1// Copyright 2013 The Servo Project Developers. See the COPYRIGHT
2// file at the top-level directory of this distribution.
3//
4// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
5// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
6// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
7// option. This file may not be copied, modified, or distributed
8// except according to those terms.
9
10#![allow(clippy::just_underscores_and_digits)]
11
12use super::{Angle, UnknownUnit};
13use crate::approxeq::ApproxEq;
14use crate::box2d::Box2D;
15use crate::num::{One, Zero};
16use crate::point::{point2, Point2D};
17use crate::rect::Rect;
18use crate::transform3d::Transform3D;
19use crate::trig::Trig;
20use crate::vector::{vec2, Vector2D};
21use core::cmp::{Eq, PartialEq};
22use core::fmt;
23use core::hash::Hash;
24use core::marker::PhantomData;
25use core::ops::{Add, Div, Mul, Sub};
26
27#[cfg(feature = "bytemuck")]
28use bytemuck::{Pod, Zeroable};
29#[cfg(feature = "mint")]
30use mint;
31use num_traits::NumCast;
32#[cfg(feature = "serde")]
33use serde::{Deserialize, Serialize};
34
35/// A 2d transform represented by a column-major 3 by 3 matrix, compressed down to 3 by 2.
36///
37/// Transforms can be parametrized over the source and destination units, to describe a
38/// transformation from a space to another.
39/// For example, `Transform2D<f32, WorldSpace, ScreenSpace>::transform_point4d`
40/// takes a `Point2D<f32, WorldSpace>` and returns a `Point2D<f32, ScreenSpace>`.
41///
42/// Transforms expose a set of convenience methods for pre- and post-transformations.
43/// Pre-transformations (`pre_*` methods) correspond to adding an operation that is
44/// applied before the rest of the transformation, while post-transformations (`then_*`
45/// methods) add an operation that is applied after.
46///
47/// The matrix representation is conceptually equivalent to a 3 by 3 matrix transformation
48/// compressed to 3 by 2 with the components that aren't needed to describe the set of 2d
49/// transformations we are interested in implicitly defined:
50///
51/// ```text
52/// | m11 m21 m31 | |x| |x'|
53/// | m12 m22 m32 | x |y| = |y'|
54/// | 0 0 1 | |1| |1 |
55/// ```
56///
57/// When translating `Transform2D` into general matrix representations, consider that the
58/// representation follows the column-major notation with column vectors.
59///
60/// The translation terms are `m31` and `m32`.
61#[repr(C)]
62#[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
63#[cfg_attr(
64 feature = "serde",
65 serde(bound(serialize = "T: Serialize", deserialize = "T: Deserialize<'de>"))
66)]
67#[rustfmt::skip]
68pub struct Transform2D<T, Src, Dst> {
69 pub m11: T, pub m12: T,
70 pub m21: T, pub m22: T,
71 pub m31: T, pub m32: T,
72 #[doc(hidden)]
73 pub _unit: PhantomData<(Src, Dst)>,
74}
75
76#[cfg(feature = "arbitrary")]
77impl<'a, T, Src, Dst> arbitrary::Arbitrary<'a> for Transform2D<T, Src, Dst>
78where
79 T: arbitrary::Arbitrary<'a>,
80{
81 fn arbitrary(u: &mut arbitrary::Unstructured<'a>) -> arbitrary::Result<Self> {
82 let (m11, m12, m21, m22, m31, m32) = arbitrary::Arbitrary::arbitrary(u)?;
83 Ok(Transform2D {
84 m11,
85 m12,
86 m21,
87 m22,
88 m31,
89 m32,
90 _unit: PhantomData,
91 })
92 }
93}
94
95#[cfg(feature = "bytemuck")]
96unsafe impl<T: Zeroable, Src, Dst> Zeroable for Transform2D<T, Src, Dst> {}
97
98#[cfg(feature = "bytemuck")]
99unsafe impl<T: Pod, Src: 'static, Dst: 'static> Pod for Transform2D<T, Src, Dst> {}
100
101impl<T: Copy, Src, Dst> Copy for Transform2D<T, Src, Dst> {}
102
103impl<T: Clone, Src, Dst> Clone for Transform2D<T, Src, Dst> {
104 fn clone(&self) -> Self {
