Struct Mat4

#[repr(C)]
pub struct Mat4 {
    pub x_axis: Vec4,
    pub y_axis: Vec4,
    pub z_axis: Vec4,
    pub w_axis: Vec4,
}

A 4x4 column major matrix.

This 4x4 matrix type features convenience methods for creating and using affine transforms and perspective projections. If you are primarily dealing with 3D affine transformations considering using Affine3A which is faster than a 4x4 matrix for some affine operations.

Affine transformations including 3D translation, rotation and scale can be created using methods such as Self::from_translation(), Self::from_quat(), Self::from_scale() and Self::from_scale_rotation_translation().

Orthographic projections can be created using the methods Self::orthographic_lh() for left-handed coordinate systems and Self::orthographic_rh() for right-handed systems. The resulting matrix is also an affine transformation.

The Self::transform_point3() and Self::transform_vector3() convenience methods are provided for performing affine transformations on 3D vectors and points. These multiply 3D inputs as 4D vectors with an implicit w value of 1 for points and 0 for vectors respectively. These methods assume that Self contains a valid affine transform.

Perspective projections can be created using methods such as Self::perspective_lh(), Self::perspective_infinite_lh() and Self::perspective_infinite_reverse_lh() for left-handed co-ordinate systems and Self::perspective_rh(), Self::perspective_infinite_rh() and Self::perspective_infinite_reverse_rh() for right-handed co-ordinate systems.

The resulting perspective project can be use to transform 3D vectors as points with perspective correction using the Self::project_point3() convenience method.

Fields

x_axis: Vec4

y_axis: Vec4

z_axis: Vec4

w_axis: Vec4

Implementations

impl Mat4

pub const ZERO: Self = _

A 4x4 matrix with all elements set to 0.0.

pub const IDENTITY: Self = _

A 4x4 identity matrix, where all diagonal elements are 1, and all off-diagonal elements are 0.

pub const NAN: Self = _

All NAN:s.

pub const fn from_cols( x_axis: Vec4, y_axis: Vec4, z_axis: Vec4, w_axis: Vec4, ) -> Self

Creates a 4x4 matrix from four column vectors.

pub const fn from_cols_array(m: &[f32; 16]) -> Self

Creates a 4x4 matrix from a [f32; 16] array stored in column major order. If your data is stored in row major you will need to transpose the returned matrix.

pub const fn to_cols_array(&self) -> [f32; 16]

Creates a [f32; 16] array storing data in column major order. If you require data in row major order transpose the matrix first.

pub const fn from_cols_array_2d(m: &[[f32; 4]; 4]) -> Self

Creates a 4x4 matrix from a [[f32; 4]; 4] 4D array stored in column major order. If your data is in row major order you will need to transpose the returned matrix.

pub const fn to_cols_array_2d(&self) -> [[f32; 4]; 4]

Creates a [[f32; 4]; 4] 4D array storing data in column major order. If you require data in row major order transpose the matrix first.

pub const fn from_diagonal(diagonal: Vec4) -> Self

Creates a 4x4 matrix with its diagonal set to diagonal and all other entries set to 0.

pub fn from_scale_rotation_translation( scale: Vec3, rotation: Quat, translation: Vec3, ) -> Self

Creates an affine transformation matrix from the given 3D scale, rotation and translation.

The resulting matrix can be used to transform 3D points and vectors. See Self::transform_point3() and Self::transform_vector3().

Panics

Will panic if rotation is not normalized when glam_assert is enabled.

pub fn from_rotation_translation(rotation: Quat, translation: Vec3) -> Self

Creates an affine transformation matrix from the given 3D translation.

The resulting matrix can be used to transform 3D points and vectors. See Self::transform_point3() and Self::transform_vector3().

Panics

Will panic if rotation is not normalized when glam_assert is enabled.

pub fn to_scale_rotation_translation(&self) -> (Vec3, Quat, Vec3)

Extracts scale, rotation and translation from self. The input matrix is expected to be a 3D affine transformation matrix otherwise the output will be invalid.

Panics

Will panic if the determinant of self is zero or if the resulting scale vector contains any zero elements when glam_assert is enabled.

pub fn from_quat(rotation: Quat) -> Self

Creates an affine transformation matrix from the given rotation quaternion.

