Struct vek::mat::repr_c::column_major::mat4::Mat4

#[repr(C)]pub struct Mat4<T> {
    pub cols: CVec4<Vec4<T>>,
}

4x4 matrix.

Fields

cols: CVec4<Vec4<T>>

Implementations

impl<T> Mat4<T>

pub fn identity() -> Self where
    T: Zero + One, 

The identity matrix, which is also the default value for square matrices.

assert_eq!(Mat4::<f32>::default(), Mat4::<f32>::identity());

pub fn zero() -> Self where
    T: Zero, 

The matrix with all elements set to zero.

pub fn apply<F>(&mut self, f: F) where
    T: Copy,
    F: FnMut(T) -> T, 

Applies the function f to each element of this matrix, in-place.

For an example, see the map() method.

pub fn apply2<F, S>(&mut self, other: Mat4<S>, f: F) where
    T: Copy,
    F: FnMut(T, S) -> T, 

Applies the function f to each element of this matrix, in-place.

For an example, see the map2() method.

pub fn numcast<D>(self) -> Option<Mat4<D>> where
    T: NumCast,
    D: NumCast, 

Returns a memberwise-converted copy of this matrix, using NumCast.

let m = Mat4::<f32>::identity();
let m: Mat4<i32> = m.numcast().unwrap();
assert_eq!(m, Mat4::identity());

pub fn broadcast_diagonal(val: T) -> Self where
    T: Zero + Copy, 

Initializes a new matrix with elements of the diagonal set to val and the other to zero.

In a way, this is the same as single-argument matrix constructors in GLSL and GLM.

assert_eq!(Mat4::broadcast_diagonal(0), Mat4::zero());
assert_eq!(Mat4::broadcast_diagonal(1), Mat4::identity());
assert_eq!(Mat4::broadcast_diagonal(2), Mat4::new(
    2,0,0,0,
    0,2,0,0,
    0,0,2,0,
    0,0,0,2,
));

pub fn with_diagonal(d: Vec4<T>) -> Self where
    T: Zero + Copy, 

Initializes a matrix by its diagonal, setting other elements to zero.

pub fn diagonal(self) -> Vec4<T>

Gets the matrix's diagonal into a vector.

assert_eq!(Mat4::<u32>::zero().diagonal(), Vec4::zero());
assert_eq!(Mat4::<u32>::identity().diagonal(), Vec4::one());

let mut m = Mat4::zero();
m[(0, 0)] = 1;
m[(1, 1)] = 2;
m[(2, 2)] = 3;
m[(3, 3)] = 4;
assert_eq!(m.diagonal(), Vec4::new(1, 2, 3, 4));
assert_eq!(m.diagonal(), Vec4::iota() + 1);

pub fn trace(self) -> T where
    T: Add<T, Output = T>, 

The sum of the diagonal's elements.

assert_eq!(Mat4::<u32>::zero().trace(), 0);
assert_eq!(Mat4::<u32>::identity().trace(), 4);

pub fn mul_memberwise(self, m: Self) -> Self where
    T: Mul<Output = T>, 

Multiply elements of this matrix with another's.

let m = Mat4::new(
    0, 1, 2, 3,
    1, 2, 3, 4,
    2, 3, 4, 5,
    3, 4, 5, 6,
);
let r = Mat4::new(
    0, 1, 4, 9,
    1, 4, 9, 16,
    4, 9, 16, 25,
    9, 16, 25, 36,
);
assert_eq!(m.mul_memberwise(m), r);

pub fn row_count(&self) -> usize

Convenience for getting the number of rows of this matrix.

pub fn col_count(&self) -> usize

Convenience for getting the number of columns of this matrix.

pub const ROW_COUNT: usize

Convenience constant representing the number of rows for matrices of this type.

pub const COL_COUNT: usize

Convenience constant representing the number of columns for matrices of this type.

pub fn is_packed(&self) -> bool

Are all elements of this matrix tightly packed together in memory ?

This might not be the case for matrices in the repr_simd module (it depends on the target architecture).

impl<T> Mat4<T>

pub fn map_cols<D, F>(self, mut f: F) -> Mat4<D> where
    F: FnMut(Vec4<T>) -> Vec4<D>, 

Returns a column-wise-converted copy of this matrix, using the given conversion closure.

use vek::mat::repr_c::column_major::Mat4;

let m = Mat4::<f32>::new(
    0.25, 1.25, 5.56, 8.66,
    8.53, 2.92, 3.86, 9.36,
    1.02, 0.28, 5.52, 6.06,
    6.20, 7.01, 4.90, 5.26
);
let m = m.map_cols(|col| col.map(|x| x.round() as i32));
assert_eq!(m, Mat4::new(
    0, 1, 6, 9,
    9, 3, 4, 9,
    1, 0, 6, 6,
    6, 7, 5, 5
));

pub fn into_col_array(self) -> [T; 16]

Converts this matrix into a fixed-size array of elements.

use vek::mat::repr_c::column_major::Mat4;

let m = Mat4::<u32>::new(
     0,  1,  2,  3,
     4,  5,  6,  7,
     8,  9, 10, 11,
    12, 13, 14, 15
);
let array = [
    0, 4, 8, 12,
    1, 5, 9, 13,
    2, 6, 10, 14,
    3, 7, 11, 15
];
assert_eq!(m.into_col_array(), array);

pub fn into_col_arrays(self) -> [[T; 4]; 4]

Converts this matrix into a fixed-size array of fixed-size arrays of elements.

use vek::mat::repr_c::column_major::Mat4;

let m = Mat4::<u32>::new(
     0,  1,  2,  3,
     4,  5,  6,  7,
     8,  9, 10, 11,
    12, 13, 14, 15
);
let array = [
    [ 0, 4,  8, 12, ],
    [ 1, 5,  9, 13, ],
    [ 2, 6, 10, 14, ],
    [ 3, 7, 11, 15, ],
];
assert_eq!(m.into_col_arrays(), array);

pub fn from_col_array(array: [T; 16]) -> Self

Converts a fixed-size array of elements into a matrix.

use vek::mat::repr_c::column_major::Mat4;

let m = Mat4::<u32>::new(
     0,  1,  2,  3,
     4,  5,  6,  7,
     8,  9, 10, 11,
    12, 13, 14, 15
);
let array = [
    0, 4, 8, 12,
    1, 5, 9, 13,
    2, 6, 10, 14,
    3, 7, 11, 15
];
assert_eq!(m, Mat4::from_col_array(array));

pub fn from_col_arrays(array: [[T; 4]; 4]) -> Self

Converts a fixed-size array of fixed-size arrays of elements into a matrix.

use vek::mat::repr_c::column_major::Mat4;

let m = Mat4::<u32>::new(
     0,  1,  2,  3,
     4,  5,  6,  7,
     8,  9, 10, 11,
    12, 13, 14, 15
);
let array = [
    [ 0, 4,  8, 12, ],
    [ 1, 5,  9, 13, ],
    [ 2, 6, 10, 14, ],
    [ 3, 7, 11, 15, ],
];
assert_eq!(m, Mat4::from_col_arrays(array));

pub fn into_row_array(self) -> [T; 16]

Converts this matrix into a fixed-size array of elements.

use vek::mat::repr_c::column_major::Mat4;

let m = Mat4::<u32>::new(
     0,  1,  2,  3,
     4,  5,  6,  7,
     8,  9, 10, 11,
    12, 13, 14, 15
);
let array = [
     0,  1,  2,  3,
     4,  5,  6,  7,
     8,  9, 10, 11,
    12, 13, 14, 15
];
assert_eq!(m.into_row_array(), array);

pub fn into_row_arrays(self) -> [[T; 4]; 4]

Converts this matrix into a fixed-size array of fixed-size arrays of elements.