105 Transform2D {
106 m11: self.m11.clone(),
107 m12: self.m12.clone(),
108 m21: self.m21.clone(),
109 m22: self.m22.clone(),
110 m31: self.m31.clone(),
111 m32: self.m32.clone(),
112 _unit: PhantomData,
113 }
114 }
115}
116
117impl<T, Src, Dst> Eq for Transform2D<T, Src, Dst> where T: Eq {}
118
119impl<T, Src, Dst> PartialEq for Transform2D<T, Src, Dst>
120where
121 T: PartialEq,
122{
123 fn eq(&self, other: &Self) -> bool {
124 self.m11 == other.m11
125 && self.m12 == other.m12
126 && self.m21 == other.m21
127 && self.m22 == other.m22
128 && self.m31 == other.m31
129 && self.m32 == other.m32
130 }
131}
132
133impl<T, Src, Dst> Hash for Transform2D<T, Src, Dst>
134where
135 T: Hash,
136{
137 fn hash<H: core::hash::Hasher>(&self, h: &mut H) {
138 self.m11.hash(state:h);
139 self.m12.hash(state:h);
140 self.m21.hash(state:h);
141 self.m22.hash(state:h);
142 self.m31.hash(state:h);
143 self.m32.hash(state:h);
144 }
145}
146
147impl<T, Src, Dst> Transform2D<T, Src, Dst> {
148 /// Create a transform specifying its components in using the column-major-column-vector
149 /// matrix notation.
150 ///
151 /// For example, the translation terms m31 and m32 are the last two parameters parameters.
152 ///
153 /// ```
154 /// use euclid::default::Transform2D;
155 /// let tx = 1.0;
156 /// let ty = 2.0;
157 /// let translation = Transform2D::new(
158 /// 1.0, 0.0,
159 /// 0.0, 1.0,
160 /// tx, ty,
161 /// );
162 /// ```
163 #[rustfmt::skip]
164 pub const fn new(m11: T, m12: T, m21: T, m22: T, m31: T, m32: T) -> Self {
165 Transform2D {
166 m11, m12,
167 m21, m22,
168 m31, m32,
169 _unit: PhantomData,
170 }
171 }
172
173 /// Returns `true` if this transform is approximately equal to the other one, using
174 /// `T`'s default epsilon value.
175 ///
176 /// The same as [`ApproxEq::approx_eq`] but available without importing trait.
177 #[inline]
178 pub fn approx_eq(&self, other: &Self) -> bool
179 where
180 T: ApproxEq<T>,
181 {
182 <Self as ApproxEq<T>>::approx_eq(&self, &other)
183 }
184
185 /// Returns `true` if this transform is approximately equal to the other one, using
186 /// a provided epsilon value.
187 ///
188 /// The same as [`ApproxEq::approx_eq_eps`] but available without importing trait.
189 #[inline]
190 pub fn approx_eq_eps(&self, other: &Self, eps: &T) -> bool
191 where
192 T: ApproxEq<T>,
193 {
194 <Self as ApproxEq<T>>::approx_eq_eps(&self, &other, &eps)
195 }
196}
197
198impl<T: Copy, Src, Dst> Transform2D<T, Src, Dst> {
199 /// Returns an array containing this transform's terms.
200 ///
201 /// The terms are laid out in the same order as they are
202 /// specified in [`Transform2D::new`], that is following the
203 /// column-major-column-vector matrix notation.
204 ///
205 /// For example the translation terms are found in the
206 /// last two slots of the array.
207 #[inline]
208 #[rustfmt::skip]
209 pub fn to_array(&self) -> [T; 6] {
210 [
211 self.m11, self.m12,
212 self.m21, self.m22,
213 self.m31, self.m32
214 ]
215 }
216
217 /// Returns an array containing this transform's terms transposed.
218 ///
219 /// The terms are laid out in transposed order from the same order of
220 /// `Transform3D::new` and `Transform3D::to_array`, that is following
221 /// the row-major-column-vector matrix notation.
222 ///
223 /// For example the translation terms are found at indices 2 and 5
224 /// in the array.
225 #[inline]
226 #[rustfmt::skip]
227 pub fn to_array_transposed(&self) -> [T; 6] {
228 [
229 self.m11, self.m21, self.m31,
230 self.m12, self.m22, self.m32
231 ]
232 }
233
234 /// Equivalent to `to_array` with elements packed two at a time
235 /// in an array of arrays.