The resulting matrix can be used to transform 3D points and vectors. See Self::transform_point3() and Self::transform_vector3().

Panics

Will panic if rotation is not normalized when glam_assert is enabled.

pub fn from_mat3(m: Mat3) -> Self

Creates an affine transformation matrix from the given 3x3 linear transformation matrix.

The resulting matrix can be used to transform 3D points and vectors. See Self::transform_point3() and Self::transform_vector3().

pub fn from_mat3a(m: Mat3A) -> Self

Creates an affine transformation matrix from the given 3x3 linear transformation matrix.

The resulting matrix can be used to transform 3D points and vectors. See Self::transform_point3() and Self::transform_vector3().

pub fn from_translation(translation: Vec3) -> Self

Creates an affine transformation matrix from the given 3D translation.

The resulting matrix can be used to transform 3D points and vectors. See Self::transform_point3() and Self::transform_vector3().

pub fn from_axis_angle(axis: Vec3, angle: f32) -> Self

Creates an affine transformation matrix containing a 3D rotation around a normalized rotation axis of angle (in radians).

The resulting matrix can be used to transform 3D points and vectors. See Self::transform_point3() and Self::transform_vector3().

Panics

Will panic if axis is not normalized when glam_assert is enabled.

pub fn from_euler(order: EulerRot, a: f32, b: f32, c: f32) -> Self

Creates a affine transformation matrix containing a rotation from the given euler rotation sequence and angles (in radians).

The resulting matrix can be used to transform 3D points and vectors. See Self::transform_point3() and Self::transform_vector3().

pub fn to_euler(&self, order: EulerRot) -> (f32, f32, f32)

Extract Euler angles with the given Euler rotation order.

Note if the upper 3x3 matrix contain scales, shears, or other non-rotation transformations then the resulting Euler angles will be ill-defined.

Panics

Will panic if any column of the upper 3x3 rotation matrix is not normalized when glam_assert is enabled.

pub fn from_rotation_x(angle: f32) -> Self

Creates an affine transformation matrix containing a 3D rotation around the x axis of angle (in radians).

The resulting matrix can be used to transform 3D points and vectors. See Self::transform_point3() and Self::transform_vector3().

pub fn from_rotation_y(angle: f32) -> Self

Creates an affine transformation matrix containing a 3D rotation around the y axis of angle (in radians).

The resulting matrix can be used to transform 3D points and vectors. See Self::transform_point3() and Self::transform_vector3().

pub fn from_rotation_z(angle: f32) -> Self

Creates an affine transformation matrix containing a 3D rotation around the z axis of angle (in radians).

The resulting matrix can be used to transform 3D points and vectors. See Self::transform_point3() and Self::transform_vector3().

pub fn from_scale(scale: Vec3) -> Self

Creates an affine transformation matrix containing the given 3D non-uniform scale.

The resulting matrix can be used to transform 3D points and vectors. See Self::transform_point3() and Self::transform_vector3().

Panics

Will panic if all elements of scale are zero when glam_assert is enabled.

pub const fn from_cols_slice(slice: &[f32]) -> Self

Creates a 4x4 matrix from the first 16 values in slice.

Panics

Panics if slice is less than 16 elements long.

pub fn write_cols_to_slice(self, slice: &mut [f32])

Writes the columns of self to the first 16 elements in slice.

Panics

Panics if slice is less than 16 elements long.

pub fn col(&self, index: usize) -> Vec4

Returns the matrix column for the given index.

Panics

Panics if index is greater than 3.

pub fn col_mut(&mut self, index: usize) -> &mut Vec4

Returns a mutable reference to the matrix column for the given index.

Panics

Panics if index is greater than 3.

pub fn row(&self, index: usize) -> Vec4

Returns the matrix row for the given index.

Panics

Panics if index is greater than 3.

pub fn is_finite(&self) -> bool

Returns true if, and only if, all elements are finite. If any element is either NaN, positive or negative infinity, this will return false.

pub fn is_nan(&self) -> bool

Returns true if any elements are NaN.

pub fn transpose(&self) -> Self

Returns the transpose of self.

pub fn determinant(&self) -> f32

Returns the determinant of self.

pub fn inverse(&self) -> Self

Returns the inverse of self.

