firefox-main/third_party/rust/euclid/src/transform2d.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
// <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.
#![allow(clippy::just_underscores_and_digits)]
use super::{Angle, UnknownUnit};
use crate::approxeq::ApproxEq;
use crate::box2d::Box2D;
use crate::num::{One, Zero};
use crate::point::{point2, Point2D};
use crate::rect::Rect;
use crate::scale::Scale;
use crate::transform3d::Transform3D;
use crate::translation::Translation2D;
use crate::trig::Trig;
use crate::vector::{vec2, Vector2D};
use crate::Rotation2D;
use core::cmp::{Eq, PartialEq};
use core::fmt;
use core::hash::Hash;
use core::marker::PhantomData;
use core::ops::{Add, Div, Mul, Neg, Sub};
#[cfg(feature = "bytemuck")]
use bytemuck::{Pod, Zeroable};
#[cfg(feature = "malloc_size_of")]
use malloc_size_of::{MallocSizeOf, MallocSizeOfOps};
#[cfg(feature = "mint")]
use mint;
use num_traits::{NumCast, Signed};
#[cfg(feature = "serde")]
use serde::{Deserialize, Serialize};
/// A 2d transform represented by a column-major 3 by 3 matrix, compressed down to 3 by 2.
///
/// Transforms can be parametrized over the source and destination units, to describe a
/// transformation from a space to another.
/// For example, `Transform2D<f32, WorldSpace, ScreenSpace>::transform_point4d`
/// takes a `Point2D<f32, WorldSpace>` and returns a `Point2D<f32, ScreenSpace>`.
///
/// Transforms expose a set of convenience methods for pre- and post-transformations.
/// Pre-transformations (`pre_*` methods) correspond to adding an operation that is
/// applied before the rest of the transformation, while post-transformations (`then_*`
/// methods) add an operation that is applied after.
///
/// The matrix representation is conceptually equivalent to a 3 by 3 matrix transformation
/// compressed to 3 by 2 with the components that aren't needed to describe the set of 2d
/// transformations we are interested in implicitly defined:
///
/// ```text
/// | m11 m21 m31 | |x| |x'|
/// | m12 m22 m32 | x |y| = |y'|
/// | 0 0 1 | |1| |1 |
/// ```
///
/// When translating `Transform2D` into general matrix representations, consider that the
/// representation follows the column-major notation with column vectors.
///
/// The translation terms are `m31` and `m32`.
#[repr(C)]
#[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
#[cfg_attr(
feature = "serde",
serde(bound(serialize = "T: Serialize", deserialize = "T: Deserialize<'de>"))
)]
#[rustfmt::skip]
pub struct Transform2D<T, Src, Dst> {
pub m11: T, pub m12: T,
pub m21: T, pub m22: T,
pub m31: T, pub m32: T,
#[doc(hidden)]
pub _unit: PhantomData<(Src, Dst)>,
}
#[cfg(feature = "arbitrary")]
impl<'a, T, Src, Dst> arbitrary::Arbitrary<'a> for Transform2D<T, Src, Dst>
where
T: arbitrary::Arbitrary<'a>,
{
fn arbitrary(u: &mut arbitrary::Unstructured<'a>) -> arbitrary::Result<Self> {
let (m11, m12, m21, m22, m31, m32) = arbitrary::Arbitrary::arbitrary(u)?;
Ok(Transform2D {
m11,
m12,
m21,
m22,
m31,
m32,
_unit: PhantomData,
})
}
}
#[cfg(feature = "bytemuck")]
unsafe impl<T: Zeroable, Src, Dst> Zeroable for Transform2D<T, Src, Dst> {}
#[cfg(feature = "bytemuck")]
unsafe impl<T: Pod, Src: 'static, Dst: 'static> Pod for Transform2D<T, Src, Dst> {}
#[cfg(feature = "malloc_size_of")]
impl<T: MallocSizeOf, Src, Dst> MallocSizeOf for Transform2D<T, Src, Dst> {
fn size_of(&self, ops: &mut MallocSizeOfOps) -> usize {
self.m11.size_of(ops)
+ self.m12.size_of(ops)
+ self.m21.size_of(ops)
+ self.m22.size_of(ops)
+ self.m31.size_of(ops)
+ self.m32.size_of(ops)
}
}
impl<T: Copy, Src, Dst> Copy for Transform2D<T, Src, Dst> {}
impl<T: Clone, Src, Dst> Clone for Transform2D<T, Src, Dst> {
fn clone(&self) -> Self {
Transform2D {
m11: self.m11.clone(),
m12: self.m12.clone(),
m21: self.m21.clone(),
m22: self.m22.clone(),
m31: self.m31.clone(),
m32: self.m32.clone(),
_unit: PhantomData,
}
}
}
impl<T, Src, Dst> Eq for Transform2D<T, Src, Dst> where T: Eq {}
impl<T, Src, Dst> PartialEq for Transform2D<T, Src, Dst>
where
T: PartialEq,
{
fn eq(&self, other: &Self) -> bool {
self.m11 == other.m11
&& self.m12 == other.m12
&& self.m21 == other.m21
&& self.m22 == other.m22
&& self.m31 == other.m31
&& self.m32 == other.m32
}
}
impl<T, Src, Dst> Hash for Transform2D<T, Src, Dst>
where
T: Hash,
{
fn hash<H: core::hash::Hasher>(&self, h: &mut H) {
self.m11.hash(h);
self.m12.hash(h);
self.m21.hash(h);
self.m22.hash(h);
self.m31.hash(h);
self.m32.hash(h);
}
}
impl<T, Src, Dst> Transform2D<T, Src, Dst> {
/// Create a transform specifying its components in using the column-major-column-vector
/// matrix notation.
///
/// For example, the translation terms m31 and m32 are the last two parameters parameters.