use vek::mat::repr_c::column_major::Mat4;

let m = Mat4::<u32>::new(
     0,  1,  2,  3,
     4,  5,  6,  7,
     8,  9, 10, 11,
    12, 13, 14, 15
);
let array = [
    [  0,  1,  2,  3, ],
    [  4,  5,  6,  7, ],
    [  8,  9, 10, 11, ],
    [ 12, 13, 14, 15, ],
];
assert_eq!(m.into_row_arrays(), array);

pub fn from_row_array(array: [T; 16]) -> Self

Converts a fixed-size array of elements into a matrix.

use vek::mat::repr_c::column_major::Mat4;

let m = Mat4::<u32>::new(
     0,  1,  2,  3,
     4,  5,  6,  7,
     8,  9, 10, 11,
    12, 13, 14, 15
);
let array = [
     0,  1,  2,  3,
     4,  5,  6,  7,
     8,  9, 10, 11,
    12, 13, 14, 15
];
assert_eq!(m, Mat4::from_row_array(array));

pub fn from_row_arrays(array: [[T; 4]; 4]) -> Self

Converts a fixed-size array of fixed-size array of elements into a matrix.

use vek::mat::repr_c::column_major::Mat4;

let m = Mat4::<u32>::new(
     0,  1,  2,  3,
     4,  5,  6,  7,
     8,  9, 10, 11,
    12, 13, 14, 15
);
let array = [
    [  0,  1,  2,  3, ],
    [  4,  5,  6,  7, ],
    [  8,  9, 10, 11, ],
    [ 12, 13, 14, 15, ],
];
assert_eq!(m, Mat4::from_row_arrays(array));

pub fn as_col_ptr(&self) -> *const T

Gets a const pointer to this matrix's elements.

Panics

Panics if the matrix's elements are not tightly packed in memory, which may be the case for matrices in the repr_simd module. You may check this with the is_packed() method.

pub fn as_mut_col_ptr(&mut self) -> *mut T

Gets a mut pointer to this matrix's elements.

Panics

Panics if the matrix's elements are not tightly packed in memory, which may be the case for matrices in the repr_simd module. You may check this with the is_packed() method.

pub fn as_col_slice(&self) -> &[T]

View this matrix as an immutable slice.

Panics

Panics if the matrix's elements are not tightly packed in memory, which may be the case for matrices in the repr_simd module. You may check this with the is_packed() method.

pub fn as_mut_col_slice(&mut self) -> &mut [T]

View this matrix as a mutable slice.

Panics

Panics if the matrix's elements are not tightly packed in memory, which may be the case for matrices in the repr_simd module. You may check this with the is_packed() method.

impl<T> Mat4<T>

pub fn gl_should_transpose(&self) -> bool

Gets the transpose parameter to pass to OpenGL glUniformMatrix*() functions.

The return value is a plain bool which you may directly cast to a GLboolean.

This takes &self to prevent surprises when changing the type of matrix you plan to send.

pub const GL_SHOULD_TRANSPOSE: bool

The transpose parameter to pass to OpenGL glUniformMatrix*() functions.

impl<T> Mat4<T>

pub fn new(
    m00: T,
    m01: T,
    m02: T,
    m03: T,
    m10: T,
    m11: T,
    m12: T,
    m13: T,
    m20: T,
    m21: T,
    m22: T,
    m23: T,
    m30: T,
    m31: T,
    m32: T,
    m33: T
) -> Self

Creates a new 4x4 matrix from elements in a layout-agnostic way.

The parameters are named mij where i is the row index and j the column index. Their order is always the same regardless of the matrix's layout.

impl<T> Mat4<T>

pub fn map<D, F>(self, mut f: F) -> Mat4<D> where
    F: FnMut(T) -> D, 

Returns an element-wise-converted copy of this matrix, using the given conversion closure.

use vek::mat::repr_c::row_major::Mat4;

let m = Mat4::<f32>::new(
    0.25, 1.25, 5.56, 8.66,
    8.53, 2.92, 3.86, 9.36,
    1.02, 0.28, 5.52, 6.06,
    6.20, 7.01, 4.90, 5.26
);
let m = m.map(|x| x.round() as i32);
assert_eq!(m, Mat4::new(
    0, 1, 6, 9,
    9, 3, 4, 9,
    1, 0, 6, 6,
    6, 7, 5, 5
));

pub fn as_<D>(self) -> Mat4<D> where
    T: AsPrimitive<D>,
    D: 'static + Copy, 

Returns a memberwise-converted copy of this matrix, using AsPrimitive.

Examples

let v = Vec4::new(0_f32, 1., 2., 3.);
let i: Vec4<i32> = v.as_();
assert_eq!(i, Vec4::new(0, 1, 2, 3));

Safety

In Rust versions before 1.45.0, some uses of the as operator were not entirely safe. In particular, it was undefined behavior if a truncated floating point value could not fit in the target integer type (#10184);

let x: u8 = (1.04E+17).as_(); // UB

pub fn map2<D, F, S>(self, other: Mat4<S>, mut f: F) -> Mat4<D> where
    F: FnMut(T, S) -> D, 

Applies the function f to each element of two matrices, pairwise, and returns the result.

use vek::mat::repr_c::row_major::Mat4;

let a = Mat4::<f32>::new(
    0.25, 1.25, 2.52, 2.99,
    0.25, 1.25, 2.52, 2.99,
    0.25, 1.25, 2.52, 2.99,
    0.25, 1.25, 2.52, 2.99
);
let b = Mat4::<i32>::new(
    0, 1, 0, 0,
    1, 0, 0, 0,
    0, 0, 1, 0,
    0, 0, 0, 1
);
let m = a.map2(b, |a, b| a.round() as i32 + b);
assert_eq!(m, Mat4::new(
    0, 2, 3, 3,
    1, 1, 3, 3,
    0, 1, 4, 3,
    0, 1, 3, 4
));

pub fn transposed(self) -> Self

The matrix's transpose.

For orthogonal matrices, the transpose is the same as the inverse. All pure rotation matrices are orthogonal, and therefore can be inverted faster by simply computing their transpose.

use std::f32::consts::PI;

let m = Mat4::new(
    0, 1, 2, 3,
    4, 5, 6, 7,
    8, 9, 0, 1,
    2, 3, 4, 5
);
let t = Mat4::new(
    0, 4, 8, 2,
    1, 5, 9, 3,
    2, 6, 0, 4,
    3, 7, 1, 5
);
assert_eq!(m.transposed(), t);
assert_eq!(m, m.transposed().transposed());

// By the way, demonstrate ways to invert a rotation matrix,
// from fastest (specific) to slowest (general-purpose).
let m = Mat4::rotation_x(PI/7.);
let id = Mat4::identity();
assert_relative_eq!(id, m * m.transposed());
assert_relative_eq!(id, m.transposed() * m);
assert_relative_eq!(id, m * m.inverted_affine_transform_no_scale());
assert_relative_eq!(id, m.inverted_affine_transform_no_scale() * m);
assert_relative_eq!(id, m * m.inverted_affine_transform());
assert_relative_eq!(id, m.inverted_affine_transform() * m);
assert_relative_eq!(id, m * m.inverted());
assert_relative_eq!(id, m.inverted() * m);

pub fn transpose(&mut self)

Transpose this matrix.

let mut m = Mat4::new(
    0, 1, 2, 3,
    4, 5, 6, 7,
    8, 9, 0, 1,
    2, 3, 4, 5
);
let t = Mat4::new(
    0, 4, 8, 2,
    1, 5, 9, 3,
    2, 6, 0, 4,
    3, 7, 1, 5
);
m.transpose();
assert_eq!(m, t);

pub fn determinant(self) -> T where
    T: Copy + Mul<T, Output = T> + Sub<T, Output = T> + Add<T, Output = T>, 

Get this matrix's determinant.