236 #[inline]
237 pub fn to_arrays(&self) -> [[T; 2]; 3] {
238 [
239 [self.m11, self.m12],
240 [self.m21, self.m22],
241 [self.m31, self.m32],
242 ]
243 }
244
245 /// Create a transform providing its components via an array
246 /// of 6 elements instead of as individual parameters.
247 ///
248 /// The order of the components corresponds to the
249 /// column-major-column-vector matrix notation (the same order
250 /// as `Transform2D::new`).
251 #[inline]
252 #[rustfmt::skip]
253 pub fn from_array(array: [T; 6]) -> Self {
254 Self::new(
255 array[0], array[1],
256 array[2], array[3],
257 array[4], array[5],
258 )
259 }
260
261 /// Equivalent to `from_array` with elements packed two at a time
262 /// in an array of arrays.
263 ///
264 /// The order of the components corresponds to the
265 /// column-major-column-vector matrix notation (the same order
266 /// as `Transform3D::new`).
267 #[inline]
268 #[rustfmt::skip]
269 pub fn from_arrays(array: [[T; 2]; 3]) -> Self {
270 Self::new(
271 array[0][0], array[0][1],
272 array[1][0], array[1][1],
273 array[2][0], array[2][1],
274 )
275 }
276
277 /// Drop the units, preserving only the numeric value.
278 #[inline]
279 #[rustfmt::skip]
280 pub fn to_untyped(&self) -> Transform2D<T, UnknownUnit, UnknownUnit> {
281 Transform2D::new(
282 self.m11, self.m12,
283 self.m21, self.m22,
284 self.m31, self.m32
285 )
286 }
287
288 /// Tag a unitless value with units.
289 #[inline]
290 #[rustfmt::skip]
291 pub fn from_untyped(p: &Transform2D<T, UnknownUnit, UnknownUnit>) -> Self {
292 Transform2D::new(
293 p.m11, p.m12,
294 p.m21, p.m22,
295 p.m31, p.m32
296 )
297 }
298
299 /// Returns the same transform with a different source unit.
300 #[inline]
301 #[rustfmt::skip]
302 pub fn with_source<NewSrc>(&self) -> Transform2D<T, NewSrc, Dst> {
303 Transform2D::new(
304 self.m11, self.m12,
305 self.m21, self.m22,
306 self.m31, self.m32,
307 )
308 }
309
310 /// Returns the same transform with a different destination unit.
311 #[inline]
312 #[rustfmt::skip]
313 pub fn with_destination<NewDst>(&self) -> Transform2D<T, Src, NewDst> {
314 Transform2D::new(
315 self.m11, self.m12,
316 self.m21, self.m22,
317 self.m31, self.m32,
318 )
319 }
320
321 /// Create a 3D transform from the current transform
322 pub fn to_3d(&self) -> Transform3D<T, Src, Dst>
323 where
324 T: Zero + One,
325 {
326 Transform3D::new_2d(self.m11, self.m12, self.m21, self.m22, self.m31, self.m32)
327 }
328}
329
330impl<T: NumCast + Copy, Src, Dst> Transform2D<T, Src, Dst> {
331 /// Cast from one numeric representation to another, preserving the units.
332 #[inline]
333 pub fn cast<NewT: NumCast>(&self) -> Transform2D<NewT, Src, Dst> {
334 self.try_cast().unwrap()
335 }
336
337 /// Fallible cast from one numeric representation to another, preserving the units.
338 #[rustfmt::skip]
339 pub fn try_cast<NewT: NumCast>(&self) -> Option<Transform2D<NewT, Src, Dst>> {
340 match (NumCast::from(self.m11), NumCast::from(self.m12),
341 NumCast::from(self.m21), NumCast::from(self.m22),
342 NumCast::from(self.m31), NumCast::from(self.m32)) {
343 (Some(m11), Some(m12),
344 Some(m21), Some(m22),
345 Some(m31), Some(m32)) => {
346 Some(Transform2D::new(
347 m11, m12,
348 m21, m22,
349 m31, m32
350 ))
351 },
352 _ => None
353 }
354 }
355}
356
357impl<T, Src, Dst> Transform2D<T, Src, Dst>
358where
359 T: Zero + One,
360{
361 /// Create an identity matrix:
362 ///
363 /// ```text
364 /// 1 0
365 /// 0 1
366 /// 0 0
367 /// ```
368 #[inline]
369 pub fn identity() -> Self {
370 Self::translation(T::zero(), T::zero())
371 }
372
373 /// Intentional not public, because it checks for exact equivalence
374 /// while most consumers will probably want some sort of approximate
375 /// equivalence to deal with floating-point errors.
