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#[cfg(feature = "zerocopy")]
14use zerocopy_derive::*;
15
16/// Creates a 3x3 matrix from three column vectors.
17#[inline(always)]
18#[must_use]
19pub const fn mat3(x_axis: Vec3, y_axis: Vec3, z_axis: Vec3) -> Mat3 {
20    Mat3::from_cols(x_axis, y_axis, z_axis)
21}
22
23/// A 3x3 column major matrix.
24///
25/// This 3x3 matrix type features convenience methods for creating and using linear and
26/// affine transformations. If you are primarily dealing with 2D affine transformations the
27/// [`Affine2`](crate::Affine2) type is much faster and more space efficient than
28/// using a 3x3 matrix.
29///
30/// Linear transformations including 3D rotation and scale can be created using methods
31/// such as [`Self::from_diagonal()`], [`Self::from_quat()`], [`Self::from_axis_angle()`],
32/// [`Self::from_rotation_x()`], [`Self::from_rotation_y()`], or
33/// [`Self::from_rotation_z()`].
34///
35/// The resulting matrices can be use to transform 3D vectors using regular vector
36/// multiplication.
37///
38/// Affine transformations including 2D translation, rotation and scale can be created
39/// using methods such as [`Self::from_translation()`], [`Self::from_angle()`],
40/// [`Self::from_scale()`] and [`Self::from_scale_angle_translation()`].
41///
42/// The [`Self::transform_point2()`] and [`Self::transform_vector2()`] convenience methods
43/// are provided for performing affine transforms on 2D vectors and points. These multiply
44/// 2D inputs as 3D vectors with an implicit `z` value of `1` for points and `0` for
45/// vectors respectively. These methods assume that `Self` contains a valid affine
46/// transform.
47#[derive(Clone, Copy)]
48#[cfg_attr(feature = "bytemuck", derive(bytemuck::Pod, bytemuck::Zeroable))]
49#[cfg_attr(
50    feature = "zerocopy",
51    derive(FromBytes, Immutable, IntoBytes, KnownLayout)
52)]
53#[repr(C)]
54pub struct Mat3 {
55    pub x_axis: Vec3,
56    pub y_axis: Vec3,
57    pub z_axis: Vec3,
58}
59
60impl Mat3 {
61    /// A 3x3 matrix with all elements set to `0.0`.
62    pub const ZERO: Self = Self::from_cols(Vec3::ZERO, Vec3::ZERO, Vec3::ZERO);
63
64    /// A 3x3 identity matrix, where all diagonal elements are `1`, and all off-diagonal elements are `0`.
65    pub const IDENTITY: Self = Self::from_cols(Vec3::X, Vec3::Y, Vec3::Z);
66
67    /// All NAN:s.
68    pub const NAN: Self = Self::from_cols(Vec3::NAN, Vec3::NAN, Vec3::NAN);
69
70    #[allow(clippy::too_many_arguments)]
71    #[inline(always)]
72    #[must_use]
73    const fn new(
74        m00: f32,
75        m01: f32,
76        m02: f32,
77        m10: f32,
78        m11: f32,
79        m12: f32,
80        m20: f32,
81        m21: f32,
82        m22: f32,
83    ) -> Self {
84        Self {
85            x_axis: Vec3::new(m00, m01, m02),
86            y_axis: Vec3::new(m10, m11, m12),
87            z_axis: Vec3::new(m20, m21, m22),
88        }
89    }
90
91    /// Creates a 3x3 matrix from three column vectors.
92    #[inline(always)]
93    #[must_use]
94    pub const fn from_cols(x_axis: Vec3, y_axis: Vec3, z_axis: Vec3) -> Self {
95        Self {
96            x_axis,
97            y_axis,
98            z_axis,
99        }
100    }
101
102    /// Creates a 3x3 matrix from a `[f32; 9]` array stored in column major order.
103    /// If your data is stored in row major you will need to `transpose` the returned
104    /// matrix.
105    #[inline]
106    #[must_use]
107    pub const fn from_cols_array(m: &[f32; 9]) -> Self {
108        Self::new(m[0], m[1], m[2], m[3], m[4], m[5], m[6], m[7], m[8])
109    }
110
111    /// Creates a `[f32; 9]` array storing data in column major order.
112    /// If you require data in row major order `transpose` the matrix first.
113    #[inline]
114    #[must_use]
115    pub const fn to_cols_array(&self) -> [f32; 9] {
116        [
117            self.x_axis.x,
118            self.x_axis.y,
119            self.x_axis.z,
120            self.y_axis.x,
121            self.y_axis.y,
122            self.y_axis.z,
123            self.z_axis.x,
124            self.z_axis.y,
125            self.z_axis.z,
126        ]
127    }
128
129    /// Creates a 3x3 matrix from a `[[f32; 3]; 3]` 3D array stored in column major order.
130    /// If your data is in row major order you will need to `transpose` the returned
131    /// matrix.
132    #[inline]
133    #[must_use]
134    pub const fn from_cols_array_2d(m: &[[f32; 3]; 3]) -> Self {
135        Self::from_cols(
136            Vec3::from_array(m[0]),
137            Vec3::from_array(m[1]),
138            Vec3::from_array(m[2]),
139        )
140    }
141
142    /// Creates a `[[f32; 3]; 3]` 3D array storing data in column major order.
143    /// If you require data in row major order `transpose` the matrix first.
144    #[inline]
145    #[must_use]
146    pub const fn to_cols_array_2d(&self) -> [[f32; 3]; 3] {
147        [
148            self.x_axis.to_array(),
149            self.y_axis.to_array(),
150            self.z_axis.to_array(),
151        ]
152    }
153
154    /// Creates a 3x3 matrix with its diagonal set to `diagonal` and all other entries set to 0.