///
/// ```
/// use euclid::default::Transform2D;
/// let tx = 1.0;
/// let ty = 2.0;
/// let translation = Transform2D::new(
/// 1.0, 0.0,
/// 0.0, 1.0,
/// tx, ty,
/// );
/// ```
#[rustfmt::skip]
pub const fn new(m11: T, m12: T, m21: T, m22: T, m31: T, m32: T) -> Self {
Transform2D {
m11, m12,
m21, m22,
m31, m32,
_unit: PhantomData,
}
}
/// Returns `true` if this transform is approximately equal to the other one, using
/// `T`'s default epsilon value.
///
/// The same as [`ApproxEq::approx_eq`] but available without importing trait.
#[inline]
pub fn approx_eq(&self, other: &Self) -> bool
where
T: ApproxEq<T>,
{
<Self as ApproxEq<T>>::approx_eq(self, other)
}
/// Returns `true` if this transform is approximately equal to the other one, using
/// a provided epsilon value.
///
/// The same as [`ApproxEq::approx_eq_eps`] but available without importing trait.
#[inline]
pub fn approx_eq_eps(&self, other: &Self, eps: &T) -> bool
where
T: ApproxEq<T>,
{
<Self as ApproxEq<T>>::approx_eq_eps(self, other, eps)
}
}
impl<T: Copy, Src, Dst> Transform2D<T, Src, Dst> {
/// Returns an array containing this transform's terms.
///
/// The terms are laid out in the same order as they are
/// specified in [`Transform2D::new`], that is following the
/// column-major-column-vector matrix notation.
///
/// For example the translation terms are found in the
/// last two slots of the array.
#[inline]
#[rustfmt::skip]
pub fn to_array(&self) -> [T; 6] {
[
self.m11, self.m12,
self.m21, self.m22,
self.m31, self.m32
]
}
/// Returns an array containing this transform's terms transposed.
///
/// The terms are laid out in transposed order from the same order of
/// `Transform3D::new` and `Transform3D::to_array`, that is following
/// the row-major-column-vector matrix notation.
///
/// For example the translation terms are found at indices 2 and 5
/// in the array.
#[inline]
#[rustfmt::skip]
pub fn to_array_transposed(&self) -> [T; 6] {
[
self.m11, self.m21, self.m31,
self.m12, self.m22, self.m32
]
}
/// Equivalent to `to_array` with elements packed two at a time
/// in an array of arrays.
#[inline]
pub fn to_arrays(&self) -> [[T; 2]; 3] {
[
[self.m11, self.m12],
[self.m21, self.m22],
[self.m31, self.m32],
]
}
/// Create a transform providing its components via an array
/// of 6 elements instead of as individual parameters.
///
/// The order of the components corresponds to the
/// column-major-column-vector matrix notation (the same order
/// as `Transform2D::new`).
#[inline]
#[rustfmt::skip]
pub fn from_array(array: [T; 6]) -> Self {
Self::new(
array[0], array[1],
array[2], array[3],
array[4], array[5],
)
}
/// Equivalent to `from_array` with elements packed two at a time
/// in an array of arrays.
///
/// The order of the components corresponds to the
/// column-major-column-vector matrix notation (the same order
/// as `Transform3D::new`).
#[inline]
#[rustfmt::skip]
pub fn from_arrays(array: [[T; 2]; 3]) -> Self {
Self::new(
array[0][0], array[0][1],
array[1][0], array[1][1],
array[2][0], array[2][1],
)
}
/// Drop the units, preserving only the numeric value.
#[inline]
#[rustfmt::skip]
pub fn to_untyped(&self) -> Transform2D<T, UnknownUnit, UnknownUnit> {
Transform2D::new(
self.m11, self.m12,
self.m21, self.m22,
self.m31, self.m32
)
}
/// Tag a unitless value with units.
#[inline]
#[rustfmt::skip]
pub fn from_untyped(p: &Transform2D<T, UnknownUnit, UnknownUnit>) -> Self {
Transform2D::new(
p.m11, p.m12,
p.m21, p.m22,
p.m31, p.m32
)
}
/// Returns the same transform with a different source unit.
#[inline]
#[rustfmt::skip]
pub fn with_source<NewSrc>(&self) -> Transform2D<T, NewSrc, Dst> {
Transform2D::new(
self.m11, self.m12,
self.m21, self.m22,
self.m31, self.m32,
)
}
/// Returns the same transform with a different destination unit.
#[inline]
#[rustfmt::skip]
pub fn with_destination<NewDst>(&self) -> Transform2D<T, Src, NewDst> {
Transform2D::new(
self.m11, self.m12,
self.m21, self.m22,
self.m31, self.m32,
)
}
/// Create a 3D transform from the current transform
#[inline]
pub fn to_3d(&self) -> Transform3D<T, Src, Dst>
where
T: Zero + One,
{
Transform3D::new_2d(self.m11, self.m12, self.m21, self.m22, self.m31, self.m32)
}
/// Returns true if self can be represented as a 2d scale+offset
/// transform, using `T`'s default epsilon value.
#[inline]
pub fn is_scale_offset(&self) -> bool
where
T: Signed + One + PartialOrd + ApproxEq<T>,
{
self.is_scale_offset_eps(T::approx_epsilon())
}
/// Returns true if self can be represented as a 2d scale+offset
/// transform.
#[inline]
pub fn is_scale_offset_eps(&self, epsilon: T) -> bool
where
T: Signed + One + PartialOrd,
{
(self.m12.abs() < epsilon) & (self.m21.abs() < epsilon)
}
/// Creates a 2D scale+offset transform from the current transform.
///
/// This method assumes that self can be represented as a 2d scale+offset
/// transformation, callers should check that [`is_scale_offset_2d`] or
/// [`is_scale_offset_2d_eps`] returns `true` beforehand.
