glam/f32/
mat3.rs

1// Generated from mat.rs.tera template. Edit the template, not the generated file.
2
3use crate::{
4    euler::{FromEuler, ToEuler},
5    f32::math,
6    swizzles::*,
7    DMat3, EulerRot, Mat2, Mat3A, Mat4, Quat, Vec2, Vec3, Vec3A,
8};
9use core::fmt;
10use core::iter::{Product, Sum};
11use core::ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, Sub, SubAssign};
12
13/// Creates a 3x3 matrix from three column vectors.
14#[inline(always)]
15#[must_use]
16pub const fn mat3(x_axis: Vec3, y_axis: Vec3, z_axis: Vec3) -> Mat3 {
17    Mat3::from_cols(x_axis, y_axis, z_axis)
18}
19
20/// A 3x3 column major matrix.
21///
22/// This 3x3 matrix type features convenience methods for creating and using linear and
23/// affine transformations. If you are primarily dealing with 2D affine transformations the
24/// [`Affine2`](crate::Affine2) type is much faster and more space efficient than
25/// using a 3x3 matrix.
26///
27/// Linear transformations including 3D rotation and scale can be created using methods
28/// such as [`Self::from_diagonal()`], [`Self::from_quat()`], [`Self::from_axis_angle()`],
29/// [`Self::from_rotation_x()`], [`Self::from_rotation_y()`], or
30/// [`Self::from_rotation_z()`].
31///
32/// The resulting matrices can be use to transform 3D vectors using regular vector
33/// multiplication.
34///
35/// Affine transformations including 2D translation, rotation and scale can be created
36/// using methods such as [`Self::from_translation()`], [`Self::from_angle()`],
37/// [`Self::from_scale()`] and [`Self::from_scale_angle_translation()`].
38///
39/// The [`Self::transform_point2()`] and [`Self::transform_vector2()`] convenience methods
40/// are provided for performing affine transforms on 2D vectors and points. These multiply
41/// 2D inputs as 3D vectors with an implicit `z` value of `1` for points and `0` for
42/// vectors respectively. These methods assume that `Self` contains a valid affine
43/// transform.
44#[derive(Clone, Copy)]
45#[repr(C)]
46pub struct Mat3 {
47    pub x_axis: Vec3,
48    pub y_axis: Vec3,
49    pub z_axis: Vec3,
50}
51
52impl Mat3 {
53    /// A 3x3 matrix with all elements set to `0.0`.
54    pub const ZERO: Self = Self::from_cols(Vec3::ZERO, Vec3::ZERO, Vec3::ZERO);
55
56    /// A 3x3 identity matrix, where all diagonal elements are `1`, and all off-diagonal elements are `0`.
57    pub const IDENTITY: Self = Self::from_cols(Vec3::X, Vec3::Y, Vec3::Z);
58
59    /// All NAN:s.
60    pub const NAN: Self = Self::from_cols(Vec3::NAN, Vec3::NAN, Vec3::NAN);
61
62    #[allow(clippy::too_many_arguments)]
63    #[inline(always)]
64    #[must_use]
65    const fn new(
66        m00: f32,
67        m01: f32,
68        m02: f32,
69        m10: f32,
70        m11: f32,
71        m12: f32,
72        m20: f32,
73        m21: f32,
74        m22: f32,
75    ) -> Self {
76        Self {
77            x_axis: Vec3::new(m00, m01, m02),
78            y_axis: Vec3::new(m10, m11, m12),
79            z_axis: Vec3::new(m20, m21, m22),
80        }
81    }
82
83    /// Creates a 3x3 matrix from three column vectors.
84    #[inline(always)]
85    #[must_use]
86    pub const fn from_cols(x_axis: Vec3, y_axis: Vec3, z_axis: Vec3) -> Self {
87        Self {
88            x_axis,
89            y_axis,
90            z_axis,
91        }
92    }
93
94    /// Creates a 3x3 matrix from a `[f32; 9]` array stored in column major order.
95    /// If your data is stored in row major you will need to `transpose` the returned
96    /// matrix.
97    #[inline]
98    #[must_use]
99    pub const fn from_cols_array(m: &[f32; 9]) -> Self {
100        Self::new(m[0], m[1], m[2], m[3], m[4], m[5], m[6], m[7], m[8])
101    }
102
103    /// Creates a `[f32; 9]` array storing data in column major order.
104    /// If you require data in row major order `transpose` the matrix first.