155    #[doc(alias = "scale")]
156    #[inline]
157    #[must_use]
158    pub const fn from_diagonal(diagonal: Vec3) -> Self {
159        Self::new(
160            diagonal.x, 0.0, 0.0, 0.0, diagonal.y, 0.0, 0.0, 0.0, diagonal.z,
161        )
162    }
163
164    /// Creates a 3x3 matrix from a 4x4 matrix, discarding the 4th row and column.
165    #[inline]
166    #[must_use]
167    pub fn from_mat4(m: Mat4) -> Self {
168        Self::from_cols(
169            Vec3::from_vec4(m.x_axis),
170            Vec3::from_vec4(m.y_axis),
171            Vec3::from_vec4(m.z_axis),
172        )
173    }
174
175    /// Creates a 3x3 matrix from the minor of the given 4x4 matrix, discarding the `i`th column
176    /// and `j`th row.
177    ///
178    /// # Panics
179    ///
180    /// Panics if `i` or `j` is greater than 3.
181    #[inline]
182    #[must_use]
183    pub fn from_mat4_minor(m: Mat4, i: usize, j: usize) -> Self {
184        match (i, j) {
185            (0, 0) => Self::from_cols(m.y_axis.yzw(), m.z_axis.yzw(), m.w_axis.yzw()),
186            (0, 1) => Self::from_cols(m.y_axis.xzw(), m.z_axis.xzw(), m.w_axis.xzw()),
187            (0, 2) => Self::from_cols(m.y_axis.xyw(), m.z_axis.xyw(), m.w_axis.xyw()),
188            (0, 3) => Self::from_cols(m.y_axis.xyz(), m.z_axis.xyz(), m.w_axis.xyz()),
189            (1, 0) => Self::from_cols(m.x_axis.yzw(), m.z_axis.yzw(), m.w_axis.yzw()),
190            (1, 1) => Self::from_cols(m.x_axis.xzw(), m.z_axis.xzw(), m.w_axis.xzw()),
191            (1, 2) => Self::from_cols(m.x_axis.xyw(), m.z_axis.xyw(), m.w_axis.xyw()),
192            (1, 3) => Self::from_cols(m.x_axis.xyz(), m.z_axis.xyz(), m.w_axis.xyz()),
193            (2, 0) => Self::from_cols(m.x_axis.yzw(), m.y_axis.yzw(), m.w_axis.yzw()),
194            (2, 1) => Self::from_cols(m.x_axis.xzw(), m.y_axis.xzw(), m.w_axis.xzw()),
195            (2, 2) => Self::from_cols(m.x_axis.xyw(), m.y_axis.xyw(), m.w_axis.xyw()),
196            (2, 3) => Self::from_cols(m.x_axis.xyz(), m.y_axis.xyz(), m.w_axis.xyz()),
197            (3, 0) => Self::from_cols(m.x_axis.yzw(), m.y_axis.yzw(), m.z_axis.yzw()),
198            (3, 1) => Self::from_cols(m.x_axis.xzw(), m.y_axis.xzw(), m.z_axis.xzw()),
199            (3, 2) => Self::from_cols(m.x_axis.xyw(), m.y_axis.xyw(), m.z_axis.xyw()),
200            (3, 3) => Self::from_cols(m.x_axis.xyz(), m.y_axis.xyz(), m.z_axis.xyz()),
201            _ => panic!("index out of bounds"),
202        }
203    }
204
205    /// Creates a 3D rotation matrix from the given quaternion.
206    ///
207    /// # Panics
208    ///
209    /// Will panic if `rotation` is not normalized when `glam_assert` is enabled.
210    #[inline]
211    #[must_use]
212    pub fn from_quat(rotation: Quat) -> Self {
213        glam_assert!(rotation.is_normalized());
214
215        let x2 = rotation.x + rotation.x;
216        let y2 = rotation.y + rotation.y;
217        let z2 = rotation.z + rotation.z;
218        let xx = rotation.x * x2;
219        let xy = rotation.x * y2;
220        let xz = rotation.x * z2;
221        let yy = rotation.y * y2;
222        let yz = rotation.y * z2;
223        let zz = rotation.z * z2;
224        let wx = rotation.w * x2;
225        let wy = rotation.w * y2;
226        let wz = rotation.w * z2;
227
228        Self::from_cols(
229            Vec3::new(1.0 - (yy + zz), xy + wz, xz - wy),
230            Vec3::new(xy - wz, 1.0 - (xx + zz), yz + wx),
231            Vec3::new(xz + wy, yz - wx, 1.0 - (xx + yy)),
232        )
233    }
234
235    /// Creates a 3D rotation matrix from a normalized rotation `axis` and `angle` (in
236    /// radians).
237    ///
238    /// # Panics
239    ///
240    /// Will panic if `axis` is not normalized when `glam_assert` is enabled.
241    #[inline]
242    #[must_use]
243    pub fn from_axis_angle(axis: Vec3, angle: f32) -> Self {
244        glam_assert!(axis.is_normalized());
245
246        let (sin, cos) = math::sin_cos(angle);
247        let (xsin, ysin, zsin) = axis.mul(sin).into();
248        let (x, y, z) = axis.into();
249        let (x2, y2, z2) = axis.mul(axis).into();
250        let omc = 1.0 - cos;
251        let xyomc = x * y * omc;
252        let xzomc = x * z * omc;
253        let yzomc = y * z * omc;
254        Self::from_cols(
255            Vec3::new(x2 * omc + cos, xyomc + zsin, xzomc - ysin),
256            Vec3::new(xyomc - zsin, y2 * omc + cos, yzomc + xsin),
257            Vec3::new(xzomc + ysin, yzomc - xsin, z2 * omc + cos),
258        )
259    }
260
261    /// Creates a 3D rotation matrix from the given euler rotation sequence and the angles (in
262    /// radians).