#[inline]
pub fn to_scale_offset(&self) -> ScaleOffset2D<T, Src, Dst> {
ScaleOffset2D::new(self.m11, self.m22, self.m31, self.m32)
}
}
impl<T: NumCast + Copy, Src, Dst> Transform2D<T, Src, Dst> {
/// Cast from one numeric representation to another, preserving the units.
#[inline]
pub fn cast<NewT: NumCast>(&self) -> Transform2D<NewT, Src, Dst> {
self.try_cast().unwrap()
}
/// Fallible cast from one numeric representation to another, preserving the units.
#[rustfmt::skip]
pub fn try_cast<NewT: NumCast>(&self) -> Option<Transform2D<NewT, Src, Dst>> {
match (NumCast::from(self.m11), NumCast::from(self.m12),
NumCast::from(self.m21), NumCast::from(self.m22),
NumCast::from(self.m31), NumCast::from(self.m32)) {
(Some(m11), Some(m12),
Some(m21), Some(m22),
Some(m31), Some(m32)) => {
Some(Transform2D::new(
m11, m12,
m21, m22,
m31, m32
))
},
_ => None
}
}
}
impl<T, Src, Dst> Transform2D<T, Src, Dst>
where
T: Zero + One,
{
/// Create an identity matrix:
///
/// ```text
/// 1 0
/// 0 1
/// 0 0
/// ```
#[inline]
pub fn identity() -> Self {
Self::translation(T::zero(), T::zero())
}
/// Intentional not public, because it checks for exact equivalence
/// while most consumers will probably want some sort of approximate
/// equivalence to deal with floating-point errors.
fn is_identity(&self) -> bool
where
T: PartialEq,
{
*self == Self::identity()
}
}
/// Methods for combining generic transformations
impl<T, Src, Dst> Transform2D<T, Src, Dst>
where
T: Copy + Add<Output = T> + Mul<Output = T>,
{
/// Returns the multiplication of the two matrices such that mat's transformation
/// applies after self's transformation.
#[must_use]
#[rustfmt::skip]
pub fn then<NewDst>(&self, mat: &Transform2D<T, Dst, NewDst>) -> Transform2D<T, Src, NewDst> {
Transform2D::new(
self.m11 * mat.m11 + self.m12 * mat.m21,
self.m11 * mat.m12 + self.m12 * mat.m22,
self.m21 * mat.m11 + self.m22 * mat.m21,
self.m21 * mat.m12 + self.m22 * mat.m22,
self.m31 * mat.m11 + self.m32 * mat.m21 + mat.m31,
self.m31 * mat.m12 + self.m32 * mat.m22 + mat.m32,
)
}
}
/// Methods for creating and combining translation transformations
impl<T, Src, Dst> Transform2D<T, Src, Dst>
where
T: Zero + One,
{
/// Create a 2d translation transform:
///
/// ```text
/// 1 0
/// 0 1
/// x y
/// ```
#[inline]
#[rustfmt::skip]
pub fn translation(x: T, y: T) -> Self {
let _0 = || T::zero();
let _1 = || T::one();
Self::new(
_1(), _0(),
_0(), _1(),
x, y,
)
}
/// Applies a translation after self's transformation and returns the resulting transform.
#[inline]
#[must_use]
pub fn then_translate(&self, v: Vector2D<T, Dst>) -> Self
where
T: Copy + Add<Output = T> + Mul<Output = T>,
{
self.then(&Transform2D::translation(v.x, v.y))
}
/// Applies a translation before self's transformation and returns the resulting transform.
#[inline]
#[must_use]
pub fn pre_translate(&self, v: Vector2D<T, Src>) -> Self
where
T: Copy + Add<Output = T> + Mul<Output = T>,
{
Transform2D::translation(v.x, v.y).then(self)
}
}
/// Methods for creating and combining rotation transformations
impl<T, Src, Dst> Transform2D<T, Src, Dst>
where
T: Copy + Add<Output = T> + Sub<Output = T> + Mul<Output = T> + Zero + Trig,
{
/// Returns a rotation transform.fn pre_translate
#[inline]
#[rustfmt::skip]
pub fn rotation(theta: Angle<T>) -> Self {
let _0 = Zero::zero();
let cos = theta.get().cos();
let sin = theta.get().sin();
Transform2D::new(
cos, sin,
_0 - sin, cos,
_0, _0
)
}
/// Applies a rotation after self's transformation and returns the resulting transform.
#[inline]
#[must_use]
pub fn then_rotate(&self, theta: Angle<T>) -> Self {
self.then(&Transform2D::rotation(theta))
}
/// Applies a rotation before self's transformation and returns the resulting transform.
#[inline]
#[must_use]
pub fn pre_rotate(&self, theta: Angle<T>) -> Self {
Transform2D::rotation(theta).then(self)
}
}
/// Methods for creating and combining scale transformations
impl<T, Src, Dst> Transform2D<T, Src, Dst> {
/// Create a 2d scale transform:
///
/// ```text
/// x 0
/// 0 y
/// 0 0
/// ```
#[inline]
#[rustfmt::skip]
pub fn scale(x: T, y: T) -> Self
where
T: Zero,
{
let _0 = || Zero::zero();
Self::new(
x, _0(),
_0(), y,
_0(), _0(),
)
}
/// Applies a scale after self's transformation and returns the resulting transform.
#[inline]
#[must_use]
pub fn then_scale(&self, x: T, y: T) -> Self
where
T: Copy + Add<Output = T> + Mul<Output = T> + Zero,
{
self.then(&Transform2D::scale(x, y))
}
/// Applies a scale before self's transformation and returns the resulting transform.
