / third_party / rust_crates / vendor / euclid / src / vector.rs
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// Copyright 2013 The Servo Project Developers. See the COPYRIGHT
// file at the top-level directory of this distribution.
//
// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
// option. This file may not be copied, modified, or distributed
// except according to those terms.
use super::UnknownUnit;
use approxeq::ApproxEq;
use length::Length;
#[cfg(feature = "mint")]
use mint;
use point::{Point2D, Point3D, point2, point3};
use size::{Size2D, size2};
use scale::Scale;
use transform2d::Transform2D;
use transform3d::Transform3D;
use trig::Trig;
use Angle;
use num::*;
use num_traits::{Float, NumCast, Signed};
use core::fmt;
use core::ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, Sub, SubAssign};
use core::marker::PhantomData;
use core::cmp::{Eq, PartialEq};
use core::hash::{Hash};
#[cfg(feature = "serde")]
use serde;
/// A 2d Vector tagged with a unit.
#[repr(C)]
pub struct Vector2D<T, U> {
pub x: T,
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) = try!(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)
}
}
impl<T, U> Eq for Vector2D<T, U> where T: Eq {}
impl<T, U> PartialEq for Vector2D<T, U>
where T: PartialEq
{
fn eq(&self, other: &Self) -> bool {
self.x == other.x && self.y == other.y
}
}
impl<T, U> Hash for Vector2D<T, U>
where T: Hash
{
fn hash<H: ::core::hash::Hasher>(&self, h: &mut H) {
self.x.hash(h);
self.y.hash(h);
}
}
impl<T: Copy + Zero, U> Vector2D<T, U> {
/// Constructor, setting all components to zero.
#[inline]
pub fn zero() -> Self {
Vector2D::new(Zero::zero(), Zero::zero())
}
/// Convert into a 3d vector.
#[inline]
pub fn to_3d(&self) -> Vector3D<T, U> {
vec3(self.x, self.y, Zero::zero())
}
}
impl<T: fmt::Debug, U> fmt::Debug for Vector2D<T, U> {
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
write!(f, "({:?},{:?})", self.x, self.y)
}
}
impl<T: fmt::Display, U> fmt::Display for Vector2D<T, U> {
fn fmt(&self, formatter: &mut fmt::Formatter) -> fmt::Result {
write!(formatter, "({},{})", self.x, self.y)
}
}
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 taking scalar values directly.
#[inline]
pub const fn new(x: T, y: T) -> Self {
Vector2D {
x,
y,
_unit: PhantomData,
}
}
}
impl<T: Copy, U> Vector2D<T, U> {
/// 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)
}
/// 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)
}
/// Tag a unit-less value with units.
#[inline]
pub fn from_untyped(p: Vector2D<T, UnknownUnit>) -> Self {
vec2(p.x, p.y)
}
/// Cast the unit
#[inline]
pub fn cast_unit<V>(&self) -> Vector2D<T, V> {
vec2(self.x, self.y)
}
#[inline]
pub fn to_array(&self) -> [T; 2] {
[self.x, self.y]
}
#[inline]
pub fn to_tuple(&self) -> (T, T) {
(self.x, self.y)
}
}
impl<T, U> Vector2D<T, U>
where
T: Copy
+ Clone
+ Add<T, Output = T>
+ Mul<T, Output = T>
+ Div<T, Output = T>
+ Sub<T, Output = T>
+ Trig
+ PartialOrd
+ One
+ Zero {
#[inline]
pub fn to_transform(&self) -> Transform2D<T, U, U> {
Transform2D::create_translation(self.x, self.y)
}
}
impl<T, U> Vector2D<T, U>
where
T: Trig + Copy + Sub<T, Output = T>,
{
/// Returns the signed angle between this vector and the x axis.
///
/// The returned angle is between -PI and PI.
pub fn angle_from_x_axis(&self) -> Angle<T> {
Angle::radians(Trig::fast_atan2(self.y, self.x))
}
}
impl<T, U> Vector2D<T, U>
where
T: Copy + Mul<T, Output = T> + Add<T, Output = T> + Sub<T, Output = T>
+ Trig + Copy + Sub<T, Output = T>,
{
/// 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> {
Angle::radians(Trig::fast_atan2(self.cross(other), self.dot(other)))
}
}
impl<T, U> Vector2D<T, U>
where
T: Copy + Mul<T, Output = T> + Add<T, Output = T> + Sub<T, Output = T>,
{
/// Dot product.