263    #[inline]
264    #[must_use]
265    pub fn from_euler(order: EulerRot, a: f32, b: f32, c: f32) -> Self {
266        Self::from_euler_angles(order, a, b, c)
267    }
268
269    /// Extract Euler angles with the given Euler rotation order.
270    ///
271    /// Note if the input matrix contains scales, shears, or other non-rotation transformations then
272    /// the resulting Euler angles will be ill-defined.
273    ///
274    /// # Panics
275    ///
276    /// Will panic if any input matrix column is not normalized when `glam_assert` is enabled.
277    #[inline]
278    #[must_use]
279    pub fn to_euler(&self, order: EulerRot) -> (f32, f32, f32) {
280        glam_assert!(
281            self.x_axis.is_normalized()
282                && self.y_axis.is_normalized()
283                && self.z_axis.is_normalized()
284        );
285        self.to_euler_angles(order)
286    }
287
288    /// Creates a 3D rotation matrix from `angle` (in radians) around the x axis.
289    #[inline]
290    #[must_use]
291    pub fn from_rotation_x(angle: f32) -> Self {
292        let (sina, cosa) = math::sin_cos(angle);
293        Self::from_cols(
294            Vec3::X,
295            Vec3::new(0.0, cosa, sina),
296            Vec3::new(0.0, -sina, cosa),
297        )
298    }
299
300    /// Creates a 3D rotation matrix from `angle` (in radians) around the y axis.
301    #[inline]
302    #[must_use]
303    pub fn from_rotation_y(angle: f32) -> Self {
304        let (sina, cosa) = math::sin_cos(angle);
305        Self::from_cols(
306            Vec3::new(cosa, 0.0, -sina),
307            Vec3::Y,
308            Vec3::new(sina, 0.0, cosa),
309        )
310    }
311
312    /// Creates a 3D rotation matrix from `angle` (in radians) around the z axis.
313    #[inline]
314    #[must_use]
315    pub fn from_rotation_z(angle: f32) -> Self {
316        let (sina, cosa) = math::sin_cos(angle);
317        Self::from_cols(
318            Vec3::new(cosa, sina, 0.0),
319            Vec3::new(-sina, cosa, 0.0),
320            Vec3::Z,
321        )
322    }
323
324    /// Creates an affine transformation matrix from the given 2D `translation`.
325    ///
326    /// The resulting matrix can be used to transform 2D points and vectors. See
327    /// [`Self::transform_point2()`] and [`Self::transform_vector2()`].
328    #[inline]
329    #[must_use]
330    pub fn from_translation(translation: Vec2) -> Self {
331        Self::from_cols(
332            Vec3::X,
333            Vec3::Y,
334            Vec3::new(translation.x, translation.y, 1.0),
335        )
336    }
337
338    /// Creates an affine transformation matrix from the given 2D rotation `angle` (in
339    /// radians).
340    ///
341    /// The resulting matrix can be used to transform 2D points and vectors. See
342    /// [`Self::transform_point2()`] and [`Self::transform_vector2()`].
343    #[inline]
344    #[must_use]
345    pub fn from_angle(angle: f32) -> Self {
346        let (sin, cos) = math::sin_cos(angle);
347        Self::from_cols(Vec3::new(cos, sin, 0.0), Vec3::new(-sin, cos, 0.0), Vec3::Z)
348    }
349
350    /// Creates an affine transformation matrix from the given 2D `scale`, rotation `angle` (in
351    /// radians) and `translation`.
352    ///
353    /// The resulting matrix can be used to transform 2D points and vectors. See
354    /// [`Self::transform_point2()`] and [`Self::transform_vector2()`].
355    #[inline]
356    #[must_use]
357    pub fn from_scale_angle_translation(scale: Vec2, angle: f32, translation: Vec2) -> Self {
358        let (sin, cos) = math::sin_cos(angle);
359        Self::from_cols(
360            Vec3::new(cos * scale.x, sin * scale.x, 0.0),
361            Vec3::new(-sin * scale.y, cos * scale.y, 0.0),
362            Vec3::new(translation.x, translation.y, 1.0),
363        )
364    }
365
366    /// Creates an affine transformation matrix from the given non-uniform 2D `scale`.
367    ///
368    /// The resulting matrix can be used to transform 2D points and vectors. See
369    /// [`Self::transform_point2()`] and [`Self::transform_vector2()`].
370    ///
371    /// # Panics
372    ///
373    /// Will panic if all elements of `scale` are zero when `glam_assert` is enabled.
374    #[inline]
375    #[must_use]
376    pub fn from_scale(scale: Vec2) -> Self {
377        // Do not panic as long as any component is non-zero
378        glam_assert!(scale.cmpne(Vec2::ZERO).any());
379
380        Self::from_cols(
381            Vec3::new(scale.x, 0.0, 0.0),
382            Vec3::new(0.0, scale.y, 0.0),
383            Vec3::Z,
384        )
385    }
386
387    /// Creates an affine transformation matrix from the given 2x2 matrix.
388    ///
389    /// The resulting matrix can be used to transform 2D points and vectors. See
390    /// [`Self::transform_point2()`] and [`Self::transform_vector2()`].
391    #[inline]
392    pub fn from_mat2(m: Mat2) -> Self {
393        Self::from_cols((m.x_axis, 0.0).into(), (m.y_axis, 0.0).into(), Vec3::Z)
394    }
395
396    /// Creates a 3x3 matrix from the first 9 values in `slice`.
397    ///
398    /// # Panics
399    ///
400    /// Panics if `slice` is less than 9 elements long.
401    #[inline]
402    #[must_use]
403    pub const fn from_cols_slice(slice: &[f32]) -> Self {
404        Self::new(
405            slice[0], slice[1], slice[2], slice[3], slice[4], slice[5], slice[6], slice[7],
406            slice[8],
407        )
408    }
409
410    /// Writes the columns of `self` to the first 9 elements in `slice`.