#[inline]
#[must_use]
#[rustfmt::skip]
pub fn pre_scale(&self, x: T, y: T) -> Self
where
T: Copy + Mul<Output = T>,
{
Transform2D::new(
self.m11 * x, self.m12 * x,
self.m21 * y, self.m22 * y,
self.m31, self.m32
)
}
}
/// Methods for apply transformations to objects
impl<T, Src, Dst> Transform2D<T, Src, Dst>
where
T: Copy + Add<Output = T> + Mul<Output = T>,
{
/// Returns the given point transformed by this transform.
#[inline]
#[must_use]
pub fn transform_point(&self, point: Point2D<T, Src>) -> Point2D<T, Dst> {
Point2D::new(
point.x * self.m11 + point.y * self.m21 + self.m31,
point.x * self.m12 + point.y * self.m22 + self.m32,
)
}
/// Returns the given vector transformed by this matrix.
#[inline]
#[must_use]
pub fn transform_vector(&self, vec: Vector2D<T, Src>) -> Vector2D<T, Dst> {
vec2(
vec.x * self.m11 + vec.y * self.m21,
vec.x * self.m12 + vec.y * self.m22,
)
}
/// Returns a rectangle that encompasses the result of transforming the given rectangle by this
/// transform.
#[inline]
#[must_use]
pub fn outer_transformed_rect(&self, rect: &Rect<T, Src>) -> Rect<T, Dst>
where
T: Sub<Output = T> + Zero + PartialOrd,
{
let min = rect.min();
let max = rect.max();
Rect::from_points(&[
self.transform_point(min),
self.transform_point(max),
self.transform_point(point2(max.x, min.y)),
self.transform_point(point2(min.x, max.y)),
])
}
/// Returns a box that encompasses the result of transforming the given box by this
/// transform.
#[inline]
#[must_use]
pub fn outer_transformed_box(&self, b: &Box2D<T, Src>) -> Box2D<T, Dst>
where
T: Sub<Output = T> + Zero + PartialOrd,
{
Box2D::from_points(&[
self.transform_point(b.min),
self.transform_point(b.max),
self.transform_point(point2(b.max.x, b.min.y)),
self.transform_point(point2(b.min.x, b.max.y)),
])
}
}
impl<T, Src, Dst> Transform2D<T, Src, Dst>
where
T: Copy + Sub<Output = T> + Mul<Output = T> + Div<Output = T> + PartialEq + Zero + One,
{
/// Computes and returns the determinant of this transform.
pub fn determinant(&self) -> T {
self.m11 * self.m22 - self.m12 * self.m21
}
/// Returns whether it is possible to compute the inverse transform.
#[inline]
pub fn is_invertible(&self) -> bool {
self.determinant() != Zero::zero()
}
/// Returns the inverse transform if possible.
#[must_use]
pub fn inverse(&self) -> Option<Transform2D<T, Dst, Src>> {
let det = self.determinant();
let _0: T = Zero::zero();
let _1: T = One::one();
if det == _0 {
return None;
}
let inv_det = _1 / det;
Some(Transform2D::new(
inv_det * self.m22,
inv_det * (_0 - self.m12),
inv_det * (_0 - self.m21),
inv_det * self.m11,
inv_det * (self.m21 * self.m32 - self.m22 * self.m31),
inv_det * (self.m31 * self.m12 - self.m11 * self.m32),
))
}
}
impl<T, Src, Dst> Default for Transform2D<T, Src, Dst>
where
T: Zero + One,
{
/// Returns the [identity transform](Transform2D::identity).
fn default() -> Self {
Self::identity()
}
}
impl<T: ApproxEq<T>, Src, Dst> ApproxEq<T> for Transform2D<T, Src, Dst> {
#[inline]
fn approx_epsilon() -> T {
T::approx_epsilon()
}
/// Returns `true` if this transform is approximately equal to the other one, using
/// a provided epsilon value.
fn approx_eq_eps(&self, other: &Self, eps: &T) -> bool {
self.m11.approx_eq_eps(&other.m11, eps)
&& self.m12.approx_eq_eps(&other.m12, eps)
&& self.m21.approx_eq_eps(&other.m21, eps)
&& self.m22.approx_eq_eps(&other.m22, eps)
&& self.m31.approx_eq_eps(&other.m31, eps)
&& self.m32.approx_eq_eps(&other.m32, eps)
}
}
impl<T, Src, Dst> fmt::Debug for Transform2D<T, Src, Dst>
where
T: Copy + fmt::Debug + PartialEq + One + Zero,
{
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
if self.is_identity() {
write!(f, "[I]")
} else {
self.to_array().fmt(f)
}
}
}
#[cfg(feature = "mint")]
impl<T, Src, Dst> From<mint::RowMatrix3x2<T>> for Transform2D<T, Src, Dst> {
#[rustfmt::skip]
fn from(m: mint::RowMatrix3x2<T>) -> Self {
Transform2D {
m11: m.x.x, m12: m.x.y,
m21: m.y.x, m22: m.y.y,
m31: m.z.x, m32: m.z.y,
_unit: PhantomData,
}
}
}
#[cfg(feature = "mint")]
impl<T, Src, Dst> From<Transform2D<T, Src, Dst>> for mint::RowMatrix3x2<T> {
fn from(t: Transform2D<T, Src, Dst>) -> Self {
mint::RowMatrix3x2 {
x: mint::Vector2 { x: t.m11, y: t.m12 },
y: mint::Vector2 { x: t.m21, y: t.m22 },
z: mint::Vector2 { x: t.m31, y: t.m32 },
}
}
}
impl<T, Src, Dst> From<Rotation2D<T, Src, Dst>> for Transform2D<T, Src, Dst>
where
T: Copy + Add<Output = T> + Sub<Output = T> + Mul<Output = T> + Zero + Trig,
{
fn from(r: Rotation2D<T, Src, Dst>) -> Self {
r.to_transform()
}
}
impl<T: Copy + Zero, Src, Dst> From<ScaleOffset2D<T, Src, Dst>> for Transform2D<T, Src, Dst> {
fn from(t: ScaleOffset2D<T, Src, Dst>) -> Self {
t.to_transform2d()
}
}
impl<T: Copy + Zero, Src, Dst> From<Scale<T, Src, Dst>> for Transform2D<T, Src, Dst> {
fn from(s: Scale<T, Src, Dst>) -> Self {
Transform2D::scale(s.0, s.0)
}
}
#[repr(C)]
#[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
#[cfg_attr(
feature = "serde",
serde(bound(serialize = "T: Serialize", deserialize = "T: Deserialize<'de>"))
)]
pub struct ScaleOffset2D<T, Src, Dst> {
pub sx: T,
pub sy: T,
pub tx: T,
pub ty: T,
#[doc(hidden)]
pub _unit: PhantomData<(Src, Dst)>,
}
impl<T, Src, Dst> ScaleOffset2D<T, Src, Dst> {
/// Create an identity transform.