#[inline]
pub fn dot(self, other: Self) -> 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 {
self.x * other.y - self.y * other.x
}
#[inline]
pub fn normalize(self) -> Self
where
T: Float,
{
self / self.length()
}
/// Return the normalized vector even if the length is larger than the max value of Float.
#[inline]
pub fn robust_normalize(self) -> Self
where
T: Float,
{
let length = self.length();
if length.is_infinite() {
let scaled = self / T::max_value();
scaled / scaled.length()
} else {
self / length
}
}
#[inline]
pub fn square_length(&self) -> T {
self.x * self.x + self.y * self.y
}
#[inline]
pub fn length(&self) -> T
where
T: Float,
{
self.square_length().sqrt()
}
/// 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: Div<T, Output = T>
{
onto * (self.dot(onto) / onto.square_length())
}
}
impl<T, U> Vector2D<T, U>
where
T: Copy + Mul<T, Output = T> + Add<T, Output = T> + Sub<T, Output = T>
+ PartialOrd + Float
{
/// 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 between this vector and another vector.
///
/// `t` is expected to be between zero and one.
#[inline]
pub fn lerp(&self, other: Self, t: T) -> Self {
let one_t = T::one() - t;
(*self) * one_t + other * t
}
}
impl<T, U> Vector2D<T, U>
where
T: Copy + One + Mul<T, Output = T> + Add<T, Output = T> + Sub<T, Output = 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: Copy + Add<T, Output = T>, U> Add for Vector2D<T, U> {
type Output = Self;
fn add(self, other: Self) -> Self {
Vector2D::new(self.x + other.x, self.y + other.y)
}
}
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: 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 + Sub<T, Output = T>, U> Sub for Vector2D<T, U> {
type Output = Self;
#[inline]
fn sub(self, other: Self) -> Self {
vec2(self.x - other.x, self.y - other.y)
}
}
impl<T: Copy + Neg<Output = T>, U> Neg for Vector2D<T, U> {
type Output = Self;
#[inline]
fn neg(self) -> Self {
vec2(-self.x, -self.y)
}
}
impl<T: Float, U> Vector2D<T, U> {
#[inline]
pub fn min(self, other: Self) -> Self {
vec2(self.x.min(other.x), self.y.min(other.y))
}
#[inline]
pub fn max(self, other: Self) -> Self {
vec2(self.x.max(other.x), self.y.max(other.y))
}
#[inline]
pub fn clamp(&self, start: Self, end: Self) -> Self {
self.max(start).min(end)
}
}
impl<T: Copy + Mul<T, Output = T>, U> Mul<T> for Vector2D<T, U> {
type Output = Self;
#[inline]
fn mul(self, scale: T) -> Self {
vec2(self.x * scale, self.y * scale)
}
}
impl<T: Copy + Div<T, Output = T>, U> Div<T> for Vector2D<T, U> {
type Output = Self;
#[inline]
fn div(self, scale: T) -> Self {
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 + 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 + Mul<T, Output = T>, U1, U2> Mul<Scale<T, U1, U2>> for Vector2D<T, U1> {
type Output = Vector2D<T, U2>;
#[inline]
fn mul(self, scale: Scale<T, U1, U2>) -> Self::Output {
vec2(self.x * scale.get(), self.y * scale.get())
}
}
impl<T: Copy + Div<T, Output = T>, U1, U2> Div<Scale<T, U1, U2>> for Vector2D<T, U2> {
type Output = Vector2D<T, U1>;
#[inline]
fn div(self, scale: Scale<T, U1, U2>) -> Self::Output {
vec2(self.x / scale.get(), self.y / scale.get())
}
}
impl<T: Round, U> Vector2D<T, U> {
/// Rounds each component to the nearest integer value.
///
/// This behavior is preserved for negative values (unlike the basic cast).
/// For example `{ -0.1, -0.8 }.round() == { 0.0, -1.0 }`.