411    ///
412    /// # Panics
413    ///
414    /// Panics if `slice` is less than 9 elements long.
415    #[inline]
416    pub fn write_cols_to_slice(&self, slice: &mut [f32]) {
417        slice[0] = self.x_axis.x;
418        slice[1] = self.x_axis.y;
419        slice[2] = self.x_axis.z;
420        slice[3] = self.y_axis.x;
421        slice[4] = self.y_axis.y;
422        slice[5] = self.y_axis.z;
423        slice[6] = self.z_axis.x;
424        slice[7] = self.z_axis.y;
425        slice[8] = self.z_axis.z;
426    }
427
428    /// Returns the matrix column for the given `index`.
429    ///
430    /// # Panics
431    ///
432    /// Panics if `index` is greater than 2.
433    #[inline]
434    #[must_use]
435    pub fn col(&self, index: usize) -> Vec3 {
436        match index {
437            0 => self.x_axis,
438            1 => self.y_axis,
439            2 => self.z_axis,
440            _ => panic!("index out of bounds"),
441        }
442    }
443
444    /// Returns a mutable reference to the matrix column for the given `index`.
445    ///
446    /// # Panics
447    ///
448    /// Panics if `index` is greater than 2.
449    #[inline]
450    pub fn col_mut(&mut self, index: usize) -> &mut Vec3 {
451        match index {
452            0 => &mut self.x_axis,
453            1 => &mut self.y_axis,
454            2 => &mut self.z_axis,
455            _ => panic!("index out of bounds"),
456        }
457    }
458
459    /// Returns the matrix row for the given `index`.
460    ///
461    /// # Panics
462    ///
463    /// Panics if `index` is greater than 2.
464    #[inline]
465    #[must_use]
466    pub fn row(&self, index: usize) -> Vec3 {
467        match index {
468            0 => Vec3::new(self.x_axis.x, self.y_axis.x, self.z_axis.x),
469            1 => Vec3::new(self.x_axis.y, self.y_axis.y, self.z_axis.y),
470            2 => Vec3::new(self.x_axis.z, self.y_axis.z, self.z_axis.z),
471            _ => panic!("index out of bounds"),
472        }
473    }
474
475    /// Returns `true` if, and only if, all elements are finite.
476    /// If any element is either `NaN`, positive or negative infinity, this will return `false`.
477    #[inline]
478    #[must_use]
479    pub fn is_finite(&self) -> bool {
480        self.x_axis.is_finite() && self.y_axis.is_finite() && self.z_axis.is_finite()
481    }
482
483    /// Returns `true` if any elements are `NaN`.
484    #[inline]
485    #[must_use]
486    pub fn is_nan(&self) -> bool {
487        self.x_axis.is_nan() || self.y_axis.is_nan() || self.z_axis.is_nan()
488    }
489
490    /// Returns the transpose of `self`.
491    #[inline]
492    #[must_use]
493    pub fn transpose(&self) -> Self {
494        Self {
495            x_axis: Vec3::new(self.x_axis.x, self.y_axis.x, self.z_axis.x),
496            y_axis: Vec3::new(self.x_axis.y, self.y_axis.y, self.z_axis.y),
497            z_axis: Vec3::new(self.x_axis.z, self.y_axis.z, self.z_axis.z),
498        }
499    }
500
501    /// Returns the diagonal of `self`.
502    #[inline]
503    #[must_use]
504    pub fn diagonal(&self) -> Vec3 {
505        Vec3::new(self.x_axis.x, self.y_axis.y, self.z_axis.z)
506    }
507
508    /// Returns the determinant of `self`.
509    #[inline]
510    #[must_use]
511    pub fn determinant(&self) -> f32 {
512        self.z_axis.dot(self.x_axis.cross(self.y_axis))
513    }
514
515    /// If `CHECKED` is true then if the determinant is zero this function will return a tuple
516    /// containing a zero matrix and false. If the determinant is non zero a tuple containing the
517    /// inverted matrix and true is returned.
518    ///
519    /// If `CHECKED` is false then the determinant is not checked and if it is zero the resulting
520    /// inverted matrix will be invalid. Will panic if the determinant of `self` is zero when
521    /// `glam_assert` is enabled.
522    ///
523    /// A tuple containing the inverted matrix and a bool is used instead of an option here as
524    /// regular Rust enums put the discriminant first which can result in a lot of padding if the
525    /// matrix is aligned.
526    #[inline(always)]
527    #[must_use]
528    fn inverse_checked<const CHECKED: bool>(&self) -> (Self, bool) {
529        let tmp0 = self.y_axis.cross(self.z_axis);
530        let tmp1 = self.z_axis.cross(self.x_axis);
531        let tmp2 = self.x_axis.cross(self.y_axis);
532        let det = self.z_axis.dot(tmp2);
533        if CHECKED {
534            if det == 0.0 {
535                return (Self::ZERO, false);
536            }
537        } else {
538            glam_assert!(det != 0.0);
539        }
540        let inv_det = Vec3::splat(det.recip());
541        (
542            Self::from_cols(tmp0.mul(inv_det), tmp1.mul(inv_det), tmp2.mul(inv_det)).transpose(),
543            true,
544        )
545    }
546
547    /// Returns the inverse of `self`.
548    ///
549    /// If the matrix is not invertible the returned matrix will be invalid.
550    ///
551    /// # Panics
552    ///
553    /// Will panic if the determinant of `self` is zero when `glam_assert` is enabled.
554    #[inline]
555    #[must_use]
556    pub fn inverse(&self) -> Self {
557        self.inverse_checked::<false>().0
558    }
559
560    /// Returns the inverse of `self` or `None` if the matrix is not invertible.