#[inline]
pub fn identity() -> Self
where
T: Zero + One,
{
ScaleOffset2D {
sx: T::one(),
sy: T::one(),
tx: T::zero(),
ty: T::zero(),
_unit: PhantomData,
}
}
/// Create a transform with provided scale and offset terms.
#[inline]
pub fn new(sx: T, sy: T, tx: T, ty: T) -> Self {
ScaleOffset2D {
sx,
sy,
tx,
ty,
_unit: PhantomData,
}
}
/// Create a transform from a scale.
#[inline]
pub fn scale(sx: T, sy: T) -> Self
where
T: Zero,
{
ScaleOffset2D {
sx,
sy,
tx: T::zero(),
ty: T::zero(),
_unit: PhantomData,
}
}
/// Create a transform from an offset.
#[inline]
pub fn offset(tx: T, ty: T) -> Self
where
T: One,
{
ScaleOffset2D {
sx: T::one(),
sy: T::one(),
tx,
ty,
_unit: PhantomData,
}
}
/// Returns true if self is an identity transform, using `T`'s
/// default epsilon value.
#[inline]
pub fn is_identity(&self) -> bool
where
T: One + Zero + ApproxEq<T>,
{
self.is_identity_eps(T::approx_epsilon())
}
/// Returns true if self is an identity transform.
#[inline]
pub fn is_identity_eps(&self, epsilon: T) -> bool
where
T: One + Zero + ApproxEq<T>,
{
self.sx.approx_eq_eps(&T::one(), &epsilon)
& self.sy.approx_eq_eps(&T::one(), &epsilon)
& self.tx.approx_eq_eps(&T::zero(), &epsilon)
& self.ty.approx_eq_eps(&T::zero(), &epsilon)
}
}
impl<T: Copy, Src, Dst> ScaleOffset2D<T, Src, Dst> {
/// Returns the given point transformed by this transform.
#[inline]
pub fn transform_point(&self, p: Point2D<T, Src>) -> Point2D<T, Dst>
where
T: Add<Output = T> + Mul<Output = T>,
{
point2(p.x * self.sx + self.tx, p.y * self.sy + self.ty)
}
/// Returns the given vector transformed by this transform.
#[inline]
pub fn transform_vector(&self, v: Vector2D<T, Src>) -> Vector2D<T, Dst>
where
T: Mul<Output = T>,
{
vec2(v.x * self.sx, v.y * self.sy)
}
/// Returns the given box transformed by this transform.
#[inline]
pub fn transform_box(&self, b: &Box2D<T, Src>) -> Box2D<T, Dst>
where
T: Zero + Add<Output = T> + Mul<Output = T> + PartialOrd,
{
let mut min = self.transform_point(b.min);
let mut max = self.transform_point(b.max);
if self.sx < T::zero() {
core::mem::swap(&mut min.x, &mut max.x);
}
if self.sy < T::zero() {
core::mem::swap(&mut min.y, &mut max.y);
}
Box2D { min, max }
}
/// Returns the given rectangle transformed by this transform.
#[inline]
pub fn transform_rect(&self, r: &Rect<T, Src>) -> Rect<T, Dst>
where
T: Zero + Add<Output = T> + Sub<Output = T> + Mul<Output = T> + PartialOrd,
{
self.transform_box(&r.to_box2d()).to_rect()
}
/// Produce a ScaleOffset2D that includes both self and other.
/// The 'other' ScaleOffset2D is applied after `self`.
///
/// This is equivalent to `Transform2D::then`.
#[inline]
pub fn then<NewDst>(
&self,
other: &ScaleOffset2D<T, Dst, NewDst>,
) -> ScaleOffset2D<T, Src, NewDst>
where
T: Add<Output = T> + Mul<Output = T>,
{
ScaleOffset2D {
sx: self.sx * other.sx,
sy: self.sy * other.sy,
tx: self.tx * other.sx + other.tx,
ty: self.ty * other.sy + other.ty,
_unit: PhantomData,
}
}
/// Applies a translation before self's transformation and returns the resulting transform.
#[inline]
#[must_use]
pub fn pre_translate(&self, v: Vector2D<T, Src>) -> Self
where
T: Add<Output = T> + Mul<Output = T>,
{
ScaleOffset2D {
sx: self.sx,
sy: self.sy,
tx: self.tx + v.x * self.sx,
ty: self.ty + v.y * self.sy,
_unit: PhantomData,
}
}
/// Applies a translation after self's transformation and returns the resulting transform.
