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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.
#![cfg_attr(feature = "cargo-clippy", allow(just_underscores_and_digits))]
use super::{UnknownUnit, Angle};
#[cfg(feature = "mint")]
use mint;
use num::{One, Zero};
use point::TypedPoint2D;
use vector::{TypedVector2D, vec2};
use rect::TypedRect;
use transform3d::TypedTransform3D;
use core::ops::{Add, Mul, Div, Sub, Neg};
use core::marker::PhantomData;
use approxeq::ApproxEq;
use trig::Trig;
use core::fmt;
use num_traits::NumCast;
define_matrix! {
/// A 2d transform stored as a 3 by 2 matrix in row-major order in memory.
///
/// Transforms can be parametrized over the source and destination units, to describe a
/// transformation from a space to another.
/// For example, `TypedTransform2D<f32, WorldSpace, ScreenSpace>::transform_point4d`
/// takes a `TypedPoint2D<f32, WorldSpace>` and returns a `TypedPoint2D<f32, ScreenSpace>`.
///
/// Transforms expose a set of convenience methods for pre- and post-transformations.
/// A pre-transformation corresponds to adding an operation that is applied before
/// the rest of the transformation, while a post-transformation adds an operation
/// that is applied after.
pub struct TypedTransform2D<T, Src, Dst> {
pub m11: T, pub m12: T,
pub m21: T, pub m22: T,
pub m31: T, pub m32: T,
}
}
/// The default 2d transform type with no units.
pub type Transform2D<T> = TypedTransform2D<T, UnknownUnit, UnknownUnit>;
impl<T: Copy, Src, Dst> TypedTransform2D<T, Src, Dst> {
/// Create a transform specifying its matrix elements in row-major order.
pub fn row_major(m11: T, m12: T, m21: T, m22: T, m31: T, m32: T) -> Self {
TypedTransform2D {
m11, m12,
m21, m22,
m31, m32,
_unit: PhantomData,
}
}
/// Create a transform specifying its matrix elements in column-major order.
pub fn column_major(m11: T, m21: T, m31: T, m12: T, m22: T, m32: T) -> Self {
TypedTransform2D {
m11, m12,
m21, m22,
m31, m32,
_unit: PhantomData,
}
}
/// Returns an array containing this transform's terms in row-major order (the order
/// in which the transform is actually laid out in memory).
pub fn to_row_major_array(&self) -> [T; 6] {
[
self.m11, self.m12,
self.m21, self.m22,
self.m31, self.m32
]
}
/// Returns an array containing this transform's terms in column-major order.
pub fn to_column_major_array(&self) -> [T; 6] {
[
self.m11, self.m21, self.m31,
self.m12, self.m22, self.m32
]
}
/// Returns an array containing this transform's 3 rows in (in row-major order)
/// as arrays.
///
/// This is a convenience method to interface with other libraries like glium.
pub fn to_row_arrays(&self) -> [[T; 2]; 3] {
[
[self.m11, self.m12],
[self.m21, self.m22],
[self.m31, self.m32],
]
}
/// Creates a transform from an array of 6 elements in row-major order.
pub fn from_row_major_array(array: [T; 6]) -> Self {
Self::row_major(
array[0], array[1],
array[2], array[3],
array[4], array[5],
)
}
/// Creates a transform from 3 rows of 2 elements (row-major order).
pub fn from_row_arrays(array: [[T; 2]; 3]) -> Self {
Self::row_major(
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.
pub fn to_untyped(&self) -> Transform2D<T> {
Transform2D::row_major(
self.m11, self.m12,
self.m21, self.m22,
self.m31, self.m32
)
}
/// Tag a unitless value with units.
pub fn from_untyped(p: &Transform2D<T>) -> Self {
TypedTransform2D::row_major(
p.m11, p.m12,
p.m21, p.m22,
p.m31, p.m32
)
}
}
impl<T0: NumCast + Copy, Src, Dst> TypedTransform2D<T0, Src, Dst> {
/// Cast from one numeric representation to another, preserving the units.