561    #[inline]
562    #[must_use]
563    pub fn try_inverse(&self) -> Option<Self> {
564        let (m, is_valid) = self.inverse_checked::<true>();
565        if is_valid {
566            Some(m)
567        } else {
568            None
569        }
570    }
571
572    /// Returns the inverse of `self` or `Mat3::ZERO` if the matrix is not invertible.
573    #[inline]
574    #[must_use]
575    pub fn inverse_or_zero(&self) -> Self {
576        self.inverse_checked::<true>().0
577    }
578
579    /// Transforms the given 2D vector as a point.
580    ///
581    /// This is the equivalent of multiplying `rhs` as a 3D vector where `z` is `1`.
582    ///
583    /// This method assumes that `self` contains a valid affine transform.
584    ///
585    /// # Panics
586    ///
587    /// Will panic if the 2nd row of `self` is not `(0, 0, 1)` when `glam_assert` is enabled.
588    #[inline]
589    #[must_use]
590    pub fn transform_point2(&self, rhs: Vec2) -> Vec2 {
591        glam_assert!(self.row(2).abs_diff_eq(Vec3::Z, 1e-6));
592        Mat2::from_cols(self.x_axis.xy(), self.y_axis.xy()) * rhs + self.z_axis.xy()
593    }
594
595    /// Rotates the given 2D vector.
596    ///
597    /// This is the equivalent of multiplying `rhs` as a 3D vector where `z` is `0`.
598    ///
599    /// This method assumes that `self` contains a valid affine transform.
600    ///
601    /// # Panics
602    ///
603    /// Will panic if the 2nd row of `self` is not `(0, 0, 1)` when `glam_assert` is enabled.
604    #[inline]
605    #[must_use]
606    pub fn transform_vector2(&self, rhs: Vec2) -> Vec2 {
607        glam_assert!(self.row(2).abs_diff_eq(Vec3::Z, 1e-6));
608        Mat2::from_cols(self.x_axis.xy(), self.y_axis.xy()) * rhs
609    }
610
611    /// Creates a left-handed view matrix using a facing direction and an up direction.
612    ///
613    /// For a view coordinate system with `+X=right`, `+Y=up` and `+Z=forward`.
614    ///
615    /// # Panics
616    ///
617    /// Will panic if `dir` or `up` are not normalized when `glam_assert` is enabled.
618    #[inline]
619    #[must_use]
620    pub fn look_to_lh(dir: Vec3, up: Vec3) -> Self {
621        Self::look_to_rh(-dir, up)
622    }
623
624    /// Creates a right-handed view matrix using a facing direction and an up direction.
625    ///
626    /// For a view coordinate system with `+X=right`, `+Y=up` and `+Z=back`.
627    ///
628    /// # Panics
629    ///
630    /// Will panic if `dir` or `up` are not normalized when `glam_assert` is enabled.
631    #[inline]
632    #[must_use]
633    pub fn look_to_rh(dir: Vec3, up: Vec3) -> Self {
634        glam_assert!(dir.is_normalized());
635        glam_assert!(up.is_normalized());
636        let f = dir;
637        let s = f.cross(up).normalize();
638        let u = s.cross(f);
639
640        Self::from_cols(
641            Vec3::new(s.x, u.x, -f.x),
642            Vec3::new(s.y, u.y, -f.y),
643            Vec3::new(s.z, u.z, -f.z),
644        )
645    }
646
647    /// Creates a left-handed view matrix using a camera position, a focal point and an up
648    /// direction.
649    ///
650    /// For a view coordinate system with `+X=right`, `+Y=up` and `+Z=forward`.
651    ///
652    /// # Panics
653    ///
654    /// Will panic if `up` is not normalized when `glam_assert` is enabled.
655    #[inline]
656    #[must_use]
657    pub fn look_at_lh(eye: Vec3, center: Vec3, up: Vec3) -> Self {
658        Self::look_to_lh(center.sub(eye).normalize(), up)
659    }
660
661    /// Creates a right-handed view matrix using a camera position, a focal point and an up
662    /// direction.
663    ///
664    /// For a view coordinate system with `+X=right`, `+Y=up` and `+Z=back`.
665    ///
666    /// # Panics
667    ///
668    /// Will panic if `up` is not normalized when `glam_assert` is enabled.
669    #[inline]
670    pub fn look_at_rh(eye: Vec3, center: Vec3, up: Vec3) -> Self {
671        Self::look_to_rh(center.sub(eye).normalize(), up)
672    }
673
674    /// Transforms a 3D vector.
675    #[inline]
676    #[must_use]
677    pub fn mul_vec3(&self, rhs: Vec3) -> Vec3 {
678        let mut res = self.x_axis.mul(rhs.x);
679        res = res.add(self.y_axis.mul(rhs.y));
680        res = res.add(self.z_axis.mul(rhs.z));
681        res
682    }
683
684    /// Transforms a [`Vec3A`].
685    #[inline]
686    #[must_use]
687    pub fn mul_vec3a(&self, rhs: Vec3A) -> Vec3A {
688        self.mul_vec3(rhs.into()).into()
689    }
690
691    /// Transforms a 3D vector by the transpose of `self`.
692    #[inline]
693    #[must_use]
694    pub fn mul_transpose_vec3(&self, rhs: Vec3) -> Vec3 {
695        Vec3::new(
696            self.x_axis.dot(rhs),
697            self.y_axis.dot(rhs),
698            self.z_axis.dot(rhs),
699        )
700    }
701
702    /// Multiplies two 3x3 matrices.
703    #[inline]
704    #[must_use]
705    pub fn mul_mat3(&self, rhs: &Self) -> Self {
706        self.mul(rhs)
707    }
708
709    /// Adds two 3x3 matrices.
710    #[inline]
711    #[must_use]
712    pub fn add_mat3(&self, rhs: &Self) -> Self {
713        self.add(rhs)
714    }
715
716    /// Subtracts two 3x3 matrices.