If the matrix is not invertible the returned matrix will be invalid.

Panics

Will panic if the determinant of self is zero when glam_assert is enabled.

pub fn look_to_lh(eye: Vec3, dir: Vec3, up: Vec3) -> Self

Creates a left-handed view matrix using a camera position, an up direction, and a facing direction.

For a view coordinate system with +X=right, +Y=up and +Z=forward.

pub fn look_to_rh(eye: Vec3, dir: Vec3, up: Vec3) -> Self

Creates a right-handed view matrix using a camera position, an up direction, and a facing direction.

For a view coordinate system with +X=right, +Y=up and +Z=back.

pub fn look_at_lh(eye: Vec3, center: Vec3, up: Vec3) -> Self

Creates a left-handed view matrix using a camera position, an up direction, and a focal point. For a view coordinate system with +X=right, +Y=up and +Z=forward.

Panics

Will panic if up is not normalized when glam_assert is enabled.

pub fn look_at_rh(eye: Vec3, center: Vec3, up: Vec3) -> Self

Creates a right-handed view matrix using a camera position, an up direction, and a focal point. For a view coordinate system with +X=right, +Y=up and +Z=back.

Panics

Will panic if up is not normalized when glam_assert is enabled.

pub fn perspective_rh_gl( fov_y_radians: f32, aspect_ratio: f32, z_near: f32, z_far: f32, ) -> Self

Creates a right-handed perspective projection matrix with [-1,1] depth range.

Useful to map the standard right-handed coordinate system into what OpenGL expects.

This is the same as the OpenGL gluPerspective function. See https://www.khronos.org/registry/OpenGL-Refpages/gl2.1/xhtml/gluPerspective.xml

pub fn perspective_lh( fov_y_radians: f32, aspect_ratio: f32, z_near: f32, z_far: f32, ) -> Self

Creates a left-handed perspective projection matrix with [0,1] depth range.

Useful to map the standard left-handed coordinate system into what WebGPU/Metal/Direct3D expect.

Panics

Will panic if z_near or z_far are less than or equal to zero when glam_assert is enabled.

pub fn perspective_rh( fov_y_radians: f32, aspect_ratio: f32, z_near: f32, z_far: f32, ) -> Self

Creates a right-handed perspective projection matrix with [0,1] depth range.

Useful to map the standard right-handed coordinate system into what WebGPU/Metal/Direct3D expect.

Panics

Will panic if z_near or z_far are less than or equal to zero when glam_assert is enabled.

pub fn perspective_infinite_lh( fov_y_radians: f32, aspect_ratio: f32, z_near: f32, ) -> Self

Creates an infinite left-handed perspective projection matrix with [0,1] depth range.

Like perspective_lh, but with an infinite value for z_far. The result is that points near z_near are mapped to depth 0, and as they move towards infinity the depth approaches 1.

Panics

Will panic if z_near or z_far are less than or equal to zero when glam_assert is enabled.

pub fn perspective_infinite_reverse_lh( fov_y_radians: f32, aspect_ratio: f32, z_near: f32, ) -> Self

Creates an infinite reverse left-handed perspective projection matrix with [0,1] depth range.

Similar to perspective_infinite_lh, but maps Z = z_near to a depth of 1 and Z = infinity to a depth of 0.

Panics

Will panic if z_near is less than or equal to zero when glam_assert is enabled.

pub fn perspective_infinite_rh( fov_y_radians: f32, aspect_ratio: f32, z_near: f32, ) -> Self

Creates an infinite right-handed perspective projection matrix with [0,1] depth range.

Like perspective_rh, but with an infinite value for z_far. The result is that points near z_near are mapped to depth 0, and as they move towards infinity the depth approaches 1.

Panics

Will panic if z_near or z_far are less than or equal to zero when glam_assert is enabled.

pub fn perspective_infinite_reverse_rh( fov_y_radians: f32, aspect_ratio: f32, z_near: f32, ) -> Self

Creates an infinite reverse right-handed perspective projection matrix with [0,1] depth range.