#[inline]
pub fn then_translate(&self, v: Vector2D<T, Dst>) -> Self
where
T: Add<Output = T> + Mul<Output = T>,
{
ScaleOffset2D {
sx: self.sx,
sy: self.sy,
tx: self.tx + v.x,
ty: self.ty + v.y,
_unit: PhantomData,
}
}
/// Applies a scale before self's transformation and returns the resulting transform.
#[inline]
pub fn pre_scale(&self, sx: T, sy: T) -> Self
where
T: Add<Output = T> + Mul<Output = T>,
{
ScaleOffset2D {
sx: self.sx * sx,
sy: self.sy * sy,
tx: self.tx,
ty: self.ty,
_unit: PhantomData,
}
}
/// Applies a scale after self's transformation and returns the resulting transform.
#[inline]
pub fn then_scale(&self, sx: T, sy: T) -> Self
where
T: Add<Output = T> + Mul<Output = T>,
{
ScaleOffset2D {
sx: self.sx * sx,
sy: self.sy * sy,
tx: self.tx * sx,
ty: self.ty * sy,
_unit: PhantomData,
}
}
/// Returns whether it is possible to compute the inverse transform.
#[inline]
pub fn is_invertible(&self) -> bool
where
T: Zero + PartialEq,
{
// Expressing the negation this way makes it so NaN scales
// count as non-invertible, although we don't attemp to check
// for NaN offsets.
!(self.sx == T::zero() || self.sy == T::zero())
}
/// Returns the inverse transform if possible.
#[must_use]
pub fn inverse(&self) -> Option<ScaleOffset2D<T, Dst, Src>>
where
T: Zero + One + PartialEq + Div<Output = T> + Mul<Output = T> + Neg<Output = T>,
{
if self.sx == T::zero() || self.sy == T::zero() {
return None;
}
let sx = T::one() / self.sx;
let sy = T::one() / self.sy;
let tx = -self.tx * sx;
let ty = -self.ty * sy;
Some(ScaleOffset2D::new(sx, sy, tx, ty))
}
/// Returns the same transform using Transform2D's matrix representation.
#[inline]
pub fn to_transform2d(&self) -> Transform2D<T, Src, Dst>
where
T: Zero,
{
Transform2D::new(self.sx, T::zero(), T::zero(), self.sy, self.tx, self.ty)
}
/// Returns the same transform using Transform3D's matrix representation.
#[inline]
#[rustfmt::skip]
pub fn to_transform3d(&self) -> Transform3D<T, Src, Dst>
where
T: Zero + One
{
Transform3D::new(
self.sx, T::zero(), T::zero(), T::zero(),
T::zero(), self.sy, T::zero(), T::zero(),
T::zero(), T::zero(), T::one(), T::zero(),
self.tx, self.ty, T::zero(), T::one(),
)
}
/// Returns an array containing this transform's terms.
///
/// The terms are laid out in the same order as they are
/// specified in [`ScaleOffset2D::new`].
#[inline]
pub fn to_array(&self) -> [T; 4] {
[self.sx, self.sy, self.tx, self.ty]
}
/// Returns the same transform with a different source unit.
#[inline]
pub fn with_source<NewSrc>(&self) -> ScaleOffset2D<T, NewSrc, Dst> {
ScaleOffset2D::new(self.sx, self.sy, self.tx, self.ty)
}
/// Returns the same transform with a different destination unit.
#[inline]
pub fn with_destination<NewDst>(&self) -> ScaleOffset2D<T, Src, NewDst> {
ScaleOffset2D::new(self.sx, self.sy, self.tx, self.ty)
}
/// Drop the units, preserving only the numeric value.
#[inline]
pub fn to_untyped(&self) -> ScaleOffset2D<T, UnknownUnit, UnknownUnit> {
ScaleOffset2D::new(self.sx, self.sy, self.tx, self.ty)
}
/// Tag a unitless value with units.
#[inline]
pub fn from_untyped(val: ScaleOffset2D<T, UnknownUnit, UnknownUnit>) -> Self {
ScaleOffset2D::new(val.sx, val.sy, val.tx, val.ty)
}
}
impl<T: Copy, Src, Dst> Copy for ScaleOffset2D<T, Src, Dst> {}
impl<T: Clone, Src, Dst> Clone for ScaleOffset2D<T, Src, Dst> {
fn clone(&self) -> Self {
ScaleOffset2D {
sx: self.sx.clone(),
sy: self.sy.clone(),
tx: self.tx.clone(),
ty: self.ty.clone(),
_unit: PhantomData,
}
}
}
impl<T, Src, Dst> Eq for ScaleOffset2D<T, Src, Dst> where T: Eq {}
impl<T, Src, Dst> PartialEq for ScaleOffset2D<T, Src, Dst>
where
T: PartialEq,
{
fn eq(&self, other: &Self) -> bool {
(self.sx == other.sx)
& (self.sy == other.sy)
& (self.tx == other.tx)
& (self.ty == other.ty)
}
}
impl<T, Src, Dst> Hash for ScaleOffset2D<T, Src, Dst>
where
T: Hash,
{
fn hash<H: core::hash::Hasher>(&self, h: &mut H) {
self.sx.hash(h);
self.sy.hash(h);
self.tx.hash(h);
self.ty.hash(h);
}
}
impl<T, Src, Dst> Default for ScaleOffset2D<T, Src, Dst>
where
T: Copy + Zero + One,
{
/// Returns the [identity transform](ScaleOffset2D::identity).
fn default() -> Self {
Self::identity()
}
}
impl<T: ApproxEq<T>, Src, Dst> ApproxEq<T> for ScaleOffset2D<T, Src, Dst> {
#[inline]
fn approx_epsilon() -> T {
T::approx_epsilon()
}
/// Returns `true` if this transform is approximately equal to the other one, using
/// a provided epsilon value.