A matrix is invertible if its determinant is non-zero.

pub fn invert(&mut self) where
    T: Real, 

Inverts this matrix, blindly assuming that it is invertible. See inverted() for more info.

pub fn inverted(self) -> Self where
    T: Real, 

Returns this matrix's inverse, blindly assuming that it is invertible.

All affine matrices have inverses; Your matrices may be affine as long as they consist of any combination of pure rotations, translations, scales and shears.

use vek::vec::repr_c::Vec3;
use vek::mat::repr_c::row_major::Mat4 as Rows4;
use vek::mat::repr_c::column_major::Mat4 as Cols4;
use std::f32::consts::PI;

let a = Rows4::scaling_3d(1.77_f32)
    .rotated_3d(PI*4./5., Vec3::new(5., 8., 10.))
    .translated_3d(Vec3::new(1., 2., 3.));
let b = a.inverted();
assert_relative_eq!(a*b, Rows4::identity(), epsilon = 0.000001);
assert_relative_eq!(b*a, Rows4::identity(), epsilon = 0.000001);

let a = Cols4::scaling_3d(1.77_f32)
    .rotated_3d(PI*4./5., Vec3::new(5., 8., 10.))
    .translated_3d(Vec3::new(1., 2., 3.));
let b = a.inverted();
assert_relative_eq!(a*b, Cols4::identity(), epsilon = 0.000001);
assert_relative_eq!(b*a, Cols4::identity(), epsilon = 0.000001);

// Beware, projection matrices are not invertible!
// Notice that we assert _inequality_ below.
let a = Cols4::perspective_rh_zo(60_f32.to_radians(), 16./9., 0.001, 1000.) * a;
let b = a.inverted();
assert_relative_ne!(a*b, Cols4::identity(), epsilon = 0.000001);
assert_relative_ne!(b*a, Cols4::identity(), epsilon = 0.000001);

pub fn invert_affine_transform_no_scale(&mut self) where
    T: Real, 

Returns this matrix's inverse, blindly assuming that it is an invertible transform matrix which scale is 1.

See inverted_affine_transform_no_scale() for more info.

pub fn inverted_affine_transform_no_scale(self) -> Self where
    T: Real, 

Returns this matrix's inverse, blindly assuming that it is an invertible transform matrix which scale is 1.

A transform matrix is invertible this way as long as it consists of translations, rotations, and shears. It's not guaranteed to work if the scale is not 1.

use vek::vec::repr_c::Vec3;
use vek::mat::repr_c::row_major::Mat4 as Rows4;
use vek::mat::repr_c::column_major::Mat4 as Cols4;
use std::f32::consts::PI;

let a = Rows4::rotation_3d(PI*4./5., Vec3::new(5., 8., 10.))
    .translated_3d(Vec3::new(1., 2., 3.));
let b = a.inverted_affine_transform_no_scale();
assert_relative_eq!(a*b, Rows4::identity(), epsilon = 0.000001);
assert_relative_eq!(b*a, Rows4::identity(), epsilon = 0.000001);

let a = Cols4::rotation_3d(PI*4./5., Vec3::new(5., 8., 10.))
    .translated_3d(Vec3::new(1., 2., 3.));
let b = a.inverted_affine_transform_no_scale();
assert_relative_eq!(a*b, Cols4::identity(), epsilon = 0.000001);
assert_relative_eq!(b*a, Cols4::identity(), epsilon = 0.000001);

// Look! It stops working as soon as we add a scale.
// Notice that we assert _inequality_ below.
let a = Rows4::scaling_3d(5_f32)
    .rotated_3d(PI*4./5., Vec3::new(5., 8., 10.))
    .translated_3d(Vec3::new(1., 2., 3.));
let b = a.inverted_affine_transform_no_scale();
assert_relative_ne!(a*b, Rows4::identity(), epsilon = 0.000001);
assert_relative_ne!(b*a, Rows4::identity(), epsilon = 0.000001);

pub fn invert_affine_transform(&mut self) where
    T: Real, 

Inverts this matrix, blindly assuming that it is an invertible transform matrix. See inverted_affine_transform() for more info.

pub fn inverted_affine_transform(self) -> Self where
    T: Real, 

Returns this matrix's inverse, blindly assuming that it is an invertible transform matrix.

A transform matrix is invertible this way as long as it consists of translations, rotations, scales and shears.

use vek::vec::repr_c::Vec3;
use vek::mat::repr_c::row_major::Mat4 as Rows4;
use vek::mat::repr_c::column_major::Mat4 as Cols4;
use std::f32::consts::PI;

let a = Rows4::scaling_3d(1.77_f32)
    .rotated_3d(PI*4./5., Vec3::new(5., 8., 10.))
    .translated_3d(Vec3::new(1., 2., 3.));
let b = a.inverted_affine_transform();
assert_relative_eq!(a*b, Rows4::identity(), epsilon = 0.000001);
assert_relative_eq!(b*a, Rows4::identity(), epsilon = 0.000001);

let a = Cols4::scaling_3d(1.77_f32)
    .rotated_3d(PI*4./5., Vec3::new(5., 8., 10.))
    .translated_3d(Vec3::new(1., 2., 3.));
let b = a.inverted_affine_transform();
assert_relative_eq!(a*b, Cols4::identity(), epsilon = 0.000001);
assert_relative_eq!(b*a, Cols4::identity(), epsilon = 0.000001);

pub fn mul_point<V: Into<Vec3<T>> + From<Vec4<T>>>(self, rhs: V) -> V where
    T: Real + MulAdd<T, T, Output = T>, 

Shortcut for self * Vec4::from_point(rhs).

pub fn mul_direction<V: Into<Vec3<T>> + From<Vec4<T>>>(self, rhs: V) -> V where
    T: Real + MulAdd<T, T, Output = T>, 

Shortcut for self * Vec4::from_direction(rhs).

pub fn translate_2d<V: Into<Vec2<T>>>(&mut self, v: V) where
    T: Real + MulAdd<T, T, Output = T>, 

Translates this matrix in 2D.

pub fn translated_2d<V: Into<Vec2<T>>>(self, v: V) -> Self where
    T: Real + MulAdd<T, T, Output = T>, 

Returns this matrix translated in 2D.

pub fn translation_2d<V: Into<Vec2<T>>>(v: V) -> Self where
    T: Zero + One, 

Creates a 2D translation matrix.

pub fn translate_3d<V: Into<Vec3<T>>>(&mut self, v: V) where
    T: Real + MulAdd<T, T, Output = T>, 

Translates this matrix in 3D.

pub fn translated_3d<V: Into<Vec3<T>>>(self, v: V) -> Self where
    T: Real + MulAdd<T, T, Output = T>, 

Returns this matrix translated in 3D.

pub fn translation_3d<V: Into<Vec3<T>>>(v: V) -> Self where
    T: Zero + One, 

Creates a 3D translation matrix.

pub fn scale_3d<V: Into<Vec3<T>>>(&mut self, v: V) where
    T: Real + MulAdd<T, T, Output = T>, 

Scales this matrix in 3D.

pub fn scaled_3d<V: Into<Vec3<T>>>(self, v: V) -> Self where
    T: Real + MulAdd<T, T, Output = T>, 

Returns this matrix scaled in 3D.

pub fn scaling_3d<V: Into<Vec3<T>>>(v: V) -> Self where
    T: Zero + One, 

Creates a 3D scaling matrix.

pub fn rotate_x(&mut self, angle_radians: T) where
    T: Real + MulAdd<T, T, Output = T>, 

Rotates this matrix around the X axis.

pub fn rotated_x(self, angle_radians: T) -> Self where
    T: Real + MulAdd<T, T, Output = T>, 

Returns this matrix rotated around the X axis.

pub fn rotation_x(angle_radians: T) -> Self where
    T: Real, 

Creates a matrix that rotates around the X axis.

pub fn rotate_y(&mut self, angle_radians: T) where
    T: Real + MulAdd<T, T, Output = T>, 