#[inline]
#[must_use]
pub fn round(&self) -> Self {
vec2(self.x.round(), self.y.round())
}
}
impl<T: Ceil, U> Vector2D<T, U> {
/// 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).
/// For example `{ -0.1, -0.8 }.ceil() == { 0.0, 0.0 }`.
#[inline]
#[must_use]
pub fn ceil(&self) -> Self {
vec2(self.x.ceil(), self.y.ceil())
}
}
impl<T: Floor, U> Vector2D<T, U> {
/// 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).
/// For example `{ -0.1, -0.8 }.floor() == { -1.0, -1.0 }`.
#[inline]
#[must_use]
pub fn floor(&self) -> Self {
vec2(self.x.floor(), self.y.floor())
}
}
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 + Copy>(&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.
#[inline]
pub fn try_cast<NewT: NumCast + Copy>(&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: Copy + 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(&self, other: &Self) -> bool {
self.x.approx_eq(&other.x) && self.y.approx_eq(&other.y)
}
#[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: Copy, U> Into<[T; 2]> for Vector2D<T, U> {
fn into(self) -> [T; 2] {
self.to_array()
}
}
impl<T: Copy, U> From<[T; 2]> for Vector2D<T, U> {
fn from(array: [T; 2]) -> Self {
vec2(array[0], array[1])
}
}
impl<T: Copy, U> Into<(T, T)> for Vector2D<T, U> {
fn into(self) -> (T, T) {
self.to_tuple()
}
}
impl<T: Copy, U> From<(T, T)> for Vector2D<T, U> {
fn from(tuple: (T, T)) -> Self {
vec2(tuple.0, tuple.1)
}
}
impl<T: Copy, U> From<Size2D<T, U>> for Vector2D<T, U> {
fn from(size: Size2D<T, U>) -> Self {
size.to_vector()
}
}
impl<T, U> Vector2D<T, U>
where
T: Signed,
{
pub fn abs(&self) -> Self {
vec2(self.x.abs(), self.y.abs())
}
}
/// A 3d Vector tagged with a unit.
#[repr(C)]
pub struct Vector3D<T, U> {
pub x: T,
pub y: T,
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) = try!(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)
}
}
impl<T, U> Eq for Vector3D<T, U> where T: Eq {}
impl<T, U> PartialEq for Vector3D<T, U>
where T: PartialEq
{
fn eq(&self, other: &Self) -> bool {
self.x == other.x && self.y == other.y && self.z == other.z
}
}
impl<T, U> Hash for Vector3D<T, U>
where T: Hash
{
fn hash<H: ::core::hash::Hasher>(&self, h: &mut H) {
self.x.hash(h);
self.y.hash(h);
self.z.hash(h);
}
}
impl<T: Copy + Zero, U> Vector3D<T, U> {
/// Constructor, setting all components to zero.
#[inline]
pub fn zero() -> Self {
vec3(Zero::zero(), Zero::zero(), Zero::zero())
}
#[inline]
pub fn to_array_4d(&self) -> [T; 4] {
[self.x, self.y, self.z, Zero::zero()]
}
#[inline]
pub fn to_tuple_4d(&self) -> (T, T, T, T) {
(self.x, self.y, self.z, Zero::zero())
}
}
impl<T: fmt::Debug, U> fmt::Debug for Vector3D<T, U> {
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
write!(f, "({:?},{:?},{:?})", self.x, self.y, self.z)
}
}
impl<T: fmt::Display, U> fmt::Display for Vector3D<T, U> {
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
write!(f, "({},{},{})", self.x, self.y, self.z)
}
}
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 taking scalar values directly.
#[inline]
pub const fn new(x: T, y: T, z: T) -> Self {
Vector3D {
x,
y,
z,
_unit: PhantomData,
}
}
}
impl<T: Copy, U> Vector3D<T, U> {
/// 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)
}
/// 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)
}
#[inline]
pub fn to_array(&self) -> [T; 3] {
[self.x, self.y, self.z]
}
#[inline]
pub fn to_tuple(&self) -> (T, T, T) {
(self.x, self.y, self.z)
}
/// Drop the units, preserving only the numeric value.