105    #[inline]
106    #[must_use]
107    pub const fn to_cols_array(&self) -> [f32; 9] {
108        [
109            self.x_axis.x,
110            self.x_axis.y,
111            self.x_axis.z,
112            self.y_axis.x,
113            self.y_axis.y,
114            self.y_axis.z,
115            self.z_axis.x,
116            self.z_axis.y,
117            self.z_axis.z,
118        ]
119    }
120
121    /// Creates a 3x3 matrix from a `[[f32; 3]; 3]` 3D array stored in column major order.
122    /// If your data is in row major order you will need to `transpose` the returned
123    /// matrix.
124    #[inline]
125    #[must_use]
126    pub const fn from_cols_array_2d(m: &[[f32; 3]; 3]) -> Self {
127        Self::from_cols(
128            Vec3::from_array(m[0]),
129            Vec3::from_array(m[1]),
130            Vec3::from_array(m[2]),
131        )
132    }
133
134    /// Creates a `[[f32; 3]; 3]` 3D array storing data in column major order.
135    /// If you require data in row major order `transpose` the matrix first.
136    #[inline]
137    #[must_use]
138    pub const fn to_cols_array_2d(&self) -> [[f32; 3]; 3] {
139        [
140            self.x_axis.to_array(),
141            self.y_axis.to_array(),
142            self.z_axis.to_array(),
143        ]
144    }
145
146    /// Creates a 3x3 matrix with its diagonal set to `diagonal` and all other entries set to 0.
147    #[doc(alias = "scale")]
148    #[inline]
149    #[must_use]
150    pub const fn from_diagonal(diagonal: Vec3) -> Self {
151        Self::new(
152            diagonal.x, 0.0, 0.0, 0.0, diagonal.y, 0.0, 0.0, 0.0, diagonal.z,
153        )
154    }
155
156    /// Creates a 3x3 matrix from a 4x4 matrix, discarding the 4th row and column.
157    #[inline]
158    #[must_use]
159    pub fn from_mat4(m: Mat4) -> Self {
160        Self::from_cols(
161            Vec3::from_vec4(m.x_axis),
162            Vec3::from_vec4(m.y_axis),
163            Vec3::from_vec4(m.z_axis),
164        )
165    }
166
167    /// Creates a 3x3 matrix from the minor of the given 4x4 matrix, discarding the `i`th column
168    /// and `j`th row.
169    ///
170    /// # Panics
171    ///
172    /// Panics if `i` or `j` is greater than 3.
173    #[inline]
174    #[must_use]
175    pub fn from_mat4_minor(m: Mat4, i: usize, j: usize) -> Self {
176        match (i, j) {
177            (0, 0) => Self::from_cols(m.y_axis.yzw(), m.z_axis.yzw(), m.w_axis.yzw()),
178            (0, 1) => Self::from_cols(m.y_axis.xzw(), m.z_axis.xzw(), m.w_axis.xzw()),
179            (0, 2) => Self::from_cols(m.y_axis.xyw(), m.z_axis.xyw(), m.w_axis.xyw()),
180            (0, 3) => Self::from_cols(m.y_axis.xyz(), m.z_axis.xyz(), m.w_axis.xyz()),
181            (1, 0) => Self::from_cols(m.x_axis.yzw(), m.z_axis.yzw(), m.w_axis.yzw()),
182            (1, 1) => Self::from_cols(m.x_axis.xzw(), m.z_axis.xzw(), m.w_axis.xzw()),
183            (1, 2) => Self::from_cols(m.x_axis.xyw(), m.z_axis.xyw(), m.w_axis.xyw()),
184            (1, 3) => Self::from_cols(m.x_axis.xyz(), m.z_axis.xyz(), m.w_axis.xyz()),
185            (2, 0) => Self::from_cols(m.x_axis.yzw(), m.y_axis.yzw(), m.w_axis.yzw()),
186            (2, 1) => Self::from_cols(m.x_axis.xzw(), m.y_axis.xzw(), m.w_axis.xzw()),
187            (2, 2) => Self::from_cols(m.x_axis.xyw(), m.y_axis.xyw(), m.w_axis.xyw()),
188            (2, 3) => Self::from_cols(m.x_axis.xyz(), m.y_axis.xyz(), m.w_axis.xyz()),
189            (3, 0) => Self::from_cols(m.x_axis.yzw(), m.y_axis.yzw(), m.z_axis.yzw()),
190            (3, 1) => Self::from_cols(m.x_axis.xzw(), m.y_axis.xzw(), m.z_axis.xzw()),
191            (3, 2) => Self::from_cols(m.x_axis.xyw(), m.y_axis.xyw(), m.z_axis.xyw()),
192            (3, 3) => Self::from_cols(m.x_axis.xyz(), m.y_axis.xyz(), m.z_axis.xyz()),
193            _ => panic!("index out of bounds"),
194        }
195    }
196
197    /// Creates a 3D rotation matrix from the given quaternion.