Similar to perspective_infinite_rh, but maps Z = z_near to a depth of 1 and Z = infinity to a depth of 0.

Panics

Will panic if z_near is less than or equal to zero when glam_assert is enabled.

pub fn orthographic_rh_gl( left: f32, right: f32, bottom: f32, top: f32, near: f32, far: f32, ) -> Self

Creates a right-handed orthographic projection matrix with [-1,1] depth range. This is the same as the OpenGL glOrtho function in OpenGL. See https://www.khronos.org/registry/OpenGL-Refpages/gl2.1/xhtml/glOrtho.xml

Useful to map a right-handed coordinate system to the normalized device coordinates that OpenGL expects.

pub fn orthographic_lh( left: f32, right: f32, bottom: f32, top: f32, near: f32, far: f32, ) -> Self

Creates a left-handed orthographic projection matrix with [0,1] depth range.

Useful to map a left-handed coordinate system to the normalized device coordinates that WebGPU/Direct3D/Metal expect.

pub fn orthographic_rh( left: f32, right: f32, bottom: f32, top: f32, near: f32, far: f32, ) -> Self

Creates a right-handed orthographic projection matrix with [0,1] depth range.

Useful to map a right-handed coordinate system to the normalized device coordinates that WebGPU/Direct3D/Metal expect.

pub fn project_point3(&self, rhs: Vec3) -> Vec3

Transforms the given 3D vector as a point, applying perspective correction.

This is the equivalent of multiplying the 3D vector as a 4D vector where w is 1.0. The perspective divide is performed meaning the resulting 3D vector is divided by w.

This method assumes that self contains a projective transform.

pub fn transform_point3(&self, rhs: Vec3) -> Vec3

Transforms the given 3D vector as a point.

This is the equivalent of multiplying the 3D vector as a 4D vector where w is 1.0.

This method assumes that self contains a valid affine transform. It does not perform a perspective divide, if self contains a perspective transform, or if you are unsure, the Self::project_point3() method should be used instead.

Panics

Will panic if the 3rd row of self is not (0, 0, 0, 1) when glam_assert is enabled.

pub fn transform_vector3(&self, rhs: Vec3) -> Vec3

Transforms the give 3D vector as a direction.

This is the equivalent of multiplying the 3D vector as a 4D vector where w is 0.0.

This method assumes that self contains a valid affine transform.

Panics

Will panic if the 3rd row of self is not (0, 0, 0, 1) when glam_assert is enabled.

pub fn project_point3a(&self, rhs: Vec3A) -> Vec3A

Transforms the given Vec3A as a 3D point, applying perspective correction.

This is the equivalent of multiplying the Vec3A as a 4D vector where w is 1.0. The perspective divide is performed meaning the resulting 3D vector is divided by w.

This method assumes that self contains a projective transform.

pub fn transform_point3a(&self, rhs: Vec3A) -> Vec3A

Transforms the given Vec3A as 3D point.

This is the equivalent of multiplying the Vec3A as a 4D vector where w is 1.0.

pub fn transform_vector3a(&self, rhs: Vec3A) -> Vec3A

Transforms the give Vec3A as 3D vector.

This is the equivalent of multiplying the Vec3A as a 4D vector where w is 0.0.

pub fn mul_vec4(&self, rhs: Vec4) -> Vec4

Transforms a 4D vector.

pub fn mul_mat4(&self, rhs: &Self) -> Self

Multiplies two 4x4 matrices.

pub fn add_mat4(&self, rhs: &Self) -> Self

Adds two 4x4 matrices.

pub fn sub_mat4(&self, rhs: &Self) -> Self

Subtracts two 4x4 matrices.

pub fn mul_scalar(&self, rhs: f32) -> Self

Multiplies a 4x4 matrix by a scalar.

pub fn div_scalar(&self, rhs: f32) -> Self

Divides a 4x4 matrix by a scalar.

pub fn abs_diff_eq(&self, rhs: Self, max_abs_diff: f32) -> bool

Returns true if the absolute difference of all elements between self and rhs is less than or equal to max_abs_diff.