717    #[inline]
718    #[must_use]
719    pub fn sub_mat3(&self, rhs: &Self) -> Self {
720        self.sub(rhs)
721    }
722
723    /// Multiplies a 3x3 matrix by a scalar.
724    #[inline]
725    #[must_use]
726    pub fn mul_scalar(&self, rhs: f32) -> Self {
727        Self::from_cols(
728            self.x_axis.mul(rhs),
729            self.y_axis.mul(rhs),
730            self.z_axis.mul(rhs),
731        )
732    }
733
734    /// Multiply `self` by a scaling vector `scale`.
735    /// This is faster than creating a whole diagonal scaling matrix and then multiplying that.
736    /// This operation is commutative.
737    #[inline]
738    #[must_use]
739    pub fn mul_diagonal_scale(&self, scale: Vec3) -> Self {
740        Self::from_cols(
741            self.x_axis * scale.x,
742            self.y_axis * scale.y,
743            self.z_axis * scale.z,
744        )
745    }
746
747    /// Divides a 3x3 matrix by a scalar.
748    #[inline]
749    #[must_use]
750    pub fn div_scalar(&self, rhs: f32) -> Self {
751        let rhs = Vec3::splat(rhs);
752        Self::from_cols(
753            self.x_axis.div(rhs),
754            self.y_axis.div(rhs),
755            self.z_axis.div(rhs),
756        )
757    }
758
759    /// Returns true if the absolute difference of all elements between `self` and `rhs`
760    /// is less than or equal to `max_abs_diff`.
761    ///
762    /// This can be used to compare if two matrices contain similar elements. It works best
763    /// when comparing with a known value. The `max_abs_diff` that should be used used
764    /// depends on the values being compared against.
765    ///
766    /// For more see
767    /// [comparing floating point numbers](https://randomascii.wordpress.com/2012/02/25/comparing-floating-point-numbers-2012-edition/).
768    #[inline]
769    #[must_use]
770    pub fn abs_diff_eq(&self, rhs: Self, max_abs_diff: f32) -> bool {
771        self.x_axis.abs_diff_eq(rhs.x_axis, max_abs_diff)
772            && self.y_axis.abs_diff_eq(rhs.y_axis, max_abs_diff)
773            && self.z_axis.abs_diff_eq(rhs.z_axis, max_abs_diff)
774    }
775
776    /// Takes the absolute value of each element in `self`
777    #[inline]
778    #[must_use]
779    pub fn abs(&self) -> Self {
780        Self::from_cols(self.x_axis.abs(), self.y_axis.abs(), self.z_axis.abs())
781    }
782
783    #[inline]
784    pub fn as_dmat3(&self) -> DMat3 {
785        DMat3::from_cols(
786            self.x_axis.as_dvec3(),
787            self.y_axis.as_dvec3(),
788            self.z_axis.as_dvec3(),
789        )
790    }
791}
792
793impl Default for Mat3 {
794    #[inline]
795    fn default() -> Self {
796        Self::IDENTITY
797    }
798}
799
800impl Add for Mat3 {
801    type Output = Self;
802    #[inline]
803    fn add(self, rhs: Self) -> Self {
804        Self::from_cols(
805            self.x_axis.add(rhs.x_axis),
806            self.y_axis.add(rhs.y_axis),
807            self.z_axis.add(rhs.z_axis),
808        )
809    }
810}
811
812impl Add<&Self> for Mat3 {
813    type Output = Self;
814    #[inline]
815    fn add(self, rhs: &Self) -> Self {
816        self.add(*rhs)
817    }
818}
819
820impl Add<&Mat3> for &Mat3 {
821    type Output = Mat3;
822    #[inline]
823    fn add(self, rhs: &Mat3) -> Mat3 {
824        (*self).add(*rhs)
825    }
826}
827
828impl Add<Mat3> for &Mat3 {
829    type Output = Mat3;
830    #[inline]
831    fn add(self, rhs: Mat3) -> Mat3 {
832        (*self).add(rhs)
833    }
834}
835
836impl AddAssign for Mat3 {
837    #[inline]
838    fn add_assign(&mut self, rhs: Self) {
839        *self = self.add(rhs);
840    }
841}
842
843impl AddAssign<&Self> for Mat3 {
844    #[inline]
845    fn add_assign(&mut self, rhs: &Self) {
846        self.add_assign(*rhs);
847    }
848}
849
850impl Sub for Mat3 {
851    type Output = Self;
852    #[inline]
853    fn sub(self, rhs: Self) -> Self {
854        Self::from_cols(
855            self.x_axis.sub(rhs.x_axis),
856            self.y_axis.sub(rhs.y_axis),
857            self.z_axis.sub(rhs.z_axis),
858        )
859    }
860}
861
862impl Sub<&Self> for Mat3 {
863    type Output = Self;
864    #[inline]
865    fn sub(self, rhs: &Self) -> Self {
866        self.sub(*rhs)
867    }
868}
869
870impl Sub<&Mat3> for &Mat3 {
871    type Output = Mat3;
872    #[inline]
873    fn sub(self, rhs: &Mat3) -> Mat3 {
874        (*self).sub(*rhs)
875    }
876}
877
878impl Sub<Mat3> for &Mat3 {
879    type Output = Mat3;
880    #[inline]