198    ///
199    /// # Panics
200    ///
201    /// Will panic if `rotation` is not normalized when `glam_assert` is enabled.
202    #[inline]
203    #[must_use]
204    pub fn from_quat(rotation: Quat) -> Self {
205        glam_assert!(rotation.is_normalized());
206
207        let x2 = rotation.x + rotation.x;
208        let y2 = rotation.y + rotation.y;
209        let z2 = rotation.z + rotation.z;
210        let xx = rotation.x * x2;
211        let xy = rotation.x * y2;
212        let xz = rotation.x * z2;
213        let yy = rotation.y * y2;
214        let yz = rotation.y * z2;
215        let zz = rotation.z * z2;
216        let wx = rotation.w * x2;
217        let wy = rotation.w * y2;
218        let wz = rotation.w * z2;
219
220        Self::from_cols(
221            Vec3::new(1.0 - (yy + zz), xy + wz, xz - wy),
222            Vec3::new(xy - wz, 1.0 - (xx + zz), yz + wx),
223            Vec3::new(xz + wy, yz - wx, 1.0 - (xx + yy)),
224        )
225    }
226
227    /// Creates a 3D rotation matrix from a normalized rotation `axis` and `angle` (in
228    /// radians).
229    ///
230    /// # Panics
231    ///
232    /// Will panic if `axis` is not normalized when `glam_assert` is enabled.
233    #[inline]
234    #[must_use]
235    pub fn from_axis_angle(axis: Vec3, angle: f32) -> Self {
236        glam_assert!(axis.is_normalized());
237
238        let (sin, cos) = math::sin_cos(angle);
239        let (xsin, ysin, zsin) = axis.mul(sin).into();
240        let (x, y, z) = axis.into();
241        let (x2, y2, z2) = axis.mul(axis).into();
242        let omc = 1.0 - cos;
243        let xyomc = x * y * omc;
244        let xzomc = x * z * omc;
245        let yzomc = y * z * omc;
246        Self::from_cols(
247            Vec3::new(x2 * omc + cos, xyomc + zsin, xzomc - ysin),
248            Vec3::new(xyomc - zsin, y2 * omc + cos, yzomc + xsin),
249            Vec3::new(xzomc + ysin, yzomc - xsin, z2 * omc + cos),
250        )
251    }
252
253    /// Creates a 3D rotation matrix from the given euler rotation sequence and the angles (in
254    /// radians).
255    #[inline]
256    #[must_use]
257    pub fn from_euler(order: EulerRot, a: f32, b: f32, c: f32) -> Self {
258        Self::from_euler_angles(order, a, b, c)
259    }
260
261    /// Extract Euler angles with the given Euler rotation order.
262    ///
263    /// Note if the input matrix contains scales, shears, or other non-rotation transformations then
264    /// the resulting Euler angles will be ill-defined.
265    ///
266    /// # Panics
267    ///
268    /// Will panic if any input matrix column is not normalized when `glam_assert` is enabled.
269    #[inline]
270    #[must_use]
271    pub fn to_euler(&self, order: EulerRot) -> (f32, f32, f32) {
272        glam_assert!(
273            self.x_axis.is_normalized()
274                && self.y_axis.is_normalized()
275                && self.z_axis.is_normalized()
276        );
277        self.to_euler_angles(order)
278    }
279
280    /// Creates a 3D rotation matrix from `angle` (in radians) around the x axis.
281    #[inline]
282    #[must_use]
283    pub fn from_rotation_x(angle: f32) -> Self {
284        let (sina, cosa) = math::sin_cos(angle);
285        Self::from_cols(
286            Vec3::X,
287            Vec3::new(0.0, cosa, sina),
288            Vec3::new(0.0, -sina, cosa),
289        )
290    }
291
292    /// Creates a 3D rotation matrix from `angle` (in radians) around the y axis.
293    #[inline]
294    #[must_use]
295    pub fn from_rotation_y(angle: f32) -> Self {
296        let (sina, cosa) = math::sin_cos(angle);
297        Self::from_cols(
298            Vec3::new(cosa, 0.0, -sina),
299            Vec3::Y,
300            Vec3::new(sina, 0.0, cosa),
301        )
302    }
303
304    /// Creates a 3D rotation matrix from `angle` (in radians) around the z axis.
