1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
// 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;

/// 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.
///
/// These transforms are for working with _row vectors_, so the matrix math for transforming
/// a vector is `v * T`. If your library is using column vectors, use `row_major` functions when you
/// are asked for `column_major` representations and vice versa.
#[repr(C)]
#[derive(EuclidMatrix)]
pub struct TypedTransform2D<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)>,
}

/// 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.
    ///
    /// Beware: This library is written with the assumption that row vectors
    /// are being used. If your matrices use column vectors (i.e. transforming a vector
    /// is `T * v`), then please use `column_major`
    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.
    ///
    /// Beware: This library is written with the assumption that row vectors
    /// are being used. If your matrices use column vectors (i.e. transforming a vector
    /// is `T * v`), then please use `row_major`
    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).
    ///
    /// Beware: This library is written with the assumption that row vectors
    /// are being used. If your matrices use column vectors (i.e. transforming a vector
    /// is `T * v`), then please use `to_column_major_array`
    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.
    ///
    /// Beware: This library is written with the assumption that row vectors
    /// are being used. If your matrices use column vectors (i.e. transforming a vector
    /// is `T * v`), then please use `to_row_major_array`
    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.
    ///
    /// Beware: This library is written with the assumption that row vectors
    /// are being used. If your matrices use column vectors (i.e. transforming a vector
    /// is `T * v`), this will return column major arrays.
    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.
    ///
    /// Beware: This library is written with the assumption that row vectors
    /// are being used. If your matrices use column vectors (i.e. transforming a vector
    /// is `T * v`), please provide a column major array.
    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).
    ///
    /// Beware: This library is written with the assumption that row vectors
    /// are being used. If your matrices use column vectors (i.e. transforming a vector
    /// is `T * v`), please provide a column major array.
    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.
    ///
    /// Assuming row vectors, this is equivalent to self * mat
    #[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.
    ///
    /// Assuming row vectors, this is equivalent to mat * self
    #[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.
    ///
    /// Assuming row vectors, this is equivalent to `p * self`
    #[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.
    ///
    /// Assuming row vectors, this is equivalent to `v * self`
    #[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);
    }
}