376 fn is_identity(&self) -> bool
377 where
378 T: PartialEq,
379 {
380 *self == Self::identity()
381 }
382}
383
384/// Methods for combining generic transformations
385impl<T, Src, Dst> Transform2D<T, Src, Dst>
386where
387 T: Copy + Add<Output = T> + Mul<Output = T>,
388{
389 /// Returns the multiplication of the two matrices such that mat's transformation
390 /// applies after self's transformation.
391 #[must_use]
392 #[rustfmt::skip]
393 pub fn then<NewDst>(&self, mat: &Transform2D<T, Dst, NewDst>) -> Transform2D<T, Src, NewDst> {
394 Transform2D::new(
395 self.m11 * mat.m11 + self.m12 * mat.m21,
396 self.m11 * mat.m12 + self.m12 * mat.m22,
397
398 self.m21 * mat.m11 + self.m22 * mat.m21,
399 self.m21 * mat.m12 + self.m22 * mat.m22,
400
401 self.m31 * mat.m11 + self.m32 * mat.m21 + mat.m31,
402 self.m31 * mat.m12 + self.m32 * mat.m22 + mat.m32,
403 )
404 }
405}
406
407/// Methods for creating and combining translation transformations
408impl<T, Src, Dst> Transform2D<T, Src, Dst>
409where
410 T: Zero + One,
411{
412 /// Create a 2d translation transform:
413 ///
414 /// ```text
415 /// 1 0
416 /// 0 1
417 /// x y
418 /// ```
419 #[inline]
420 #[rustfmt::skip]
421 pub fn translation(x: T, y: T) -> Self {
422 let _0 = || T::zero();
423 let _1 = || T::one();
424
425 Self::new(
426 _1(), _0(),
427 _0(), _1(),
428 x, y,
429 )
430 }
431
432 /// Applies a translation after self's transformation and returns the resulting transform.
433 #[inline]
434 #[must_use]
435 pub fn then_translate(&self, v: Vector2D<T, Dst>) -> Self
436 where
437 T: Copy + Add<Output = T> + Mul<Output = T>,
438 {
439 self.then(&Transform2D::translation(v.x, v.y))
440 }
441
442 /// Applies a translation before self's transformation and returns the resulting transform.
443 #[inline]
444 #[must_use]
445 pub fn pre_translate(&self, v: Vector2D<T, Src>) -> Self
446 where
447 T: Copy + Add<Output = T> + Mul<Output = T>,
448 {
449 Transform2D::translation(v.x, v.y).then(self)
450 }
451}
452
453/// Methods for creating and combining rotation transformations
454impl<T, Src, Dst> Transform2D<T, Src, Dst>
455where
456 T: Copy + Add<Output = T> + Sub<Output = T> + Mul<Output = T> + Zero + Trig,
457{
458 /// Returns a rotation transform.
459 #[inline]
460 #[rustfmt::skip]
461 pub fn rotation(theta: Angle<T>) -> Self {
462 let _0 = Zero::zero();
463 let cos = theta.get().cos();
464 let sin = theta.get().sin();
465 Transform2D::new(
466 cos, sin,
467 _0 - sin, cos,
468 _0, _0
469 )
470 }
471
472 /// Applies a rotation after self's transformation and returns the resulting transform.
473 #[inline]
474 #[must_use]
475 pub fn then_rotate(&self, theta: Angle<T>) -> Self {
476 self.then(&Transform2D::rotation(theta))
477 }
478
479 /// Applies a rotation before self's transformation and returns the resulting transform.
480 #[inline]
481 #[must_use]
482 pub fn pre_rotate(&self, theta: Angle<T>) -> Self {
483 Transform2D::rotation(theta).then(self)
484 }
485}
486
487/// Methods for creating and combining scale transformations
488impl<T, Src, Dst> Transform2D<T, Src, Dst> {
489 /// Create a 2d scale transform:
490 ///
491 /// ```text
492 /// x 0
493 /// 0 y
494 /// 0 0
495 /// ```
496 #[inline]
497 #[rustfmt::skip]
498 pub fn scale(x: T, y: T) -> Self
499 where
500 T: Zero,
501 {
502 let _0 = || Zero::zero();
503
504 Self::new(
505 x, _0(),
506 _0(), y,
507 _0(), _0(),
508 )
509 }
510
511 /// Applies a scale after self's transformation and returns the resulting transform.