305    #[inline]
306    #[must_use]
307    pub fn from_rotation_z(angle: f32) -> Self {
308        let (sina, cosa) = math::sin_cos(angle);
309        Self::from_cols(
310            Vec3::new(cosa, sina, 0.0),
311            Vec3::new(-sina, cosa, 0.0),
312            Vec3::Z,
313        )
314    }
315
316    /// Creates an affine transformation matrix from the given 2D `translation`.
317    ///
318    /// The resulting matrix can be used to transform 2D points and vectors. See
319    /// [`Self::transform_point2()`] and [`Self::transform_vector2()`].
320    #[inline]
321    #[must_use]
322    pub fn from_translation(translation: Vec2) -> Self {
323        Self::from_cols(
324            Vec3::X,
325            Vec3::Y,
326            Vec3::new(translation.x, translation.y, 1.0),
327        )
328    }
329
330    /// Creates an affine transformation matrix from the given 2D rotation `angle` (in
331    /// radians).
332    ///
333    /// The resulting matrix can be used to transform 2D points and vectors. See
334    /// [`Self::transform_point2()`] and [`Self::transform_vector2()`].
335    #[inline]
336    #[must_use]
337    pub fn from_angle(angle: f32) -> Self {
338        let (sin, cos) = math::sin_cos(angle);
339        Self::from_cols(Vec3::new(cos, sin, 0.0), Vec3::new(-sin, cos, 0.0), Vec3::Z)
340    }
341
342    /// Creates an affine transformation matrix from the given 2D `scale`, rotation `angle` (in
343    /// radians) and `translation`.
344    ///
345    /// The resulting matrix can be used to transform 2D points and vectors. See
346    /// [`Self::transform_point2()`] and [`Self::transform_vector2()`].
347    #[inline]
348    #[must_use]
349    pub fn from_scale_angle_translation(scale: Vec2, angle: f32, translation: Vec2) -> Self {
350        let (sin, cos) = math::sin_cos(angle);
351        Self::from_cols(
352            Vec3::new(cos * scale.x, sin * scale.x, 0.0),
353            Vec3::new(-sin * scale.y, cos * scale.y, 0.0),
354            Vec3::new(translation.x, translation.y, 1.0),
355        )
356    }
357
358    /// Creates an affine transformation matrix from the given non-uniform 2D `scale`.
359    ///
360    /// The resulting matrix can be used to transform 2D points and vectors. See
361    /// [`Self::transform_point2()`] and [`Self::transform_vector2()`].
362    ///
363    /// # Panics
364    ///
365    /// Will panic if all elements of `scale` are zero when `glam_assert` is enabled.
366    #[inline]
367    #[must_use]
368    pub fn from_scale(scale: Vec2) -> Self {
369        // Do not panic as long as any component is non-zero
370        glam_assert!(scale.cmpne(Vec2::ZERO).any());
371
372        Self::from_cols(
373            Vec3::new(scale.x, 0.0, 0.0),
374            Vec3::new(0.0, scale.y, 0.0),
375            Vec3::Z,
376        )
377    }
378
379    /// Creates an affine transformation matrix from the given 2x2 matrix.
380    ///
381    /// The resulting matrix can be used to transform 2D points and vectors. See
382    /// [`Self::transform_point2()`] and [`Self::transform_vector2()`].
383    #[inline]
384    pub fn from_mat2(m: Mat2) -> Self {
385        Self::from_cols((m.x_axis, 0.0).into(), (m.y_axis, 0.0).into(), Vec3::Z)
386    }
387
388    /// Creates a 3x3 matrix from the first 9 values in `slice`.
389    ///
390    /// # Panics
391    ///
392    /// Panics if `slice` is less than 9 elements long.
393    #[inline]
394    #[must_use]
395    pub const fn from_cols_slice(slice: &[f32]) -> Self {
396        Self::new(
397            slice[0], slice[1], slice[2], slice[3], slice[4], slice[5], slice[6], slice[7],
398            slice[8],
399        )
400    }
401
402    /// Writes the columns of `self` to the first 9 elements in `slice`.
403    ///
404    /// # Panics
405    ///
406    /// Panics if `slice` is less than 9 elements long.
407    #[inline]
408    pub fn write_cols_to_slice(self, slice: &mut [f32]) {
409        slice[0] = self.x_axis.x;
410        slice[1] = self.x_axis.y;
411        slice[2] = self.x_axis.z;
412        slice[3] = self.y_axis.x;
413        slice[4] = self.y_axis.y;
414        slice[5] = self.y_axis.z;
415        slice[6] = self.z_axis.x;
416        slice[7] = self.z_axis.y;
417        slice[8] = self.z_axis.z;
418    }
419
420    /// Returns the matrix column for the given `index`.