#[inline]
pub fn to_untyped(&self) -> Vector3D<T, UnknownUnit> {
vec3(self.x, self.y, self.z)
}
/// Tag a unitless value with units.
#[inline]
pub fn from_untyped(p: Vector3D<T, UnknownUnit>) -> Self {
vec3(p.x, p.y, p.z)
}
/// Cast the unit
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()
}
}
impl<T, U> Vector3D<T, U>
where
T: Copy
+ Clone
+ Add<T, Output = T>
+ Mul<T, Output = T>
+ Div<T, Output = T>
+ Sub<T, Output = T>
+ Trig
+ PartialOrd
+ One
+ Zero
+ Neg<Output = T> {
#[inline]
pub fn to_transform(&self) -> Transform3D<T, U, U> {
Transform3D::create_translation(self.x, self.y, self.z)
}
}
impl<T, U> Vector3D<T, U>
where
T: Copy + Mul<T, Output = T> + Add<T, Output = T> + Sub<T, Output = T>
+ Trig + Copy + Sub<T, Output = T>
+ Float
{
/// 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> {
Angle::radians(Trig::fast_atan2(self.cross(other).length(), self.dot(other)))
}
}
impl<T: Mul<T, Output = T> + Add<T, Output = T> + Sub<T, Output = T> + Copy, U>
Vector3D<T, U> {
// Dot product.
#[inline]
pub fn dot(self, other: Self) -> T {
self.x * other.x + self.y * other.y + self.z * other.z
}
// Cross product.
#[inline]
pub fn cross(self, other: Self) -> Self {
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,
)
}
#[inline]
pub fn normalize(self) -> Self
where
T: Float,
{
self / self.length()
}
/// Return the normalized vector even if the length is larger than the max value of Float.
#[inline]
pub fn robust_normalize(self) -> Self
where
T: Float,
{
let length = self.length();
if length.is_infinite() {
let scaled = self / T::max_value();
scaled / scaled.length()
} else {
self / length
}
}
#[inline]
pub fn square_length(&self) -> T {
self.x * self.x + self.y * self.y + self.z * self.z
}
#[inline]
pub fn length(&self) -> T
where
T: Float,
{
self.square_length().sqrt()
}
/// 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: Div<T, Output = T>
{
onto * (self.dot(onto) / onto.square_length())
}
}
impl<T, U> Vector3D<T, U>
where
T: Copy + Mul<T, Output = T> + Add<T, Output = T> + Sub<T, Output = T>
+ PartialOrd + Float
{
/// 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 between this vector and another vector.
///
/// `t` is expected to be between zero and one.
#[inline]
pub fn lerp(&self, other: Self, t: T) -> Self {
let one_t = T::one() - t;
(*self) * one_t + other * t
}
}
impl<T, U> Vector3D<T, U>
where
T: Copy + One + Mul<T, Output = T> + Add<T, Output = T> + Sub<T, Output = 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: Copy + Add<T, Output = T>, U> Add for Vector3D<T, U> {
type Output = Self;
#[inline]
fn add(self, other: Self) -> Self {
vec3(self.x + other.x, self.y + other.y, self.z + other.z)
}
}
impl<T: Copy + Sub<T, Output = T>, U> Sub for Vector3D<T, U> {
type Output = Self;
#[inline]
fn sub(self, other: Self) -> Self {
vec3(self.x - other.x, self.y - other.y, self.z - other.z)
}
}
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: 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 + Neg<Output = T>, U> Neg for Vector3D<T, U> {
type Output = Self;
#[inline]
fn neg(self) -> Self {
vec3(-self.x, -self.y, -self.z)
}
}
impl<T: Copy + Mul<T, Output = T>, U> Mul<T> for Vector3D<T, U> {
type Output = Self;
#[inline]
fn mul(self, scale: T) -> Self {
Self::new(self.x * scale, self.y * scale, self.z * scale)
}
}
impl<T: Copy + Div<T, Output = T>, U> Div<T> for Vector3D<T, U> {
type Output = Self;
#[inline]
fn div(self, scale: T) -> Self {
Self::new(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 + Div<T, Output = T>, U> DivAssign<T> for Vector3D<T, U> {
#[inline]
fn div_assign(&mut self, scale: T) {
*self = *self / scale
}
}