512 #[inline]
513 #[must_use]
514 pub fn then_scale(&self, x: T, y: T) -> Self
515 where
516 T: Copy + Add<Output = T> + Mul<Output = T> + Zero,
517 {
518 self.then(&Transform2D::scale(x, y))
519 }
520
521 /// Applies a scale before self's transformation and returns the resulting transform.
522 #[inline]
523 #[must_use]
524 #[rustfmt::skip]
525 pub fn pre_scale(&self, x: T, y: T) -> Self
526 where
527 T: Copy + Mul<Output = T>,
528 {
529 Transform2D::new(
530 self.m11 * x, self.m12 * x,
531 self.m21 * y, self.m22 * y,
532 self.m31, self.m32
533 )
534 }
535}
536
537/// Methods for apply transformations to objects
538impl<T, Src, Dst> Transform2D<T, Src, Dst>
539where
540 T: Copy + Add<Output = T> + Mul<Output = T>,
541{
542 /// Returns the given point transformed by this transform.
543 #[inline]
544 #[must_use]
545 pub fn transform_point(&self, point: Point2D<T, Src>) -> Point2D<T, Dst> {
546 Point2D::new(
547 point.x * self.m11 + point.y * self.m21 + self.m31,
548 point.x * self.m12 + point.y * self.m22 + self.m32,
549 )
550 }
551
552 /// Returns the given vector transformed by this matrix.
553 #[inline]
554 #[must_use]
555 pub fn transform_vector(&self, vec: Vector2D<T, Src>) -> Vector2D<T, Dst> {
556 vec2(
557 vec.x * self.m11 + vec.y * self.m21,
558 vec.x * self.m12 + vec.y * self.m22,
559 )
560 }
561
562 /// Returns a rectangle that encompasses the result of transforming the given rectangle by this
563 /// transform.
564 #[inline]
565 #[must_use]
566 pub fn outer_transformed_rect(&self, rect: &Rect<T, Src>) -> Rect<T, Dst>
567 where
568 T: Sub<Output = T> + Zero + PartialOrd,
569 {
570 let min = rect.min();
571 let max = rect.max();
572 Rect::from_points(&[
573 self.transform_point(min),
574 self.transform_point(max),
575 self.transform_point(point2(max.x, min.y)),
576 self.transform_point(point2(min.x, max.y)),
577 ])
578 }
579
580 /// Returns a box that encompasses the result of transforming the given box by this
581 /// transform.
582 #[inline]
583 #[must_use]
584 pub fn outer_transformed_box(&self, b: &Box2D<T, Src>) -> Box2D<T, Dst>
585 where
586 T: Sub<Output = T> + Zero + PartialOrd,
587 {
588 Box2D::from_points(&[
589 self.transform_point(b.min),
590 self.transform_point(b.max),
591 self.transform_point(point2(b.max.x, b.min.y)),
592 self.transform_point(point2(b.min.x, b.max.y)),
593 ])
594 }
595}
596
597impl<T, Src, Dst> Transform2D<T, Src, Dst>
598where
599 T: Copy + Sub<Output = T> + Mul<Output = T> + Div<Output = T> + PartialEq + Zero + One,
600{
601 /// Computes and returns the determinant of this transform.
602 pub fn determinant(&self) -> T {
603 self.m11 * self.m22 - self.m12 * self.m21
604 }
605
606 /// Returns whether it is possible to compute the inverse transform.
607 #[inline]
608 pub fn is_invertible(&self) -> bool {
609 self.determinant() != Zero::zero()
610 }
611
612 /// Returns the inverse transform if possible.
613 #[must_use]
614 pub fn inverse(&self) -> Option<Transform2D<T, Dst, Src>> {
615 let det = self.determinant();
616
617 let _0: T = Zero::zero();
618 let _1: T = One::one();
619
620 if det == _0 {
621 return None;
622 }
623
624 let inv_det = _1 / det;
625 Some(Transform2D::new(
626 inv_det * self.m22,
627 inv_det * (_0 - self.m12),
628 inv_det * (_0 - self.m21),
629 inv_det * self.m11,
630 inv_det * (self.m21 * self.m32 - self.m22 * self.m31),
631 inv_det * (self.m31 * self.m12 - self.m11 * self.m32),
632 ))
633 }
634}
635
636impl<T, Src, Dst> Default for Transform2D<T, Src, Dst>
637where
638 T: Zero + One,
639{
640 /// Returns the [identity transform](Transform2D::identity).