pub fn cast<T1: NumCast + Copy>(&self) -> TypedTransform2D<T1, Src, Dst> {
self.try_cast().unwrap()
}
/// Fallible cast from one numeric representation to another, preserving the units.
pub fn try_cast<T1: NumCast + Copy>(&self) -> Option<TypedTransform2D<T1, 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(TypedTransform2D::row_major(
m11, m12,
m21, m22,
m31, m32
))
},
_ => None
}
}
}
impl<T, Src, Dst> TypedTransform2D<T, Src, Dst>
where T: Copy +
PartialEq +
One + Zero {
pub fn identity() -> Self {
let (_0, _1) = (Zero::zero(), One::one());
TypedTransform2D::row_major(
_1, _0,
_0, _1,
_0, _0
)
}
// 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 {
*self == TypedTransform2D::identity()
}
}
impl<T, Src, Dst> TypedTransform2D<T, Src, Dst>
where T: Copy + Clone +
Add<T, Output=T> +
Mul<T, Output=T> +
Div<T, Output=T> +
Sub<T, Output=T> +
Trig +
PartialOrd +
One + Zero {
/// Returns the multiplication of the two matrices such that mat's transformation
/// applies after self's transformation.
#[cfg_attr(feature = "unstable", must_use)]
pub fn post_mul<NewDst>(&self, mat: &TypedTransform2D<T, Dst, NewDst>) -> TypedTransform2D<T, Src, NewDst> {
TypedTransform2D::row_major(
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,
)
}
/// Returns the multiplication of the two matrices such that mat's transformation
/// applies before self's transformation.
#[cfg_attr(feature = "unstable", must_use)]
pub fn pre_mul<NewSrc>(&self, mat: &TypedTransform2D<T, NewSrc, Src>) -> TypedTransform2D<T, NewSrc, Dst> {
mat.post_mul(self)
}
/// Returns a translation transform.
pub fn create_translation(x: T, y: T) -> Self {
let (_0, _1): (T, T) = (Zero::zero(), One::one());
TypedTransform2D::row_major(
_1, _0,
_0, _1,
x, y
)
}
/// Applies a translation after self's transformation and returns the resulting transform.
#[cfg_attr(feature = "unstable", must_use)]
pub fn post_translate(&self, v: TypedVector2D<T, Dst>) -> Self {
self.post_mul(&TypedTransform2D::create_translation(v.x, v.y))
}
/// Applies a translation before self's transformation and returns the resulting transform.
#[cfg_attr(feature = "unstable", must_use)]
pub fn pre_translate(&self, v: TypedVector2D<T, Src>) -> Self {
self.pre_mul(&TypedTransform2D::create_translation(v.x, v.y))
}
/// Returns a scale transform.
pub fn create_scale(x: T, y: T) -> Self {
let _0 = Zero::zero();
TypedTransform2D::row_major(
x, _0,
_0, y,
_0, _0
)
}
/// Applies a scale after self's transformation and returns the resulting transform.
#[cfg_attr(feature = "unstable", must_use)]
pub fn post_scale(&self, x: T, y: T) -> Self {
self.post_mul(&TypedTransform2D::create_scale(x, y))
}
/// Applies a scale before self's transformation and returns the resulting transform.
#[cfg_attr(feature = "unstable", must_use)]
pub fn pre_scale(&self, x: T, y: T) -> Self {
TypedTransform2D::row_major(
self.m11 * x, self.m12,
self.m21, self.m22 * y,
self.m31, self.m32
)
}
/// Returns a rotation transform.
pub fn create_rotation(theta: Angle<T>) -> Self {
let _0 = Zero::zero();
let cos = theta.get().cos();
let sin = theta.get().sin();
TypedTransform2D::row_major(
cos, _0 - sin,
sin, cos,
_0, _0
)
}
/// Applies a rotation after self's transformation and returns the resulting transform.
#[cfg_attr(feature = "unstable", must_use)]
pub fn post_rotate(&self, theta: Angle<T>) -> Self {
self.post_mul(&TypedTransform2D::create_rotation(theta))
}
/// Applies a rotation after self's transformation and returns the resulting transform.