421    ///
422    /// # Panics
423    ///
424    /// Panics if `index` is greater than 2.
425    #[inline]
426    #[must_use]
427    pub fn col(&self, index: usize) -> Vec3 {
428        match index {
429            0 => self.x_axis,
430            1 => self.y_axis,
431            2 => self.z_axis,
432            _ => panic!("index out of bounds"),
433        }
434    }
435
436    /// Returns a mutable reference to the matrix column for the given `index`.
437    ///
438    /// # Panics
439    ///
440    /// Panics if `index` is greater than 2.
441    #[inline]
442    pub fn col_mut(&mut self, index: usize) -> &mut Vec3 {
443        match index {
444            0 => &mut self.x_axis,
445            1 => &mut self.y_axis,
446            2 => &mut self.z_axis,
447            _ => panic!("index out of bounds"),
448        }
449    }
450
451    /// Returns the matrix row for the given `index`.
452    ///
453    /// # Panics
454    ///
455    /// Panics if `index` is greater than 2.
456    #[inline]
457    #[must_use]
458    pub fn row(&self, index: usize) -> Vec3 {
459        match index {
460            0 => Vec3::new(self.x_axis.x, self.y_axis.x, self.z_axis.x),
461            1 => Vec3::new(self.x_axis.y, self.y_axis.y, self.z_axis.y),
462            2 => Vec3::new(self.x_axis.z, self.y_axis.z, self.z_axis.z),
463            _ => panic!("index out of bounds"),
464        }
465    }
466
467    /// Returns `true` if, and only if, all elements are finite.
468    /// If any element is either `NaN`, positive or negative infinity, this will return `false`.
469    #[inline]
470    #[must_use]
471    pub fn is_finite(&self) -> bool {
472        self.x_axis.is_finite() && self.y_axis.is_finite() && self.z_axis.is_finite()
473    }
474
475    /// Returns `true` if any elements are `NaN`.
476    #[inline]
477    #[must_use]
478    pub fn is_nan(&self) -> bool {
479        self.x_axis.is_nan() || self.y_axis.is_nan() || self.z_axis.is_nan()
480    }
481
482    /// Returns the transpose of `self`.
483    #[inline]
484    #[must_use]
485    pub fn transpose(&self) -> Self {
486        Self {
487            x_axis: Vec3::new(self.x_axis.x, self.y_axis.x, self.z_axis.x),
488            y_axis: Vec3::new(self.x_axis.y, self.y_axis.y, self.z_axis.y),
489            z_axis: Vec3::new(self.x_axis.z, self.y_axis.z, self.z_axis.z),
490        }
491    }
492
493    /// Returns the determinant of `self`.
494    #[inline]
495    #[must_use]
496    pub fn determinant(&self) -> f32 {
497        self.z_axis.dot(self.x_axis.cross(self.y_axis))
498    }
499
500    /// Returns the inverse of `self`.
501    ///
502    /// If the matrix is not invertible the returned matrix will be invalid.
503    ///
504    /// # Panics
505    ///
506    /// Will panic if the determinant of `self` is zero when `glam_assert` is enabled.
507    #[inline]
508    #[must_use]
509    pub fn inverse(&self) -> Self {
510        let tmp0 = self.y_axis.cross(self.z_axis);
511        let tmp1 = self.z_axis.cross(self.x_axis);
512        let tmp2 = self.x_axis.cross(self.y_axis);
513        let det = self.z_axis.dot(tmp2);
514        glam_assert!(det != 0.0);
515        let inv_det = Vec3::splat(det.recip());
516        Self::from_cols(tmp0.mul(inv_det), tmp1.mul(inv_det), tmp2.mul(inv_det)).transpose()
517    }
518
519    /// Transforms the given 2D vector as a point.
520    ///
521    /// This is the equivalent of multiplying `rhs` as a 3D vector where `z` is `1`.
522    ///
523    /// This method assumes that `self` contains a valid affine transform.
524    ///
525    /// # Panics
526    ///
527    /// Will panic if the 2nd row of `self` is not `(0, 0, 1)` when `glam_assert` is enabled.
528    #[inline]
529    #[must_use]
530    pub fn transform_point2(&self, rhs: Vec2) -> Vec2 {
531        glam_assert!(self.row(2).abs_diff_eq(Vec3::Z, 1e-6));
532        Mat2::from_cols(self.x_axis.xy(), self.y_axis.xy()) * rhs + self.z_axis.xy()
533    }
534
535    /// Rotates the given 2D vector.