Rotates this matrix around the Y axis.

pub fn rotated_y(self, angle_radians: T) -> Self where
    T: Real + MulAdd<T, T, Output = T>, 

Returns this matrix rotated around the Y axis.

pub fn rotation_y(angle_radians: T) -> Self where
    T: Real, 

Creates a matrix that rotates around the Y axis.

pub fn rotate_z(&mut self, angle_radians: T) where
    T: Real + MulAdd<T, T, Output = T>, 

Rotates this matrix around the Z axis.

pub fn rotated_z(self, angle_radians: T) -> Self where
    T: Real + MulAdd<T, T, Output = T>, 

Returns this matrix rotated around the Z axis.

pub fn rotation_z(angle_radians: T) -> Self where
    T: Real, 

Creates a matrix that rotates around the Z axis.

pub fn rotate_3d<V: Into<Vec3<T>>>(&mut self, angle_radians: T, axis: V) where
    T: Real + MulAdd<T, T, Output = T> + Add<T, Output = T>, 

Rotates this matrix around a 3D axis. The axis is not required to be normalized.

pub fn rotated_3d<V: Into<Vec3<T>>>(self, angle_radians: T, axis: V) -> Self where
    T: Real + MulAdd<T, T, Output = T> + Add<T, Output = T>, 

Returns this matrix rotated around a 3D axis. The axis is not required to be normalized.

pub fn rotation_3d<V: Into<Vec3<T>>>(angle_radians: T, axis: V) -> Self where
    T: Real + Add<T, Output = T>, 

Creates a matrix that rotates around a 3D axis. The axis is not required to be normalized.

use std::f32::consts::PI;

let v = Vec4::unit_x();

let m = Mat4::rotation_z(PI);
assert_relative_eq!(m * v, -v);

let m = Mat4::rotation_z(PI * 0.5);
assert_relative_eq!(m * v, Vec4::unit_y());

let m = Mat4::rotation_z(PI * 1.5);
assert_relative_eq!(m * v, -Vec4::unit_y());

let angles = 32;
for i in 0..angles {
    let theta = PI * 2. * (i as f32) / (angles as f32);

    // See what rotating unit vectors do for most angles between 0 and 2*PI.
    // It's helpful to picture this as a right-handed coordinate system.

    let v = Vec4::unit_y();
    let m = Mat4::rotation_x(theta);
    assert_relative_eq!(m * v, Vec4::new(0., theta.cos(), theta.sin(), 0.));

    let v = Vec4::unit_z();
    let m = Mat4::rotation_y(theta);
    assert_relative_eq!(m * v, Vec4::new(theta.sin(), 0., theta.cos(), 0.));

    let v = Vec4::unit_x();
    let m = Mat4::rotation_z(theta);
    assert_relative_eq!(m * v, Vec4::new(theta.cos(), theta.sin(), 0., 0.));

    assert_relative_eq!(Mat4::rotation_x(theta), Mat4::rotation_3d(theta, Vec4::unit_x()));
    assert_relative_eq!(Mat4::rotation_y(theta), Mat4::rotation_3d(theta, Vec4::unit_y()));
    assert_relative_eq!(Mat4::rotation_z(theta), Mat4::rotation_3d(theta, Vec4::unit_z()));
}

pub fn rotation_from_to_3d<V: Into<Vec3<T>>>(from: V, to: V) -> Self where
    T: Real + Add<T, Output = T>, 

Creates a matrix that would rotate a from direction to to.

let (from, to) = (Vec4::<f32>::unit_x(), Vec4::<f32>::unit_z());
let m = Mat4::<f32>::rotation_from_to_3d(from, to);
assert_relative_eq!(m * from, to);

let (from, to) = (Vec4::<f32>::unit_x(), -Vec4::<f32>::unit_x());
let m = Mat4::<f32>::rotation_from_to_3d(from, to);
assert_relative_eq!(m * from, to);

pub fn basis_to_local<V: Into<Vec3<T>>>(origin: V, i: V, j: V, k: V) -> Self where
    T: Zero + One + Neg<Output = T> + Real + Add<T, Output = T>, 

Builds a change of basis matrix that transforms points and directions from any space to the canonical one.

origin is the origin of the child space. i, j and k are all required to be normalized; They are the unit basis vector along the target space x-axis, y-axis and z-axis respectively, expressed in canonical-space coordinates.

    let origin = Vec3::new(1_f32, 2., 3.);
    let i = Vec3::unit_z();
    let j = Vec3::unit_y();
    let k = Vec3::unit_x();
    let m = Mat4::basis_to_local(origin, i, j, k);
    assert_relative_eq!(m.mul_point(origin), Vec3::zero());
    assert_relative_eq!(m.mul_point(origin+i), Vec3::unit_x());
    assert_relative_eq!(m.mul_point(origin+j), Vec3::unit_y());
    assert_relative_eq!(m.mul_point(origin+k), Vec3::unit_z());

    // `local_to_basis` and `basis_to_local` undo each other
    let a = Mat4::<f32>::basis_to_local(origin, i, j, k);
    let b = Mat4::<f32>::local_to_basis(origin, i, j, k);
    assert_relative_eq!(a*b, Mat4::identity());
    assert_relative_eq!(b*a, Mat4::identity());

Slightly more contrived example:

    let origin = Vec3::new(1_f32, 2., 3.);
    let r = Mat4::rotation_3d(3., Vec3::new(2_f32, 1., 3.));
    let i = r.mul_direction(Vec3::unit_x());
    let j = r.mul_direction(Vec3::unit_y());
    let k = r.mul_direction(Vec3::unit_z());
    let m = Mat4::basis_to_local(origin, i, j, k);
    assert_relative_eq!(m.mul_point(origin), Vec3::zero(), epsilon = 0.000001);
    assert_relative_eq!(m.mul_point(origin+i), Vec3::unit_x(), epsilon = 0.000001);
    assert_relative_eq!(m.mul_point(origin+j), Vec3::unit_y(), epsilon = 0.000001);
    assert_relative_eq!(m.mul_point(origin+k), Vec3::unit_z(), epsilon = 0.000001);

pub fn local_to_basis<V: Into<Vec3<T>>>(origin: V, i: V, j: V, k: V) -> Self where
    T: Zero + One, 

Builds a change of basis matrix that transforms points and directions from canonical space to another space.

origin is the origin of the child space. i, j and k are all required to be normalized; They are the unit basis vector along the target space x-axis, y-axis and z-axis respectively, expressed in canonical-space coordinates.

    let origin = Vec3::new(1_f32, 2., 3.);
    let i = Vec3::unit_z();
    let j = Vec3::unit_y();
    let k = Vec3::unit_x();
    let m = Mat4::local_to_basis(origin, i, j, k);
    assert_relative_eq!(origin,   m.mul_point(Vec3::zero()));
    assert_relative_eq!(origin+i, m.mul_point(Vec3::unit_x()));
    assert_relative_eq!(origin+j, m.mul_point(Vec3::unit_y()));
    assert_relative_eq!(origin+k, m.mul_point(Vec3::unit_z()));

    // `local_to_basis` and `basis_to_local` undo each other
    let a = Mat4::<f32>::local_to_basis(origin, i, j, k);
    let b = Mat4::<f32>::basis_to_local(origin, i, j, k);
    assert_relative_eq!(a*b, Mat4::identity());
    assert_relative_eq!(b*a, Mat4::identity());

Slightly more contrived example:

    // Sanity test
    let origin = Vec3::new(1_f32, 2., 3.);
    let r = Mat4::rotation_3d(3., Vec3::new(2_f32, 1., 3.));
    let i = r.mul_direction(Vec3::unit_x());
    let j = r.mul_direction(Vec3::unit_y());
    let k = r.mul_direction(Vec3::unit_z());
    let m = Mat4::local_to_basis(origin, i, j, k);
    assert_relative_eq!(origin,   m.mul_point(Vec3::zero()));
    assert_relative_eq!(origin+i, m.mul_point(Vec3::unit_x()));
    assert_relative_eq!(origin+j, m.mul_point(Vec3::unit_y()));
    assert_relative_eq!(origin+k, m.mul_point(Vec3::unit_z()));

pub fn look_at<V: Into<Vec3<T>>>(eye: V, target: V, up: V) -> Self where
    T: Real + Add<T, Output = T>, 