881    fn sub(self, rhs: Mat3) -> Mat3 {
882        (*self).sub(rhs)
883    }
884}
885
886impl SubAssign for Mat3 {
887    #[inline]
888    fn sub_assign(&mut self, rhs: Self) {
889        *self = self.sub(rhs);
890    }
891}
892
893impl SubAssign<&Self> for Mat3 {
894    #[inline]
895    fn sub_assign(&mut self, rhs: &Self) {
896        self.sub_assign(*rhs);
897    }
898}
899
900impl Neg for Mat3 {
901    type Output = Self;
902    #[inline]
903    fn neg(self) -> Self::Output {
904        Self::from_cols(self.x_axis.neg(), self.y_axis.neg(), self.z_axis.neg())
905    }
906}
907
908impl Neg for &Mat3 {
909    type Output = Mat3;
910    #[inline]
911    fn neg(self) -> Mat3 {
912        (*self).neg()
913    }
914}
915
916impl Mul for Mat3 {
917    type Output = Self;
918    #[inline]
919    fn mul(self, rhs: Self) -> Self {
920        Self::from_cols(
921            self.mul(rhs.x_axis),
922            self.mul(rhs.y_axis),
923            self.mul(rhs.z_axis),
924        )
925    }
926}
927
928impl Mul<&Self> for Mat3 {
929    type Output = Self;
930    #[inline]
931    fn mul(self, rhs: &Self) -> Self {
932        self.mul(*rhs)
933    }
934}
935
936impl Mul<&Mat3> for &Mat3 {
937    type Output = Mat3;
938    #[inline]
939    fn mul(self, rhs: &Mat3) -> Mat3 {
940        (*self).mul(*rhs)
941    }
942}
943
944impl Mul<Mat3> for &Mat3 {
945    type Output = Mat3;
946    #[inline]
947    fn mul(self, rhs: Mat3) -> Mat3 {
948        (*self).mul(rhs)
949    }
950}
951
952impl MulAssign for Mat3 {
953    #[inline]
954    fn mul_assign(&mut self, rhs: Self) {
955        *self = self.mul(rhs);
956    }
957}
958
959impl MulAssign<&Self> for Mat3 {
960    #[inline]
961    fn mul_assign(&mut self, rhs: &Self) {
962        self.mul_assign(*rhs);
963    }
964}
965
966impl Mul<Vec3> for Mat3 {
967    type Output = Vec3;
968    #[inline]
969    fn mul(self, rhs: Vec3) -> Self::Output {
970        self.mul_vec3(rhs)
971    }
972}
973
974impl Mul<&Vec3> for Mat3 {
975    type Output = Vec3;
976    #[inline]
977    fn mul(self, rhs: &Vec3) -> Vec3 {
978        self.mul(*rhs)
979    }
980}
981
982impl Mul<&Vec3> for &Mat3 {
983    type Output = Vec3;
984    #[inline]
985    fn mul(self, rhs: &Vec3) -> Vec3 {
986        (*self).mul(*rhs)
987    }
988}
989
990impl Mul<Vec3> for &Mat3 {
991    type Output = Vec3;
992    #[inline]
993    fn mul(self, rhs: Vec3) -> Vec3 {
994        (*self).mul(rhs)
995    }
996}
997
998impl Mul<Mat3> for f32 {
999    type Output = Mat3;
1000    #[inline]
1001    fn mul(self, rhs: Mat3) -> Self::Output {
1002        rhs.mul_scalar(self)
1003    }
1004}
1005
1006impl Mul<&Mat3> for f32 {
1007    type Output = Mat3;
1008    #[inline]
1009    fn mul(self, rhs: &Mat3) -> Mat3 {
1010        self.mul(*rhs)
1011    }
1012}
1013
1014impl Mul<&Mat3> for &f32 {
1015    type Output = Mat3;
1016    #[inline]
1017    fn mul(self, rhs: &Mat3) -> Mat3 {
1018        (*self).mul(*rhs)
1019    }
1020}
1021
1022impl Mul<Mat3> for &f32 {
1023    type Output = Mat3;
1024    #[inline]
1025    fn mul(self, rhs: Mat3) -> Mat3 {
1026        (*self).mul(rhs)
1027    }
1028}
1029
1030impl Mul<f32> for Mat3 {
1031    type Output = Self;
1032    #[inline]
1033    fn mul(self, rhs: f32) -> Self {
1034        self.mul_scalar(rhs)
1035    }
1036}
1037
1038impl Mul<&f32> for Mat3 {
1039    type Output = Self;
1040    #[inline]
1041    fn mul(self, rhs: &f32) -> Self {
1042        self.mul(*rhs)
1043    }
1044}
1045
1046impl Mul<&f32> for &Mat3 {
1047    type Output = Mat3;
1048    #[inline]
1049    fn mul(self, rhs: &f32) -> Mat3 {
1050        (*self).mul(*rhs)
1051    }
1052}
1053
1054impl Mul<f32> for &Mat3 {
1055    type Output = Mat3;
1056    #[inline]
1057    fn mul(self, rhs: f32) -> Mat3 {
1058        (*self).mul(rhs)
1059    }
1060}
1061
1062impl MulAssign<f32> for Mat3 {
1063    #[inline]
1064    fn mul_assign(&mut self, rhs: f32) {
1065        *self = self.mul(rhs);
1066    }
1067}
1068
1069impl MulAssign<&f32> for Mat3 {
1070    #[inline]
1071    fn mul_assign(&mut self, rhs: &f32) {
1072        self.mul_assign(*rhs);
1073    }
1074}
1075
1076impl Div<Mat3> for f32 {
1077    type Output = Mat3;
1078    #[inline]
1079    fn div(self, rhs: Mat3) -> Self::Output {
1080        rhs.div_scalar(self)
1081    }
1082}
1083
1084impl Div<&Mat3> for f32 {
1085    type Output = Mat3;
1086    #[inline]
1087    fn div(self, rhs: &Mat3) -> Mat3 {
1088        self.div(*rhs)
1089    }
1090}
1091
1092impl Div<&Mat3> for &f32 {
