Struct Mat3A

#[repr(C)]
pub struct Mat3A {
    pub x_axis: Vec3A,
    pub y_axis: Vec3A,
    pub z_axis: Vec3A,
}

A 3x3 column major matrix.

This 3x3 matrix type features convenience methods for creating and using linear and affine transformations. If you are primarily dealing with 2D affine transformations the Affine2 type is much faster and more space efficient than using a 3x3 matrix.

Linear transformations including 3D rotation and scale can be created using methods such as Self::from_diagonal(), Self::from_quat(), Self::from_axis_angle(), Self::from_rotation_x(), Self::from_rotation_y(), or Self::from_rotation_z().

The resulting matrices can be use to transform 3D vectors using regular vector multiplication.

Affine transformations including 2D translation, rotation and scale can be created using methods such as Self::from_translation(), Self::from_angle(), Self::from_scale() and Self::from_scale_angle_translation().

The Self::transform_point2() and Self::transform_vector2() convenience methods are provided for performing affine transforms on 2D vectors and points. These multiply 2D inputs as 3D vectors with an implicit z value of 1 for points and 0 for vectors respectively. These methods assume that Self contains a valid affine transform.

Fields

x_axis: Vec3A

y_axis: Vec3A

z_axis: Vec3A

Implementations

impl Mat3A

pub const ZERO: Self = _

A 3x3 matrix with all elements set to 0.0.

pub const IDENTITY: Self = _

A 3x3 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: Vec3A, y_axis: Vec3A, z_axis: Vec3A) -> Self

Creates a 3x3 matrix from three column vectors.

pub const fn from_cols_array(m: &[f32; 9]) -> Self

Creates a 3x3 matrix from a [f32; 9] 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; 9]

Creates a [f32; 9] 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; 3]; 3]) -> Self

Creates a 3x3 matrix from a [[f32; 3]; 3] 3D 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; 3]; 3]

Creates a [[f32; 3]; 3] 3D 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: Vec3) -> Self

Creates a 3x3 matrix with its diagonal set to diagonal and all other entries set to 0.

pub fn from_mat4(m: Mat4) -> Self

Creates a 3x3 matrix from a 4x4 matrix, discarding the 4th row and column.

pub fn from_mat4_minor(m: Mat4, i: usize, j: usize) -> Self

Creates a 3x3 matrix from the minor of the given 4x4 matrix, discarding the ith column and jth row.

Panics

Panics if i or j is greater than 3.

pub fn from_quat(rotation: Quat) -> Self

Creates a 3D rotation matrix from the given quaternion.

Panics

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

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

Creates a 3D rotation matrix from a normalized rotation axis and angle (in radians).

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 3D rotation matrix from the given euler rotation sequence and the angles (in radians).

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

Extract Euler angles with the given Euler rotation order.

Note if the input matrix contains scales, shears, or other non-rotation transformations then the resulting Euler angles will be ill-defined.

Panics

Will panic if any input matrix column is not normalized when glam_assert is enabled.

pub fn from_rotation_x(angle: f32) -> Self

Creates a 3D rotation matrix from angle (in radians) around the x axis.

pub fn from_rotation_y(angle: f32) -> Self

Creates a 3D rotation matrix from angle (in radians) around the y axis.

pub fn from_rotation_z(angle: f32) -> Self

Creates a 3D rotation matrix from angle (in radians) around the z axis.

pub fn from_translation(translation: Vec2) -> Self

Creates an affine transformation matrix from the given 2D translation.

The resulting matrix can be used to transform 2D points and vectors. See Self::transform_point2() and Self::transform_vector2().

pub fn from_angle(angle: f32) -> Self

Creates an affine transformation matrix from the given 2D rotation angle (in radians).

The resulting matrix can be used to transform 2D points and vectors. See Self::transform_point2() and Self::transform_vector2().

pub fn from_scale_angle_translation( scale: Vec2, angle: f32, translation: Vec2, ) -> Self

Creates an affine transformation matrix from the given 2D scale, rotation angle (in radians) and translation.

The resulting matrix can be used to transform 2D points and vectors. See Self::transform_point2() and Self::transform_vector2().

pub fn from_scale(scale: Vec2) -> Self

Creates an affine transformation matrix from the given non-uniform 2D scale.

The resulting matrix can be used to transform 2D points and vectors. See Self::transform_point2() and Self::transform_vector2().

Panics

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

pub fn from_mat2(m: Mat2) -> Self

Creates an affine transformation matrix from the given 2x2 matrix.

The resulting matrix can be used to transform 2D points and vectors. See Self::transform_point2() and Self::transform_vector2().

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

Creates a 3x3 matrix from the first 9 values in slice.

Panics

Panics if slice is less than 9 elements long.

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

Writes the columns of self to the first 9 elements in slice.

Panics

Panics if slice is less than 9 elements long.

pub fn col(&self, index: usize) -> Vec3A

Returns the matrix column for the given index.