641 fn default() -> Self {
642 Self::identity()
643 }
644}
645
646impl<T: ApproxEq<T>, Src, Dst> ApproxEq<T> for Transform2D<T, Src, Dst> {
647 #[inline]
648 fn approx_epsilon() -> T {
649 T::approx_epsilon()
650 }
651
652 /// Returns `true` if this transform is approximately equal to the other one, using
653 /// a provided epsilon value.
654 fn approx_eq_eps(&self, other: &Self, eps: &T) -> bool {
655 self.m11.approx_eq_eps(&other.m11, approx_epsilon:eps)
656 && self.m12.approx_eq_eps(&other.m12, approx_epsilon:eps)
657 && self.m21.approx_eq_eps(&other.m21, approx_epsilon:eps)
658 && self.m22.approx_eq_eps(&other.m22, approx_epsilon:eps)
659 && self.m31.approx_eq_eps(&other.m31, approx_epsilon:eps)
660 && self.m32.approx_eq_eps(&other.m32, approx_epsilon:eps)
661 }
662}
663
664impl<T, Src, Dst> fmt::Debug for Transform2D<T, Src, Dst>
665where
666 T: Copy + fmt::Debug + PartialEq + One + Zero,
667{
668 fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
669 if self.is_identity() {
670 write!(f, "[I]")
671 } else {
672 self.to_array().fmt(f)
673 }
674 }
675}
676
677#[cfg(feature = "mint")]
678impl<T, Src, Dst> From<mint::RowMatrix3x2<T>> for Transform2D<T, Src, Dst> {
679 #[rustfmt::skip]
680 fn from(m: mint::RowMatrix3x2<T>) -> Self {
681 Transform2D {
682 m11: m.x.x, m12: m.x.y,
683 m21: m.y.x, m22: m.y.y,
684 m31: m.z.x, m32: m.z.y,
685 _unit: PhantomData,
686 }
687 }
688}
689#[cfg(feature = "mint")]
690impl<T, Src, Dst> From<Transform2D<T, Src, Dst>> for mint::RowMatrix3x2<T> {
691 fn from(t: Transform2D<T, Src, Dst>) -> Self {
692 mint::RowMatrix3x2 {
693 x: mint::Vector2 { x: t.m11, y: t.m12 },
694 y: mint::Vector2 { x: t.m21, y: t.m22 },
695 z: mint::Vector2 { x: t.m31, y: t.m32 },
696 }
697 }
698}
699
700#[cfg(test)]
701mod test {
702 use super::*;
703 use crate::approxeq::ApproxEq;
704 use crate::default;
705 #[cfg(feature = "mint")]
706 use mint;
707
708 use core::f32::consts::FRAC_PI_2;
709
710 type Mat = default::Transform2D<f32>;
711
712 fn rad(v: f32) -> Angle<f32> {
713 Angle::radians(v)
714 }
715
716 #[test]
717 pub fn test_translation() {
718 let t1 = Mat::translation(1.0, 2.0);
719 let t2 = Mat::identity().pre_translate(vec2(1.0, 2.0));
720 let t3 = Mat::identity().then_translate(vec2(1.0, 2.0));
721 assert_eq!(t1, t2);
722 assert_eq!(t1, t3);
723
724 assert_eq!(
725 t1.transform_point(Point2D::new(1.0, 1.0)),
726 Point2D::new(2.0, 3.0)
727 );
728
729 assert_eq!(t1.then(&t1), Mat::translation(2.0, 4.0));
730 }
731
732 #[test]
733 pub fn test_rotation() {
734 let r1 = Mat::rotation(rad(FRAC_PI_2));
735 let r2 = Mat::identity().pre_rotate(rad(FRAC_PI_2));
736 let r3 = Mat::identity().then_rotate(rad(FRAC_PI_2));
737 assert_eq!(r1, r2);
738 assert_eq!(r1, r3);
739
740 assert!(r1
741 .transform_point(Point2D::new(1.0, 2.0))
742 .approx_eq(&Point2D::new(-2.0, 1.0)));
743
744 assert!(r1.then(&r1).approx_eq(&Mat::rotation(rad(FRAC_PI_2 * 2.0))));
745 }
746
747 #[test]
748 pub fn test_scale() {