fn approx_eq_eps(&self, other: &Self, eps: &T) -> bool {
self.sx.approx_eq_eps(&other.sx, eps)
&& self.sy.approx_eq_eps(&other.sy, eps)
&& self.tx.approx_eq_eps(&other.tx, eps)
&& self.ty.approx_eq_eps(&other.ty, eps)
}
}
impl<T, Src, Dst> fmt::Debug for ScaleOffset2D<T, Src, Dst>
where
T: Copy + fmt::Debug + PartialEq + One + Zero + ApproxEq<T>,
{
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
if self.is_identity() {
write!(f, "[I]")
} else {
self.to_array().fmt(f)
}
}
}
impl<T: Copy + Zero, Src, Dst> From<Scale<T, Src, Dst>> for ScaleOffset2D<T, Src, Dst> {
fn from(s: Scale<T, Src, Dst>) -> Self {
ScaleOffset2D::scale(s.0, s.0)
}
}
impl<T: Copy + One, Src, Dst> From<Translation2D<T, Src, Dst>> for ScaleOffset2D<T, Src, Dst> {
fn from(t: Translation2D<T, Src, Dst>) -> Self {
ScaleOffset2D::offset(t.x, t.y)
}
}
#[cfg(feature = "arbitrary")]
impl<'a, T, Src, Dst> arbitrary::Arbitrary<'a> for ScaleOffset2D<T, Src, Dst>
where
T: arbitrary::Arbitrary<'a>,
{
fn arbitrary(u: &mut arbitrary::Unstructured<'a>) -> arbitrary::Result<Self> {
let (sx, sy, tx, ty) = arbitrary::Arbitrary::arbitrary(u)?;
Ok(ScaleOffset2D::new(sx, sy, tx, ty))
}
}
#[cfg(feature = "bytemuck")]
unsafe impl<T: Zeroable, Src, Dst> Zeroable for ScaleOffset2D<T, Src, Dst> {}
#[cfg(feature = "bytemuck")]
unsafe impl<T: Pod, Src: 'static, Dst: 'static> Pod for ScaleOffset2D<T, Src, Dst> {}
#[cfg(feature = "malloc_size_of")]
impl<T: MallocSizeOf, Src, Dst> MallocSizeOf for ScaleOffset2D<T, Src, Dst> {
fn size_of(&self, ops: &mut MallocSizeOfOps) -> usize {
self.sx.size_of(ops) + self.sy.size_of(ops) + self.tx.size_of(ops) + self.ty.size_of(ops)
}
}
#[cfg(test)]
mod test {
use super::*;
use crate::approxeq::ApproxEq;
use crate::default;
#[cfg(feature = "mint")]
use mint;
type ScaleOffset = crate::default::ScaleOffset2D<f32>;
type IntScaleOffset = crate::default::ScaleOffset2D<i32>;
use core::f32::consts::FRAC_PI_2;
type Mat = default::Transform2D<f32>;
fn rad(v: f32) -> Angle<f32> {
Angle::radians(v)
}
#[test]
pub fn test_translation() {
let t1 = Mat::translation(1.0, 2.0);
let t2 = Mat::identity().pre_translate(vec2(1.0, 2.0));
let t3 = Mat::identity().then_translate(vec2(1.0, 2.0));
assert_eq!(t1, t2);
assert_eq!(t1, t3);
assert_eq!(
t1.transform_point(Point2D::new(1.0, 1.0)),
Point2D::new(2.0, 3.0)
);
assert_eq!(t1.then(&t1), Mat::translation(2.0, 4.0));
}
#[test]
pub fn test_rotation() {
let r1 = Mat::rotation(rad(FRAC_PI_2));
let r2 = Mat::identity().pre_rotate(rad(FRAC_PI_2));
let r3 = Mat::identity().then_rotate(rad(FRAC_PI_2));
assert_eq!(r1, r2);
assert_eq!(r1, r3);
assert!(r1
.transform_point(Point2D::new(1.0, 2.0))
.approx_eq(&Point2D::new(-2.0, 1.0)));
assert!(r1.then(&r1).approx_eq(&Mat::rotation(rad(FRAC_PI_2 * 2.0))));
}
#[test]
pub fn test_scale() {
let s1 = Mat::scale(2.0, 3.0);
let s2 = Mat::identity().pre_scale(2.0, 3.0);
let s3 = Mat::identity().then_scale(2.0, 3.0);
assert_eq!(s1, s2);
assert_eq!(s1, s3);
assert!(s1
.transform_point(Point2D::new(2.0, 2.0))
.approx_eq(&Point2D::new(4.0, 6.0)));
}
#[test]
pub fn test_pre_then_scale() {
let m = Mat::rotation(rad(FRAC_PI_2)).then_translate(vec2(6.0, 7.0));
let s = Mat::scale(2.0, 3.0);
assert_eq!(m.then(&s), m.then_scale(2.0, 3.0));
}
#[test]
pub fn test_inverse_simple() {
let m1 = Mat::identity();
let m2 = m1.inverse().unwrap();
assert!(m1.approx_eq(&m2));
}
#[test]
pub fn test_inverse_scale() {
let m1 = Mat::scale(1.5, 0.3);
let m2 = m1.inverse().unwrap();
assert!(m1.then(&m2).approx_eq(&Mat::identity()));
assert!(m2.then(&m1).approx_eq(&Mat::identity()));
}
#[test]
pub fn test_inverse_translate() {
let m1 = Mat::translation(-132.0, 0.3);
let m2 = m1.inverse().unwrap();
assert!(m1.then(&m2).approx_eq(&Mat::identity()));
assert!(m2.then(&m1).approx_eq(&Mat::identity()));
}
#[test]
fn test_inverse_none() {
assert!(Mat::scale(2.0, 0.0).inverse().is_none());
assert!(Mat::scale(2.0, 2.0).inverse().is_some());
}
#[test]
pub fn test_pre_post() {
let m1 = default::Transform2D::identity()
.then_scale(1.0, 2.0)
.then_translate(vec2(1.0, 2.0));
let m2 = default::Transform2D::identity()
.pre_translate(vec2(1.0, 2.0))
.pre_scale(1.0, 2.0);
assert!(m1.approx_eq(&m2));
let r = Mat::rotation(rad(FRAC_PI_2));
let t = Mat::translation(2.0, 3.0);
let a = Point2D::new(1.0, 1.0);
assert!(r
.then(&t)
.transform_point(a)
.approx_eq(&Point2D::new(1.0, 4.0)));
assert!(t
.then(&r)
.transform_point(a)
.approx_eq(&Point2D::new(-4.0, 3.0)));
assert!(t
.then(&r)
.transform_point(a)
.approx_eq(&r.transform_point(t.transform_point(a))));
}
#[test]
fn test_size_of() {
use core::mem::size_of;
assert_eq!(size_of::<default::Transform2D<f32>>(), 6 * size_of::<f32>());
assert_eq!(size_of::<default::Transform2D<f64>>(), 6 * size_of::<f64>());
}
#[test]
pub fn test_is_identity() {
let m1 = default::Transform2D::identity();
assert!(m1.is_identity());
let m2 = m1.then_translate(vec2(0.1, 0.0));
assert!(!m2.is_identity());
}
#[test]
pub fn test_transform_vector() {
// Translation does not apply to vectors.