This can be used to compare if two matrices contain similar elements. It works best when comparing with a known value. The max_abs_diff that should be used used depends on the values being compared against.

For more see comparing floating point numbers.

pub fn abs(&self) -> Self

Takes the absolute value of each element in self

pub fn as_dmat4(&self) -> DMat4

Trait Implementations

impl Add for Mat4

type Output = Mat4

The resulting type after applying the + operator.

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

Performs the + operation.

impl AddAssign for Mat4

fn add_assign(&mut self, rhs: Self)

Performs the += operation.

impl AsMut<[f32; 16]> for Mat4

fn as_mut(&mut self) -> &mut [f32; 16]

Converts this type into a mutable reference of the (usually inferred) input type.

impl AsRef<[f32; 16]> for Mat4

fn as_ref(&self) -> &[f32; 16]

Converts this type into a shared reference of the (usually inferred) input type.

impl Clone for Mat4

fn clone(&self) -> Mat4

Returns a copy of the value.

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

Performs copy-assignment from source.

impl Debug for Mat4

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

Formats the value using the given formatter.

impl Default for Mat4

fn default() -> Self

Returns the “default value” for a type.

impl Display for Mat4

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

Formats the value using the given formatter.

impl Div<Mat4> for f32

type Output = Mat4

The resulting type after applying the / operator.

fn div(self, rhs: Mat4) -> Self::Output

Performs the / operation.

impl Div<f32> for Mat4

type Output = Mat4

The resulting type after applying the / operator.

fn div(self, rhs: f32) -> Self::Output

Performs the / operation.

impl DivAssign<f32> for Mat4

fn div_assign(&mut self, rhs: f32)

Performs the /= operation.

impl From<Affine3A> for Mat4

fn from(m: Affine3A) -> Mat4

Converts to this type from the input type.

impl Mul<Affine3A> for Mat4

type Output = Mat4

The resulting type after applying the * operator.

fn mul(self, rhs: Affine3A) -> Self::Output

Performs the * operation.

impl Mul<Mat4> for Affine3A

type Output = Mat4

The resulting type after applying the * operator.

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

Performs the * operation.

impl Mul<Mat4> for f32

type Output = Mat4

The resulting type after applying the * operator.

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

Performs the * operation.

impl Mul<Vec4> for Mat4

type Output = Vec4

The resulting type after applying the * operator.

fn mul(self, rhs: Vec4) -> Self::Output

Performs the * operation.

impl Mul<f32> for Mat4

type Output = Mat4

The resulting type after applying the * operator.

fn mul(self, rhs: f32) -> Self::Output

Performs the * operation.

impl Mul for Mat4

type Output = Mat4

The resulting type after applying the * operator.

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

Performs the * operation.

impl MulAssign<f32> for Mat4

fn mul_assign(&mut self, rhs: f32)

Performs the *= operation.

impl MulAssign for Mat4

fn mul_assign(&mut self, rhs: Self)

Performs the *= operation.

impl Neg for Mat4

type Output = Mat4

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl PartialEq for Mat4

fn eq(&self, rhs: &Self) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl<'a> Product<&'a Mat4> for Mat4

fn product<I>(iter: I) -> Self

where I: Iterator<Item = &'a Self>,

Takes an iterator and generates Self from the elements by multiplying the items.

impl Product for Mat4

fn product<I>(iter: I) -> Self

where I: Iterator<Item = Self>,

Takes an iterator and generates Self from the elements by multiplying the items.

impl Sub for Mat4

type Output = Mat4

The resulting type after applying the - operator.

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

Performs the - operation.

impl SubAssign for Mat4

fn sub_assign(&mut self, rhs: Self)

Performs the -= operation.

impl<'a> Sum<&'a Mat4> for Mat4

fn sum<I>(iter: I) -> Self

where I: Iterator<Item = &'a Self>,

Takes an iterator and generates Self from the elements by “summing up” the items.

impl Sum for Mat4

fn sum<I>(iter: I) -> Self

where I: Iterator<Item = Self>,

Takes an iterator and generates Self from the elements by “summing up” the items.

impl Zeroable for Mat4

fn zeroed() -> Self

Calls zeroed.

impl Copy for Mat4

impl Pod for Mat4