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
// Generated from affine.rs.tera template. Edit the template, not the generated file.

use crate::{DMat2, DMat3, DVec2};
use core::ops::{Deref, DerefMut, Mul, MulAssign};

/// A 2D affine transform, which can represent translation, rotation, scaling and shear.
#[derive(Copy, Clone)]
#[repr(C)]
pub struct DAffine2 {
    pub matrix2: DMat2,
    pub translation: DVec2,
}

impl DAffine2 {
    /// The degenerate zero transform.
    ///
    /// This transforms any finite vector and point to zero.
    /// The zero transform is non-invertible.
    pub const ZERO: Self = Self {
        matrix2: DMat2::ZERO,
        translation: DVec2::ZERO,
    };

    /// The identity transform.
    ///
    /// Multiplying a vector with this returns the same vector.
    pub const IDENTITY: Self = Self {
        matrix2: DMat2::IDENTITY,
        translation: DVec2::ZERO,
    };

    /// All NAN:s.
    pub const NAN: Self = Self {
        matrix2: DMat2::NAN,
        translation: DVec2::NAN,
    };

    /// Creates an affine transform from three column vectors.
    #[inline(always)]
    #[must_use]
    pub const fn from_cols(x_axis: DVec2, y_axis: DVec2, z_axis: DVec2) -> Self {
        Self {
            matrix2: DMat2::from_cols(x_axis, y_axis),
            translation: z_axis,
        }
    }

    /// Creates an affine transform from a `[f64; 6]` array stored in column major order.
    #[inline]
    #[must_use]
    pub fn from_cols_array(m: &[f64; 6]) -> Self {
        Self {
            matrix2: DMat2::from_cols_slice(&m[0..4]),
            translation: DVec2::from_slice(&m[4..6]),
        }
    }

    /// Creates a `[f64; 6]` array storing data in column major order.
    #[inline]
    #[must_use]
    pub fn to_cols_array(&self) -> [f64; 6] {
        let x = &self.matrix2.x_axis;
        let y = &self.matrix2.y_axis;
        let z = &self.translation;
        [x.x, x.y, y.x, y.y, z.x, z.y]
    }

    /// Creates an affine transform from a `[[f64; 2]; 3]`
    /// 2D array stored in column major order.
    /// If your data is in row major order you will need to `transpose` the returned
    /// matrix.
    #[inline]
    #[must_use]
    pub fn from_cols_array_2d(m: &[[f64; 2]; 3]) -> Self {
        Self {
            matrix2: DMat2::from_cols(m[0].into(), m[1].into()),
            translation: m[2].into(),
        }
    }

    /// Creates a `[[f64; 2]; 3]` 2D array storing data in
    /// column major order.
    /// If you require data in row major order `transpose` the matrix first.
    #[inline]
    #[must_use]
    pub fn to_cols_array_2d(&self) -> [[f64; 2]; 3] {
        [
            self.matrix2.x_axis.into(),
            self.matrix2.y_axis.into(),
            self.translation.into(),
        ]
    }

    /// Creates an affine transform from the first 6 values in `slice`.
    ///
    /// # Panics
    ///
    /// Panics if `slice` is less than 6 elements long.
    #[inline]
    #[must_use]
    pub fn from_cols_slice(slice: &[f64]) -> Self {
        Self {
            matrix2: DMat2::from_cols_slice(&slice[0..4]),
            translation: DVec2::from_slice(&slice[4..6]),
        }
    }

    /// Writes the columns of `self` to the first 6 elements in `slice`.
    ///
    /// # Panics
    ///
    /// Panics if `slice` is less than 6 elements long.
    #[inline]
    pub fn write_cols_to_slice(self, slice: &mut [f64]) {
        self.matrix2.write_cols_to_slice(&mut slice[0..4]);
        self.translation.write_to_slice(&mut slice[4..6]);
    }

    /// Creates an affine transform that changes scale.
    /// Note that if any scale is zero the transform will be non-invertible.
    #[inline]
    #[must_use]
    pub fn from_scale(scale: DVec2) -> Self {
        Self {
            matrix2: DMat2::from_diagonal(scale),
            translation: DVec2::ZERO,
        }
    }

    /// Creates an affine transform from the given rotation `angle`.
    #[inline]
    #[must_use]
    pub fn from_angle(angle: f64) -> Self {
        Self {
            matrix2: DMat2::from_angle(angle),
            translation: DVec2::ZERO,
        }
    }