👎 Deprecated since 0.9.7:

Use look_at_lh() or look_at_rh() instead depending on your space's handedness

Builds a "look at" view transform from an eye position, a target position, and up vector. Commonly used for cameras - in short, it maps points from world-space to eye-space.

pub fn look_at_lh<V: Into<Vec3<T>>>(eye: V, target: V, up: V) -> Self where
    T: Real + Add<T, Output = T>, 

Builds a "look at" view transform for left-handed spaces from an eye position, a target position, and up vector. Commonly used for cameras - in short, it maps points from world-space to eye-space.

let eye = Vec4::new(1_f32, 0., 1., 1.);
let target = Vec4::new(2_f32, 0., 2., 1.);
let view = Mat4::<f32>::look_at_lh(eye, target, Vec4::up());
assert_relative_eq!(view * eye, Vec4::unit_w());
assert_relative_eq!(view * target, Vec4::new(0_f32, 0., 2_f32.sqrt(), 1.));

pub fn look_at_rh<V: Into<Vec3<T>>>(eye: V, target: V, up: V) -> Self where
    T: Real + Add<T, Output = T>, 

Builds a "look at" view transform for right-handed spaces from an eye position, a target position, and up vector. Commonly used for cameras - in short, it maps points from world-space to eye-space.

let eye = Vec4::new(1_f32, 0., 1., 1.);
let target = Vec4::new(2_f32, 0., 2., 1.);
let view = Mat4::<f32>::look_at_rh(eye, target, Vec4::up());
assert_relative_eq!(view * eye, Vec4::unit_w());
assert_relative_eq!(view * target, Vec4::new(0_f32, 0., -2_f32.sqrt(), 1.));

pub fn model_look_at<V: Into<Vec3<T>>>(eye: V, target: V, up: V) -> Self where
    T: Real + Add<T, Output = T>, 

👎 Deprecated since 0.9.7:

Use model_look_at_lh() or model_look_at_rh() instead depending on your space's handedness

Builds a "look at" model transform from an eye position, a target position, and up vector. Preferred for transforming objects.

pub fn model_look_at_lh<V: Into<Vec3<T>>>(eye: V, target: V, up: V) -> Self where
    T: Real + Add<T, Output = T>, 

Builds a "look at" model transform for left-handed spaces from an eye position, a target position, and up vector. Preferred for transforming objects.

let eye = Vec4::new(1_f32, 0., 1., 1.);
let target = Vec4::new(2_f32, 0., 2., 1.);
let model = Mat4::<f32>::model_look_at_lh(eye, target, Vec4::up());
assert_relative_eq!(model * Vec4::unit_w(), eye);
let d = 2_f32.sqrt();
assert_relative_eq!(model * Vec4::new(0_f32, 0., d, 1.), target);

// A "model" look-at essentially undoes a "view" look-at
let view = Mat4::look_at_lh(eye, target, Vec4::up());
assert_relative_eq!(view * model, Mat4::identity());
assert_relative_eq!(model * view, Mat4::identity());

pub fn model_look_at_rh<V: Into<Vec3<T>>>(eye: V, target: V, up: V) -> Self where
    T: Real + Add<T, Output = T> + MulAdd<T, T, Output = T>, 

Builds a "look at" model transform for right-handed spaces from an eye position, a target position, and up vector. Preferred for transforming objects.

let eye = Vec4::new(1_f32, 0., -1., 1.);
let forward = Vec4::new(0_f32, 0., -1., 0.);
let model = Mat4::<f32>::model_look_at_rh(eye, eye + forward, Vec4::up());
assert_relative_eq!(model * Vec4::unit_w(), eye);
assert_relative_eq!(model * forward, forward);

// A "model" look-at essentially undoes a "view" look-at
let view = Mat4::look_at_rh(eye, eye + forward, Vec4::up());
assert_relative_eq!(view * model, Mat4::identity());
assert_relative_eq!(model * view, Mat4::identity());

pub fn orthographic_without_depth_planes(o: FrustumPlanes<T>) -> Self where
    T: Real, 

Returns an orthographic projection matrix that doesn't use near and far planes.

pub fn orthographic_lh_zo(o: FrustumPlanes<T>) -> Self where
    T: Real, 

Returns an orthographic projection matrix for left-handed spaces, for a depth clip space ranging from 0 to 1 (GL_DEPTH_ZERO_TO_ONE, hence the _zo suffix).

let m = Mat4::orthographic_lh_zo(FrustumPlanes {
    left: -1_f32, right: 1., bottom: -1., top: 1.,
    near: 0., far: 1.
});
let v = Vec4::new(0_f32, 0., 1., 1.); // "forward"
assert_relative_eq!(m * v, Vec4::new(0., 0., 1., 1.)); // "far"

pub fn orthographic_lh_no(o: FrustumPlanes<T>) -> Self where
    T: Real, 

Returns an orthographic projection matrix for left-handed spaces, for a depth clip space ranging from -1 to 1 (GL_DEPTH_NEGATIVE_ONE_TO_ONE, hence the _no suffix).

let m = Mat4::orthographic_lh_no(FrustumPlanes {
    left: -1_f32, right: 1., bottom: -1., top: 1.,
    near: 0., far: 1.
});
let v = Vec4::new(0_f32, 0., 1., 1.); // "forward"
assert_relative_eq!(m * v, Vec4::new(0., 0., 1., 1.)); // "far"

pub fn orthographic_rh_zo(o: FrustumPlanes<T>) -> Self where
    T: Real, 

Returns an orthographic projection matrix for right-handed spaces, for a depth clip space ranging from 0 to 1 (GL_DEPTH_ZERO_TO_ONE, hence the _zo suffix).

let m = Mat4::orthographic_rh_zo(FrustumPlanes {
    left: -1_f32, right: 1., bottom: -1., top: 1.,
    near: 0., far: 1.
});
let v = Vec4::new(0_f32, 0., -1., 1.); // "forward"
assert_relative_eq!(m * v, Vec4::new(0., 0., 1., 1.)); // "far"

pub fn orthographic_rh_no(o: FrustumPlanes<T>) -> Self where
    T: Real, 

Returns an orthographic projection matrix for right-handed spaces, for a depth clip space ranging from -1 to 1 (GL_DEPTH_NEGATIVE_ONE_TO_ONE, hence the _no suffix).

let m = Mat4::orthographic_rh_no(FrustumPlanes {
    left: -1_f32, right: 1., bottom: -1., top: 1.,
    near: 0., far: 1.
});
let v = Vec4::new(0_f32, 0., -1., 1.); // "forward"
assert_relative_eq!(m * v, Vec4::new(0., 0., 1., 1.)); // "far"

pub fn frustum_lh_zo(o: FrustumPlanes<T>) -> Self where
    T: Real, 

Creates a perspective projection matrix from a frustum (left-handed, zero-to-one depth clip planes).

pub fn frustum_lh_no(o: FrustumPlanes<T>) -> Self where
    T: Real, 

Creates a perspective projection matrix from a frustum (left-handed, negative-one-to-one depth clip planes).

pub fn frustum_rh_zo(o: FrustumPlanes<T>) -> Self where
    T: Real, 

Creates a perspective projection matrix from a frustum (right-handed, zero-to-one depth clip planes).

pub fn frustum_rh_no(o: FrustumPlanes<T>) -> Self where
    T: Real, 

Creates a perspective projection matrix from a frustum (right-handed, negative-one-to-one depth clip planes).