536    ///
537    /// This is the equivalent of multiplying `rhs` as a 3D vector where `z` is `0`.
538    ///
539    /// This method assumes that `self` contains a valid affine transform.
540    ///
541    /// # Panics
542    ///
543    /// Will panic if the 2nd row of `self` is not `(0, 0, 1)` when `glam_assert` is enabled.
544    #[inline]
545    #[must_use]
546    pub fn transform_vector2(&self, rhs: Vec2) -> Vec2 {
547        glam_assert!(self.row(2).abs_diff_eq(Vec3::Z, 1e-6));
548        Mat2::from_cols(self.x_axis.xy(), self.y_axis.xy()) * rhs
549    }
550
551    /// Creates a left-handed view matrix using a facing direction and an up direction.
552    ///
553    /// For a view coordinate system with `+X=right`, `+Y=up` and `+Z=forward`.
554    ///
555    /// # Panics
556    ///
557    /// Will panic if `dir` or `up` are not normalized when `glam_assert` is enabled.
558    #[inline]
559    #[must_use]
560    pub fn look_to_lh(dir: Vec3, up: Vec3) -> Self {
561        Self::look_to_rh(-dir, up)
562    }
563
564    /// Creates a right-handed view matrix using a facing direction and an up direction.
565    ///
566    /// For a view coordinate system with `+X=right`, `+Y=up` and `+Z=back`.
567    ///
568    /// # Panics
569    ///
570    /// Will panic if `dir` or `up` are not normalized when `glam_assert` is enabled.
571    #[inline]
572    #[must_use]
573    pub fn look_to_rh(dir: Vec3, up: Vec3) -> Self {
574        glam_assert!(dir.is_normalized());
575        glam_assert!(up.is_normalized());
576        let f = dir;
577        let s = f.cross(up).normalize();
578        let u = s.cross(f);
579
580        Self::from_cols(
581            Vec3::new(s.x, u.x, -f.x),
582            Vec3::new(s.y, u.y, -f.y),
583            Vec3::new(s.z, u.z, -f.z),
584        )
585    }
586
587    /// Creates a left-handed view matrix using a camera position, a focal point and an up
588    /// direction.
589    ///
590    /// For a view coordinate system with `+X=right`, `+Y=up` and `+Z=forward`.
591    ///
592    /// # Panics
593    ///
594    /// Will panic if `up` is not normalized when `glam_assert` is enabled.
595    #[inline]
596    #[must_use]
597    pub fn look_at_lh(eye: Vec3, center: Vec3, up: Vec3) -> Self {
598        Self::look_to_lh(center.sub(eye).normalize(), up)
599    }
600
601    /// Creates a right-handed view matrix using a camera position, a focal point and an up
602    /// direction.
603    ///
604    /// For a view coordinate system with `+X=right`, `+Y=up` and `+Z=back`.
605    ///
606    /// # Panics
607    ///
608    /// Will panic if `up` is not normalized when `glam_assert` is enabled.
609    #[inline]
610    pub fn look_at_rh(eye: Vec3, center: Vec3, up: Vec3) -> Self {
611        Self::look_to_rh(center.sub(eye).normalize(), up)
612    }
613
614    /// Transforms a 3D vector.
615    #[inline]
616    #[must_use]
617    pub fn mul_vec3(&self, rhs: Vec3) -> Vec3 {
618        let mut res = self.x_axis.mul(rhs.x);
619        res = res.add(self.y_axis.mul(rhs.y));
620        res = res.add(self.z_axis.mul(rhs.z));
621        res
622    }
623
624    /// Transforms a [`Vec3A`].
625    #[inline]
626    #[must_use]
627    pub fn mul_vec3a(&self, rhs: Vec3A) -> Vec3A {
628        self.mul_vec3(rhs.into()).into()
629    }
630
631    /// Multiplies two 3x3 matrices.
632    #[inline]
633    #[must_use]
634    pub fn mul_mat3(&self, rhs: &Self) -> Self {
635        Self::from_cols(
636            self.mul(rhs.x_axis),
637            self.mul(rhs.y_axis),
638            self.mul(rhs.z_axis),
639        )
640    }
641
642    /// Adds two 3x3 matrices.
643    #[inline]
644    #[must_use]
645    pub fn add_mat3(&self, rhs: &Self) -> Self {
646        Self::from_cols(
647            self.x_axis.add(rhs.x_axis),
648            self.y_axis.add(rhs.y_axis),
649            self.z_axis.add(rhs.z_axis),
650        )
651    }
652
653    /// Subtracts two 3x3 matrices.