    /// Creates an affine transformation from the given 2D `translation`.
    #[inline]
    #[must_use]
    pub fn from_translation(translation: DVec2) -> Self {
        Self {
            matrix2: DMat2::IDENTITY,
            translation,
        }
    }

    /// Creates an affine transform from a 2x2 matrix (expressing scale, shear and rotation)
    #[inline]
    #[must_use]
    pub fn from_mat2(matrix2: DMat2) -> Self {
        Self {
            matrix2,
            translation: DVec2::ZERO,
        }
    }

    /// Creates an affine transform from a 2x2 matrix (expressing scale, shear and rotation) and a
    /// translation vector.
    ///
    /// Equivalent to
    /// `DAffine2::from_translation(translation) * DAffine2::from_mat2(mat2)`
    #[inline]
    #[must_use]
    pub fn from_mat2_translation(matrix2: DMat2, translation: DVec2) -> Self {
        Self {
            matrix2,
            translation,
        }
    }

    /// Creates an affine transform from the given 2D `scale`, rotation `angle` (in radians) and
    /// `translation`.
    ///
    /// Equivalent to `DAffine2::from_translation(translation) *
    /// DAffine2::from_angle(angle) * DAffine2::from_scale(scale)`
    #[inline]
    #[must_use]
    pub fn from_scale_angle_translation(scale: DVec2, angle: f64, translation: DVec2) -> Self {
        let rotation = DMat2::from_angle(angle);
        Self {
            matrix2: DMat2::from_cols(rotation.x_axis * scale.x, rotation.y_axis * scale.y),
            translation,
        }
    }

    /// Creates an affine transform from the given 2D rotation `angle` (in radians) and
    /// `translation`.
    ///
    /// Equivalent to `DAffine2::from_translation(translation) * DAffine2::from_angle(angle)`
    #[inline]
    #[must_use]
    pub fn from_angle_translation(angle: f64, translation: DVec2) -> Self {
        Self {
            matrix2: DMat2::from_angle(angle),
            translation,
        }
    }

    /// The given `DMat3` must be an affine transform,
    #[inline]
    #[must_use]
    pub fn from_mat3(m: DMat3) -> Self {
        use crate::swizzles::Vec3Swizzles;
        Self {
            matrix2: DMat2::from_cols(m.x_axis.xy(), m.y_axis.xy()),
            translation: m.z_axis.xy(),
        }
    }

    /// Extracts `scale`, `angle` and `translation` from `self`.
    ///
    /// The transform is expected to be non-degenerate and without shearing, or the output
    /// will be invalid.
    ///
    /// # Panics
    ///
    /// Will panic if the determinant `self.matrix2` is zero or if the resulting scale
    /// vector contains any zero elements when `glam_assert` is enabled.
    #[inline]
    #[must_use]
    pub fn to_scale_angle_translation(self) -> (DVec2, f64, DVec2) {
        use crate::f64::math;
        let det = self.matrix2.determinant();
        glam_assert!(det != 0.0);

        let scale = DVec2::new(
            self.matrix2.x_axis.length() * math::signum(det),
            self.matrix2.y_axis.length(),
        );

        glam_assert!(scale.cmpne(DVec2::ZERO).all());

        let angle = math::atan2(-self.matrix2.y_axis.x, self.matrix2.y_axis.y);

        (scale, angle, self.translation)
    }

    /// Transforms the given 2D point, applying shear, scale, rotation and translation.
    #[inline]
    #[must_use]
    pub fn transform_point2(&self, rhs: DVec2) -> DVec2 {
        self.matrix2 * rhs + self.translation
    }

    /// Transforms the given 2D vector, applying shear, scale and rotation (but NOT
    /// translation).
    ///
    /// To also apply translation, use [`Self::transform_point2()`] instead.
    #[inline]
    pub fn transform_vector2(&self, rhs: DVec2) -> DVec2 {
        self.matrix2 * rhs
    }

    /// Returns `true` if, and only if, all elements are finite.
    ///
    /// If any element is either `NaN`, positive or negative infinity, this will return
    /// `false`.
    #[inline]
    #[must_use]
    pub fn is_finite(&self) -> bool {
        self.matrix2.is_finite() && self.translation.is_finite()
    }

    /// Returns `true` if any elements are `NaN`.
    #[inline]
    #[must_use]
    pub fn is_nan(&self) -> bool {
        self.matrix2.is_nan() || self.translation.is_nan()
    }