#[cfg_attr(feature = "unstable", must_use)]
pub fn pre_rotate(&self, theta: Angle<T>) -> Self {
self.pre_mul(&TypedTransform2D::create_rotation(theta))
}
/// Returns the given point transformed by this transform.
#[inline]
#[cfg_attr(feature = "unstable", must_use)]
pub fn transform_point(&self, point: &TypedPoint2D<T, Src>) -> TypedPoint2D<T, Dst> {
TypedPoint2D::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]
#[cfg_attr(feature = "unstable", must_use)]
pub fn transform_vector(&self, vec: &TypedVector2D<T, Src>) -> TypedVector2D<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]
#[cfg_attr(feature = "unstable", must_use)]
pub fn transform_rect(&self, rect: &TypedRect<T, Src>) -> TypedRect<T, Dst> {
TypedRect::from_points(&[
self.transform_point(&rect.origin),
self.transform_point(&rect.top_right()),
self.transform_point(&rect.bottom_left()),
self.transform_point(&rect.bottom_right()),
])
}
/// Computes and returns the determinant of this transform.
pub fn determinant(&self) -> T {
self.m11 * self.m22 - self.m12 * self.m21
}
/// Returns the inverse transform if possible.
#[cfg_attr(feature = "unstable", must_use)]
pub fn inverse(&self) -> Option<TypedTransform2D<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(TypedTransform2D::row_major(
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),
))
}
/// Returns the same transform with a different destination unit.
#[inline]
pub fn with_destination<NewDst>(&self) -> TypedTransform2D<T, Src, NewDst> {
TypedTransform2D::row_major(
self.m11, self.m12,
self.m21, self.m22,
self.m31, self.m32,
)
}
/// Returns the same transform with a different source unit.
#[inline]
pub fn with_source<NewSrc>(&self) -> TypedTransform2D<T, NewSrc, Dst> {
TypedTransform2D::row_major(
self.m11, self.m12,
self.m21, self.m22,
self.m31, self.m32,
)
}
}
impl <T, Src, Dst> TypedTransform2D<T, Src, Dst>
where T: Copy + Clone +
Add<T, Output=T> +
Sub<T, Output=T> +
Mul<T, Output=T> +
Div<T, Output=T> +
Neg<Output=T> +
PartialOrd +
Trig +
One + Zero {
/// Create a 3D transform from the current transform
pub fn to_3d(&self) -> TypedTransform3D<T, Src, Dst> {
TypedTransform3D::row_major_2d(self.m11, self.m12, self.m21, self.m22, self.m31, self.m32)
}
}
impl <T, Src, Dst> Default for TypedTransform2D<T, Src, Dst>
where T: Copy + PartialEq + One + Zero
{
fn default() -> Self {
Self::identity()
}
}
impl<T: ApproxEq<T>, Src, Dst> TypedTransform2D<T, Src, Dst> {
pub fn approx_eq(&self, other: &Self) -> bool {
self.m11.approx_eq(&other.m11) && self.m12.approx_eq(&other.m12) &&
self.m21.approx_eq(&other.m21) && self.m22.approx_eq(&other.m22) &&
self.m31.approx_eq(&other.m31) && self.m32.approx_eq(&other.m32)
}
}
impl<T: Copy + fmt::Debug, Src, Dst> fmt::Debug for TypedTransform2D<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_row_major_array().fmt(f)
}
}
}
#[cfg(feature = "mint")]
impl<T, Src, Dst> From<mint::RowMatrix3x2<T>> for TypedTransform2D<T, Src, Dst> {
fn from(m: mint::RowMatrix3x2<T>) -> Self {
TypedTransform2D {
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> Into<mint::RowMatrix3x2<T>> for TypedTransform2D<T, Src, Dst> {
fn into(self) -> mint::RowMatrix3x2<T> {
mint::RowMatrix3x2 {