pub fn perspective_rh_zo(
    fov_y_radians: T,
    aspect_ratio: T,
    near: T,
    far: T
) -> Self where
    T: Real + FloatConst + Debug, 

Creates a perspective projection matrix for right-handed spaces, with zero-to-one depth clip planes.

pub fn perspective_lh_zo(
    fov_y_radians: T,
    aspect_ratio: T,
    near: T,
    far: T
) -> Self where
    T: Real + FloatConst + Debug, 

Creates a perspective projection matrix for left-handed spaces, with zero-to-one depth clip planes.

pub fn perspective_rh_no(
    fov_y_radians: T,
    aspect_ratio: T,
    near: T,
    far: T
) -> Self where
    T: Real + FloatConst + Debug, 

Creates a perspective projection matrix for right-handed spaces, with negative-one-to-one depth clip planes.

pub fn perspective_lh_no(
    fov_y_radians: T,
    aspect_ratio: T,
    near: T,
    far: T
) -> Self where
    T: Real + FloatConst + Debug, 

Creates a perspective projection matrix for left-handed spaces, with negative-one-to-one depth clip planes.

pub fn perspective_fov_rh_zo(
    fov_y_radians: T,
    width: T,
    height: T,
    near: T,
    far: T
) -> Self where
    T: Real + FloatConst + Debug, 

Creates a perspective projection matrix for right-handed spaces, with zero-to-one depth clip planes.

Panics

width, height and fov_y_radians must all be strictly greater than zero.

pub fn perspective_fov_lh_zo(
    fov_y_radians: T,
    width: T,
    height: T,
    near: T,
    far: T
) -> Self where
    T: Real + FloatConst + Debug, 

Creates a perspective projection matrix for left-handed spaces, with zero-to-one depth clip planes.

Panics

width, height and fov_y_radians must all be strictly greater than zero.

pub fn perspective_fov_rh_no(
    fov_y_radians: T,
    width: T,
    height: T,
    near: T,
    far: T
) -> Self where
    T: Real + FloatConst + Debug, 

Creates a perspective projection matrix for right-handed spaces, with negative-one-to-one depth clip planes.

Panics

width, height and fov_y_radians must all be strictly greater than zero.

pub fn perspective_fov_lh_no(
    fov_y_radians: T,
    width: T,
    height: T,
    near: T,
    far: T
) -> Self where
    T: Real + FloatConst + Debug, 

Creates a perspective projection matrix for left-handed spaces, with negative-one-to-one depth clip planes.

Panics

width, height and fov_y_radians must all be strictly greater than zero.

pub fn tweaked_infinite_perspective_rh(
    fov_y_radians: T,
    aspect_ratio: T,
    near: T,
    epsilon: T
) -> Self where
    T: Real + FloatConst + Debug, 

Creates an infinite perspective projection matrix for right-handed spaces.

Link to PDF

pub fn tweaked_infinite_perspective_lh(
    fov_y_radians: T,
    aspect_ratio: T,
    near: T,
    epsilon: T
) -> Self where
    T: Real + FloatConst + Debug, 

Creates an infinite perspective projection matrix for left-handed spaces.

pub fn infinite_perspective_rh(
    fov_y_radians: T,
    aspect_ratio: T,
    near: T
) -> Self where
    T: Real + FloatConst + Debug, 

Creates an infinite perspective projection matrix for right-handed spaces.

pub fn infinite_perspective_lh(
    fov_y_radians: T,
    aspect_ratio: T,
    near: T
) -> Self where
    T: Real + FloatConst + Debug, 

Creates an infinite perspective projection matrix for left-handed spaces.

pub fn picking_region<V2: Into<Vec2<T>>>(
    center: V2,
    delta: V2,
    viewport: Rect<T, T>
) -> Self where
    T: Real + MulAdd<T, T, Output = T>, 

GLM's pickMatrix. Creates a projection matrix that can be used to restrict drawing to a small region of the viewport.

Panics

delta's x and y are required to be strictly greater than zero.

pub fn world_to_viewport_no<V3>(
    obj: V3,
    modelview: Self,
    proj: Self,
    viewport: Rect<T, T>
) -> Vec3<T> where
    T: Real + MulAdd<T, T, Output = T>,
    V3: Into<Vec3<T>>, 

Projects a world-space coordinate into screen space, for a depth clip space ranging from -1 to 1 (GL_DEPTH_NEGATIVE_ONE_TO_ONE, hence the _no suffix).

pub fn world_to_viewport_zo<V3>(
    obj: V3,
    modelview: Self,
    proj: Self,
    viewport: Rect<T, T>
) -> Vec3<T> where
    T: Real + MulAdd<T, T, Output = T>,
    V3: Into<Vec3<T>>, 

Projects a world-space coordinate into screen space, for a depth clip space ranging from 0 to 1 (GL_DEPTH_ZERO_TO_ONE, hence the _zo suffix).

pub fn viewport_to_world_zo<V3>(
    ray: V3,
    modelview: Self,
    proj: Self,
    viewport: Rect<T, T>
) -> Vec3<T> where
    T: Real + MulAdd<T, T, Output = T>,
    V3: Into<Vec3<T>>, 

Projects a screen-space coordinate into world space, for a depth clip space ranging from 0 to 1 (GL_DEPTH_ZERO_TO_ONE, hence the _zo suffix).

pub fn viewport_to_world_no<V3>(
    ray: V3,
    modelview: Self,
    proj: Self,
    viewport: Rect<T, T>
) -> Vec3<T> where
    T: Real + MulAdd<T, T, Output = T>,
    V3: Into<Vec3<T>>, 

Projects a screen-space coordinate into world space, for a depth clip space ranging from -1 to 1 (GL_DEPTH_NEGATIVE_ONE_TO_ONE, hence the _no suffix).

Trait Implementations

impl<T: AbsDiffEq> AbsDiffEq<Mat4<T>> for Mat4<T> where
    T::Epsilon: Copy, 

type Epsilon = T::Epsilon

Used for specifying relative comparisons.

pub fn default_epsilon() -> T::Epsilon

The default tolerance to use when testing values that are close together.

pub fn abs_diff_eq(&self, other: &Self, epsilon: Self::Epsilon) -> bool

A test for equality that uses the absolute difference to compute the approximate equality of two numbers.

pub fn abs_diff_ne(&self, other: &Rhs, epsilon: Self::Epsilon) -> bool

The inverse of AbsDiffEq::abs_diff_eq.

impl<T> Add<Mat4<T>> for Mat4<T> where
    T: Add<Output = T>, 

type Output = Self

The resulting type after applying the + operator.

pub fn add(self, rhs: Self) -> Self::Output

Performs the + operation.

impl<T> Add<T> for Mat4<T> where
    T: Copy + Add<Output = T>, 

type Output = Self

The resulting type after applying the + operator.

pub fn add(self, rhs: T) -> Self::Output

Performs the + operation.

impl<T: Add<Output = T> + Copy> AddAssign<Mat4<T>> for Mat4<T>

pub fn add_assign(&mut self, rhs: Self)

Performs the += operation.

impl<T: Add<Output = T> + Copy> AddAssign<T> for Mat4<T>

pub fn add_assign(&mut self, rhs: T)

Performs the += operation.

impl<T: Clone> Clone for Mat4<T>

pub fn clone(&self) -> Mat4<T>

Returns a copy of the value.

pub fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<T: Copy> Copy for Mat4<T>

impl<T: Debug> Debug for Mat4<T>

pub fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<T: Zero + One> Default for Mat4<T>

The default value for a square matrix is the identity.

assert_eq!(Mat4::<f32>::default(), Mat4::<f32>::identity());

pub fn default() -> Self

Returns the "default value" for a type.

impl<'de, T> Deserialize<'de> for Mat4<T> where
    T: Deserialize<'de>, 

pub fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error> where
    __D: Deserializer<'de>, 