654    #[inline]
655    #[must_use]
656    pub fn sub_mat3(&self, rhs: &Self) -> Self {
657        Self::from_cols(
658            self.x_axis.sub(rhs.x_axis),
659            self.y_axis.sub(rhs.y_axis),
660            self.z_axis.sub(rhs.z_axis),
661        )
662    }
663
664    /// Multiplies a 3x3 matrix by a scalar.
665    #[inline]
666    #[must_use]
667    pub fn mul_scalar(&self, rhs: f32) -> Self {
668        Self::from_cols(
669            self.x_axis.mul(rhs),
670            self.y_axis.mul(rhs),
671            self.z_axis.mul(rhs),
672        )
673    }
674
675    /// Divides a 3x3 matrix by a scalar.
676    #[inline]
677    #[must_use]
678    pub fn div_scalar(&self, rhs: f32) -> Self {
679        let rhs = Vec3::splat(rhs);
680        Self::from_cols(
681            self.x_axis.div(rhs),
682            self.y_axis.div(rhs),
683            self.z_axis.div(rhs),
684        )
685    }
686
687    /// Returns true if the absolute difference of all elements between `self` and `rhs`
688    /// is less than or equal to `max_abs_diff`.
689    ///
690    /// This can be used to compare if two matrices contain similar elements. It works best
691    /// when comparing with a known value. The `max_abs_diff` that should be used used
692    /// depends on the values being compared against.
693    ///
694    /// For more see
695    /// [comparing floating point numbers](https://randomascii.wordpress.com/2012/02/25/comparing-floating-point-numbers-2012-edition/).
696    #[inline]
697    #[must_use]
698    pub fn abs_diff_eq(&self, rhs: Self, max_abs_diff: f32) -> bool {
699        self.x_axis.abs_diff_eq(rhs.x_axis, max_abs_diff)
700            && self.y_axis.abs_diff_eq(rhs.y_axis, max_abs_diff)
701            && self.z_axis.abs_diff_eq(rhs.z_axis, max_abs_diff)
702    }
703
704    /// Takes the absolute value of each element in `self`
705    #[inline]
706    #[must_use]
707    pub fn abs(&self) -> Self {
708        Self::from_cols(self.x_axis.abs(), self.y_axis.abs(), self.z_axis.abs())
709    }
710
711    #[inline]
712    pub fn as_dmat3(&self) -> DMat3 {
713        DMat3::from_cols(
714            self.x_axis.as_dvec3(),
715            self.y_axis.as_dvec3(),
716            self.z_axis.as_dvec3(),
717        )
718    }
719}
720
721impl Default for Mat3 {
722    #[inline]
723    fn default() -> Self {
724        Self::IDENTITY
725    }
726}
727
728impl Add<Mat3> for Mat3 {
729    type Output = Self;
730    #[inline]
731    fn add(self, rhs: Self) -> Self::Output {
732        self.add_mat3(&rhs)
733    }
734}
735
736impl AddAssign<Mat3> for Mat3 {
737    #[inline]
738    fn add_assign(&mut self, rhs: Self) {
739        *self = self.add_mat3(&rhs);
740    }
741}
742
743impl Sub<Mat3> for Mat3 {
744    type Output = Self;
745    #[inline]
746    fn sub(self, rhs: Self) -> Self::Output {
747        self.sub_mat3(&rhs)
748    }
749}
750
751impl SubAssign<Mat3> for Mat3 {
752    #[inline]
753    fn sub_assign(&mut self, rhs: Self) {
754        *self = self.sub_mat3(&rhs);
755    }
756}
757
758impl Neg for Mat3 {
759    type Output = Self;
760    #[inline]
761    fn neg(self) -> Self::Output {
762        Self::from_cols(self.x_axis.neg(), self.y_axis.neg(), self.z_axis.neg())
763    }
764}
765
766impl Mul<Mat3> for Mat3 {
767    type Output = Self;
768    #[inline]
769    fn mul(self, rhs: Self) -> Self::Output {
770        self.mul_mat3(&rhs)
771    }
772}
773
774impl MulAssign<Mat3> for Mat3 {
775    #[inline]
776    fn mul_assign(&mut self, rhs: Self) {
777        *self = self.mul_mat3(&rhs);
778    }
779}
780
781impl Mul<Vec3> for Mat3 {
782    type Output = Vec3;
783    #[inline]
784    fn mul(self, rhs: Vec3) -> Self::Output {