1093    type Output = Mat3;
1094    #[inline]
1095    fn div(self, rhs: &Mat3) -> Mat3 {
1096        (*self).div(*rhs)
1097    }
1098}
1099
1100impl Div<Mat3> for &f32 {
1101    type Output = Mat3;
1102    #[inline]
1103    fn div(self, rhs: Mat3) -> Mat3 {
1104        (*self).div(rhs)
1105    }
1106}
1107
1108impl Div<f32> for Mat3 {
1109    type Output = Self;
1110    #[inline]
1111    fn div(self, rhs: f32) -> Self {
1112        self.div_scalar(rhs)
1113    }
1114}
1115
1116impl Div<&f32> for Mat3 {
1117    type Output = Self;
1118    #[inline]
1119    fn div(self, rhs: &f32) -> Self {
1120        self.div(*rhs)
1121    }
1122}
1123
1124impl Div<&f32> for &Mat3 {
1125    type Output = Mat3;
1126    #[inline]
1127    fn div(self, rhs: &f32) -> Mat3 {
1128        (*self).div(*rhs)
1129    }
1130}
1131
1132impl Div<f32> for &Mat3 {
1133    type Output = Mat3;
1134    #[inline]
1135    fn div(self, rhs: f32) -> Mat3 {
1136        (*self).div(rhs)
1137    }
1138}
1139
1140impl DivAssign<f32> for Mat3 {
1141    #[inline]
1142    fn div_assign(&mut self, rhs: f32) {
1143        *self = self.div(rhs);
1144    }
1145}
1146
1147impl DivAssign<&f32> for Mat3 {
1148    #[inline]
1149    fn div_assign(&mut self, rhs: &f32) {
1150        self.div_assign(*rhs);
1151    }
1152}
1153
1154impl Mul<Vec3A> for Mat3 {
1155    type Output = Vec3A;
1156    #[inline]
1157    fn mul(self, rhs: Vec3A) -> Vec3A {
1158        self.mul_vec3a(rhs)
1159    }
1160}
1161
1162impl Mul<&Vec3A> for Mat3 {
1163    type Output = Vec3A;
1164    #[inline]
1165    fn mul(self, rhs: &Vec3A) -> Vec3A {
1166        self.mul(*rhs)
1167    }
1168}
1169
1170impl Mul<&Vec3A> for &Mat3 {
1171    type Output = Vec3A;
1172    #[inline]
1173    fn mul(self, rhs: &Vec3A) -> Vec3A {
1174        (*self).mul(*rhs)
1175    }
1176}
1177
1178impl Mul<Vec3A> for &Mat3 {
1179    type Output = Vec3A;
1180    #[inline]
1181    fn mul(self, rhs: Vec3A) -> Vec3A {
1182        (*self).mul(rhs)
1183    }
1184}
1185
1186impl From<Mat3A> for Mat3 {
1187    #[inline]
1188    fn from(m: Mat3A) -> Self {
1189        Self {
1190            x_axis: m.x_axis.into(),
1191            y_axis: m.y_axis.into(),
1192            z_axis: m.z_axis.into(),
1193        }
1194    }
1195}
1196
1197impl Sum<Self> for Mat3 {
1198    fn sum<I>(iter: I) -> Self
1199    where
1200        I: Iterator<Item = Self>,
1201    {
1202        iter.fold(Self::ZERO, Self::add)
1203    }
1204}
1205
1206impl<'a> Sum<&'a Self> for Mat3 {
1207    fn sum<I>(iter: I) -> Self
1208    where
1209        I: Iterator<Item = &'a Self>,
1210    {
1211        iter.fold(Self::ZERO, |a, &b| Self::add(a, b))
1212    }
1213}
1214
1215impl Product for Mat3 {
1216    fn product<I>(iter: I) -> Self
1217    where
1218        I: Iterator<Item = Self>,
1219    {
1220        iter.fold(Self::IDENTITY, Self::mul)
1221    }
1222}
1223
1224impl<'a> Product<&'a Self> for Mat3 {
1225    fn product<I>(iter: I) -> Self
1226    where
1227        I: Iterator<Item = &'a Self>,
1228    {
1229        iter.fold(Self::IDENTITY, |a, &b| Self::mul(a, b))
1230    }
1231}
1232
1233impl PartialEq for Mat3 {
1234    #[inline]
1235    fn eq(&self, rhs: &Self) -> bool {
1236        self.x_axis.eq(&rhs.x_axis) && self.y_axis.eq(&rhs.y_axis) && self.z_axis.eq(&rhs.z_axis)
1237    }
1238}
1239
1240impl AsRef<[f32; 9]> for Mat3 {
1241    #[inline]
1242    fn as_ref(&self) -> &[f32; 9] {
1243        unsafe { &*(self as *const Self as *const [f32; 9]) }
1244    }
1245}
1246
1247impl AsMut<[f32; 9]> for Mat3 {
1248    #[inline]
1249    fn as_mut(&mut self) -> &mut [f32; 9] {
1250        unsafe { &mut *(self as *mut Self as *mut [f32; 9]) }
1251    }
1252}
1253
1254impl fmt::Debug for Mat3 {
1255    fn fmt(&self, fmt: &mut fmt::Formatter<'_>) -> fmt::Result {
1256        fmt.debug_struct(stringify!(Mat3))
1257            .field("x_axis", &self.x_axis)
1258            .field("y_axis", &self.y_axis)
1259            .field("z_axis", &self.z_axis)
1260            .finish()
1261    }
1262}
1263
1264impl fmt::Display for Mat3 {
1265    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
1266        if let Some(p) = f.precision() {
1267            write!(
1268                f,
1269                "[{:.*}, {:.*}, {:.*}]",
1270                p, self.x_axis, p, self.y_axis, p, self.z_axis
1271            )
1272        } else {
1273            write!(f, "[{}, {}, {}]", self.x_axis, self.y_axis, self.z_axis)
1274        }
1275    }
1276}
glam/f32/mat3.rs

glam/f32/
mat3.rs