Deserialize this value from the given Serde deserializer.

impl<T: Display> Display for Mat4<T>

Displays this matrix using the following format:

(i being the number of rows and j the number of columns)

( m00 ... m0j
  ... ... ...
  mi0 ... mij )

Note that elements are not comma-separated. This format doesn't depend on the matrix's storage layout.

pub fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<T> Div<Mat4<T>> for Mat4<T> where
    T: Div<Output = T>, 

type Output = Self

The resulting type after applying the / operator.

pub fn div(self, rhs: Self) -> Self::Output

Performs the / operation.

impl<T> Div<T> for Mat4<T> where
    T: Copy + Div<Output = T>, 

type Output = Self

The resulting type after applying the / operator.

pub fn div(self, rhs: T) -> Self::Output

Performs the / operation.

impl<T: Div<Output = T> + Copy> DivAssign<Mat4<T>> for Mat4<T>

pub fn div_assign(&mut self, rhs: Self)

Performs the /= operation.

impl<T: Div<Output = T> + Copy> DivAssign<T> for Mat4<T>

pub fn div_assign(&mut self, rhs: T)

Performs the /= operation.

impl<T: Eq> Eq for Mat4<T>

impl<T> From<Mat2<T>> for Mat4<T> where
    T: Zero + One, 

pub fn from(m: Mat2<T>) -> Self

Performs the conversion.

impl<T> From<Mat3<T>> for Mat4<T> where
    T: Zero + One, 

pub fn from(m: Mat3<T>) -> Self

Performs the conversion.

impl<T> From<Mat4<T>> for Mat4<T>

pub fn from(m: Transpose<T>) -> Self

Performs the conversion.

impl<T> From<Mat4<T>> for Mat3<T>

pub fn from(m: Mat4<T>) -> Self

Performs the conversion.

impl<T> From<Mat4<T>> for Mat2<T>

pub fn from(m: Mat4<T>) -> Self

Performs the conversion.

impl<T> From<Mat4<T>> for Mat4<T>

pub fn from(m: Transpose<T>) -> Self

Performs the conversion.

impl<T> From<Quaternion<T>> for Mat4<T> where
    T: Copy + Zero + One + Mul<Output = T> + Add<Output = T> + Sub<Output = T>, 

Rotation matrices can be obtained from quaternions. This implementation only works properly if the quaternion is normalized.

use std::f32::consts::PI;

let angles = 32;
for i in 0..angles {
    let theta = PI * 2. * (i as f32) / (angles as f32);

    assert_relative_eq!(Mat4::rotation_x(theta), Mat4::from(Quaternion::rotation_x(theta)), epsilon = 0.000001);
    assert_relative_eq!(Mat4::rotation_y(theta), Mat4::from(Quaternion::rotation_y(theta)), epsilon = 0.000001);
    assert_relative_eq!(Mat4::rotation_z(theta), Mat4::from(Quaternion::rotation_z(theta)), epsilon = 0.000001);

    assert_relative_eq!(Mat4::rotation_x(theta), Mat4::rotation_3d(theta, Vec4::unit_x()));
    assert_relative_eq!(Mat4::rotation_y(theta), Mat4::rotation_3d(theta, Vec4::unit_y()));
    assert_relative_eq!(Mat4::rotation_z(theta), Mat4::rotation_3d(theta, Vec4::unit_z()));

    // See what rotating unit vectors do for most angles between 0 and 2*PI.
    // It's helpful to picture this as a right-handed coordinate system.

    let v = Vec4::unit_y();
    let m = Mat4::rotation_x(theta);
    assert_relative_eq!(m * v, Vec4::new(0., theta.cos(), theta.sin(), 0.));

    let v = Vec4::unit_z();
    let m = Mat4::rotation_y(theta);
    assert_relative_eq!(m * v, Vec4::new(theta.sin(), 0., theta.cos(), 0.));

    let v = Vec4::unit_x();
    let m = Mat4::rotation_z(theta);
    assert_relative_eq!(m * v, Vec4::new(theta.cos(), theta.sin(), 0., 0.));
}

pub fn from(q: Quaternion<T>) -> Self

Performs the conversion.

impl<T> From<Transform<T, T, T>> for Mat4<T> where
    T: Real + MulAdd<T, T, Output = T>, 

A Mat4 can be obtained from a Transform, by rotating, then scaling, then translating.

pub fn from(xform: Transform<T, T, T>) -> Self

Performs the conversion.

impl<T: Hash> Hash for Mat4<T>

pub fn hash<__H: Hasher>(&self, state: &mut __H)

Feeds this value into the given Hasher.

pub fn hash_slice<H>(data: &[Self], state: &mut H) where
    H: Hasher, 

Feeds a slice of this type into the given Hasher.

impl<T> Index<(usize, usize)> for Mat4<T>

Index this matrix in a layout-agnostic way with an (i, j) (row index, column index) tuple.

Matrices cannot be indexed by Vec2s because that would be likely to cause confusion: should x be the row index (because it's the first element) or the column index (because it's a horizontal position) ?

type Output = T

The returned type after indexing.

pub fn index(&self, t: (usize, usize)) -> &Self::Output

Performs the indexing (container[index]) operation.

impl<T> IndexMut<(usize, usize)> for Mat4<T>

pub fn index_mut(&mut self, t: (usize, usize)) -> &mut Self::Output

Performs the mutable indexing (container[index]) operation.

impl<T> Mul<CubicBezier3<T>> for Cols4<T> where
    T: Real + MulAdd<T, T, Output = T>, 

type Output = CubicBezier3<T>

The resulting type after applying the * operator.

pub fn mul(self, rhs: CubicBezier3<T>) -> CubicBezier3<T>

Performs the * operation.

impl<T: MulAdd<T, T, Output = T> + Mul<Output = T> + Copy> Mul<Mat4<T>> for Vec4<T>

Multiplies a row vector with a column-major matrix, giving a row vector.

use vek::mat::column_major::Mat4;
use vek::vec::Vec4;

let m = Mat4::new(
    0, 1, 2, 3,
    4, 5, 6, 7,
    8, 9, 0, 1,
    2, 3, 4, 5
);
let v = Vec4::new(0, 1, 2, 3);
let r = Vec4::new(26, 32, 18, 24);
assert_eq!(v * m, r);

type Output = Self

The resulting type after applying the * operator.

pub fn mul(self, rhs: Mat4<T>) -> Self::Output

Performs the * operation.

impl<T: MulAdd<T, T, Output = T> + Mul<Output = T> + Copy> Mul<Mat4<T>> for Mat4<T>

Multiplies a column-major matrix with another.

use vek::mat::column_major::Mat4;

let m = Mat4::<u32>::new(
    0, 1, 2, 3,
    4, 5, 6, 7,
    8, 9, 0, 1,
    2, 3, 4, 5
);
let r = Mat4::<u32>::new(
    26, 32, 18, 24,
    82, 104, 66, 88,
    38, 56, 74, 92,
    54, 68, 42, 56
);
assert_eq!(m * m, r);
assert_eq!(m, m * Mat4::<u32>::identity());
assert_eq!(m, Mat4::<u32>::identity() * m);

type Output = Self

The resulting type after applying the * operator.

pub fn mul(self, rhs: Self) -> Self::Output

Performs the * operation.

impl<T: MulAdd<T, T, Output = T> + Mul<Output = T> + Copy> Mul<Mat4<T>> for Mat4<T>

Multiplies a column-major matrix with a row-major matrix.