impl<T: Float, U> Vector3D<T, U> {
#[inline]
pub fn min(self, other: Self) -> Self {
vec3(
self.x.min(other.x),
self.y.min(other.y),
self.z.min(other.z),
)
}
#[inline]
pub fn max(self, other: Self) -> Self {
vec3(
self.x.max(other.x),
self.y.max(other.y),
self.z.max(other.z),
)
}
#[inline]
pub fn clamp(&self, start: Self, end: Self) -> Self {
self.max(start).min(end)
}
}
impl<T: Copy + Mul<T, Output = T>, U1, U2> Mul<Scale<T, U1, U2>> for Vector3D<T, U1> {
type Output = Vector3D<T, U2>;
#[inline]
fn mul(self, scale: Scale<T, U1, U2>) -> Self::Output {
vec3(self.x * scale.get(), self.y * scale.get(), self.z * scale.get())
}
}
impl<T: Copy + Div<T, Output = T>, U1, U2> Div<Scale<T, U1, U2>> for Vector3D<T, U2> {
type Output = Vector3D<T, U1>;
#[inline]
fn div(self, scale: Scale<T, U1, U2>) -> Self::Output {
vec3(self.x / scale.get(), self.y / scale.get(), self.z / scale.get())
}
}
impl<T: Round, U> Vector3D<T, U> {
/// Rounds each component to the nearest integer value.
///
/// This behavior is preserved for negative values (unlike the basic cast).
#[inline]
#[must_use]
pub fn round(&self) -> Self {
vec3(self.x.round(), self.y.round(), self.z.round())
}
}
impl<T: Ceil, U> Vector3D<T, U> {
/// 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).
#[inline]
#[must_use]
pub fn ceil(&self) -> Self {
vec3(self.x.ceil(), self.y.ceil(), self.z.ceil())
}
}
impl<T: Floor, U> Vector3D<T, U> {
/// 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).
#[inline]
#[must_use]
pub fn floor(&self) -> Self {
vec3(self.x.floor(), self.y.floor(), self.z.floor())
}
}
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 + Copy>(&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.
#[inline]
pub fn try_cast<NewT: NumCast + Copy>(&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: Copy + 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(&self, other: &Self) -> bool {
self.x.approx_eq(&other.x) && self.y.approx_eq(&other.y) && self.z.approx_eq(&other.z)
}
#[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: Copy, U> Into<[T; 3]> for Vector3D<T, U> {
fn into(self) -> [T; 3] {
self.to_array()
}
}
impl<T: Copy, U> From<[T; 3]> for Vector3D<T, U> {
fn from(array: [T; 3]) -> Self {
vec3(array[0], array[1], array[2])
}
}
impl<T: Copy, U> Into<(T, T, T)> for Vector3D<T, U> {
fn into(self) -> (T, T, T) {
self.to_tuple()
}
}
impl<T: Copy, U> From<(T, T, T)> for Vector3D<T, U> {
fn from(tuple: (T, T, T)) -> Self {
vec3(tuple.0, tuple.1, tuple.2)
}
}
impl<T, U> Vector3D<T, U>
where
T: Signed,
{
pub fn abs(&self) -> Self {
vec3(self.x.abs(), self.y.abs(), self.z.abs())
}
}
#[derive(Copy, Clone, Debug, PartialEq, Eq, Hash)]
pub struct BoolVector2D {
pub x: bool,
pub y: bool,
}
#[derive(Copy, Clone, Debug, PartialEq, Eq, Hash)]
pub struct BoolVector3D {
pub x: bool,
pub y: bool,
pub z: bool,
}
impl BoolVector2D {
#[inline]
pub fn all(&self) -> bool {
self.x && self.y
}
#[inline]
pub fn any(&self) -> bool {
self.x || self.y
}
#[inline]
pub fn none(&self) -> bool {
!self.any()
}
#[inline]
pub fn and(&self, other: Self) -> Self {
BoolVector2D {
x: self.x && other.x,
y: self.y && other.y,
}
}
#[inline]
pub fn or(&self, other: Self) -> Self {
BoolVector2D {
x: self.x || other.x,
y: self.y || other.y,
}
}
#[inline]
pub fn not(&self) -> Self {
BoolVector2D {
x: !self.x,
y: !self.y,
}
}
#[inline]
pub fn select_point<T: Copy, 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 },
)
}
#[inline]
pub fn select_vector<T: Copy, 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 },
)
}
#[inline]
pub fn select_size<T: Copy, 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 {
#[inline]
pub fn all(&self) -> bool {