x: mint::Vector2 { x: self.m11, y: self.m12 },
y: mint::Vector2 { x: self.m21, y: self.m22 },
z: mint::Vector2 { x: self.m31, y: self.m32 },
}
}
}
#[cfg(test)]
mod test {
use super::*;
use approxeq::ApproxEq;
use point::Point2D;
use Angle;
#[cfg(feature = "mint")]
use mint;
use core::f32::consts::FRAC_PI_2;
type Mat = Transform2D<f32>;
fn rad(v: f32) -> Angle<f32> { Angle::radians(v) }
#[test]
pub fn test_translation() {
let t1 = Mat::create_translation(1.0, 2.0);
let t2 = Mat::identity().pre_translate(vec2(1.0, 2.0));
let t3 = Mat::identity().post_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.post_mul(&t1), Mat::create_translation(2.0, 4.0));
}
#[test]
pub fn test_rotation() {
let r1 = Mat::create_rotation(rad(FRAC_PI_2));
let r2 = Mat::identity().pre_rotate(rad(FRAC_PI_2));
let r3 = Mat::identity().post_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.post_mul(&r1).approx_eq(&Mat::create_rotation(rad(FRAC_PI_2*2.0))));
}
#[test]
pub fn test_scale() {
let s1 = Mat::create_scale(2.0, 3.0);
let s2 = Mat::identity().pre_scale(2.0, 3.0);
let s3 = Mat::identity().post_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]
fn test_column_major() {
assert_eq!(
Mat::row_major(
1.0, 2.0,
3.0, 4.0,
5.0, 6.0
),
Mat::column_major(
1.0, 3.0, 5.0,
2.0, 4.0, 6.0,
)
);
}
#[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::create_scale(1.5, 0.3);
let m2 = m1.inverse().unwrap();
assert!(m1.pre_mul(&m2).approx_eq(&Mat::identity()));
}
#[test]
pub fn test_inverse_translate() {
let m1 = Mat::create_translation(-132.0, 0.3);
let m2 = m1.inverse().unwrap();
assert!(m1.pre_mul(&m2).approx_eq(&Mat::identity()));
}
#[test]
fn test_inverse_none() {
assert!(Mat::create_scale(2.0, 0.0).inverse().is_none());
assert!(Mat::create_scale(2.0, 2.0).inverse().is_some());
}
#[test]
pub fn test_pre_post() {
let m1 = Transform2D::identity().post_scale(1.0, 2.0).post_translate(vec2(1.0, 2.0));
let m2 = Transform2D::identity().pre_translate(vec2(1.0, 2.0)).pre_scale(1.0, 2.0);
assert!(m1.approx_eq(&m2));
let r = Mat::create_rotation(rad(FRAC_PI_2));
let t = Mat::create_translation(2.0, 3.0);
let a = Point2D::new(1.0, 1.0);
assert!(r.post_mul(&t).transform_point(&a).approx_eq(&Point2D::new(3.0, 2.0)));
assert!(t.post_mul(&r).transform_point(&a).approx_eq(&Point2D::new(4.0, -3.0)));
assert!(t.post_mul(&r).transform_point(&a).approx_eq(&r.transform_point(&t.transform_point(&a))));
assert!(r.pre_mul(&t).transform_point(&a).approx_eq(&Point2D::new(4.0, -3.0)));
assert!(t.pre_mul(&r).transform_point(&a).approx_eq(&Point2D::new(3.0, 2.0)));
assert!(t.pre_mul(&r).transform_point(&a).approx_eq(&t.transform_point(&r.transform_point(&a))));
}
#[test]
fn test_size_of() {
use core::mem::size_of;
assert_eq!(size_of::<Transform2D<f32>>(), 6*size_of::<f32>());
assert_eq!(size_of::<Transform2D<f64>>(), 6*size_of::<f64>());
}
#[test]
pub fn test_is_identity() {
let m1 = Transform2D::identity();
assert!(m1.is_identity());
let m2 = m1.post_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::create_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::create_rotation(rad(FRAC_PI_2));
let mm: mint::RowMatrix3x2<_> = m1.into();
let m2 = Mat::from(mm);
assert_eq!(m1, m2);
}
}