Panics

Panics if index is greater than 2.

pub fn col_mut(&mut self, index: usize) -> &mut Vec3A

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

Panics

Panics if index is greater than 2.

pub fn row(&self, index: usize) -> Vec3A

Returns the matrix row for the given index.

Panics

Panics if index is greater than 2.

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 transform_point2(&self, rhs: Vec2) -> Vec2

Transforms the given 2D vector as a point.

This is the equivalent of multiplying rhs as a 3D vector where z is 1.

This method assumes that self contains a valid affine transform.

Panics

Will panic if the 2nd row of self is not (0, 0, 1) when glam_assert is enabled.

pub fn transform_vector2(&self, rhs: Vec2) -> Vec2

Rotates the given 2D vector.

This is the equivalent of multiplying rhs as a 3D vector where z is 0.

This method assumes that self contains a valid affine transform.

Panics

Will panic if the 2nd row of self is not (0, 0, 1) when glam_assert is enabled.

pub fn mul_vec3(&self, rhs: Vec3) -> Vec3

Transforms a 3D vector.

pub fn mul_vec3a(&self, rhs: Vec3A) -> Vec3A

Transforms a Vec3A.

pub fn mul_mat3(&self, rhs: &Self) -> Self

Multiplies two 3x3 matrices.

pub fn add_mat3(&self, rhs: &Self) -> Self

Adds two 3x3 matrices.

pub fn sub_mat3(&self, rhs: &Self) -> Self

Subtracts two 3x3 matrices.

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

Multiplies a 3x3 matrix by a scalar.

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

Divides a 3x3 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_dmat3(&self) -> DMat3

Trait Implementations

impl Add for Mat3A

type Output = Mat3A

The resulting type after applying the + operator.

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

Performs the + operation.

impl AddAssign for Mat3A

fn add_assign(&mut self, rhs: Self)

Performs the += operation.

impl Clone for Mat3A

fn clone(&self) -> Mat3A

Returns a copy of the value.

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

Performs copy-assignment from source.

impl Debug for Mat3A

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

Formats the value using the given formatter.

impl Default for Mat3A

fn default() -> Self

Returns the “default value” for a type.

impl Display for Mat3A

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

Formats the value using the given formatter.

impl Div<Mat3A> for f32

type Output = Mat3A

The resulting type after applying the / operator.

fn div(self, rhs: Mat3A) -> Self::Output

Performs the / operation.

impl Div<f32> for Mat3A

type Output = Mat3A

The resulting type after applying the / operator.

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

Performs the / operation.

impl DivAssign<f32> for Mat3A

fn div_assign(&mut self, rhs: f32)

Performs the /= operation.

impl From<Affine2> for Mat3A

fn from(m: Affine2) -> Mat3A

Converts to this type from the input type.

impl From<Mat3> for Mat3A

fn from(m: Mat3) -> Self

Converts to this type from the input type.

impl From<Mat3A> for Mat3

fn from(m: Mat3A) -> Self

Converts to this type from the input type.

impl Mul<Affine2> for Mat3A

type Output = Mat3A

The resulting type after applying the * operator.

fn mul(self, rhs: Affine2) -> Self::Output

Performs the * operation.

impl Mul<Mat3A> for Affine2

type Output = Mat3A

The resulting type after applying the * operator.

fn mul(self, rhs: Mat3A) -> Self::Output

Performs the * operation.

impl Mul<Mat3A> for f32

type Output = Mat3A

The resulting type after applying the * operator.

fn mul(self, rhs: Mat3A) -> Self::Output

Performs the * operation.

impl Mul<Vec3> for Mat3A

type Output = Vec3

The resulting type after applying the * operator.

fn mul(self, rhs: Vec3) -> Vec3

Performs the * operation.

impl Mul<Vec3A> for Mat3A

type Output = Vec3A

The resulting type after applying the * operator.

fn mul(self, rhs: Vec3A) -> Self::Output

Performs the * operation.

impl Mul<f32> for Mat3A

type Output = Mat3A

The resulting type after applying the * operator.

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

Performs the * operation.

impl Mul for Mat3A

type Output = Mat3A

The resulting type after applying the * operator.

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

Performs the * operation.

impl MulAssign<f32> for Mat3A

fn mul_assign(&mut self, rhs: f32)

Performs the *= operation.

impl MulAssign for Mat3A

fn mul_assign(&mut self, rhs: Self)

Performs the *= operation.

impl Neg for Mat3A

type Output = Mat3A

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl PartialEq for Mat3A

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 Mat3A> for Mat3A

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 Mat3A

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 Mat3A

type Output = Mat3A

The resulting type after applying the - operator.

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

Performs the - operation.

impl SubAssign for Mat3A

fn sub_assign(&mut self, rhs: Self)

Performs the -= operation.

impl<'a> Sum<&'a Mat3A> for Mat3A

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 Mat3A

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 Mat3A

fn zeroed() -> Self

Calls zeroed.

impl AnyBitPattern for Mat3A

impl Copy for Mat3A