use vek::mat::row_major::Mat4 as Rows4;
use vek::mat::column_major::Mat4 as Cols4;

let m = Cols4::<u32>::new(
    0, 1, 2, 3,
    4, 5, 6, 7,
    8, 9, 0, 1,
    2, 3, 4, 5
);
let b = Rows4::from(m);
let r = Rows4::<u32>::new(
    26, 32, 18, 24,
    82, 104, 66, 88,
    38, 56, 74, 92,
    54, 68, 42, 56
);
assert_eq!(m * b, r);
assert_eq!(m * Rows4::<u32>::identity(), m.into());
assert_eq!(Cols4::<u32>::identity() * b, m.into());

type Output = Transpose<T>

The resulting type after applying the * operator.

pub fn mul(self, rhs: Transpose<T>) -> Self::Output

Performs the * operation.

impl<T: MulAdd<T, T, Output = T> + Mul<Output = T> + Copy> Mul<Mat4<T>> for Mat4<T>

Multiplies a row-major matrix with a column-major matrix, producing a column-major matrix.

use vek::mat::row_major::Mat4 as Rows4;
use vek::mat::column_major::Mat4 as Cols4;

let m = Rows4::<u32>::new(
    0, 1, 2, 3,
    4, 5, 6, 7,
    8, 9, 0, 1,
    2, 3, 4, 5
);
let b = Cols4::from(m);
let r = Cols4::<u32>::new(
    26, 32, 18, 24,
    82, 104, 66, 88,
    38, 56, 74, 92,
    54, 68, 42, 56
);
assert_eq!(m * b, r);
assert_eq!(m * Cols4::<u32>::identity(), m.into());
assert_eq!(Rows4::<u32>::identity() * b, m.into());

type Output = Transpose<T>

The resulting type after applying the * operator.

pub fn mul(self, rhs: Transpose<T>) -> Self::Output

Performs the * operation.

impl<T> Mul<QuadraticBezier3<T>> for Cols4<T> where
    T: Real + MulAdd<T, T, Output = T>, 

type Output = QuadraticBezier3<T>

The resulting type after applying the * operator.

pub fn mul(self, rhs: QuadraticBezier3<T>) -> QuadraticBezier3<T>

Performs the * operation.

impl<T> Mul<T> for Mat4<T> where
    T: Copy + Zero + Add<Output = T> + Mul<Output = T>, 

type Output = Self

The resulting type after applying the * operator.

pub fn mul(self, rhs: T) -> Self::Output

Performs the * operation.

impl<T: MulAdd<T, T, Output = T> + Mul<Output = T> + Copy> Mul<Vec4<T>> for Mat4<T>

Multiplies a column-major matrix with a column vector, giving a column vector.

With SIMD vectors, this is the most efficient way.

use vek::mat::column_major::Mat4;
use vek::vec::Vec4;

let m = Mat4::new(
    0, 1, 2, 3,
    4, 5, 6, 7,
    8, 9, 0, 1,
    2, 3, 4, 5
);
let v = Vec4::new(0, 1, 2, 3);
let r = Vec4::new(14, 38, 12, 26);
assert_eq!(m * v, r);

type Output = Vec4<T>

The resulting type after applying the * operator.

pub fn mul(self, v: Vec4<T>) -> Self::Output

Performs the * operation.

impl<T> MulAssign<Mat4<T>> for Mat4<T> where
    T: Copy + Zero + Add<Output = T> + Mul<Output = T> + MulAdd<T, T, Output = T>, 

pub fn mul_assign(&mut self, rhs: Self)

Performs the *= operation.

impl<T> MulAssign<T> for Mat4<T> where
    T: Copy + Zero + Add<Output = T> + Mul<Output = T>, 

pub fn mul_assign(&mut self, rhs: T)

Performs the *= operation.

impl<T> Neg for Mat4<T> where
    T: Neg<Output = T>, 

type Output = Self

The resulting type after applying the - operator.

pub fn neg(self) -> Self::Output

Performs the unary - operation.

impl<T: Zero + One + Copy + MulAdd<T, T, Output = T>> One for Mat4<T>

pub fn one() -> Self

Returns the multiplicative identity element of Self, 1.

pub fn set_one(&mut self)

Sets self to the multiplicative identity element of Self, 1.

pub fn is_one(&self) -> bool where
    Self: PartialEq<Self>, 

Returns true if self is equal to the multiplicative identity.

impl<T: PartialEq> PartialEq<Mat4<T>> for Mat4<T>

pub fn eq(&self, other: &Mat4<T>) -> bool

This method tests for self and other values to be equal, and is used by ==.

pub fn ne(&self, other: &Mat4<T>) -> bool

This method tests for !=.

impl<T: RelativeEq> RelativeEq<Mat4<T>> for Mat4<T> where
    T::Epsilon: Copy, 

pub fn default_max_relative() -> T::Epsilon

The default relative tolerance for testing values that are far-apart.

pub fn relative_eq(
    &self,
    other: &Self,
    epsilon: T::Epsilon,
    max_relative: T::Epsilon
) -> bool

A test for equality that uses a relative comparison if the values are far apart.

pub fn relative_ne(
    &self,
    other: &Rhs,
    epsilon: Self::Epsilon,
    max_relative: Self::Epsilon
) -> bool

The inverse of RelativeEq::relative_eq.

impl<T> Rem<Mat4<T>> for Mat4<T> where
    T: Rem<Output = T>, 

type Output = Self

The resulting type after applying the % operator.

pub fn rem(self, rhs: Self) -> Self::Output

Performs the % operation.

impl<T> Rem<T> for Mat4<T> where
    T: Copy + Rem<Output = T>, 

type Output = Self

The resulting type after applying the % operator.

pub fn rem(self, rhs: T) -> Self::Output

Performs the % operation.

impl<T: Rem<Output = T> + Copy> RemAssign<Mat4<T>> for Mat4<T>

pub fn rem_assign(&mut self, rhs: Self)

Performs the %= operation.

impl<T: Rem<Output = T> + Copy> RemAssign<T> for Mat4<T>

pub fn rem_assign(&mut self, rhs: T)

Performs the %= operation.

impl<T> Serialize for Mat4<T> where
    T: Serialize, 

pub fn serialize<__S>(&self, __serializer: __S) -> Result<__S::Ok, __S::Error> where
    __S: Serializer, 

Serialize this value into the given Serde serializer.

impl<T> StructuralEq for Mat4<T>

impl<T> StructuralPartialEq for Mat4<T>

impl<T> Sub<Mat4<T>> for Mat4<T> where
    T: Sub<Output = T>, 

type Output = Self

The resulting type after applying the - operator.

pub fn sub(self, rhs: Self) -> Self::Output

Performs the - operation.

impl<T> Sub<T> for Mat4<T> where
    T: Copy + Sub<Output = T>, 

type Output = Self

The resulting type after applying the - operator.

pub fn sub(self, rhs: T) -> Self::Output

Performs the - operation.

impl<T: Sub<Output = T> + Copy> SubAssign<Mat4<T>> for Mat4<T>

pub fn sub_assign(&mut self, rhs: Self)

Performs the -= operation.

impl<T: Sub<Output = T> + Copy> SubAssign<T> for Mat4<T>

pub fn sub_assign(&mut self, rhs: T)

Performs the -= operation.

impl<T: UlpsEq> UlpsEq<Mat4<T>> for Mat4<T> where
    T::Epsilon: Copy, 

pub fn default_max_ulps() -> u32

The default ULPs to tolerate when testing values that are far-apart.

pub fn ulps_eq(&self, other: &Self, epsilon: T::Epsilon, max_ulps: u32) -> bool

A test for equality that uses units in the last place (ULP) if the values are far apart.

pub fn ulps_ne(
    &self,
    other: &Rhs,
    epsilon: Self::Epsilon,
    max_ulps: u32
) -> bool

The inverse of UlpsEq::ulps_eq.

impl<T: Zero + PartialEq> Zero for Mat4<T>

pub fn zero() -> Self

Returns the additive identity element of Self, 0.

pub fn is_zero(&self) -> bool

Returns true if self is equal to the additive identity.

pub fn set_zero(&mut self)

Sets self to the additive identity element of Self, 0.