785        self.mul_vec3(rhs)
786    }
787}
788
789impl Mul<Mat3> for f32 {
790    type Output = Mat3;
791    #[inline]
792    fn mul(self, rhs: Mat3) -> Self::Output {
793        rhs.mul_scalar(self)
794    }
795}
796
797impl Mul<f32> for Mat3 {
798    type Output = Self;
799    #[inline]
800    fn mul(self, rhs: f32) -> Self::Output {
801        self.mul_scalar(rhs)
802    }
803}
804
805impl MulAssign<f32> for Mat3 {
806    #[inline]
807    fn mul_assign(&mut self, rhs: f32) {
808        *self = self.mul_scalar(rhs);
809    }
810}
811
812impl Div<Mat3> for f32 {
813    type Output = Mat3;
814    #[inline]
815    fn div(self, rhs: Mat3) -> Self::Output {
816        rhs.div_scalar(self)
817    }
818}
819
820impl Div<f32> for Mat3 {
821    type Output = Self;
822    #[inline]
823    fn div(self, rhs: f32) -> Self::Output {
824        self.div_scalar(rhs)
825    }
826}
827
828impl DivAssign<f32> for Mat3 {
829    #[inline]
830    fn div_assign(&mut self, rhs: f32) {
831        *self = self.div_scalar(rhs);
832    }
833}
834
835impl Mul<Vec3A> for Mat3 {
836    type Output = Vec3A;
837    #[inline]
838    fn mul(self, rhs: Vec3A) -> Vec3A {
839        self.mul_vec3a(rhs)
840    }
841}
842
843impl From<Mat3A> for Mat3 {
844    #[inline]
845    fn from(m: Mat3A) -> Self {
846        Self {
847            x_axis: m.x_axis.into(),
848            y_axis: m.y_axis.into(),
849            z_axis: m.z_axis.into(),
850        }
851    }
852}
853
854impl Sum<Self> for Mat3 {
855    fn sum<I>(iter: I) -> Self
856    where
857        I: Iterator<Item = Self>,
858    {
859        iter.fold(Self::ZERO, Self::add)
860    }
861}
862
863impl<'a> Sum<&'a Self> for Mat3 {
864    fn sum<I>(iter: I) -> Self
865    where
866        I: Iterator<Item = &'a Self>,
867    {
868        iter.fold(Self::ZERO, |a, &b| Self::add(a, b))
869    }
870}
871
872impl Product for Mat3 {
873    fn product<I>(iter: I) -> Self
874    where
875        I: Iterator<Item = Self>,
876    {
877        iter.fold(Self::IDENTITY, Self::mul)
878    }
879}
880
881impl<'a> Product<&'a Self> for Mat3 {
882    fn product<I>(iter: I) -> Self
883    where
884        I: Iterator<Item = &'a Self>,
885    {
886        iter.fold(Self::IDENTITY, |a, &b| Self::mul(a, b))
887    }
888}
889
890impl PartialEq for Mat3 {
891    #[inline]
892    fn eq(&self, rhs: &Self) -> bool {
893        self.x_axis.eq(&rhs.x_axis) && self.y_axis.eq(&rhs.y_axis) && self.z_axis.eq(&rhs.z_axis)
894    }
895}
896
897#[cfg(not(target_arch = "spirv"))]
898impl AsRef<[f32; 9]> for Mat3 {
899    #[inline]
900    fn as_ref(&self) -> &[f32; 9] {
901        unsafe { &*(self as *const Self as *const [f32; 9]) }
902    }
903}
904
905#[cfg(not(target_arch = "spirv"))]
906impl AsMut<[f32; 9]> for Mat3 {
907    #[inline]
908    fn as_mut(&mut self) -> &mut [f32; 9] {
909        unsafe { &mut *(self as *mut Self as *mut [f32; 9]) }
910    }
911}
912
913impl fmt::Debug for Mat3 {
914    fn fmt(&self, fmt: &mut fmt::Formatter<'_>) -> fmt::Result {
915        fmt.debug_struct(stringify!(Mat3))
916            .field("x_axis", &self.x_axis)
917            .field("y_axis", &self.y_axis)
918            .field("z_axis", &self.z_axis)
919            .finish()
920    }
921}
922
923impl fmt::Display for Mat3 {
924    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
925        if let Some(p) = f.precision() {
926            write!(
927                f,
928                "[{:.*}, {:.*}, {:.*}]",
929                p, self.x_axis, p, self.y_axis, p, self.z_axis
930            )
931        } else {
932            write!(f, "[{}, {}, {}]", self.x_axis, self.y_axis, self.z_axis)
933        }
934    }
935}
glam/f32/mat3.rs

glam/f32/
mat3.rs