self.x && self.y && self.z
}
#[inline]
pub fn any(&self) -> bool {
self.x || self.y || self.z
}
#[inline]
pub fn none(&self) -> bool {
!self.any()
}
#[inline]
pub fn and(&self, other: Self) -> Self {
BoolVector3D {
x: self.x && other.x,
y: self.y && other.y,
z: self.z && other.z,
}
}
#[inline]
pub fn or(&self, other: Self) -> Self {
BoolVector3D {
x: self.x || other.x,
y: self.y || other.y,
z: self.z || other.z,
}
}
#[inline]
pub fn not(&self) -> Self {
BoolVector3D {
x: !self.x,
y: !self.y,
z: !self.z,
}
}
#[inline]
pub fn select_point<T: Copy, 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 },
)
}
#[inline]
pub fn select_vector<T: Copy, 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 },
)
}
#[inline]
pub fn xy(&self) -> BoolVector2D {
BoolVector2D {
x: self.x,
y: self.y,
}
}
#[inline]
pub fn xz(&self) -> BoolVector2D {
BoolVector2D {
x: self.x,
y: self.z,
}
}
#[inline]
pub fn yz(&self) -> BoolVector2D {
BoolVector2D {
x: self.y,
y: self.z,
}
}
}
impl<T: PartialOrd, U> Vector2D<T, U> {
#[inline]
pub fn greater_than(&self, other: Self) -> BoolVector2D {
BoolVector2D {
x: self.x > other.x,
y: self.y > other.y,
}
}
#[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> {
#[inline]
pub fn equal(&self, other: Self) -> BoolVector2D {
BoolVector2D {
x: self.x == other.x,
y: self.y == other.y,
}
}
#[inline]
pub fn not_equal(&self, other: Self) -> BoolVector2D {
BoolVector2D {
x: self.x != other.x,
y: self.y != other.y,
}
}
}
impl<T: PartialOrd, U> Vector3D<T, U> {
#[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,
}
}
#[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> {
#[inline]
pub fn equal(&self, other: Self) -> BoolVector3D {
BoolVector3D {
x: self.x == other.x,
y: self.y == other.y,
z: self.z == other.z,
}
}
#[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,
}
}
}
/// Convenience constructor.
#[inline]
pub fn vec2<T, U>(x: T, y: T) -> Vector2D<T, U> {
Vector2D {
x,
y,
_unit: PhantomData,
}
}
/// Convenience constructor.
#[inline]
pub fn vec3<T, U>(x: T, y: T, z: T) -> Vector3D<T, U> {
Vector3D {
x,
y,
z,
_unit: PhantomData,
}
}
#[inline]
pub fn bvec2(x: bool, y: bool) -> BoolVector2D {
BoolVector2D { x, y }
}
#[inline]
pub fn bvec3(x: bool, y: bool, z: bool) -> BoolVector3D {
BoolVector3D { x, y, z }
}
#[cfg(test)]
mod vector2d {
use {default, vec2};
use scale::Scale;
#[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() {
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()));
}
#[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 core::f32::consts::FRAC_PI_2;
use approxeq::ApproxEq;
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 core::f32::consts::FRAC_PI_2;
use approxeq::ApproxEq;
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 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 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);
let result = p1 + p2;
assert_eq!(result, vec2(4.0, 6.0));
}
#[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 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 {
#[cfg(feature = "mint")]
use mint;
use {default, vec2, vec3};
use scale::Scale;
type Vec3 = default::Vector3D<f32>;
#[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() {
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));
}
#[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 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 core::f32::consts::FRAC_PI_2;
use approxeq::ApproxEq;
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 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 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 default;
use super::*;
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),
);
}
}