let m1 = Mat::translation(1.0, 1.0);
let v1 = vec2(10.0, -10.0);
assert_eq!(v1, m1.transform_vector(v1));
}
#[cfg(feature = "mint")]
#[test]
pub fn test_mint() {
let m1 = Mat::rotation(rad(FRAC_PI_2));
let mm: mint::RowMatrix3x2<_> = m1.into();
let m2 = Mat::from(mm);
assert_eq!(m1, m2);
}
#[test]
pub fn scale_offset_transform_point() {
let t1 = IntScaleOffset::new(2, 3, 4, 5);
let p = point2(6, 7);
assert_eq!(
t1.transform_point(p),
t1.to_transform2d().transform_point(p),
);
}
#[test]
pub fn scale_offset_transform_vector() {
let t1 = IntScaleOffset::new(2, 3, 4, 5);
let v = vec2(6, 7);
assert_eq!(
t1.transform_vector(v),
t1.to_transform2d().transform_vector(v),
);
}
#[test]
pub fn scale_offset_transform_box() {
let transforms = [
ScaleOffset::identity(),
ScaleOffset::new(2.0, 3.0, 4.0, 5.0),
ScaleOffset::new(-2.0, 3.0, 4.0, -5.0),
ScaleOffset::new(2.0, -3.0, 4.0, -5.0),
ScaleOffset::new(-2.0, -3.0, -4.0, 5.0),
];
let boxes = [
default::Box2D {
min: point2(0.0, 0.0),
max: point2(1.0, 1.0),
},
Box2D {
min: point2(-10.0, -10.0),
max: point2(10.0, 10.0),
},
Box2D {
min: point2(100.0, 130.0),
max: point2(150.0, 160.0),
},
Box2D {
min: point2(-100.0, -130.0),
max: point2(-50.0, 160.0),
},
Box2D {
min: point2(0.0, 0.0),
max: point2(0.0, 0.0),
},
Box2D {
min: point2(1.0, 0.0),
max: point2(-1.0, 1.0),
},
Box2D {
min: point2(1.0, 1.0),
max: point2(1.0, -1.0),
},
Box2D {
min: point2(1.0, 1.0),
max: point2(-1.0, -1.0),
},
];
for b in &boxes {
for transform in &transforms {
let b2 = transform.transform_box(b);
assert_eq!(
b2.is_empty(),
b.is_empty(),
"transform: {transform:?}, box: {b:?}, empty before: {:?} after {:?}",
b.is_empty(),
b2.is_empty()
);
let mat = transform.to_transform2d();
// We don't guarantee that Transform2D and ScaleOffset2D
// deal with empty boxes the same way.
if !b.is_empty() {
assert_eq!(b2, mat.outer_transformed_box(b));
}
}
}
}
#[test]
pub fn scale_offset_then() {
let t1 = IntScaleOffset::new(2, 3, 4, 5);
let t2 = IntScaleOffset::new(6, 7, 8, 9);
let t3 = t1.then(&t2).to_transform2d();
let t3_tx = t1.to_transform2d().then(&t2.to_transform2d());
assert_eq!(t3, t3_tx);
}
#[test]
pub fn scale_offset_pre_post() {
let t1 = ScaleOffset::new(2.0, 3.0, 4.0, 5.0);
let v = vec2(100.0, 200.0);
assert!(t1
.then_translate(v)
.to_transform2d()
.approx_eq(&t1.to_transform2d().then_translate(v)));
assert!(t1
.pre_translate(v)
.to_transform2d()
.approx_eq(&t1.to_transform2d().pre_translate(v)));
let sx = 100.0;
let sy = 120.0;
assert!(t1
.then_scale(sx, sy)
.to_transform2d()
.approx_eq(&t1.to_transform2d().then_scale(sx, sy)));
assert!(t1
.pre_scale(sx, sy)
.to_transform2d()
.approx_eq(&t1.to_transform2d().pre_scale(sx, sy)));
}
#[test]
pub fn scale_offset_inverse() {
let t1 = ScaleOffset::new(2.0, 3.0, 4.0, 5.0);
assert_eq!(
t1.inverse().unwrap().to_transform2d(),
t1.to_transform2d().inverse().unwrap(),
)
}
#[test]
pub fn scale_offset_identity() {
assert!(ScaleOffset::identity().is_identity())
}
}