749 let s1 = Mat::scale(2.0, 3.0);
750 let s2 = Mat::identity().pre_scale(2.0, 3.0);
751 let s3 = Mat::identity().then_scale(2.0, 3.0);
752 assert_eq!(s1, s2);
753 assert_eq!(s1, s3);
754
755 assert!(s1
756 .transform_point(Point2D::new(2.0, 2.0))
757 .approx_eq(&Point2D::new(4.0, 6.0)));
758 }
759
760 #[test]
761 pub fn test_pre_then_scale() {
762 let m = Mat::rotation(rad(FRAC_PI_2)).then_translate(vec2(6.0, 7.0));
763 let s = Mat::scale(2.0, 3.0);
764 assert_eq!(m.then(&s), m.then_scale(2.0, 3.0));
765 }
766
767 #[test]
768 pub fn test_inverse_simple() {
769 let m1 = Mat::identity();
770 let m2 = m1.inverse().unwrap();
771 assert!(m1.approx_eq(&m2));
772 }
773
774 #[test]
775 pub fn test_inverse_scale() {
776 let m1 = Mat::scale(1.5, 0.3);
777 let m2 = m1.inverse().unwrap();
778 assert!(m1.then(&m2).approx_eq(&Mat::identity()));
779 assert!(m2.then(&m1).approx_eq(&Mat::identity()));
780 }
781
782 #[test]
783 pub fn test_inverse_translate() {
784 let m1 = Mat::translation(-132.0, 0.3);
785 let m2 = m1.inverse().unwrap();
786 assert!(m1.then(&m2).approx_eq(&Mat::identity()));
787 assert!(m2.then(&m1).approx_eq(&Mat::identity()));
788 }
789
790 #[test]
791 fn test_inverse_none() {
792 assert!(Mat::scale(2.0, 0.0).inverse().is_none());
793 assert!(Mat::scale(2.0, 2.0).inverse().is_some());
794 }
795
796 #[test]
797 pub fn test_pre_post() {
798 let m1 = default::Transform2D::identity()
799 .then_scale(1.0, 2.0)
800 .then_translate(vec2(1.0, 2.0));
801 let m2 = default::Transform2D::identity()
802 .pre_translate(vec2(1.0, 2.0))
803 .pre_scale(1.0, 2.0);
804 assert!(m1.approx_eq(&m2));
805
806 let r = Mat::rotation(rad(FRAC_PI_2));
807 let t = Mat::translation(2.0, 3.0);
808
809 let a = Point2D::new(1.0, 1.0);
810
811 assert!(r
812 .then(&t)
813 .transform_point(a)
814 .approx_eq(&Point2D::new(1.0, 4.0)));
815 assert!(t
816 .then(&r)
817 .transform_point(a)
818 .approx_eq(&Point2D::new(-4.0, 3.0)));
819 assert!(t
820 .then(&r)
821 .transform_point(a)
822 .approx_eq(&r.transform_point(t.transform_point(a))));
823 }
824
825 #[test]
826 fn test_size_of() {
827 use core::mem::size_of;
828 assert_eq!(size_of::<default::Transform2D<f32>>(), 6 * size_of::<f32>());
829 assert_eq!(size_of::<default::Transform2D<f64>>(), 6 * size_of::<f64>());
830 }
831
832 #[test]
833 pub fn test_is_identity() {
834 let m1 = default::Transform2D::identity();
835 assert!(m1.is_identity());
836 let m2 = m1.then_translate(vec2(0.1, 0.0));
837 assert!(!m2.is_identity());
838 }
839
840 #[test]
841 pub fn test_transform_vector() {
842 // Translation does not apply to vectors.
843 let m1 = Mat::translation(1.0, 1.0);
844 let v1 = vec2(10.0, -10.0);
845 assert_eq!(v1, m1.transform_vector(v1));
846 }
847
848 #[cfg(feature = "mint")]
849 #[test]
850 pub fn test_mint() {
851 let m1 = Mat::rotation(rad(FRAC_PI_2));
852 let mm: mint::RowMatrix3x2<_> = m1.into();
853 let m2 = Mat::from(mm);
854
855 assert_eq!(m1, m2);
856 }
857}
858