    /// Returns true if the absolute difference of all elements between `self` and `rhs`
    /// is less than or equal to `max_abs_diff`.
    ///
    /// This can be used to compare if two 3x4 matrices contain similar elements. It works
    /// best when comparing with a known value. The `max_abs_diff` that should be used used
    /// depends on the values being compared against.
    ///
    /// For more see
    /// [comparing floating point numbers](https://randomascii.wordpress.com/2012/02/25/comparing-floating-point-numbers-2012-edition/).
    #[inline]
    #[must_use]
    pub fn abs_diff_eq(&self, rhs: Self, max_abs_diff: f64) -> bool {
        self.matrix2.abs_diff_eq(rhs.matrix2, max_abs_diff)
            && self.translation.abs_diff_eq(rhs.translation, max_abs_diff)
    }

    /// Return the inverse of this transform.
    ///
    /// Note that if the transform is not invertible the result will be invalid.
    #[inline]
    #[must_use]
    pub fn inverse(&self) -> Self {
        let matrix2 = self.matrix2.inverse();
        // transform negative translation by the matrix inverse:
        let translation = -(matrix2 * self.translation);

        Self {
            matrix2,
            translation,
        }
    }
}

impl Default for DAffine2 {
    #[inline(always)]
    fn default() -> Self {
        Self::IDENTITY
    }
}

impl Deref for DAffine2 {
    type Target = crate::deref::Cols3<DVec2>;
    #[inline(always)]
    fn deref(&self) -> &Self::Target {
        unsafe { &*(self as *const Self as *const Self::Target) }
    }
}

impl DerefMut for DAffine2 {
    #[inline(always)]
    fn deref_mut(&mut self) -> &mut Self::Target {
        unsafe { &mut *(self as *mut Self as *mut Self::Target) }
    }
}

impl PartialEq for DAffine2 {
    #[inline]
    fn eq(&self, rhs: &Self) -> bool {
        self.matrix2.eq(&rhs.matrix2) && self.translation.eq(&rhs.translation)
    }
}

#[cfg(not(target_arch = "spirv"))]
impl core::fmt::Debug for DAffine2 {
    fn fmt(&self, fmt: &mut core::fmt::Formatter<'_>) -> core::fmt::Result {
        fmt.debug_struct(stringify!(DAffine2))
            .field("matrix2", &self.matrix2)
            .field("translation", &self.translation)
            .finish()
    }
}

#[cfg(not(target_arch = "spirv"))]
impl core::fmt::Display for DAffine2 {
    fn fmt(&self, f: &mut core::fmt::Formatter<'_>) -> core::fmt::Result {
        if let Some(p) = f.precision() {
            write!(
                f,
                "[{:.*}, {:.*}, {:.*}]",
                p, self.matrix2.x_axis, p, self.matrix2.y_axis, p, self.translation
            )
        } else {
            write!(
                f,
                "[{}, {}, {}]",
                self.matrix2.x_axis, self.matrix2.y_axis, self.translation
            )
        }
    }
}

impl<'a> core::iter::Product<&'a Self> for DAffine2 {
    fn product<I>(iter: I) -> Self
    where
        I: Iterator<Item = &'a Self>,
    {
        iter.fold(Self::IDENTITY, |a, &b| a * b)
    }
}

impl Mul for DAffine2 {
    type Output = DAffine2;

    #[inline]
    fn mul(self, rhs: DAffine2) -> Self::Output {
        Self {
            matrix2: self.matrix2 * rhs.matrix2,
            translation: self.matrix2 * rhs.translation + self.translation,
        }
    }
}

impl MulAssign for DAffine2 {
    #[inline]
    fn mul_assign(&mut self, rhs: DAffine2) {
        *self = self.mul(rhs);
    }
}

impl From<DAffine2> for DMat3 {
    #[inline]
    fn from(m: DAffine2) -> DMat3 {
        Self::from_cols(
            m.matrix2.x_axis.extend(0.0),
            m.matrix2.y_axis.extend(0.0),
            m.translation.extend(1.0),
        )
    }
}

impl Mul<DMat3> for DAffine2 {
    type Output = DMat3;

    #[inline]
    fn mul(self, rhs: DMat3) -> Self::Output {
        DMat3::from(self) * rhs
    }
}

impl Mul<DAffine2> for DMat3 {
    type Output = DMat3;

    #[inline]
    fn mul(self, rhs: DAffine2) -> Self::Output {
        self * DMat3::from(rhs)
    }
}